Introduction to The Design and Analysis of Algorithms

{"title":"Introduction to The Design and Analysis of Algorithms","price":"۷","ebook_price":"۷","rent_3_price":"۶","rent_6_price":"۲","rent_12_price":"-۱","print_price":"-۱","front_cover":{"thumbnail":"/storage/files/styles/thumbnail/books/4a8b03583f119702/front.jpg","medium":"/storage/files/styles/medium/books/4a8b03583f119702/front.jpg","medium_rounded":"/storage/files/styles/medium_rounded/books/4a8b03583f119702/front.png","large":"/storage/files/styles/large/books/4a8b03583f119702/front.jpg","medium_trans":"/storage/files/styles/medium_trans/books/4a8b03583f119702/front.png","medium_zoom_fit":"/storage/files/styles/medium_zoom_fit/books/4a8b03583f119702/front.png"},"back_cover":{"thumbnail":"/storage/files/styles/thumbnail/books/4a8b03583f119702/back.jpg","medium":"/storage/files/styles/medium/books/4a8b03583f119702/back.jpg","medium_rounded":"/storage/files/styles/medium_rounded/books/4a8b03583f119702/back.png","large":"/storage/files/styles/large/books/4a8b03583f119702/back.jpg","medium_trans":"/storage/files/styles/medium_trans/books/4a8b03583f119702/back.png","medium_zoom_fit":"/storage/files/styles/medium_zoom_fit/books/4a8b03583f119702/back.png"},"print_book":false,"isbn":"9780132316811","lang":"null","cover_type":"null","dimension":"null","year":"۲۰۱۱","nobat_chap":1,"description":["Based on a new classification of algorithm design techniques and a clear delineation of analysis methods, Introduction to the Design and Analysis of Algorithms presents the subject in a truly innovative manner. Written in a reader-friendly style, the book encourages broad problem-solving skills while thoroughly covering the material required for introductory algorithms. The author emphasizes conceptual understanding before the introduction of the formal treatment of each technique. Popular puzzles are used to motivate readers' interest and strengthen their skills in algorithmic problem solving. Other enhancement features include chapter summaries, hints to the exercises, and a solution manual. For those interested in learning more about algorithms."],"pages_count":592,"token":"4a8b03583f119702","deleted_at":null,"published_at":"2017-12-12 14:32:47","available_for_web":true,"publisher_title":"Pearson","edition":null,"currency":"EUR","subtitle":"null","country":"null","rent_1_week_price":"-۱","meta_desc":null,"meta_title":null,"stock":0,"cache":1,"bookmark":"false","has_book":"false","has_file":"true","writer_authors":[{"id":1055,"title":"Anany Levitin","meta_title":"Anany Levitin","meta_description":"Anany Levitin - بوکت، نخستین و بزرگ‌ترین سامانه‌ی یادگیری و آموزش با قابلیت کرایه و خرید نسخه‌ی الکترونیکی کتاب‌های دانشگاهی است ","faq":null,"keywords":"بوکت,کرایه کتاب,کتاب الکترونیک/ نسخه الکترونیک,ئی بوک/ایبوک,مطالعه آنلاین,کتاب تخصصی,کتاب دانشگاهی,دانلود کتاب,خرید کتاب,جستجوی کتاب,خرید کتاب الکترونیک,ناشرشو,چاپ کتاب,چاپ رایگان کتاب,کتاب مهندسی,کتاب پزشکی,کتاب مدیریت,جیتجو در متن کتاب,دانلود اپلیکیشن کتابخوان","description":null,"firstname":"Anany","lastname":"Levitin","token":"ac5211b9343c3ed5","national_code":null,"pivot":{"book_id":573,"author_id":1055,"created_at":"2017-12-09 19:25:09","updated_at":"2019-03-12 15:13:25","role":"writer"}}],"translator_authors":[],"available_e_book":true,"dir":true,"vitrines":[{"title":"کتاب‌های مشابه","url":"/api/bookstore/vitrines/similar-books/4a8b03583f119702","type":"books","books":[]},{"title":"کتاب‌های دیگر ناشر","url":"/api/bookstore/vitrines/publisher-books/4a8b03583f119702","type":"books","books":[]}],"authors":[{"id":1055,"title":"Anany Levitin","meta_title":"Anany Levitin","meta_description":"Anany Levitin - بوکت، نخستین و بزرگ‌ترین سامانه‌ی یادگیری و آموزش با قابلیت کرایه و خرید نسخه‌ی الکترونیکی کتاب‌های دانشگاهی است ","faq":null,"keywords":"بوکت,کرایه کتاب,کتاب الکترونیک/ نسخه الکترونیک,ئی بوک/ایبوک,مطالعه آنلاین,کتاب تخصصی,کتاب دانشگاهی,دانلود کتاب,خرید کتاب,جستجوی کتاب,خرید کتاب الکترونیک,ناشرشو,چاپ کتاب,چاپ رایگان کتاب,کتاب مهندسی,کتاب پزشکی,کتاب مدیریت,جیتجو در متن کتاب,دانلود اپلیکیشن کتابخوان","description":null,"firstname":"Anany","lastname":"Levitin","token":"ac5211b9343c3ed5","national_code":null,"pivot":{"book_id":573,"author_id":1055,"created_at":"2017-12-09 19:25:09","updated_at":"2019-03-12 15:13:25","role":"writer"}}],"e_book":{"toc":[{"page":2,"title":"Copyright Page"},{"page":3,"title":"Title Page"},{"page":5,"title":"Brief Contents"},{"page":7,"title":"Contents"},{"page":17,"title":"New to the Third Edition"},{"page":19,"title":"Preface"},{"page":24,"title":"Acknowledgments"},{"page":27,"title":"1 Introduction","children":[{"page":29,"title":"1.1 What Is an Algorithm?","children":[{"page":33,"title":"Exercises 1.1"}]},{"page":35,"title":"1.2 Fundamentals of Algorithmic Problem Solving","children":[{"page":35,"title":"Understanding the Problem"},{"page":35,"title":"Ascertaining the Capabilities of the Computational Device"},{"page":37,"title":"Choosing between Exact and Approximate Problem Solving"},{"page":37,"title":"Algorithm Design Techniques"},{"page":38,"title":"Designing an Algorithm and Data Structures"},{"page":38,"title":"Methods of Specifying an Algorithm"},{"page":39,"title":"Proving an Algorithm’s Correctness"},{"page":40,"title":"Analyzing an Algorithm"},{"page":41,"title":"Coding an Algorithm"},{"page":43,"title":"Exercises 1.2"}]},{"page":44,"title":"1.3 Important Problem Types","children":[{"page":45,"title":"Sorting"},{"page":46,"title":"Searching"},{"page":46,"title":"String Processing"},{"page":47,"title":"Graph Problems"},{"page":47,"title":"Combinatorial Problems"},{"page":48,"title":"Geometric Problems"},{"page":48,"title":"Numerical Problems"},{"page":49,"title":"Exercises 1.3"}]},{"page":51,"title":"1.4 Fundamental Data Structures","children":[{"page":51,"title":"Linear Data Structures"},{"page":54,"title":"Graphs"},{"page":57,"title":"Trees"},{"page":61,"title":"Sets and Dictionaries"},{"page":63,"title":"Exercises 1.4"},{"page":64,"title":"Summary"}]}]},{"page":67,"title":"2 Fundamentals of the Analysis of Algorithm Efficiency","children":[{"page":68,"title":"2.1 The Analysis Framework","children":[{"page":69,"title":"Measuring an Input’s Size"},{"page":70,"title":"Units for Measuring Running Time"},{"page":71,"title":"Orders of Growth"},{"page":73,"title":"Worst-Case, Best-Case, and Average-Case Efficiencies"},{"page":76,"title":"Recapitulation of the Analysis Framework"},{"page":76,"title":"Exercises 2.1"}]},{"page":78,"title":"2.2 Asymptotic Notations and Basic Efficiency Classes","children":[{"page":78,"title":"Informal Introduction"},{"page":79,"title":"O-notation"},{"page":80,"title":"Ω-notation"},{"page":81,"title":"Θ-notation"},{"page":81,"title":"Useful Property Involving the Asymptotic Notations"},{"page":82,"title":"Using Limits for Comparing Orders of Growth"},{"page":84,"title":"Basic Efficiency Classes"},{"page":84,"title":"Exercises 2.2"}]},{"page":87,"title":"2.3 Mathematical Analysis of Nonrecursive Algorithms","children":[{"page":93,"title":"Exercises 2.3"}]},{"page":96,"title":"2.4 Mathematical Analysis of Recursive Algorithms","children":[{"page":102,"title":"Exercises 2.4"}]},{"page":106,"title":"2.5 Example: Computing the nth Fibonacci Number","children":[{"page":109,"title":"Exercises 2.5"}]},{"page":110,"title":"2.6 Empirical Analysis of Algorithms","children":[{"page":115,"title":"Exercises 2.6"}]},{"page":117,"title":"2.7 Algorithm Visualization","children":[{"page":120,"title":"Summary"}]}]},{"page":123,"title":"3 Brute Force and Exhaustive Search","children":[{"page":124,"title":"3.1 Selection Sort and Bubble Sort","children":[{"page":124,"title":"Selection Sort"},{"page":126,"title":"Bubble Sort"},{"page":128,"title":"Exercises 3.1"}]},{"page":130,"title":"3.2 Sequential Search and Brute-Force String Matching","children":[{"page":130,"title":"Sequential Search"},{"page":131,"title":"Brute-Force String Matching"},{"page":132,"title":"Exercises 3.2"}]},{"page":134,"title":"3.3 Closest-Pair and Convex-Hull Problems by Brute Force","children":[{"page":134,"title":"Closest-Pair Problem"},{"page":135,"title":"Convex-Hull Problem"},{"page":139,"title":"Exercises 3.3"}]},{"page":141,"title":"3.4 Exhaustive Search","children":[{"page":142,"title":"Traveling Salesman Problem"},{"page":142,"title":"Knapsack Problem"},{"page":145,"title":"Assignment Problem"},{"page":146,"title":"Exercises 3.4"}]},{"page":148,"title":"3.5 Depth-First Search and Breadth-First Search","children":[{"page":148,"title":"Depth-First Search"},{"page":151,"title":"Breadth-First Search"},{"page":154,"title":"Exercises 3.5"},{"page":156,"title":"Summary"}]}]},{"page":157,"title":"4 Decrease-and-Conquer","children":[{"page":160,"title":"4.1 Insertion Sort","children":[{"page":162,"title":"Exercises 4.1"}]},{"page":164,"title":"4.2 Topological Sorting","children":[{"page":168,"title":"Exercises 4.2"}]},{"page":170,"title":"4.3 Algorithms for Generating Combinatorial Objects","children":[{"page":170,"title":"Generating Permutations"},{"page":172,"title":"Generating Subsets"},{"page":174,"title":"Exercises 4.3"}]},{"page":176,"title":"4.4 Decrease-by-a-Constant-Factor Algorithms","children":[{"page":176,"title":"Binary Search"},{"page":178,"title":"Fake-Coin Problem"},{"page":179,"title":"Russian Peasant Multiplication"},{"page":180,"title":"Josephus Problem"},{"page":182,"title":"Exercises 4.4"}]},{"page":183,"title":"4.5 Variable-Size-Decrease Algorithms","children":[{"page":184,"title":"Computing a Median and the Selection Problem"},{"page":187,"title":"Interpolation Search"},{"page":189,"title":"Searching and Insertion in a Binary Search Tree"},{"page":190,"title":"The Game of Nim"},{"page":192,"title":"Exercises 4.5"},{"page":193,"title":"Summary"}]}]},{"page":195,"title":"5 Divide-and-Conquer","children":[{"page":198,"title":"5.1 Mergesort","children":[{"page":200,"title":"Exercises 5.1"}]},{"page":202,"title":"5.2 Quicksort","children":[{"page":207,"title":"Exercises 5.2"}]},{"page":208,"title":"5.3 Binary Tree Traversals and Related Properties","children":[{"page":211,"title":"Exercises 5.3"}]},{"page":212,"title":"5.4 Multiplication of Large Integers and Strassen’s Matrix Multiplication","children":[{"page":213,"title":"Multiplication of Large Integers"},{"page":215,"title":"Strassen’s Matrix Multiplication"},{"page":217,"title":"Exercises 5.4"}]},{"page":218,"title":"5.5 The Closest-Pair and Convex-Hull Problems by Divide-and-Conquer","children":[{"page":218,"title":"The Closest-Pair Problem"},{"page":221,"title":"Convex-Hull Problem"},{"page":223,"title":"Exercises 5.5"},{"page":224,"title":"Summary"}]}]},{"page":227,"title":"6 Transform-and-Conquer","children":[{"page":228,"title":"6.1 Presorting","children":[{"page":231,"title":"Exercises 6.1"}]},{"page":234,"title":"6.2 Gaussian Elimination","children":[{"page":238,"title":"LU Decomposition"},{"page":240,"title":"Computing a Matrix Inverse"},{"page":241,"title":"Computing a Determinant"},{"page":242,"title":"Exercises 6.2"}]},{"page":244,"title":"6.3 Balanced Search Trees","children":[{"page":244,"title":"AVL Trees"},{"page":249,"title":"2-3 Trees"},{"page":251,"title":"Exercises 6.3"}]},{"page":252,"title":"6.4 Heaps and Heapsort","children":[{"page":253,"title":"Notion of the Heap"},{"page":257,"title":"Heapsort"},{"page":259,"title":"Exercises 6.4"}]},{"page":260,"title":"6.5 Horner’s Rule and Binary Exponentiation","children":[{"page":260,"title":"Horner’s Rule"},{"page":262,"title":"Binary Exponentiation"},{"page":265,"title":"Exercises 6.5"}]},{"page":266,"title":"6.6 Problem Reduction","children":[{"page":267,"title":"Computing the Least Common Multiple"},{"page":268,"title":"Counting Paths in a Graph"},{"page":269,"title":"Reduction of Optimization Problems"},{"page":270,"title":"Linear Programming"},{"page":272,"title":"Reduction to Graph Problems"},{"page":274,"title":"Exercises 6.6"},{"page":276,"title":"Summary"}]}]},{"page":279,"title":"7 Space and Time Trade-Offs","children":[{"page":280,"title":"7.1 Sorting by Counting","children":[{"page":283,"title":"Exercises 7.1"}]},{"page":284,"title":"7.2 Input Enhancement in String Matching","children":[{"page":285,"title":"Horspool’s Algorithm"},{"page":289,"title":"Boyer-Moore Algorithm"},{"page":293,"title":"Exercises 7.2"}]},{"page":295,"title":"7.3 Hashing","children":[{"page":296,"title":"Open Hashing (Separate Chaining)"},{"page":298,"title":"Closed Hashing (Open Addressing)"},{"page":300,"title":"Exercises 7.3"}]},{"page":302,"title":"7.4 B-Trees","children":[{"page":305,"title":"Exercises 7.4"},{"page":306,"title":"Summary"}]}]},{"page":309,"title":"8 Dynamic Programming","children":[{"page":311,"title":"8.1 Three Basic Examples","children":[{"page":316,"title":"Exercises 8.1"}]},{"page":318,"title":"8.2 The Knapsack Problem and Memory Functions","children":[{"page":320,"title":"Memory Functions"},{"page":322,"title":"Exercises 8.2"}]},{"page":323,"title":"8.3 Optimal Binary Search Trees","children":[{"page":329,"title":"Exercises 8.3"}]},{"page":330,"title":"8.4 Warshall’s and Floyd’s Algorithms","children":[{"page":330,"title":"Warshall’s Algorithm"},{"page":334,"title":"Floyd’s Algorithm for the All-Pairs Shortest-Paths Problem"},{"page":337,"title":"Exercises 8.4"},{"page":338,"title":"Summary"}]}]},{"page":341,"title":"9 Greedy Technique","children":[{"page":344,"title":"9.1 Prim’s Algorithm","children":[{"page":348,"title":"Exercises 9.1"}]},{"page":351,"title":"9.2 Kruskal’s Algorithm","children":[{"page":353,"title":"Disjoint Subsets and Union-Find Algorithms"},{"page":357,"title":"Exercises 9.2"}]},{"page":359,"title":"9.3 Dijkstra’s Algorithm","children":[{"page":363,"title":"Exercises 9.3"}]},{"page":364,"title":"9.4 Huffman Trees and Codes","children":[{"page":368,"title":"Exercises 9.4"},{"page":370,"title":"Summary"}]}]},{"page":371,"title":"10 Iterative Improvement","children":[{"page":372,"title":"10.1 The Simplex Method","children":[{"page":373,"title":"Geometric Interpretation of Linear Programming"},{"page":377,"title":"An Outline of the Simplex Method"},{"page":383,"title":"Further Notes on the Simplex Method"},{"page":385,"title":"Exercises 10.1"}]},{"page":387,"title":"10.2 The Maximum-Flow Problem","children":[{"page":397,"title":"Exercises 10.2"}]},{"page":398,"title":"10.3 Maximum Matching in Bipartite Graphs","children":[{"page":404,"title":"Exercises 10.3"}]},{"page":406,"title":"10.4 The Stable Marriage Problem","children":[{"page":409,"title":"Exercises 10.4"},{"page":410,"title":"Summary"}]}]},{"page":413,"title":"11 Limitations of Algorithm Power","children":[{"page":414,"title":"11.1 Lower-Bound Arguments","children":[{"page":415,"title":"Trivial Lower Bounds"},{"page":416,"title":"Information-Theoretic Arguments"},{"page":416,"title":"Adversary Arguments"},{"page":417,"title":"Problem Reduction"},{"page":419,"title":"Exercises 11.1"}]},{"page":420,"title":"11.2 Decision Trees","children":[{"page":421,"title":"Decision Trees for Sorting"},{"page":423,"title":"Decision Trees for Searching a Sorted Array"},{"page":425,"title":"Exercises 11.2"}]},{"page":427,"title":"11.3 P, NP, and NP-Complete Problems","children":[{"page":428,"title":"P and NP Problems"},{"page":432,"title":"NP-Complete Problems"},{"page":435,"title":"Exercises 11.3"}]},{"page":438,"title":"11.4 Challenges of Numerical Algorithms","children":[{"page":445,"title":"Exercises 11.4"},{"page":446,"title":"Summary"}]}]},{"page":449,"title":"12 Coping with the Limitations of Algorithm Power","children":[{"page":450,"title":"12.1 Backtracking","children":[{"page":451,"title":"n-Queens Problem"},{"page":452,"title":"Hamiltonian Circuit Problem"},{"page":453,"title":"Subset-Sum Problem"},{"page":454,"title":"General Remarks"},{"page":456,"title":"Exercises 12.1"}]},{"page":458,"title":"12.2 Branch-and-Bound","children":[{"page":459,"title":"Assignment Problem"},{"page":462,"title":"Knapsack Problem"},{"page":464,"title":"Traveling Salesman Problem"},{"page":466,"title":"Exercises 12.2"}]},{"page":467,"title":"12.3 Approximation Algorithms for NP-Hard Problems","children":[{"page":469,"title":"Approximation Algorithms for the Traveling Salesman Problem"},{"page":479,"title":"Approximation Algorithms for the Knapsack Problem"},{"page":483,"title":"Exercises 12.3"}]},{"page":485,"title":"12.4 Algorithms for Solving Nonlinear Equations","children":[{"page":486,"title":"Bisection Method"},{"page":490,"title":"Method of False Position"},{"page":490,"title":"Newton’s Method"},{"page":493,"title":"Exercises 12.4"},{"page":494,"title":"Summary"}]}]},{"page":497,"title":"Epilogue"},{"page":501,"title":"APPENDIX A: Useful Formulas for the Analysis of Algorithms","children":[{"page":501,"title":"Properties of Logarithms"},{"page":501,"title":"Combinatorics"},{"page":502,"title":"Important Summation Formulas"},{"page":502,"title":"Sum Manipulation Rules"},{"page":503,"title":"Approximation of a Sum by a Definite Integral"},{"page":503,"title":"Floor and Ceiling Formulas"},{"page":503,"title":"Miscellaneous"}]},{"page":505,"title":"APPENDIX B: Short Tutorial on Recurrence Relations","children":[{"page":505,"title":"Sequences and Recurrence Relations"},{"page":506,"title":"Methods for Solving Recurrence Relations"},{"page":511,"title":"Common Recurrence Types in Algorithm Analysis"}]},{"page":519,"title":"References"},{"page":529,"title":"Hints to Exercises"},{"page":573,"title":"Index","children":[{"page":573,"title":"A"},{"page":574,"title":"B"},{"page":576,"title":"C"},{"page":577,"title":"D"},{"page":578,"title":"E"},{"page":579,"title":"F"},{"page":580,"title":"G"},{"page":581,"title":"H"},{"page":581,"title":"I"},{"page":582,"title":"J"},{"page":582,"title":"K"},{"page":582,"title":"L"},{"page":584,"title":"M"},{"page":585,"title":"N"},{"page":585,"title":"O"},{"page":585,"title":"P"},{"page":588,"title":"Q"},{"page":588,"title":"R"},{"page":588,"title":"S"},{"page":590,"title":"T"},{"page":590,"title":"U"},{"page":591,"title":"V"},{"page":591,"title":"W"}]}],"pages_count":592,"version":"6.15.2","dir":"ltr","state":"converting","token":"4a8b03583f119702","status":"SUCCEED","pages_count_fa":"۵۹۲"},"publisher":{"id":105,"title":"Pearson","description":null,"logo":null,"token":"4e9e4a99eea1a798","slug":"Pearson"},"tags":[{"title":"algorithms","token":"cd7cf7ad54e27c11","pivot":{"taggable_id":573,"tag_id":2731}},{"title":"طراحی الگوریتم","token":"2cce625e6845ad2d","pivot":{"taggable_id":573,"tag_id":2732}}],"study_subjects":[{"id":26035,"title":"طراحی الگوریتم ها","meta_title":"طراحی الگوریتم ها","meta_description":"طراحی الگوریتم ها - بوکت، نخستین و بزرگ‌ترین سامانه‌ی یادگیری و آموزش با قابلیت کرایه و خرید نسخه‌ی الکترونیکی کتاب‌های دانشگاهی است ","faq":null,"keywords":"بوکت,کرایه کتاب,کتاب الکترونیک/ نسخه الکترونیک,ئی بوک/ایبوک,مطالعه آنلاین,کتاب تخصصی,کتاب دانشگاهی,دانلود کتاب,خرید کتاب,جستجوی کتاب,خرید کتاب الکترونیک,ناشرشو,چاپ کتاب,چاپ رایگان کتاب,کتاب مهندسی,کتاب پزشکی,کتاب مدیریت,جیتجو در متن کتاب,دانلود اپلیکیشن کتابخوان","description":null,"token":"05ba630232278efd","type":"","books_count":5,"created_at":"2017-10-07 11:39:18","updated_at":"2022-11-27 13:23:09","study_fields":[{"id":898,"title":"مهندسی کامپیوتر","meta_title":"مهندسی کامپیوتر","meta_description":"مهندسی کامپیوتر - بوکت، نخستین و بزرگ‌ترین سامانه‌ی یادگیری و آموزش با قابلیت کرایه و خرید نسخه‌ی الکترونیکی کتاب‌های دانشگاهی است ","faq":null,"keywords":"بوکت,کرایه کتاب,کتاب الکترونیک/ نسخه الکترونیک,ئی بوک/ایبوک,مطالعه آنلاین,کتاب تخصصی,کتاب دانشگاهی,دانلود کتاب,خرید کتاب,جستجوی کتاب,خرید کتاب الکترونیک,ناشرشو,چاپ کتاب,چاپ رایگان کتاب,کتاب مهندسی,کتاب پزشکی,کتاب مدیریت,جیتجو در متن کتاب,دانلود اپلیکیشن کتابخوان","description":null,"token":"57bea94f4a51f6b8","books_count":33,"created_at":"2017-10-07 11:22:53","updated_at":"2024-11-22 18:27:59","study_groups":[{"id":10,"title":"فنی و مهندسی","meta_title":"فنی و مهندسی","meta_description":"فنی و مهندسی - بوکت، نخستین و بزرگ‌ترین سامانه‌ی یادگیری و آموزش با قابلیت کرایه و خرید نسخه‌ی الکترونیکی کتاب‌های دانشگاهی است ","faq":null,"keywords":"بوکت,کرایه کتاب,کتاب الکترونیک/ نسخه الکترونیک,ئی بوک/ایبوک,مطالعه آنلاین,کتاب تخصصی,کتاب دانشگاهی,دانلود کتاب,خرید کتاب,جستجوی کتاب,خرید کتاب الکترونیک,ناشرشو,چاپ کتاب,چاپ رایگان کتاب,کتاب مهندسی,کتاب پزشکی,کتاب مدیریت,جیتجو در متن کتاب,دانلود اپلیکیشن کتابخوان","description":null,"token":"cd075d6bdb3fbd29","style":{"first_color":"#F47820","second_color":"#F47820","icon":"images/categories/mohandesi.png"},"books_count":750,"created_at":"2017-10-07 11:22:44","updated_at":"2025-03-20 07:43:52"}]}]}],"study_fields":[{"id":898,"title":"مهندسی کامپیوتر","meta_title":"مهندسی کامپیوتر","meta_description":"مهندسی کامپیوتر - بوکت، نخستین و بزرگ‌ترین سامانه‌ی یادگیری و آموزش با قابلیت کرایه و خرید نسخه‌ی الکترونیکی کتاب‌های دانشگاهی است ","faq":null,"keywords":"بوکت,کرایه کتاب,کتاب الکترونیک/ نسخه الکترونیک,ئی بوک/ایبوک,مطالعه آنلاین,کتاب تخصصی,کتاب دانشگاهی,دانلود کتاب,خرید کتاب,جستجوی کتاب,خرید کتاب الکترونیک,ناشرشو,چاپ کتاب,چاپ رایگان کتاب,کتاب مهندسی,کتاب پزشکی,کتاب مدیریت,جیتجو در متن کتاب,دانلود اپلیکیشن کتابخوان","description":null,"token":"57bea94f4a51f6b8","books_count":33,"created_at":"2017-10-07 11:22:53","updated_at":"2024-11-22 18:27:59","study_groups":[{"id":10,"title":"فنی و مهندسی","meta_title":"فنی و مهندسی","meta_description":"فنی و مهندسی - بوکت، نخستین و بزرگ‌ترین سامانه‌ی یادگیری و آموزش با قابلیت کرایه و خرید نسخه‌ی الکترونیکی کتاب‌های دانشگاهی است ","faq":null,"keywords":"بوکت,کرایه کتاب,کتاب الکترونیک/ نسخه الکترونیک,ئی بوک/ایبوک,مطالعه آنلاین,کتاب تخصصی,کتاب دانشگاهی,دانلود کتاب,خرید کتاب,جستجوی کتاب,خرید کتاب الکترونیک,ناشرشو,چاپ کتاب,چاپ رایگان کتاب,کتاب مهندسی,کتاب پزشکی,کتاب مدیریت,جیتجو در متن کتاب,دانلود اپلیکیشن کتابخوان","description":null,"token":"cd075d6bdb3fbd29","style":{"first_color":"#F47820","second_color":"#F47820","icon":"images/categories/mohandesi.png"},"books_count":750,"created_at":"2017-10-07 11:22:44","updated_at":"2025-03-20 07:43:52"}]}],"study_groups":[{"id":10,"title":"فنی و مهندسی","meta_title":"فنی و مهندسی","meta_description":"فنی و مهندسی - بوکت، نخستین و بزرگ‌ترین سامانه‌ی یادگیری و آموزش با قابلیت کرایه و خرید نسخه‌ی الکترونیکی کتاب‌های دانشگاهی است ","faq":null,"keywords":"بوکت,کرایه کتاب,کتاب الکترونیک/ نسخه الکترونیک,ئی بوک/ایبوک,مطالعه آنلاین,کتاب تخصصی,کتاب دانشگاهی,دانلود کتاب,خرید کتاب,جستجوی کتاب,خرید کتاب الکترونیک,ناشرشو,چاپ کتاب,چاپ رایگان کتاب,کتاب مهندسی,کتاب پزشکی,کتاب مدیریت,جیتجو در متن کتاب,دانلود اپلیکیشن کتابخوان","description":null,"token":"cd075d6bdb3fbd29","style":{"first_color":"#F47820","second_color":"#F47820","icon":"images/categories/mohandesi.png"},"books_count":750,"created_at":"2017-10-07 11:22:44","updated_at":"2025-03-20 07:43:52"}],"views":1,"titleLink":"Introduction-to-The-Design-and-Analysis-of-Algorithms","ebook_price_en":7,"urlify":"Introduction-to-The-Design-and-Analysis-of-Algorithms","pages_count_fa":"۵۹۲","authorTitle":"Anany Levitin","tocStr":"Copyright Page, Title Page, Brief Contents, Contents, New to the Third Edition, Preface, Acknowledgments, 1 Introduction, 2 Fundamentals of the Analysis of Algorithm Efficiency, 3 Brute Force and Exhaustive Search, 4 Decrease-and-Conquer, 5 Divide-and-Conquer, 6 Transform-and-Conquer, 7 Space and Time Trade-Offs, 8 Dynamic Programming, 9 Greedy Technique, 10 Iterative Improvement, 11 Limitations of Algorithm Power, 12 Coping with the Limitations of Algorithm Power, Epilogue, APPENDIX A: Useful Formulas for the Analysis of Algorithms, APPENDIX B: Short Tutorial on Recurrence Relations, References, Hints to Exercises, Index","url":"/preview/4a8b03583f119702/Introduction-to-The-Design-and-Analysis-of-Algorithms"}

{"toc":[{"page":2,"title":"Copyright Page"},{"page":3,"title":"Title Page"},{"page":5,"title":"Brief Contents"},{"page":7,"title":"Contents"},{"page":17,"title":"New to the Third Edition"},{"page":19,"title":"Preface"},{"page":24,"title":"Acknowledgments"},{"page":27,"title":"1 Introduction","children":[{"page":29,"title":"1.1 What Is an Algorithm?","children":[{"page":33,"title":"Exercises 1.1"}]},{"page":35,"title":"1.2 Fundamentals of Algorithmic Problem Solving","children":[{"page":35,"title":"Understanding the Problem"},{"page":35,"title":"Ascertaining the Capabilities of the Computational Device"},{"page":37,"title":"Choosing between Exact and Approximate Problem Solving"},{"page":37,"title":"Algorithm Design Techniques"},{"page":38,"title":"Designing an Algorithm and Data Structures"},{"page":38,"title":"Methods of Specifying an Algorithm"},{"page":39,"title":"Proving an Algorithm’s Correctness"},{"page":40,"title":"Analyzing an Algorithm"},{"page":41,"title":"Coding an Algorithm"},{"page":43,"title":"Exercises 1.2"}]},{"page":44,"title":"1.3 Important Problem Types","children":[{"page":45,"title":"Sorting"},{"page":46,"title":"Searching"},{"page":46,"title":"String Processing"},{"page":47,"title":"Graph Problems"},{"page":47,"title":"Combinatorial Problems"},{"page":48,"title":"Geometric Problems"},{"page":48,"title":"Numerical Problems"},{"page":49,"title":"Exercises 1.3"}]},{"page":51,"title":"1.4 Fundamental Data Structures","children":[{"page":51,"title":"Linear Data Structures"},{"page":54,"title":"Graphs"},{"page":57,"title":"Trees"},{"page":61,"title":"Sets and Dictionaries"},{"page":63,"title":"Exercises 1.4"},{"page":64,"title":"Summary"}]}]},{"page":67,"title":"2 Fundamentals of the Analysis of Algorithm Efficiency","children":[{"page":68,"title":"2.1 The Analysis Framework","children":[{"page":69,"title":"Measuring an Input’s Size"},{"page":70,"title":"Units for Measuring Running Time"},{"page":71,"title":"Orders of Growth"},{"page":73,"title":"Worst-Case, Best-Case, and Average-Case Efficiencies"},{"page":76,"title":"Recapitulation of the Analysis Framework"},{"page":76,"title":"Exercises 2.1"}]},{"page":78,"title":"2.2 Asymptotic Notations and Basic Efficiency Classes","children":[{"page":78,"title":"Informal Introduction"},{"page":79,"title":"O-notation"},{"page":80,"title":"Ω-notation"},{"page":81,"title":"Θ-notation"},{"page":81,"title":"Useful Property Involving the Asymptotic Notations"},{"page":82,"title":"Using Limits for Comparing Orders of Growth"},{"page":84,"title":"Basic Efficiency Classes"},{"page":84,"title":"Exercises 2.2"}]},{"page":87,"title":"2.3 Mathematical Analysis of Nonrecursive Algorithms","children":[{"page":93,"title":"Exercises 2.3"}]},{"page":96,"title":"2.4 Mathematical Analysis of Recursive Algorithms","children":[{"page":102,"title":"Exercises 2.4"}]},{"page":106,"title":"2.5 Example: Computing the nth Fibonacci Number","children":[{"page":109,"title":"Exercises 2.5"}]},{"page":110,"title":"2.6 Empirical Analysis of Algorithms","children":[{"page":115,"title":"Exercises 2.6"}]},{"page":117,"title":"2.7 Algorithm Visualization","children":[{"page":120,"title":"Summary"}]}]},{"page":123,"title":"3 Brute Force and Exhaustive Search","children":[{"page":124,"title":"3.1 Selection Sort and Bubble Sort","children":[{"page":124,"title":"Selection Sort"},{"page":126,"title":"Bubble Sort"},{"page":128,"title":"Exercises 3.1"}]},{"page":130,"title":"3.2 Sequential Search and Brute-Force String Matching","children":[{"page":130,"title":"Sequential Search"},{"page":131,"title":"Brute-Force String Matching"},{"page":132,"title":"Exercises 3.2"}]},{"page":134,"title":"3.3 Closest-Pair and Convex-Hull Problems by Brute Force","children":[{"page":134,"title":"Closest-Pair Problem"},{"page":135,"title":"Convex-Hull Problem"},{"page":139,"title":"Exercises 3.3"}]},{"page":141,"title":"3.4 Exhaustive Search","children":[{"page":142,"title":"Traveling Salesman Problem"},{"page":142,"title":"Knapsack Problem"},{"page":145,"title":"Assignment Problem"},{"page":146,"title":"Exercises 3.4"}]},{"page":148,"title":"3.5 Depth-First Search and Breadth-First Search","children":[{"page":148,"title":"Depth-First Search"},{"page":151,"title":"Breadth-First Search"},{"page":154,"title":"Exercises 3.5"},{"page":156,"title":"Summary"}]}]},{"page":157,"title":"4 Decrease-and-Conquer","children":[{"page":160,"title":"4.1 Insertion Sort","children":[{"page":162,"title":"Exercises 4.1"}]},{"page":164,"title":"4.2 Topological Sorting","children":[{"page":168,"title":"Exercises 4.2"}]},{"page":170,"title":"4.3 Algorithms for Generating Combinatorial Objects","children":[{"page":170,"title":"Generating Permutations"},{"page":172,"title":"Generating Subsets"},{"page":174,"title":"Exercises 4.3"}]},{"page":176,"title":"4.4 Decrease-by-a-Constant-Factor Algorithms","children":[{"page":176,"title":"Binary Search"},{"page":178,"title":"Fake-Coin Problem"},{"page":179,"title":"Russian Peasant Multiplication"},{"page":180,"title":"Josephus Problem"},{"page":182,"title":"Exercises 4.4"}]},{"page":183,"title":"4.5 Variable-Size-Decrease Algorithms","children":[{"page":184,"title":"Computing a Median and the Selection Problem"},{"page":187,"title":"Interpolation Search"},{"page":189,"title":"Searching and Insertion in a Binary Search Tree"},{"page":190,"title":"The Game of Nim"},{"page":192,"title":"Exercises 4.5"},{"page":193,"title":"Summary"}]}]},{"page":195,"title":"5 Divide-and-Conquer","children":[{"page":198,"title":"5.1 Mergesort","children":[{"page":200,"title":"Exercises 5.1"}]},{"page":202,"title":"5.2 Quicksort","children":[{"page":207,"title":"Exercises 5.2"}]},{"page":208,"title":"5.3 Binary Tree Traversals and Related Properties","children":[{"page":211,"title":"Exercises 5.3"}]},{"page":212,"title":"5.4 Multiplication of Large Integers and Strassen’s Matrix Multiplication","children":[{"page":213,"title":"Multiplication of Large Integers"},{"page":215,"title":"Strassen’s Matrix Multiplication"},{"page":217,"title":"Exercises 5.4"}]},{"page":218,"title":"5.5 The Closest-Pair and Convex-Hull Problems by Divide-and-Conquer","children":[{"page":218,"title":"The Closest-Pair Problem"},{"page":221,"title":"Convex-Hull Problem"},{"page":223,"title":"Exercises 5.5"},{"page":224,"title":"Summary"}]}]},{"page":227,"title":"6 Transform-and-Conquer","children":[{"page":228,"title":"6.1 Presorting","children":[{"page":231,"title":"Exercises 6.1"}]},{"page":234,"title":"6.2 Gaussian Elimination","children":[{"page":238,"title":"LU Decomposition"},{"page":240,"title":"Computing a Matrix Inverse"},{"page":241,"title":"Computing a Determinant"},{"page":242,"title":"Exercises 6.2"}]},{"page":244,"title":"6.3 Balanced Search Trees","children":[{"page":244,"title":"AVL Trees"},{"page":249,"title":"2-3 Trees"},{"page":251,"title":"Exercises 6.3"}]},{"page":252,"title":"6.4 Heaps and Heapsort","children":[{"page":253,"title":"Notion of the Heap"},{"page":257,"title":"Heapsort"},{"page":259,"title":"Exercises 6.4"}]},{"page":260,"title":"6.5 Horner’s Rule and Binary Exponentiation","children":[{"page":260,"title":"Horner’s Rule"},{"page":262,"title":"Binary Exponentiation"},{"page":265,"title":"Exercises 6.5"}]},{"page":266,"title":"6.6 Problem Reduction","children":[{"page":267,"title":"Computing the Least Common Multiple"},{"page":268,"title":"Counting Paths in a Graph"},{"page":269,"title":"Reduction of Optimization Problems"},{"page":270,"title":"Linear Programming"},{"page":272,"title":"Reduction to Graph Problems"},{"page":274,"title":"Exercises 6.6"},{"page":276,"title":"Summary"}]}]},{"page":279,"title":"7 Space and Time Trade-Offs","children":[{"page":280,"title":"7.1 Sorting by Counting","children":[{"page":283,"title":"Exercises 7.1"}]},{"page":284,"title":"7.2 Input Enhancement in String Matching","children":[{"page":285,"title":"Horspool’s Algorithm"},{"page":289,"title":"Boyer-Moore Algorithm"},{"page":293,"title":"Exercises 7.2"}]},{"page":295,"title":"7.3 Hashing","children":[{"page":296,"title":"Open Hashing (Separate Chaining)"},{"page":298,"title":"Closed Hashing (Open Addressing)"},{"page":300,"title":"Exercises 7.3"}]},{"page":302,"title":"7.4 B-Trees","children":[{"page":305,"title":"Exercises 7.4"},{"page":306,"title":"Summary"}]}]},{"page":309,"title":"8 Dynamic Programming","children":[{"page":311,"title":"8.1 Three Basic Examples","children":[{"page":316,"title":"Exercises 8.1"}]},{"page":318,"title":"8.2 The Knapsack Problem and Memory Functions","children":[{"page":320,"title":"Memory Functions"},{"page":322,"title":"Exercises 8.2"}]},{"page":323,"title":"8.3 Optimal Binary Search Trees","children":[{"page":329,"title":"Exercises 8.3"}]},{"page":330,"title":"8.4 Warshall’s and Floyd’s Algorithms","children":[{"page":330,"title":"Warshall’s Algorithm"},{"page":334,"title":"Floyd’s Algorithm for the All-Pairs Shortest-Paths Problem"},{"page":337,"title":"Exercises 8.4"},{"page":338,"title":"Summary"}]}]},{"page":341,"title":"9 Greedy Technique","children":[{"page":344,"title":"9.1 Prim’s Algorithm","children":[{"page":348,"title":"Exercises 9.1"}]},{"page":351,"title":"9.2 Kruskal’s Algorithm","children":[{"page":353,"title":"Disjoint Subsets and Union-Find Algorithms"},{"page":357,"title":"Exercises 9.2"}]},{"page":359,"title":"9.3 Dijkstra’s Algorithm","children":[{"page":363,"title":"Exercises 9.3"}]},{"page":364,"title":"9.4 Huffman Trees and Codes","children":[{"page":368,"title":"Exercises 9.4"},{"page":370,"title":"Summary"}]}]},{"page":371,"title":"10 Iterative Improvement","children":[{"page":372,"title":"10.1 The Simplex Method","children":[{"page":373,"title":"Geometric Interpretation of Linear Programming"},{"page":377,"title":"An Outline of the Simplex Method"},{"page":383,"title":"Further Notes on the Simplex Method"},{"page":385,"title":"Exercises 10.1"}]},{"page":387,"title":"10.2 The Maximum-Flow Problem","children":[{"page":397,"title":"Exercises 10.2"}]},{"page":398,"title":"10.3 Maximum Matching in Bipartite Graphs","children":[{"page":404,"title":"Exercises 10.3"}]},{"page":406,"title":"10.4 The Stable Marriage Problem","children":[{"page":409,"title":"Exercises 10.4"},{"page":410,"title":"Summary"}]}]},{"page":413,"title":"11 Limitations of Algorithm Power","children":[{"page":414,"title":"11.1 Lower-Bound Arguments","children":[{"page":415,"title":"Trivial Lower Bounds"},{"page":416,"title":"Information-Theoretic Arguments"},{"page":416,"title":"Adversary Arguments"},{"page":417,"title":"Problem Reduction"},{"page":419,"title":"Exercises 11.1"}]},{"page":420,"title":"11.2 Decision Trees","children":[{"page":421,"title":"Decision Trees for Sorting"},{"page":423,"title":"Decision Trees for Searching a Sorted Array"},{"page":425,"title":"Exercises 11.2"}]},{"page":427,"title":"11.3 P, NP, and NP-Complete Problems","children":[{"page":428,"title":"P and NP Problems"},{"page":432,"title":"NP-Complete Problems"},{"page":435,"title":"Exercises 11.3"}]},{"page":438,"title":"11.4 Challenges of Numerical Algorithms","children":[{"page":445,"title":"Exercises 11.4"},{"page":446,"title":"Summary"}]}]},{"page":449,"title":"12 Coping with the Limitations of Algorithm Power","children":[{"page":450,"title":"12.1 Backtracking","children":[{"page":451,"title":"n-Queens Problem"},{"page":452,"title":"Hamiltonian Circuit Problem"},{"page":453,"title":"Subset-Sum Problem"},{"page":454,"title":"General Remarks"},{"page":456,"title":"Exercises 12.1"}]},{"page":458,"title":"12.2 Branch-and-Bound","children":[{"page":459,"title":"Assignment Problem"},{"page":462,"title":"Knapsack Problem"},{"page":464,"title":"Traveling Salesman Problem"},{"page":466,"title":"Exercises 12.2"}]},{"page":467,"title":"12.3 Approximation Algorithms for NP-Hard Problems","children":[{"page":469,"title":"Approximation Algorithms for the Traveling Salesman Problem"},{"page":479,"title":"Approximation Algorithms for the Knapsack Problem"},{"page":483,"title":"Exercises 12.3"}]},{"page":485,"title":"12.4 Algorithms for Solving Nonlinear Equations","children":[{"page":486,"title":"Bisection Method"},{"page":490,"title":"Method of False Position"},{"page":490,"title":"Newton’s Method"},{"page":493,"title":"Exercises 12.4"},{"page":494,"title":"Summary"}]}]},{"page":497,"title":"Epilogue"},{"page":501,"title":"APPENDIX A: Useful Formulas for the Analysis of Algorithms","children":[{"page":501,"title":"Properties of Logarithms"},{"page":501,"title":"Combinatorics"},{"page":502,"title":"Important Summation Formulas"},{"page":502,"title":"Sum Manipulation Rules"},{"page":503,"title":"Approximation of a Sum by a Definite Integral"},{"page":503,"title":"Floor and Ceiling Formulas"},{"page":503,"title":"Miscellaneous"}]},{"page":505,"title":"APPENDIX B: Short Tutorial on Recurrence Relations","children":[{"page":505,"title":"Sequences and Recurrence Relations"},{"page":506,"title":"Methods for Solving Recurrence Relations"},{"page":511,"title":"Common Recurrence Types in Algorithm Analysis"}]},{"page":519,"title":"References"},{"page":529,"title":"Hints to Exercises"},{"page":573,"title":"Index","children":[{"page":573,"title":"A"},{"page":574,"title":"B"},{"page":576,"title":"C"},{"page":577,"title":"D"},{"page":578,"title":"E"},{"page":579,"title":"F"},{"page":580,"title":"G"},{"page":581,"title":"H"},{"page":581,"title":"I"},{"page":582,"title":"J"},{"page":582,"title":"K"},{"page":582,"title":"L"},{"page":584,"title":"M"},{"page":585,"title":"N"},{"page":585,"title":"O"},{"page":585,"title":"P"},{"page":588,"title":"Q"},{"page":588,"title":"R"},{"page":588,"title":"S"},{"page":590,"title":"T"},{"page":590,"title":"U"},{"page":591,"title":"V"},{"page":591,"title":"W"}]}],"pages_count":592,"version":"6.15.2","dir":"ltr","state":"converting","token":"4a8b03583f119702","status":"SUCCEED","pages":[{"token":null,"index":0,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/7594374b5cec75028ef1d6e26d7e3e9f.jpg","blurred":"/storage/books/4a8b03583f119702/pages/f41d2a4e5da4de461eba8781eeb7eb24.jpg"},"info":{"width":559.44,"height":795.6,"margin":[0.35709,0.23928,0.35915,0.74564]},"elements":[{"words":[{"str":"This","boundary":[0.3570897683397683,0.23927657192684773,0.39406531531531525,0.2543595281862746],"dir":"ltr"},{"str":"page","boundary":[0.3994278206778206,0.23927657192684773,0.4411438223938223,0.2543595281862746],"dir":"ltr"},{"str":"intentionally","boundary":[0.4465063277563277,0.23927657192684773,0.5550134062634061,0.2543595281862746],"dir":"ltr"},{"str":"left","boundary":[0.5603759116259115,0.23927657192684773,0.5878061990561989,0.2543595281862746],"dir":"ltr"},{"str":"blank","boundary":[0.5931687044187043,0.23927657192684773,0.640852102102102,0.2543595281862746],"dir":"ltr"}],"boundary":[0.35709,0.23928,0.64085,0.25436],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":1,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/6ae87982a6bc225f77af698f514cb854.jpg","blurred":"/storage/books/4a8b03583f119702/pages/8aceb138758e65974261ebe17e815ab7.jpg"},"info":{"width":503.999986,"height":652.3200059999999,"margin":[0,0,0,0]},"elements":[]},{"token":null,"index":2,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/508a403e985414575c4d25320bb9e27d.jpg","blurred":"/storage/books/4a8b03583f119702/pages/72cb38ab21f5858084e98e496b18aef2.jpg"},"info":{"width":504,"height":652.32001,"margin":[0.23869,0.05937,0.07337,0.06327]},"elements":[{"words":[{"str":"Vice","boundary":[0.23869047619047618,0.05936832598466516,0.27167277103174603,0.07234999122593225],"dir":"ltr"},{"str":"President","boundary":[0.2758732670634921,0.05936832598466516,0.3449630257936508,0.07234999122593225],"dir":"ltr"},{"str":"and","boundary":[0.3491635218253968,0.05936832598466516,0.3762483202380952,0.07234999122593225],"dir":"ltr"},{"str":"Editorial","boundary":[0.3804488162698413,0.05936832598466516,0.4458085345238096,0.07234999122593225],"dir":"ltr"},{"str":"Director,","boundary":[0.4500090305555556,0.05936832598466516,0.5164440757936508,0.07234999122593225],"dir":"ltr"},{"str":"ECS","boundary":[0.5206445718253969,0.05936832598466516,0.5542485400793651,0.07234999122593225],"dir":"ltr"},{"str":"Marcia","boundary":[0.5710522044047619,0.05936832598466516,0.6223822659126984,0.07234999122593225],"dir":"ltr"},{"str":"Horton","boundary":[0.6265827619444443,0.05936832598466516,0.67981144765873,0.07234999122593225],"dir":"ltr"},{"str":"Editor-in-Chief","boundary":[0.4422129099206349,0.07693251905609946,0.5542485400793651,0.08991418429736656],"dir":"ltr"},{"str":"Michael","boundary":[0.5710522044047619,0.07693251905609946,0.6287166139285714,0.08991418429736656],"dir":"ltr"},{"str":"Hirsch","boundary":[0.6329171099603174,0.07693251905609946,0.6812564182936507,0.08991418429736656],"dir":"ltr"},{"str":"Acquisitions","boundary":[0.41084360555555555,0.09449541396100965,0.5024312210317461,0.10747707920227674],"dir":"ltr"},{"str":"Editor","boundary":[0.5066317170634921,0.09449541396100965,0.5542485400793651,0.10747707920227674],"dir":"ltr"},{"str":"Matt","boundary":[0.5710522044047619,0.09449541396100965,0.6046561726587301,0.10747707920227674],"dir":"ltr"},{"str":"Goldstein","boundary":[0.6088566686904762,0.09449541396100965,0.678887338531746,0.10747707920227674],"dir":"ltr"},{"str":"Editorial","boundary":[0.417398059563492,0.11205701069939573,0.4827577778174603,0.1250386759406628],"dir":"ltr"},{"str":"Assistant","boundary":[0.4869582738492063,0.11205701069939573,0.5542502202777777,0.1250386759406628],"dir":"ltr"},{"str":"Chelsea","boundary":[0.5710522044047619,0.11205701069939573,0.6270532174999999,0.1250386759406628],"dir":"ltr"},{"str":"Bell","boundary":[0.631253713531746,0.11205701069939573,0.6601867301984126,0.1250386759406628],"dir":"ltr"},{"str":"Vice","boundary":[0.3630268389285714,0.12961990560430592,0.3960091337698412,0.142601570845573],"dir":"ltr"},{"str":"President,","boundary":[0.40020962980158725,0.12961990560430592,0.473499884563492,0.142601570845573],"dir":"ltr"},{"str":"Marketing","boundary":[0.47770038059523806,0.12961990560430592,0.5542502202777778,0.142601570845573],"dir":"ltr"},{"str":"Patrice","boundary":[0.5710522044047619,0.12961990560430592,0.6205340476587301,0.142601570845573],"dir":"ltr"},{"str":"Jones","boundary":[0.6247345436904762,0.12961990560430592,0.6637823548015873,0.142601570845573],"dir":"ltr"},{"str":"Marketing","boundary":[0.40815528809523804,0.14718150234269198,0.48470512777777774,0.16016316758395907],"dir":"ltr"},{"str":"Manager","boundary":[0.48890562380952374,0.14718150234269198,0.554248540079365,0.16016316758395907],"dir":"ltr"},{"str":"Yezan","boundary":[0.5710522044047619,0.14718150234269198,0.61524142265873,0.16016316758395907],"dir":"ltr"},{"str":"Alayan","boundary":[0.6194419186904762,0.14718150234269198,0.671427257579365,0.16016316758395907],"dir":"ltr"},{"str":"Senior","boundary":[0.33108626710317457,0.16474439724760218,0.3787198921031746,0.17772606248886927],"dir":"ltr"},{"str":"Marketing","boundary":[0.3829203881349206,0.16474439724760218,0.4594702278174602,0.17772606248886927],"dir":"ltr"},{"str":"Coordinator","boundary":[0.46367072384920627,0.16474439724760218,0.5542502202777777,0.17772606248886927],"dir":"ltr"},{"str":"Kathryn","boundary":[0.5710522044047619,0.16474439724760218,0.6308168619444444,0.17772606248886927],"dir":"ltr"},{"str":"Ferranti","boundary":[0.6350173579761904,0.16474439724760218,0.6919760841666667,0.17772606248886927],"dir":"ltr"},{"str":"Marketing","boundary":[0.4062062579365079,0.18230729215251237,0.48275609761904764,0.19528895739377944],"dir":"ltr"},{"str":"Assistant","boundary":[0.48695659365079363,0.18230729215251237,0.554248540079365,0.19528895739377944],"dir":"ltr"},{"str":"Emma","boundary":[0.5710522044047619,0.18230729215251237,0.6195763345634919,0.19528895739377944],"dir":"ltr"},{"str":"Snider","boundary":[0.623776830595238,0.18230729215251237,0.6704695444841269,0.19528895739377944],"dir":"ltr"},{"str":"Vice","boundary":[0.3583374051587301,0.1998688888908984,0.39131969999999994,0.2128505541321655],"dir":"ltr"},{"str":"President,","boundary":[0.395520196031746,0.1998688888908984,0.46881045079365075,0.2128505541321655],"dir":"ltr"},{"str":"Production","boundary":[0.4730109468253968,0.1998688888908984,0.554248540079365,0.2128505541321655],"dir":"ltr"},{"str":"Vince","boundary":[0.5710522044047619,0.1998688888908984,0.611192144484127,0.2128505541321655],"dir":"ltr"},{"str":"O’Brien","boundary":[0.615392640515873,0.1998688888908984,0.6741995849603175,0.2128505541321655],"dir":"ltr"},{"str":"Managing","boundary":[0.42961142182539674,0.2174343801288569,0.502431221031746,0.230416045370124],"dir":"ltr"},{"str":"Editor","boundary":[0.506631717063492,0.2174343801288569,0.554248540079365,0.230416045370124],"dir":"ltr"},{"str":"Jeff","boundary":[0.5710522044047619,0.2174343801288569,0.5960703587698413,0.230416045370124],"dir":"ltr"},{"str":"Holcomb","boundary":[0.6002708548015873,0.2174343801288569,0.6684197024206349,0.230416045370124],"dir":"ltr"},{"str":"Production","boundary":[0.3469960658730158,0.23499597686724308,0.4282336591269841,0.24797764210851014],"dir":"ltr"},{"str":"Project","boundary":[0.43243415515873007,0.23499597686724308,0.4847051277777777,0.24797764210851014],"dir":"ltr"},{"str":"Manager","boundary":[0.48890562380952374,0.23499597686724308,0.554248540079365,0.24797764210851014],"dir":"ltr"},{"str":"Kayla","boundary":[0.5710522044047619,0.23499597686724308,0.6136956401190475,0.24797764210851014],"dir":"ltr"},{"str":"Smith-Tarbox","boundary":[0.6178961361507935,0.23499597686724308,0.716893426626984,0.24797764210851014],"dir":"ltr"},{"str":"Senior","boundary":[0.33760375674603166,0.25256016993867747,0.38523738174603167,0.26554183517994456],"dir":"ltr"},{"str":"Operations","boundary":[0.38943787777777766,0.25256016993867747,0.47159958015873005,0.26554183517994456],"dir":"ltr"},{"str":"Supervisor","boundary":[0.47580007619047615,0.25256016993867747,0.554248540079365,0.26554183517994456],"dir":"ltr"},{"str":"Alan","boundary":[0.5710522044047619,0.25256016993867747,0.6065379948809523,0.26554183517994456],"dir":"ltr"},{"str":"Fischer","boundary":[0.6107384909126983,0.25256016993867747,0.6628078397222221,0.26554183517994456],"dir":"ltr"},{"str":"Manufacturing","boundary":[0.39694836468253963,0.2701230648435877,0.5052371523809523,0.2831047300848548],"dir":"ltr"},{"str":"Buyer","boundary":[0.5094376484126983,0.2701230648435877,0.554248540079365,0.2831047300848548],"dir":"ltr"},{"str":"Lisa","boundary":[0.5710522044047619,0.2701230648435877,0.6027911524206349,0.2831047300848548],"dir":"ltr"},{"str":"McDowell","boundary":[0.6069916484523808,0.2701230648435877,0.6822813393253968,0.2831047300848548],"dir":"ltr"},{"str":"Art","boundary":[0.46129996388888883,0.28768595974849803,0.48751105912698406,0.30066762498976507],"dir":"ltr"},{"str":"Director","boundary":[0.4917115551587301,0.28768595974849803,0.554248540079365,0.30066762498976507],"dir":"ltr"},{"str":"Anthony","boundary":[0.5710522044047619,0.28768595974849803,0.6345637044047618,0.30066762498976507],"dir":"ltr"},{"str":"Gemmellaro","boundary":[0.6387642004365078,0.28768595974849803,0.7292932909126983,0.30066762498976507],"dir":"ltr"},{"str":"Text","boundary":[0.4520269488492063,0.3052475564868842,0.4837658968650793,0.31822922172815127],"dir":"ltr"},{"str":"Designer","boundary":[0.48796639289682536,0.3052475564868842,0.5542502202777777,0.31822922172815127],"dir":"ltr"},{"str":"Sandra","boundary":[0.5710522044047619,0.3052475564868842,0.6224158698809523,0.31822922172815127],"dir":"ltr"},{"str":"Rigney","boundary":[0.6266163659126983,0.3052475564868842,0.6770223182936508,0.31822922172815127],"dir":"ltr"},{"str":"Cover","boundary":[0.43895500519841263,0.32281045139179443,0.4837658968650793,0.3357921166330615],"dir":"ltr"},{"str":"Designer","boundary":[0.48796639289682536,0.32281045139179443,0.5542502202777777,0.3357921166330615],"dir":"ltr"},{"str":"Anthony","boundary":[0.5710522044047619,0.32281045139179443,0.6345637044047618,0.3357921166330615],"dir":"ltr"},{"str":"Gemmellaro","boundary":[0.6387642004365078,0.32281045139179443,0.7292932909126983,0.3357921166330615],"dir":"ltr"},{"str":"Cover","boundary":[0.42400123932539674,0.34037334629670474,0.4688121309920634,0.3533550115379718],"dir":"ltr"},{"str":"Illustration","boundary":[0.4730126270238095,0.34037334629670474,0.5542502202777777,0.3533550115379718],"dir":"ltr"},{"str":"Jennifer","boundary":[0.5710522044047619,0.34037334629670474,0.6278261087698411,0.3533550115379718],"dir":"ltr"},{"str":"Kohnke","boundary":[0.6320266048015872,0.34037334629670474,0.6890021329761904,0.3533550115379718],"dir":"ltr"},{"str":"Media","boundary":[0.4557569893253968,0.3579349430350909,0.5024329012301587,0.370916608276358],"dir":"ltr"},{"str":"Editor","boundary":[0.5066333972619048,0.3579349430350909,0.5542502202777778,0.370916608276358],"dir":"ltr"},{"str":"Daniel","boundary":[0.5710522044047619,0.3579349430350909,0.619593136547619,0.370916608276358],"dir":"ltr"},{"str":"Sandin","boundary":[0.623793632579365,0.3579349430350909,0.6742331889285713,0.370916608276358],"dir":"ltr"},{"str":"Full-Service","boundary":[0.30967885912698406,0.37549783794000113,0.3974356222222222,0.3884795031812682],"dir":"ltr"},{"str":"Project","boundary":[0.4016361182539682,0.37549783794000113,0.45390709087301584,0.3884795031812682],"dir":"ltr"},{"str":"Management","boundary":[0.4581075869047619,0.37549783794000113,0.554248540079365,0.3884795031812682],"dir":"ltr"},{"str":"Windfall","boundary":[0.5710522044047619,0.37549783794000113,0.6333035555952381,0.3884795031812682],"dir":"ltr"},{"str":"Software","boundary":[0.6375040516269841,0.37549783794000113,0.7009819476587302,0.3884795031812682],"dir":"ltr"},{"str":"Composition","boundary":[0.4599390031746031,0.39306073284491144,0.554248540079365,0.4060423980861786],"dir":"ltr"},{"str":"Windfall","boundary":[0.5710522044047619,0.39306073284491144,0.6333035555952381,0.4060423980861786],"dir":"ltr"},{"str":"Software,","boundary":[0.6375040516269841,0.39306073284491144,0.7047623940873016,0.4060423980861786],"dir":"ltr"},{"str":"using","boundary":[0.7089628901190476,0.39306073284491144,0.7472546119444443,0.4060423980861786],"dir":"ltr"},{"str":"ZzTEX","boundary":[0.7514551079761904,0.3930594346783873,0.8027381239285714,0.40936180988837056],"dir":"ltr"},{"str":"Printer/Binder","boundary":[0.44780965083333324,0.4106210314167734,0.5542502202777777,0.42360269665804057],"dir":"ltr"},{"str":"Courier","boundary":[0.5710538846031745,0.4106210314167734,0.6270716996825396,0.42360269665804057],"dir":"ltr"},{"str":"Westford","boundary":[0.6312721957142857,0.4106210314167734,0.6953885671428571,0.42360269665804057],"dir":"ltr"},{"str":"Cover","boundary":[0.45389364928571424,0.42818392632168367,0.4987045409523809,0.4411655915629508],"dir":"ltr"},{"str":"Printer","boundary":[0.5029050369841269,0.42818392632168367,0.5542519004761904,0.4411655915629508],"dir":"ltr"},{"str":"Courier","boundary":[0.5710538846031745,0.42818392632168367,0.6270716996825396,0.4411655915629508],"dir":"ltr"},{"str":"Westford","boundary":[0.6312721957142857,0.42818392632168367,0.6953885671428571,0.4411655915629508],"dir":"ltr"},{"str":"Text","boundary":[0.48469000599206347,0.445746821226594,0.5164289540079364,0.4587284864678611],"dir":"ltr"},{"str":"Font","boundary":[0.5206294500396825,0.445746821226594,0.5542502202777777,0.4587284864678611],"dir":"ltr"},{"str":"Times","boundary":[0.5710538846031745,0.445746821226594,0.6143021917460317,0.4587284864678611],"dir":"ltr"},{"str":"Ten","boundary":[0.6185026877777777,0.445746821226594,0.6449658127777778,0.4587284864678611],"dir":"ltr"},{"str":"Copyright","boundary":[0.23869215638888883,0.470182209710231,0.31245286670634914,0.4831638749514981],"dir":"ltr"},{"str":"©","boundary":[0.31603168932539677,0.470182209710231,0.3294732766269841,0.4831638749514981],"dir":"ltr"},{"str":"2012,","boundary":[0.33305209924603174,0.470182209710231,0.370856563531746,0.4831638749514981],"dir":"ltr"},{"str":"2007,","boundary":[0.3745530000396825,0.470182209710231,0.41235746432539677,0.4831638749514981],"dir":"ltr"},{"str":"2003","boundary":[0.41605390083333327,0.470182209710231,0.4496578690873015,0.4831638749514981],"dir":"ltr"},{"str":"Pearson","boundary":[0.4532366917063491,0.470182209710231,0.5120604381349206,0.4831638749514981],"dir":"ltr"},{"str":"Education,","boundary":[0.5156392607539683,0.470182209710231,0.5954654873412698,0.4831638749514981],"dir":"ltr"},{"str":"Inc.,","boundary":[0.5991619238492063,0.470182209710231,0.6305984361507935,0.4831638749514981],"dir":"ltr"},{"str":"publishing","boundary":[0.6342948726587301,0.470182209710231,0.7099542071825397,0.4831638749514981],"dir":"ltr"},{"str":"as","boundary":[0.7135330298015873,0.470182209710231,0.7284699936904762,0.4831638749514981],"dir":"ltr"},{"str":"Addison-Wesley.","boundary":[0.7320488163095237,0.470182209710231,0.8549217262301586,0.4831638749514981],"dir":"ltr"},{"str":"All","boundary":[0.8585005488492063,0.470182209710231,0.8819225147222222,0.4831638749514981],"dir":"ltr"},{"str":"rights","boundary":[0.8855013373412697,0.470182209710231,0.9265821885317459,0.4831638749514981],"dir":"ltr"},{"str":"reserved.","boundary":[0.23869215638888883,0.485836799824675,0.3054464393253968,0.4988184650659421],"dir":"ltr"},{"str":"Printed","boundary":[0.3098989651190476,0.485836799824675,0.36405175996031747,0.4988184650659421],"dir":"ltr"},{"str":"in","boundary":[0.36850428575396815,0.485836799824675,0.38251714051587293,0.4988184650659421],"dir":"ltr"},{"str":"the","boundary":[0.3869696663095238,0.485836799824675,0.4103076222619047,0.4988184650659421],"dir":"ltr"},{"str":"United","boundary":[0.4147601480555555,0.485836799824675,0.466107011547619,0.4988184650659421],"dir":"ltr"},{"str":"States","boundary":[0.4705595373412698,0.485836799824675,0.5144295178968253,0.4988184650659421],"dir":"ltr"},{"str":"of","boundary":[0.5188820436904761,0.485836799824675,0.5338190075793651,0.4988184650659421],"dir":"ltr"},{"str":"America.","boundary":[0.5382715333730158,0.485836799824675,0.6060171333730159,0.4988184650659421],"dir":"ltr"},{"str":"This","boundary":[0.6104696591666667,0.485836799824675,0.6415533298015874,0.4988184650659421],"dir":"ltr"},{"str":"publication","boundary":[0.6460058555952382,0.485836799824675,0.7281843599603175,0.4988184650659421],"dir":"ltr"},{"str":"is","boundary":[0.7326368857539683,0.485836799824675,0.7438438091666668,0.4988184650659421],"dir":"ltr"},{"str":"protected","boundary":[0.7482963349603176,0.485836799824675,0.8183102028174604,0.4988184650659421],"dir":"ltr"},{"str":"by","boundary":[0.8227627286111112,0.485836799824675,0.8405056238492065,0.4988184650659421],"dir":"ltr"},{"str":"Copyright,","boundary":[0.8449581496428572,0.485836799824675,0.9229193559920635,0.4988184650659421],"dir":"ltr"},{"str":"and","boundary":[0.23869215638888883,0.5014913899391189,0.26577695480158725,0.5144730551803861],"dir":"ltr"},{"str":"permission","boundary":[0.27069993615079363,0.5014913899391189,0.3500725091666666,0.5144730551803861],"dir":"ltr"},{"str":"should","boundary":[0.354995490515873,0.5014913899391189,0.4035700266269841,0.5144730551803861],"dir":"ltr"},{"str":"be","boundary":[0.4084930079761905,0.5014913899391189,0.42623590321428567,0.5144730551803861],"dir":"ltr"},{"str":"obtained","boundary":[0.431158884563492,0.5014913899391189,0.49559449369047615,0.5144730551803861],"dir":"ltr"},{"str":"from","boundary":[0.5005174750396825,0.5014913899391189,0.5359864635317461,0.5144730551803861],"dir":"ltr"},{"str":"the","boundary":[0.5409094448809524,0.5014913899391189,0.5642474008333332,0.5144730551803861],"dir":"ltr"},{"str":"publisher","boundary":[0.5691703821825397,0.5014913899391189,0.6373528337698412,0.5144730551803861],"dir":"ltr"},{"str":"prior","boundary":[0.6422758151190475,0.5014913899391189,0.6787025167063492,0.5144730551803861],"dir":"ltr"},{"str":"to","boundary":[0.6836254980555555,0.5014913899391189,0.6985624619444445,0.5144730551803861],"dir":"ltr"},{"str":"any","boundary":[0.7034854432936507,0.5014913899391189,0.7296293305952379,0.5144730551803861],"dir":"ltr"},{"str":"prohibited","boundary":[0.7345523119444443,0.5014913899391189,0.811135755595238,0.5144730551803861],"dir":"ltr"},{"str":"reproduction,","boundary":[0.8160587369444443,0.5014913899391189,0.9155096809920634,0.5144730551803861],"dir":"ltr"},{"str":"storage","boundary":[0.23869215638888883,0.5171459800535629,0.2919040401190475,0.53012764529483],"dir":"ltr"},{"str":"in","boundary":[0.2946595655158729,0.5171459800535629,0.3086724202777777,0.53012764529483],"dir":"ltr"},{"str":"a","boundary":[0.3114279456746031,0.5171459800535629,0.3198289377380952,0.53012764529483],"dir":"ltr"},{"str":"retrieval","boundary":[0.32258446313492056,0.5171459800535629,0.3841973389285714,0.53012764529483],"dir":"ltr"},{"str":"system,","boundary":[0.3869528643253968,0.5171459800535629,0.44061840162698407,0.53012764529483],"dir":"ltr"},{"str":"or","boundary":[0.4436595607539682,0.5171459800535629,0.45953743575396816,0.53012764529483],"dir":"ltr"},{"str":"transmission","boundary":[0.4622929611507936,0.5171459800535629,0.5537965667063491,0.53012764529483],"dir":"ltr"},{"str":"in","boundary":[0.5565520921031746,0.5171459800535629,0.5705649468650793,0.53012764529483],"dir":"ltr"},{"str":"any","boundary":[0.5733204722619046,0.5171459800535629,0.5994643595634919,0.53012764529483],"dir":"ltr"},{"str":"form","boundary":[0.6022198849603175,0.5171459800535629,0.637688873452381,0.53012764529483],"dir":"ltr"},{"str":"or","boundary":[0.6404443988492063,0.5171459800535629,0.6563222738492064,0.53012764529483],"dir":"ltr"},{"str":"by","boundary":[0.6590777992460318,0.5171459800535629,0.6768206944841271,0.53012764529483],"dir":"ltr"},{"str":"any","boundary":[0.6795762198809524,0.5171459800535629,0.7057201071825397,0.53012764529483],"dir":"ltr"},{"str":"means,","boundary":[0.7084756325793652,0.5171459800535629,0.758427931388889,0.53012764529483],"dir":"ltr"},{"str":"electronic,","boundary":[0.7614690905158732,0.5171459800535629,0.8372460389285715,0.53012764529483],"dir":"ltr"},{"str":"mechanical,","boundary":[0.8402871980555556,0.5171459800535629,0.926632594484127,0.53012764529483],"dir":"ltr"},{"str":"photocopying,","boundary":[0.23869215638888883,0.5327992720014828,0.34251161630952376,0.5457809372427499],"dir":"ltr"},{"str":"recording,","boundary":[0.34733378575396817,0.5327992720014828,0.4212625159126983,0.5457809372427499],"dir":"ltr"},{"str":"or","boundary":[0.4260846853571428,0.5327992720014828,0.4419625603571428,0.5457809372427499],"dir":"ltr"},{"str":"likewise.","boundary":[0.44666711591269836,0.5327992720014828,0.5090696849603173,0.5457809372427499],"dir":"ltr"},{"str":"To","boundary":[0.513774240515873,0.5327992720014828,0.5326428686904761,0.5457809372427499],"dir":"ltr"},{"str":"obtain","boundary":[0.5373474242460317,0.5327992720014828,0.5840401381349206,0.5457809372427499],"dir":"ltr"},{"str":"permission(s)","boundary":[0.5887446936904762,0.5327992720014828,0.6877251821825396,0.5457809372427499],"dir":"ltr"},{"str":"to","boundary":[0.6924297377380952,0.5327992720014828,0.7073667016269841,0.5457809372427499],"dir":"ltr"},{"str":"use","boundary":[0.7120712571825397,0.5327992720014828,0.7363501242460319,0.5457809372427499],"dir":"ltr"},{"str":"material","boundary":[0.7410546798015873,0.5327992720014828,0.801726644484127,0.5457809372427499],"dir":"ltr"},{"str":"from","boundary":[0.8064312000396825,0.5327992720014828,0.841900188531746,0.5457809372427499],"dir":"ltr"},{"str":"this","boundary":[0.8466047440873015,0.5327992720014828,0.8727486313888887,0.5457809372427499],"dir":"ltr"},{"str":"work,","boundary":[0.8774531869444443,0.5327992720014828,0.919004493690476,0.5457809372427499],"dir":"ltr"},{"str":"please","boundary":[0.23869215638888883,0.5484538621159267,0.2844439591666666,0.5614355273571938],"dir":"ltr"},{"str":"submit","boundary":[0.2880059798015872,0.5484538621159267,0.33748782305555547,0.5614355273571938],"dir":"ltr"},{"str":"a","boundary":[0.3410498436904762,0.5484538621159267,0.34945083575396824,0.5614355273571938],"dir":"ltr"},{"str":"written","boundary":[0.35301285638888885,0.5484538621159267,0.4052838290079364,0.5614355273571938],"dir":"ltr"},{"str":"request","boundary":[0.4088458496428571,0.5484538621159267,0.4629986444841269,0.5614355273571938],"dir":"ltr"},{"str":"to","boundary":[0.4665606651190476,0.5484538621159267,0.48149762900793647,0.5614355273571938],"dir":"ltr"},{"str":"Pearson","boundary":[0.4850596496428571,0.5484538621159267,0.5438833960714285,0.5614355273571938],"dir":"ltr"},{"str":"Education,","boundary":[0.547445416706349,0.5484538621159267,0.6272716432936507,0.5614355273571938],"dir":"ltr"},{"str":"Inc.,","boundary":[0.6309512778174603,0.5484538621159267,0.6623877901190476,0.5614355273571938],"dir":"ltr"},{"str":"Permissions","boundary":[0.6660674246428571,0.5484538621159267,0.7529000786111111,0.5614355273571938],"dir":"ltr"},{"str":"Department,","boundary":[0.7564620992460317,0.5484538621159267,0.8502675766269842,0.5614355273571938],"dir":"ltr"},{"str":"One","boundary":[0.8539472111507938,0.5484538621159267,0.8856861591666667,0.5614355273571938],"dir":"ltr"},{"str":"Lake","boundary":[0.8892481798015875,0.5484538621159267,0.9265989905158731,0.5614355273571938],"dir":"ltr"},{"str":"Street,","boundary":[0.23869215638888883,0.5641084522303708,0.2867626329761904,0.5770901174716379],"dir":"ltr"},{"str":"Upper","boundary":[0.29096312900793647,0.5641084522303708,0.33857995202380947,0.5770901174716379],"dir":"ltr"},{"str":"Saddle","boundary":[0.3427804480555555,0.5641084522303708,0.39227909329365074,0.5770901174716379],"dir":"ltr"},{"str":"River,","boundary":[0.3964795893253968,0.5641084522303708,0.44145850083333327,0.5770901174716379],"dir":"ltr"},{"str":"New","boundary":[0.4456589968650793,0.5641084522303708,0.47926296511904753,0.5770901174716379],"dir":"ltr"},{"str":"Jersey","boundary":[0.4834634611507936,0.5641084522303708,0.5283583627380951,0.5770901174716379],"dir":"ltr"},{"str":"07458,","boundary":[0.5325588587698412,0.5641084522303708,0.5787643151190476,0.5770901174716379],"dir":"ltr"},{"str":"or","boundary":[0.5829648111507936,0.5641084522303708,0.5988426861507936,0.5770901174716379],"dir":"ltr"},{"str":"you","boundary":[0.6030431821825396,0.5641084522303708,0.6301279805952381,0.5770901174716379],"dir":"ltr"},{"str":"may","boundary":[0.634328476626984,0.5641084522303708,0.6651265135317459,0.5770901174716379],"dir":"ltr"},{"str":"fax","boundary":[0.6693270095634918,0.5641084522303708,0.6917240544047616,0.5770901174716379],"dir":"ltr"},{"str":"your","boundary":[0.6959245504365078,0.5641084522303708,0.729545320674603,0.5770901174716379],"dir":"ltr"},{"str":"request","boundary":[0.733745816706349,0.5641084522303708,0.7878986115476189,0.5770901174716379],"dir":"ltr"},{"str":"to","boundary":[0.792099107579365,0.5641084522303708,0.8070360714682538,0.5770901174716379],"dir":"ltr"},{"str":"201-236-3290.","boundary":[0.8112365674999998,0.5641084522303708,0.9106371055952379,0.5770901174716379],"dir":"ltr"},{"str":"This","boundary":[0.23869215638888883,0.5889280980051492,0.2697758270238095,0.6019097632464163],"dir":"ltr"},{"str":"is","boundary":[0.2740603329761904,0.5889280980051492,0.28526725638888883,0.6019097632464163],"dir":"ltr"},{"str":"the","boundary":[0.2895517623412698,0.5889280980051492,0.31288971829365075,0.6019097632464163],"dir":"ltr"},{"str":"eBook","boundary":[0.3171742242460317,0.5889280980051492,0.3657319583730158,0.6019097632464163],"dir":"ltr"},{"str":"of","boundary":[0.37001646432539675,0.5889280980051492,0.38495342821428563,0.6019097632464163],"dir":"ltr"},{"str":"the","boundary":[0.38923793416666663,0.5889280980051492,0.4125758901190476,0.6019097632464163],"dir":"ltr"},{"str":"printed","boundary":[0.41686039607142855,0.5889280980051492,0.4700890817857143,0.6019097632464163],"dir":"ltr"},{"str":"book","boundary":[0.47437358773809524,0.5889280980051492,0.511741200436508,0.6019097632464163],"dir":"ltr"},{"str":"and","boundary":[0.5160257063888889,0.5889280980051492,0.5431105048015874,0.6019097632464163],"dir":"ltr"},{"str":"may","boundary":[0.5473950107539681,0.5889280980051492,0.57819304765873,0.6019097632464163],"dir":"ltr"},{"str":"not","boundary":[0.5824775536111111,0.5889280980051492,0.6067564206746031,0.6019097632464163],"dir":"ltr"},{"str":"include","boundary":[0.6110409266269841,0.5889280980051492,0.6642696123412698,0.6019097632464163],"dir":"ltr"},{"str":"any","boundary":[0.6685541182936506,0.5889280980051492,0.6946980055952379,0.6019097632464163],"dir":"ltr"},{"str":"media,","boundary":[0.6989825115476189,0.5889280980051492,0.7479938992460317,0.6019097632464163],"dir":"ltr"},{"str":"Website","boundary":[0.7522952071825395,0.5889280980051492,0.8107997159126983,0.6019097632464163],"dir":"ltr"},{"str":"access","boundary":[0.8150842218650793,0.5889280980051492,0.8598783115476191,0.6019097632464163],"dir":"ltr"},{"str":"codes","boundary":[0.8641628175,0.5889280980051492,0.9052436686904761,0.6019097632464163],"dir":"ltr"},{"str":"or","boundary":[0.9095281746428572,0.5889280980051492,0.9254060496428572,0.6019097632464163],"dir":"ltr"},{"str":"print","boundary":[0.23869215638888883,0.6045813899530691,0.27417794686507935,0.6175630551943362],"dir":"ltr"},{"str":"supplements","boundary":[0.2783784428968254,0.6045813899530691,0.36988204845238093,0.6175630551943362],"dir":"ltr"},{"str":"that","boundary":[0.374082544484127,0.6045813899530691,0.4030155611507936,0.6175630551943362],"dir":"ltr"},{"str":"may","boundary":[0.40721605718253967,0.6045813899530691,0.4380140940873015,0.6175630551943362],"dir":"ltr"},{"str":"come","boundary":[0.44221459011904757,0.6045813899530691,0.48141361908730157,0.6175630551943362],"dir":"ltr"},{"str":"packaged","boundary":[0.48561411511904756,0.6045813899530691,0.5547038738492063,0.6175630551943362],"dir":"ltr"},{"str":"with","boundary":[0.5589043698809523,0.6045813899530691,0.5906433178968253,0.6175630551943362],"dir":"ltr"},{"str":"the","boundary":[0.5948438139285713,0.6045813899530691,0.6181817698809523,0.6175630551943362],"dir":"ltr"},{"str":"bound","boundary":[0.6223822659126983,0.6045813899530691,0.6690917817857143,0.6175630551943362],"dir":"ltr"},{"str":"book.","boundary":[0.6732922778174603,0.6045813899530691,0.714860386547619,0.6175630551943362],"dir":"ltr"},{"str":"Many","boundary":[0.23869215638888883,0.6294010357278476,0.28069711670634917,0.6423827009691147],"dir":"ltr"},{"str":"of","boundary":[0.28447756313492056,0.6294010357278476,0.29941452702380944,0.6423827009691147],"dir":"ltr"},{"str":"the","boundary":[0.3032117754365079,0.6294010357278476,0.3265497313888888,0.6423827009691147],"dir":"ltr"},{"str":"designations","boundary":[0.3303301778174602,0.6294010357278476,0.4209096742460317,0.6423827009691147],"dir":"ltr"},{"str":"by","boundary":[0.42470692265873006,0.6294010357278476,0.4424498178968253,0.6423827009691147],"dir":"ltr"},{"str":"manufacturers","boundary":[0.44624706630952377,0.6294010357278476,0.5517299226587301,0.6423827009691147],"dir":"ltr"},{"str":"and","boundary":[0.5555271710714285,0.6294010357278476,0.582611969484127,0.6423827009691147],"dir":"ltr"},{"str":"sellers","boundary":[0.5863924159126983,0.6294010357278476,0.6321442186904761,0.6423827009691147],"dir":"ltr"},{"str":"to","boundary":[0.6359414671031746,0.6294010357278476,0.6508784309920636,0.6423827009691147],"dir":"ltr"},{"str":"distinguish","boundary":[0.6546756794047618,0.6294010357278476,0.7331241432936507,0.6423827009691147],"dir":"ltr"},{"str":"their","boundary":[0.7369213917063491,0.6294010357278476,0.7714662710714284,0.6423827009691147],"dir":"ltr"},{"str":"products","boundary":[0.7752467175000001,0.6294010357278476,0.8387414155158731,0.6423827009691147],"dir":"ltr"},{"str":"are","boundary":[0.8425386639285714,0.6294010357278476,0.8658766198809522,0.6423827009691147],"dir":"ltr"},{"str":"claimed","boundary":[0.8696570663095237,0.6294010357278476,0.9265989905158729,0.6423827009691147],"dir":"ltr"},{"str":"as","boundary":[0.23869215638888883,0.6450556258422916,0.25362912027777773,0.6580372910835587],"dir":"ltr"},{"str":"trademarks.","boundary":[0.2577960123412698,0.6450556258422916,0.34415821075396824,0.6580372910835587],"dir":"ltr"},{"str":"Where","boundary":[0.34832510281746026,0.6450556258422916,0.3975045103571428,0.6580372910835587],"dir":"ltr"},{"str":"those","boundary":[0.40167140242063487,0.6450556258422916,0.4408872333730158,0.6580372910835587],"dir":"ltr"},{"str":"designations","boundary":[0.44505412543650785,0.6450556258422916,0.5356336218650793,0.6580372910835587],"dir":"ltr"},{"str":"appear","boundary":[0.5398005139285713,0.6450556258422916,0.5902232682936507,0.6580372910835587],"dir":"ltr"},{"str":"in","boundary":[0.5943901603571429,0.6450556258422916,0.6084030151190476,0.6580372910835587],"dir":"ltr"},{"str":"this","boundary":[0.6125699071825398,0.6450556258422916,0.638713794484127,0.6580372910835587],"dir":"ltr"},{"str":"book,","boundary":[0.6428806865476192,0.6450556258422916,0.6844487952777779,0.6580372910835587],"dir":"ltr"},{"str":"and","boundary":[0.6886324893253969,0.6450556258422916,0.7157172877380953,0.6580372910835587],"dir":"ltr"},{"str":"the","boundary":[0.7198841798015874,0.6450556258422916,0.7432221357539682,0.6580372910835587],"dir":"ltr"},{"str":"publisher","boundary":[0.7473890278174604,0.6450556258422916,0.8155714794047619,0.6580372910835587],"dir":"ltr"},{"str":"was","boundary":[0.8197383714682541,0.6450556258422916,0.8468063678968255,0.6580372910835587],"dir":"ltr"},{"str":"aware","boundary":[0.8509732599603174,0.6450556258422916,0.8948432405158729,0.6580372910835587],"dir":"ltr"},{"str":"of","boundary":[0.8990101325793649,0.6450556258422916,0.9139470964682539,0.6580372910835587],"dir":"ltr"},{"str":"a","boundary":[0.918113988531746,0.6450556258422916,0.9265149805952381,0.6580372910835587],"dir":"ltr"},{"str":"trademark","boundary":[0.23869215638888883,0.6607089177902113,0.3152419960714285,0.6736905830314786],"dir":"ltr"},{"str":"claim,","boundary":[0.31944249210317455,0.6607089177902113,0.3628420171031746,0.6736905830314786],"dir":"ltr"},{"str":"the","boundary":[0.36704251313492053,0.6607089177902113,0.3903804690873015,0.6736905830314786],"dir":"ltr"},{"str":"designations","boundary":[0.39458096511904756,0.6607089177902113,0.485160461547619,0.6736905830314786],"dir":"ltr"},{"str":"have","boundary":[0.48936095757936504,0.6607089177902113,0.5239058369444444,0.6736905830314786],"dir":"ltr"},{"str":"been","boundary":[0.5281063329761905,0.6607089177902113,0.5635921234523809,0.6736905830314786],"dir":"ltr"},{"str":"printed","boundary":[0.5677926194841271,0.6607089177902113,0.6210213051984127,0.6736905830314786],"dir":"ltr"},{"str":"in","boundary":[0.6252218012301588,0.6607089177902113,0.6392346559920635,0.6736905830314786],"dir":"ltr"},{"str":"initial","boundary":[0.6434351520238095,0.6607089177902113,0.6854569143253968,0.6736905830314786],"dir":"ltr"},{"str":"caps","boundary":[0.6896574103571429,0.6607089177902113,0.7213963583730159,0.6736905830314786],"dir":"ltr"},{"str":"or","boundary":[0.7255968544047618,0.6607089177902113,0.7414747294047619,0.6736905830314786],"dir":"ltr"},{"str":"all","boundary":[0.7456752254365079,0.6607089177902113,0.7634181206746031,0.6736905830314786],"dir":"ltr"},{"str":"caps.","boundary":[0.7676186167063491,0.6607089177902113,0.802633951626984,0.6736905830314786],"dir":"ltr"},{"str":"Library","boundary":[0.23869215638888883,0.68552856356499,0.2937858623412698,0.6985102288062571],"dir":"ltr"},{"str":"of","boundary":[0.29798635837301585,0.68552856356499,0.31294012424603174,0.6985102288062571],"dir":"ltr"},{"str":"Congress","boundary":[0.3171406202777777,0.68552856356499,0.38421414091269834,0.6985102288062571],"dir":"ltr"},{"str":"Cataloging-in-Publication","boundary":[0.3884146369444444,0.68552856356499,0.5770505127380953,0.6985102288062571],"dir":"ltr"},{"str":"Data","boundary":[0.5812510087698413,0.68552856356499,0.6176441063888889,0.6985102288062571],"dir":"ltr"},{"str":"Levitin,","boundary":[0.23869215638888883,0.705097125749676,0.2951804270238095,0.7180787909909431],"dir":"ltr"},{"str":"Anany.","boundary":[0.29938092305555547,0.705097125749676,0.3516014897222221,0.7180787909909431],"dir":"ltr"},{"str":"Introduction","boundary":[0.25549414051587294,0.72075171586412,0.34793865718253963,0.7337333811053871],"dir":"ltr"},{"str":"to","boundary":[0.3521391532142856,0.72075171586412,0.3670761171031745,0.7337333811053871],"dir":"ltr"},{"str":"the","boundary":[0.3712766131349206,0.72075171586412,0.3946145690873016,0.7337333811053871],"dir":"ltr"},{"str":"design","boundary":[0.3988150651190476,0.72075171586412,0.4455077790079364,0.7337333811053871],"dir":"ltr"},{"str":"&","boundary":[0.44970827503968247,0.72075171586412,0.46370432781746024,0.7337333811053871],"dir":"ltr"},{"str":"analysis","boundary":[0.46790482384920634,0.72075171586412,0.5248635500396825,0.7337333811053871],"dir":"ltr"},{"str":"of","boundary":[0.5290640460714284,0.72075171586412,0.5440010099603174,0.7337333811053871],"dir":"ltr"},{"str":"algorithms","boundary":[0.5482015059920634,0.72075171586412,0.6256922567857142,0.7337333811053871],"dir":"ltr"},{"str":"/","boundary":[0.6298927528174603,0.72075171586412,0.6345637044047618,0.7337333811053871],"dir":"ltr"},{"str":"Anany","boundary":[0.6387642004365078,0.72075171586412,0.6883300536111111,0.7337333811053871],"dir":"ltr"},{"str":"Levitin.","boundary":[0.692530549642857,0.72075171586412,0.7490188202777777,0.7337333811053871],"dir":"ltr"},{"str":"—","boundary":[0.7532193163095238,0.72075171586412,0.770021300436508,0.7337333811053871],"dir":"ltr"},{"str":"3rd","boundary":[0.7742217964682538,0.72075171586412,0.798500663531746,0.7337333811053871],"dir":"ltr"},{"str":"ed.","boundary":[0.8027011595634919,0.72075171586412,0.8246445508333332,0.7337333811053871],"dir":"ltr"},{"str":"p.","boundary":[0.27229780484126975,0.7364050078120398,0.2851681246825396,0.749386673053307],"dir":"ltr"},{"str":"cm.","boundary":[0.30197010880952374,0.7364050078120398,0.3276267385714285,0.749386673053307],"dir":"ltr"},{"str":"Includes","boundary":[0.25549414051587294,0.7520595979264838,0.31712381829365077,0.7650412631677509],"dir":"ltr"},{"str":"bibliographical","boundary":[0.3213243143253968,0.7520595979264838,0.43058761710317456,0.7650412631677509],"dir":"ltr"},{"str":"references","boundary":[0.4347881131349206,0.7520595979264838,0.5103970417063491,0.7650412631677509],"dir":"ltr"},{"str":"and","boundary":[0.5145975377380951,0.7520595979264838,0.5416823361507935,0.7650412631677509],"dir":"ltr"},{"str":"index.","boundary":[0.5458828321825397,0.7520595979264838,0.5902400702777778,0.7650412631677509],"dir":"ltr"},{"str":"ISBN-13:","boundary":[0.25549414051587294,0.7677141880409277,0.323172532579365,0.7806958532821949],"dir":"ltr"},{"str":"978-0-13-231681-1","boundary":[0.327373028611111,0.7677141880409277,0.45896616829365067,0.7806958532821949],"dir":"ltr"},{"str":"ISBN-10:","boundary":[0.25549414051587294,0.7833687781553718,0.323172532579365,0.7963504433966389],"dir":"ltr"},{"str":"0-13-231681-1","boundary":[0.327373028611111,0.7833687781553718,0.4281681313888888,0.7963504433966389],"dir":"ltr"},{"str":"1.","boundary":[0.25549414051587294,0.7990233682698157,0.268095628611111,0.8120050335110829],"dir":"ltr"},{"str":"Computer","boundary":[0.27232972861111104,0.7990233682698157,0.3470145480555554,0.8120050335110829],"dir":"ltr"},{"str":"algorithms.","boundary":[0.3512486480555555,0.7990233682698157,0.4320157857539682,0.8120050335110829],"dir":"ltr"},{"str":"I.","boundary":[0.44881776988095234,0.7990233682698157,0.45955423773809523,0.8120050335110829],"dir":"ltr"},{"str":"Title.","boundary":[0.46378833773809514,0.7990233682698157,0.5010719405158729,0.8120050335110829],"dir":"ltr"},{"str":"II.","boundary":[0.517873924642857,0.7990233682698157,0.5351463643253968,0.8120050335110829],"dir":"ltr"},{"str":"Title:","boundary":[0.5393804643253967,0.7990233682698157,0.5772857405158729,0.8120050335110829],"dir":"ltr"},{"str":"Introduction","boundary":[0.5815198405158729,0.7990233682698157,0.6739643571825396,0.8120050335110829],"dir":"ltr"},{"str":"to","boundary":[0.6781984571825396,0.7990233682698157,0.6931354210714286,0.8120050335110829],"dir":"ltr"},{"str":"the","boundary":[0.6973695210714285,0.7990233682698157,0.7207074770238093,0.8120050335110829],"dir":"ltr"},{"str":"design","boundary":[0.7249415770238093,0.7990233682698157,0.7716342909126983,0.8120050335110829],"dir":"ltr"},{"str":"and","boundary":[0.7758683909126982,0.7990233682698157,0.8029531893253966,0.8120050335110829],"dir":"ltr"},{"str":"analysis","boundary":[0.8071872893253966,0.7990233682698157,0.8641460155158728,0.8120050335110829],"dir":"ltr"},{"str":"of","boundary":[0.8683801155158729,0.7990233682698157,0.8833170794047618,0.8120050335110829],"dir":"ltr"},{"str":"algorithms.","boundary":[0.23869215638888883,0.8146779583842597,0.31945929408730156,0.8276596236255268],"dir":"ltr"},{"str":"QA76.9.A43L48","boundary":[0.25549414051587294,0.8303312503321796,0.37606517861111105,0.8433129155734467],"dir":"ltr"},{"str":"2012","boundary":[0.38026567464285704,0.8303312503321796,0.41386964289682526,0.8433129155734467],"dir":"ltr"},{"str":"005.1—dc23","boundary":[0.25549414051587294,0.8459858404466235,0.34370455718253967,0.8589675056878906],"dir":"ltr"},{"str":"2011027089","boundary":[0.7998784262301586,0.8459858404466235,0.8838883468650792,0.8589675056878906],"dir":"ltr"},{"str":"15","boundary":[0.23869215638888877,0.870805486221402,0.2554941405158729,0.8837871514626692],"dir":"ltr"},{"str":"14","boundary":[0.263895132579365,0.870805486221402,0.2806971167063491,0.8837871514626692],"dir":"ltr"},{"str":"13","boundary":[0.28909810876984116,0.870805486221402,0.30590009289682524,0.8837871514626692],"dir":"ltr"},{"str":"12","boundary":[0.31430108496031733,0.870805486221402,0.33110306908730147,0.8837871514626692],"dir":"ltr"},{"str":"11—CRW—10987654321","boundary":[0.33950406115079357,0.870805486221402,0.6058491135317459,0.8837871514626692],"dir":"ltr"},{"str":"ISBN","boundary":[0.4165952380952381,0.9023642353083727,0.4576760892857143,0.9153459005496398],"dir":"ltr"},{"str":"10:","boundary":[0.4618765853174603,0.9023642353083727,0.48287906547619047,0.9153459005496398],"dir":"ltr"},{"str":"0-13-231681-1","boundary":[0.4870795615079365,0.9023642353083727,0.5878746642857143,0.9153459005496398],"dir":"ltr"},{"str":"ISBN","boundary":[0.4165952380952381,0.9237463361272638,0.4576760892857143,0.9367280013685308],"dir":"ltr"},{"str":"13:","boundary":[0.4618765853174603,0.9237463361272638,0.48287906547619047,0.9367280013685308],"dir":"ltr"},{"str":"978-0-13-231681-1","boundary":[0.4870795615079365,0.9237463361272638,0.6186727011904762,0.9367280013685308],"dir":"ltr"}],"boundary":[0.23869,0.05937,0.92663,0.93673],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":3,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/fb3992ba07885f6ee6cf2286e84ffc3a.jpg","blurred":"/storage/books/4a8b03583f119702/pages/7b15b4f18793f4a3f96e55c21ea85e03.jpg"},"info":{"width":503.99998500000004,"height":652.319995,"margin":[0.19756,0.89355,0.14119,0.0574]},"elements":[{"words":[{"str":"Boston","boundary":[0.24418609655315765,0.8935485183157692,0.2934272314156749,0.9058124379584593],"dir":"ltr"},{"str":"Columbus","boundary":[0.3052944715014359,0.8935485183157692,0.37564347072982657,0.9058124379584593],"dir":"ltr"},{"str":"Indianapolis","boundary":[0.3875107108155874,0.8935485183157692,0.47282825553881785,0.9058124379584593],"dir":"ltr"},{"str":"New","boundary":[0.4846954956245789,0.8935485183157692,0.5163414691866081,0.9058124379584593],"dir":"ltr"},{"str":"York","boundary":[0.5202972158818616,0.8935485183157692,0.5548248938848619,0.9058124379584593],"dir":"ltr"},{"str":"San","boundary":[0.5666364139331816,0.8935485183157692,0.5920233076903701,0.9058124379584593],"dir":"ltr"},{"str":"Francisco","boundary":[0.5959604810398101,0.8935485183157692,0.6617892835849986,0.9058124379584593],"dir":"ltr"},{"str":"Upper","boundary":[0.6736940458440689,0.8935485183157692,0.7186781741670093,0.9058124379584593],"dir":"ltr"},{"str":"Saddle","boundary":[0.722646428253366,0.8935485183157692,0.7694083344069942,0.9058124379584593],"dir":"ltr"},{"str":"River","boundary":[0.7733765884933509,0.8935485183157692,0.8121861134579201,0.9058124379584593],"dir":"ltr"},{"str":"Amsterdam","boundary":[0.19755911103846563,0.9119443977798044,0.2790812180294013,0.9242083174224944],"dir":"ltr"},{"str":"Cape","boundary":[0.29085926034958076,0.9119443977798044,0.3266331008900726,0.9242083174224944],"dir":"ltr"},{"str":"Town","boundary":[0.330559114996799,0.9119443977798044,0.36858503229930284,0.9242083174224944],"dir":"ltr"},{"str":"Dubai","boundary":[0.3804549547507669,0.9119443977798044,0.4235667163246579,0.9242083174224944],"dir":"ltr"},{"str":"London","boundary":[0.43544299980526574,0.9119443977798044,0.49002639868213915,0.9242083174224944],"dir":"ltr"},{"str":"Madrid","boundary":[0.501902682162747,0.9119443977798044,0.5529390310400789,0.9242083174224944],"dir":"ltr"},{"str":"Milan","boundary":[0.5648153145206866,0.9119443977798044,0.605289688622598,0.9242083174224944],"dir":"ltr"},{"str":"Munich","boundary":[0.6171659721032058,0.9119443977798044,0.6699600109356677,0.9242083174224944],"dir":"ltr"},{"str":"Paris","boundary":[0.6818362944162755,0.9119443977798044,0.7161370491179188,0.9242083174224944],"dir":"ltr"},{"str":"Montreal","boundary":[0.7280066871767753,0.9119443977798044,0.7917073864466307,0.9242083174224944],"dir":"ltr"},{"str":"Toronto","boundary":[0.8032892877963081,0.9119443977798044,0.858813098972612,0.9242083174224944],"dir":"ltr"},{"str":"Delhi","boundary":[0.22384482610649287,0.9303402772438395,0.26250537652330075,0.9426041968865296],"dir":"ltr"},{"str":"Mexico","boundary":[0.27436444106833385,0.9303402772438395,0.3253109823537961,0.9426041968865296],"dir":"ltr"},{"str":"City","boundary":[0.3292640038688071,0.9303402772438395,0.358247557616868,0.9426041968865296],"dir":"ltr"},{"str":"Sao","boundary":[0.3701066221619011,0.9303402772438395,0.39559570489069223,0.9426041968865296],"dir":"ltr"},{"str":"Paulo","boundary":[0.3995487264057033,0.9303402772438395,0.43874057519644055,0.9426041968865296],"dir":"ltr"},{"str":"Sydney","boundary":[0.4504590927393176,0.9303402772438395,0.5003034448939895,0.9426041968865296],"dir":"ltr"},{"str":"Hong","boundary":[0.512121120377207,0.9303402772438395,0.5506467424524962,0.9426041968865296],"dir":"ltr"},{"str":"Kong","boundary":[0.5545859676135687,0.9303402772438395,0.5923915195997081,0.9426041968865296],"dir":"ltr"},{"str":"Seoul","boundary":[0.6042773834109125,0.9303402772438395,0.6430411472538534,0.9426041968865296],"dir":"ltr"},{"str":"Singapore","boundary":[0.6549270110650577,0.9303402772438395,0.7241781743306998,0.9426041968865296],"dir":"ltr"},{"str":"Taipei","boundary":[0.7355591270503707,0.9303402772438395,0.7774386996920813,0.9426041968865296],"dir":"ltr"},{"str":"Tokyo","boundary":[0.7891146841998418,0.9303402772438395,0.8325273839045848,0.9426041968865296],"dir":"ltr"}],"boundary":[0.19756,0.89355,0.85881,0.9426],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":4,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/5e2f0442f63f76211e8ec9356431c63b.jpg","blurred":"/storage/books/4a8b03583f119702/pages/f87efaf0551450339c0f1a120e5dc6ff.jpg"},"info":{"width":559.44,"height":795.6,"margin":[0.35709,0.23928,0.35915,0.74564]},"elements":[{"words":[{"str":"This","boundary":[0.3570897683397683,0.23927657192684773,0.39406531531531525,0.2543595281862746],"dir":"ltr"},{"str":"page","boundary":[0.3994278206778206,0.23927657192684773,0.4411438223938223,0.2543595281862746],"dir":"ltr"},{"str":"intentionally","boundary":[0.4465063277563277,0.23927657192684773,0.5550134062634061,0.2543595281862746],"dir":"ltr"},{"str":"left","boundary":[0.5603759116259115,0.23927657192684773,0.5878061990561989,0.2543595281862746],"dir":"ltr"},{"str":"blank","boundary":[0.5931687044187043,0.23927657192684773,0.640852102102102,0.2543595281862746],"dir":"ltr"}],"boundary":[0.35709,0.23928,0.64085,0.25436],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":5,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/7eb31051e3bc8ee4ffc470366faf4897.jpg","blurred":"/storage/books/4a8b03583f119702/pages/2ef5ad580e5271cde24c6694962cd851.jpg"},"info":{"width":503.99999,"height":652.3200119999999,"margin":[0.07371,0.16303,0.073,0.05179]},"elements":[{"words":[{"str":"Brief","boundary":[0.14421784016305234,0.16302940802619442,0.25826617814020186,0.19968365680003092],"dir":"ltr"},{"str":"Contents","boundary":[0.2740640552393661,0.16302940802619442,0.4920083417065147,0.19968365680003092],"dir":"ltr"}],"boundary":[0.14422,0.16303,0.49201,0.19968],"dir":"ltr","type":"paragraph"},{"words":[{"str":"New","boundary":[0.11456903005097278,0.32398094847962455,0.16290560779574614,0.3407808316633402],"dir":"ltr"},{"str":"to","boundary":[0.16895039799504755,0.32398094847962455,0.19069424763282233,0.3407808316633402],"dir":"ltr"},{"str":"the","boundary":[0.19673903783212374,0.32398094847962455,0.2305724678685013,0.3407808316633402],"dir":"ltr"},{"str":"Third","boundary":[0.23661725806780268,0.32398094847962455,0.2909768821622396,0.3407808316633402],"dir":"ltr"},{"str":"Edition","boundary":[0.29702167236154103,0.32398094847962455,0.3707115787839598,0.3407808316633402],"dir":"ltr"},{"str":"Preface","boundary":[0.11456903005097284,0.35147227732145686,0.1906942476328224,0.36827216050517253],"dir":"ltr"},{"str":"1","boundary":[0.08820461236517084,0.3850720436888882,0.10270776007356663,0.40187192687260387],"dir":"ltr"},{"str":"Introduction","boundary":[0.11456903005097278,0.3850720436888882,0.24261856056782855,0.40187192687260387],"dir":"ltr"},{"str":"2","boundary":[0.0882067867501346,0.4110362631493208,0.10270993445853038,0.4278361463330364],"dir":"ltr"},{"str":"Fundamentals","boundary":[0.11457120443593653,0.4110362631493208,0.2619727611304119,0.4278361463330364],"dir":"ltr"},{"str":"of","boundary":[0.2680175513297133,0.4110362631493208,0.2885437453877727,0.4278361463330364],"dir":"ltr"},{"str":"the","boundary":[0.2945885355870741,0.4110362631493208,0.32842196562345166,0.4278361463330364],"dir":"ltr"},{"str":"Analysis","boundary":[0.3344667558227531,0.4110362631493208,0.42146389822349,0.4278361463330364],"dir":"ltr"},{"str":"of","boundary":[0.4275086884227914,0.4110362631493208,0.44803488248085077,0.4278361463330364],"dir":"ltr"},{"str":"Algorithm","boundary":[0.4540796726801522,0.4110362631493208,0.5591676979795177,0.4278361463330364],"dir":"ltr"},{"str":"Efficiency","boundary":[0.5652124881788192,0.4110362631493208,0.6642774671285212,0.4278361463330364],"dir":"ltr"},{"str":"3","boundary":[0.0882067867501346,0.4370004826097534,0.10270993445853038,0.453800365793469],"dir":"ltr"},{"str":"Brute","boundary":[0.11457120443593653,0.4370004826097534,0.1713661396898043,0.453800365793469],"dir":"ltr"},{"str":"Force","boundary":[0.1774109298891057,0.4370004826097534,0.23420586514297345,0.453800365793469],"dir":"ltr"},{"str":"and","boundary":[0.24025065534227485,0.4370004826097534,0.2789112199982384,0.453800365793469],"dir":"ltr"},{"str":"Exhaustive","boundary":[0.28495601019753986,0.4370004826097534,0.39854588070527536,0.453800365793469],"dir":"ltr"},{"str":"Search","boundary":[0.4045906709045768,0.4370004826097534,0.4758887538668403,0.453800365793469],"dir":"ltr"},{"str":"4","boundary":[0.0882067867501346,0.462964702070186,0.10270993445853038,0.4797645852539016],"dir":"ltr"},{"str":"Decrease-and-Conquer","boundary":[0.11457120443593653,0.462964702070186,0.3501658152612264,0.4797645852539016],"dir":"ltr"},{"str":"5","boundary":[0.08820896113509846,0.48892892153061857,0.10271210884349424,0.5057288047143341],"dir":"ltr"},{"str":"Divide-and-Conquer","boundary":[0.1145733788209004,0.48892892153061857,0.32116169422939866,0.5057288047143341],"dir":"ltr"},{"str":"6","boundary":[0.08821113552006221,0.5148931409910511,0.102714283228458,0.5316930241747668],"dir":"ltr"},{"str":"Transform-and-Conquer","boundary":[0.11457555320586416,0.5148931409910511,0.3614117342938836,0.5316930241747668],"dir":"ltr"},{"str":"7","boundary":[0.08821330990502597,0.5408573604514838,0.10271645761342175,0.5576572436351994],"dir":"ltr"},{"str":"Space","boundary":[0.1145777275908279,0.5408573604514838,0.17741745304399706,0.5576572436351994],"dir":"ltr"},{"str":"and","boundary":[0.1834622432432985,0.5408573604514838,0.22212280789926206,0.5576572436351994],"dir":"ltr"},{"str":"Time","boundary":[0.22816759809856343,0.5408573604514838,0.27850461001001203,0.5576572436351994],"dir":"ltr"},{"str":"Trade-Offs","boundary":[0.28454940020931346,0.5408573604514838,0.3912682142315122,0.5576572436351994],"dir":"ltr"},{"str":"8","boundary":[0.08821330990502597,0.5668215799119164,0.10271645761342175,0.583621463095632],"dir":"ltr"},{"str":"Dynamic","boundary":[0.1145777275908279,0.5668215799119164,0.20518434903143545,0.583621463095632],"dir":"ltr"},{"str":"Programming","boundary":[0.21122913923073686,0.5668215799119164,0.35376007360635064,0.583621463095632],"dir":"ltr"},{"str":"9","boundary":[0.08821548428998972,0.5927857993723489,0.1027186319983855,0.6095856825560646],"dir":"ltr"},{"str":"Greedy","boundary":[0.11457990197579167,0.5927857993723489,0.18950920782756359,0.6095856825560646],"dir":"ltr"},{"str":"Technique","boundary":[0.195553998026865,0.5927857993723489,0.3010769003189861,0.6095856825560646],"dir":"ltr"},{"str":"10","boundary":[0.07371451096655773,0.6187500188327815,0.10272080638334931,0.6355499020164972],"dir":"ltr"},{"str":"Iterative","boundary":[0.11458207636075547,0.6187500188327815,0.20040505088105257,0.6355499020164972],"dir":"ltr"},{"str":"Improvement","boundary":[0.206449841080354,0.6187500188327815,0.3465889519958125,0.6355499020164972],"dir":"ltr"},{"str":"11","boundary":[0.07371451096655773,0.6447142382932141,0.10272080638334931,0.6615141214769298],"dir":"ltr"},{"str":"Limitations","boundary":[0.11458207636075547,0.6447142382932141,0.23178142590836162,0.6615141214769298],"dir":"ltr"},{"str":"of","boundary":[0.237826216107663,0.6447142382932141,0.2583524101657224,0.6615141214769298],"dir":"ltr"},{"str":"Algorithm","boundary":[0.2643972003650238,0.6447142382932141,0.36948522566438935,0.6615141214769298],"dir":"ltr"},{"str":"Power","boundary":[0.3755300158636907,0.6447142382932141,0.44197922035673054,0.6615141214769298],"dir":"ltr"},{"str":"12","boundary":[0.07371451096655773,0.6706784577536465,0.10272080638334931,0.6874783409373622],"dir":"ltr"},{"str":"Coping","boundary":[0.11458207636075547,0.6706784577536465,0.18827198278317425,0.6874783409373622],"dir":"ltr"},{"str":"with","boundary":[0.19431677298247563,0.6706784577536465,0.2414356951475336,0.6874783409373622],"dir":"ltr"},{"str":"the","boundary":[0.24748048534683503,0.6706784577536465,0.2813139153832126,0.6874783409373622],"dir":"ltr"},{"str":"Limitations","boundary":[0.287358705582514,0.6706784577536465,0.4045580551301201,0.6874783409373622],"dir":"ltr"},{"str":"of","boundary":[0.41060284532942154,0.6706784577536465,0.43112903938748093,0.6874783409373622],"dir":"ltr"},{"str":"Algorithm","boundary":[0.4371738295867823,0.6706784577536465,0.5422618548861479,0.6874783409373622],"dir":"ltr"},{"str":"Power","boundary":[0.5483066450854492,0.6706784577536465,0.614755849578489,0.6874783409373622],"dir":"ltr"},{"str":"Epilogue","boundary":[0.11458207636075547,0.7042782241210779,0.205188697801363,0.7210781073047936],"dir":"ltr"},{"str":"APPENDIX","boundary":[0.07661466421854489,0.7400736330621728,0.17223847563965228,0.7538190338394833],"dir":"ltr"},{"str":"A","boundary":[0.17718422811873466,0.7400736330621728,0.19074057124485255,0.7538190338394833],"dir":"ltr"},{"str":"Useful","boundary":[0.11456903005097278,0.7577235821488183,0.18101823454401256,0.774523465332534],"dir":"ltr"},{"str":"Formulas","boundary":[0.18706302474331396,0.7577235821488183,0.2837144363832229,0.774523465332534],"dir":"ltr"},{"str":"for","boundary":[0.2897592265825243,0.7577235821488183,0.3187437781496781,0.774523465332534],"dir":"ltr"},{"str":"the","boundary":[0.3247885683489795,0.7577235821488183,0.3586219983853571,0.774523465332534],"dir":"ltr"},{"str":"Analysis","boundary":[0.3646667885846585,0.7577235821488183,0.4516639309853954,0.774523465332534],"dir":"ltr"},{"str":"of","boundary":[0.4577087211846968,0.7577235821488183,0.4782349152427562,0.774523465332534],"dir":"ltr"},{"str":"Algorithms","boundary":[0.4842797054420576,0.7577235821488183,0.6002396555603106,0.774523465332534],"dir":"ltr"},{"str":"APPENDIX","boundary":[0.07661466421854489,0.7858916356532079,0.17223847563965228,0.7996370364305184],"dir":"ltr"},{"str":"B","boundary":[0.17718422811873466,0.7858916356532079,0.18976209503496216,0.7996370364305184],"dir":"ltr"},{"str":"Short","boundary":[0.11456903005097278,0.8035415847398535,0.17258162088455592,0.8203414679235691],"dir":"ltr"},{"str":"Tutorial","boundary":[0.17862641108385735,0.8035415847398535,0.25761311927803804,0.8203414679235691],"dir":"ltr"},{"str":"on","boundary":[0.26365790947733947,0.8035415847398535,0.2902375912745554,0.8203414679235691],"dir":"ltr"},{"str":"Recurrence","boundary":[0.29628238147385677,0.8035415847398535,0.4123293069906608,0.8203414679235691],"dir":"ltr"},{"str":"Relations","boundary":[0.4183740971899622,0.8035415847398535,0.515086391608857,0.8203414679235691],"dir":"ltr"},{"str":"References","boundary":[0.11456903005097273,0.8371396711189664,0.22815890055870824,0.853939554302682],"dir":"ltr"},{"str":"Hints","boundary":[0.11456903005097273,0.8646326799491171,0.1689286541454097,0.8814325631328327],"dir":"ltr"},{"str":"to","boundary":[0.1749734443447111,0.8646326799491171,0.19671729398248589,0.8814325631328327],"dir":"ltr"},{"str":"Exercises","boundary":[0.2027620841817873,0.8646326799491171,0.299435239671334,0.8814325631328327],"dir":"ltr"},{"str":"Index","boundary":[0.11456903005097273,0.8921240087909493,0.17136396530484047,0.9089238919746649],"dir":"ltr"}],"boundary":[0.07371,0.32398,0.66428,0.90892],"dir":"ltr","type":"paragraph"},{"words":[{"str":"xvii","boundary":[0.7246862301921871,0.32398094847962455,0.7609549713879955,0.3407808316633402],"dir":"ltr"},{"str":"xix","boundary":[0.7307288460065247,0.35147227732145686,0.7609527970030316,0.36827216050517253],"dir":"ltr"},{"str":"1","boundary":[0.7488653909893925,0.3850720436888882,0.7609549713879954,0.40187192687260387],"dir":"ltr"},{"str":"41","boundary":[0.7367758105907898,0.4110362631493208,0.7609549713879953,0.4278361463330364],"dir":"ltr"},{"str":"97","boundary":[0.7367758105907898,0.4370004826097534,0.7609549713879953,0.453800365793469],"dir":"ltr"},{"str":"131","boundary":[0.7246884045771509,0.462964702070186,0.7609571457729593,0.4797645852539016],"dir":"ltr"},{"str":"169","boundary":[0.7246905789621146,0.48892892153061857,0.760959320157923,0.5057288047143341],"dir":"ltr"},{"str":"201","boundary":[0.7246927533470784,0.5148931409910511,0.7609614945428868,0.5316930241747668],"dir":"ltr"},{"str":"253","boundary":[0.7246927533470784,0.5408573604514838,0.7609614945428868,0.5576572436351994],"dir":"ltr"},{"str":"283","boundary":[0.7246949277320421,0.5668215799119164,0.7609636689278505,0.583621463095632],"dir":"ltr"},{"str":"315","boundary":[0.7246971021170059,0.5927857993723489,0.7609658433128142,0.6095856825560646],"dir":"ltr"},{"str":"345","boundary":[0.7246971021170059,0.6187500188327815,0.7609658433128142,0.6355499020164972],"dir":"ltr"},{"str":"387","boundary":[0.7246971021170059,0.6447142382932141,0.7609658433128142,0.6615141214769298],"dir":"ltr"},{"str":"423","boundary":[0.7246971021170059,0.6706784577536465,0.7609658433128142,0.6874783409373622],"dir":"ltr"},{"str":"471","boundary":[0.7246992765019697,0.7042782241210779,0.7609680176977781,0.7210781073047936],"dir":"ltr"}],"boundary":[0.72469,0.32398,0.76097,0.72108],"dir":"ltr","type":"paragraph"},{"words":[{"str":"475","boundary":[0.7246818814222594,0.7577235821488183,0.7609506226180678,0.774523465332534],"dir":"ltr"},{"str":"479","boundary":[0.7246818814222594,0.8035415847398535,0.7609506226180678,0.8203414679235691],"dir":"ltr"},{"str":"493","boundary":[0.724686230192187,0.8371396711189664,0.7609549713879954,0.853939554302682],"dir":"ltr"},{"str":"503","boundary":[0.724686230192187,0.8646326799491171,0.7609549713879954,0.8814325631328327],"dir":"ltr"},{"str":"547","boundary":[0.724686230192187,0.8921240087909493,0.7609549713879954,0.9089238919746649],"dir":"ltr"}],"boundary":[0.72468,0.75772,0.76095,0.90892],"dir":"ltr","type":"paragraph"},{"words":[{"str":"v","boundary":[0.9160075380160224,0.9329341022884333,0.926998025535675,0.9482066676194506],"dir":"ltr"}],"boundary":[0.91601,0.93293,0.927,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":6,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/636a4ce23478003c2197c9dd13d529cc.jpg","blurred":"/storage/books/4a8b03583f119702/pages/eb4aba963c4c3aae0ad009024d0d989b.jpg"},"info":{"width":559.44,"height":795.6,"margin":[0.35709,0.23928,0.35915,0.74564]},"elements":[{"words":[{"str":"This","boundary":[0.3570897683397683,0.23927657192684773,0.39406531531531525,0.2543595281862746],"dir":"ltr"},{"str":"page","boundary":[0.3994278206778206,0.23927657192684773,0.4411438223938223,0.2543595281862746],"dir":"ltr"},{"str":"intentionally","boundary":[0.4465063277563277,0.23927657192684773,0.5550134062634061,0.2543595281862746],"dir":"ltr"},{"str":"left","boundary":[0.5603759116259115,0.23927657192684773,0.5878061990561989,0.2543595281862746],"dir":"ltr"},{"str":"blank","boundary":[0.5931687044187043,0.23927657192684773,0.640852102102102,0.2543595281862746],"dir":"ltr"}],"boundary":[0.35709,0.23928,0.64085,0.25436],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":7,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/237ce3bcc5920a8ed0026f333c6f49c0.jpg","blurred":"/storage/books/4a8b03583f119702/pages/b30cbc529d4371ff19a7861605910ef4.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.0962,0.16303,0.073,0.05179]},"elements":[{"words":[{"str":"Contents","boundary":[0.14421784044919886,0.16302940802619442,0.36216212734877656,0.19968365680003092],"dir":"ltr"}],"boundary":[0.14422,0.16303,0.36216,0.19968],"dir":"ltr","type":"paragraph"},{"words":[{"str":"New","boundary":[0.138289268891234,0.3051001409412534,0.1910202414706798,0.32342734197766737],"dir":"ltr"},{"str":"to","boundary":[0.19761457812254035,0.3051001409412534,0.22133521356088756,0.32342734197766737],"dir":"ltr"},{"str":"the","boundary":[0.22792955021274805,0.3051001409412534,0.2648388589548163,0.32342734197766737],"dir":"ltr"},{"str":"Third","boundary":[0.2714331956066768,0.3051001409412534,0.3307347842025448,0.32342734197766737],"dir":"ltr"},{"str":"Edition","boundary":[0.33732912085440536,0.3051001409412534,0.417718354354964,0.32342734197766737],"dir":"ltr"},{"str":"Preface","boundary":[0.138289268891234,0.34175546280803065,0.22133521356088756,0.36008266384444465],"dir":"ltr"},{"str":"1","boundary":[0.09972776011310584,0.3847074147404819,0.1313709554465883,0.42136166351431836],"dir":"ltr"},{"str":"Introduction","boundary":[0.138289268891234,0.39793954320690095,0.27798009098766063,0.41626674424331495],"dir":"ltr"},{"str":"1.1","boundary":[0.09620395051238777,0.4280602328048769,0.1264279015688629,0.44486011598859254],"dir":"ltr"},{"str":"What","boundary":[0.13827829964496285,0.4280602328048769,0.19263792384725623,0.44486011598859254],"dir":"ltr"},{"str":"Is","boundary":[0.19868271405855129,0.4280602328048769,0.21559942911030497,0.44486011598859254],"dir":"ltr"},{"str":"an","boundary":[0.2216442193216,0.4280602328048769,0.24701929189923058,0.44486011598859254],"dir":"ltr"},{"str":"Algorithm?","boundary":[0.2530640821105256,0.4280602328048769,0.36780637687672646,0.44486011598859254],"dir":"ltr"},{"str":"Exercises","boundary":[0.138289268891234,0.4526232639939308,0.2217796814277311,0.4671322470480947],"dir":"ltr"},{"str":"1.1","boundary":[0.22700017955754356,0.4526232639939308,0.2531026702066059,0.4671322470480947],"dir":"ltr"},{"str":"1.2","boundary":[0.09620395051238777,0.4799872002087222,0.1264279015688629,0.49678708339243793],"dir":"ltr"},{"str":"Fundamentals","boundary":[0.13827829964496285,0.4799872002087222,0.2844622010497702,0.49678708339243793],"dir":"ltr"},{"str":"of","boundary":[0.2905069912610653,0.4799872002087222,0.31103318535985125,0.49678708339243793],"dir":"ltr"},{"str":"Algorithmic","boundary":[0.31707797557114625,0.4799872002087222,0.43786506054864216,0.49678708339243793],"dir":"ltr"},{"str":"Problem","boundary":[0.4439098507599373,0.4799872002087222,0.5308852494836066,0.49678708339243793],"dir":"ltr"},{"str":"Solving","boundary":[0.5369300396949016,0.4799872002087222,0.6154688247423752,0.49678708339243793],"dir":"ltr"},{"str":"Understanding","boundary":[0.138289268891234,0.5014965154863287,0.2603888330640419,0.5160054985404926],"dir":"ltr"},{"str":"the","boundary":[0.26560933119385444,0.5014965154863287,0.2927446542067285,0.5160054985404926],"dir":"ltr"},{"str":"Problem","boundary":[0.297965152336541,0.5014965154863287,0.3678785139814755,0.5160054985404926],"dir":"ltr"},{"str":"Ascertaining","boundary":[0.138289268891234,0.5213506078976465,0.24159128404266686,0.5358595909518105],"dir":"ltr"},{"str":"the","boundary":[0.24681178217247932,0.5213506078976465,0.27394710518535337,0.5358595909518105],"dir":"ltr"},{"str":"Capabilities","boundary":[0.27916760331516594,0.5213506078976465,0.3741130657048486,0.5358595909518105],"dir":"ltr"},{"str":"of","boundary":[0.37933356383466105,0.5213506078976465,0.3960278905879102,0.5358595909518105],"dir":"ltr"},{"str":"the","boundary":[0.4012483887177227,0.5213506078976465,0.4283837117305968,0.5358595909518105],"dir":"ltr"},{"str":"Computational","boundary":[0.4336042098604093,0.5213506078976465,0.5546521628991543,0.5358595909518105],"dir":"ltr"},{"str":"Device","boundary":[0.5598726610289668,0.5213506078976465,0.6172605829164016,0.5358595909518105],"dir":"ltr"},{"str":"Choosing","boundary":[0.138289268891234,0.5412047003089644,0.21657796206816976,0.5557136833631283],"dir":"ltr"},{"str":"between","boundary":[0.22179846019798224,0.5412047003089644,0.2958994876089173,0.5557136833631283],"dir":"ltr"},{"str":"Exact","boundary":[0.30111998573872983,0.5412047003089644,0.34701530023247673,0.5557136833631283],"dir":"ltr"},{"str":"and","boundary":[0.35223579836228924,0.5412047003089644,0.38250717600710105,0.5557136833631283],"dir":"ltr"},{"str":"Approximate","boundary":[0.38772767413691345,0.5412047003089644,0.494165743920284,0.5557136833631283],"dir":"ltr"},{"str":"Problem","boundary":[0.49938624205009646,0.5412047003089644,0.569299603695031,0.5557136833631283],"dir":"ltr"},{"str":"Solving","boundary":[0.5745201018248434,0.5412047003089644,0.6350440783442158,0.5557136833631283],"dir":"ltr"},{"str":"Algorithm","boundary":[0.138289268891234,0.5610587927202823,0.2196764591596052,0.5755677757744462],"dir":"ltr"},{"str":"Design","boundary":[0.22489695728941766,0.5610587927202823,0.2833364903109154,0.5755677757744462],"dir":"ltr"},{"str":"Techniques","boundary":[0.28855698844072786,0.5610587927202823,0.38286397264187233,0.5755677757744462],"dir":"ltr"},{"str":"Designing","boundary":[0.138289268891234,0.5809143360299056,0.2217796814277311,0.5954233190840695],"dir":"ltr"},{"str":"an","boundary":[0.22700017955754356,0.5809143360299056,0.24683056094273048,0.5954233190840695],"dir":"ltr"},{"str":"Algorithm","boundary":[0.25205105907254294,0.5809143360299056,0.3334382493409141,0.5954233190840695],"dir":"ltr"},{"str":"and","boundary":[0.33865874747072655,0.5809143360299056,0.36893012511553835,0.5954233190840695],"dir":"ltr"},{"str":"Data","boundary":[0.3741506232453508,0.5809143360299056,0.4127409961114105,0.5954233190840695],"dir":"ltr"},{"str":"Structures","boundary":[0.41796149424122303,0.5809143360299056,0.5045504038691555,0.5954233190840695],"dir":"ltr"},{"str":"Methods","boundary":[0.138289268891234,0.6007684284412235,0.21342312866598093,0.6152774114953874],"dir":"ltr"},{"str":"of","boundary":[0.21864362679579338,0.6007684284412235,0.23533795354904258,0.6152774114953874],"dir":"ltr"},{"str":"Specifying","boundary":[0.24055845167885503,0.6007684284412235,0.3271661400770387,0.6152774114953874],"dir":"ltr"},{"str":"an","boundary":[0.33238663820685116,0.6007684284412235,0.35221701959203805,0.6152774114953874],"dir":"ltr"},{"str":"Algorithm","boundary":[0.3574375177218505,0.6007684284412235,0.4388247079902218,0.6152774114953874],"dir":"ltr"},{"str":"Proving","boundary":[0.138289268891234,0.6206225208525413,0.20089768890848125,0.6351315039067053],"dir":"ltr"},{"str":"an","boundary":[0.2061181870382937,0.6206225208525413,0.2259485684234806,0.6351315039067053],"dir":"ltr"},{"str":"Algorithm’s","boundary":[0.23116906655329306,0.6206225208525413,0.32577651107845557,0.6351315039067053],"dir":"ltr"},{"str":"Correctness","boundary":[0.33099700920826797,0.6206225208525413,0.43221458086182607,0.6351315039067053],"dir":"ltr"},{"str":"Analyzing","boundary":[0.138289268891234,0.6404766132638593,0.21759201566173048,0.6549855963180231],"dir":"ltr"},{"str":"an","boundary":[0.22281251379154296,0.6404766132638593,0.24264289517672985,0.6549855963180231],"dir":"ltr"},{"str":"Algorithm","boundary":[0.24786339330654225,0.6404766132638593,0.32925058357491344,0.6549855963180231],"dir":"ltr"},{"str":"Coding","boundary":[0.138289268891234,0.6603321565734825,0.1967475806829829,0.6748411396276465],"dir":"ltr"},{"str":"an","boundary":[0.20196807881279533,0.6603321565734825,0.22179846019798224,0.6748411396276465],"dir":"ltr"},{"str":"Algorithm","boundary":[0.2270189583277947,0.6603321565734825,0.3084061485961659,0.6748411396276465],"dir":"ltr"},{"str":"Exercises","boundary":[0.138289268891234,0.6832389390193966,0.2217796814277311,0.6977479220735604],"dir":"ltr"},{"str":"1.2","boundary":[0.22700017955754356,0.6832389390193966,0.2531026702066059,0.6977479220735604],"dir":"ltr"},{"str":"1.3","boundary":[0.09620395051238777,0.7106040711196212,0.1264279015688629,0.7274039543033369],"dir":"ltr"},{"str":"Important","boundary":[0.13827829964496285,0.7106040711196212,0.2397351022561232,0.7274039543033369],"dir":"ltr"},{"str":"Problem","boundary":[0.24577989246741827,0.7106040711196212,0.33275529119108765,0.7274039543033369],"dir":"ltr"},{"str":"Types","boundary":[0.3388000814023827,0.7106040711196212,0.39881310652171464,0.7274039543033369],"dir":"ltr"},{"str":"Sorting","boundary":[0.138289268891234,0.7321118534073122,0.19776163427654356,0.746620836461476],"dir":"ltr"},{"str":"Searching","boundary":[0.138289268891234,0.7519673967169355,0.22072807029366814,0.7664763797710994],"dir":"ltr"},{"str":"String","boundary":[0.138289268891234,0.7718214891282533,0.18732063801691864,0.7863304721824174],"dir":"ltr"},{"str":"Processing","boundary":[0.1925411361467311,0.7718214891282533,0.2843693226747272,0.7863304721824174],"dir":"ltr"},{"str":"Graph","boundary":[0.138289268891234,0.7916755815395714,0.18837224915098158,0.8061845645937354],"dir":"ltr"},{"str":"Problems","boundary":[0.19359274728079404,0.7916755815395714,0.27289549405129043,0.8061845645937354],"dir":"ltr"},{"str":"Combinatorial","boundary":[0.138289268891234,0.8115296739508893,0.2530651126661036,0.8260386570050533],"dir":"ltr"},{"str":"Problems","boundary":[0.25828561079591605,0.8115296739508893,0.3375883575664125,0.8260386570050533],"dir":"ltr"},{"str":"Geometric","boundary":[0.138289268891234,0.8313837663622072,0.2259297896532295,0.8458927494163712],"dir":"ltr"},{"str":"Problems","boundary":[0.23115028778304195,0.8313837663622072,0.3104530345535384,0.8458927494163712],"dir":"ltr"},{"str":"Numerical","boundary":[0.138289268891234,0.8512393096718305,0.2227937350212918,0.8657482927259945],"dir":"ltr"},{"str":"Problems","boundary":[0.22801423315110425,0.8512393096718305,0.3073169799216007,0.8657482927259945],"dir":"ltr"},{"str":"Exercises","boundary":[0.138289268891234,0.8741460921177445,0.2217796814277311,0.8886550751719084],"dir":"ltr"},{"str":"1.3","boundary":[0.22700017955754356,0.8741460921177445,0.2531026702066059,0.8886550751719084],"dir":"ltr"}],"boundary":[0.0962,0.3051,0.63504,0.88866],"dir":"ltr","type":"paragraph"},{"words":[{"str":"xvii","boundary":[0.7279777738249117,0.3073055879205498,0.7609492364492888,0.3225781532515671],"dir":"ltr"},{"str":"xix","boundary":[0.7334757898179239,0.343960909787327,0.7609520086715715,0.35923347511834436],"dir":"ltr"}],"boundary":[0.72798,0.30731,0.76095,0.35923],"dir":"ltr","type":"paragraph"},{"words":[{"str":"1","boundary":[0.7499599171618235,0.40014499018619737,0.7609504047032826,0.4154175555172147],"dir":"ltr"},{"str":"3","boundary":[0.749961901288851,0.42916295629452517,0.76095238883031,0.4444355216255425],"dir":"ltr"},{"str":"7","boundary":[0.7499658695429058,0.4520719575900427,0.7609563570843648,0.46734452292106005],"dir":"ltr"},{"str":"9","boundary":[0.749961901288851,0.4810899236983705,0.76095238883031,0.49636248902938784],"dir":"ltr"},{"str":"9","boundary":[0.750514736618377,0.5014965154863287,0.760955732878002,0.5160054985404926],"dir":"ltr"},{"str":"9","boundary":[0.7505147366183773,0.5213506078976465,0.7609557328780023,0.5358595909518105],"dir":"ltr"},{"str":"11","boundary":[0.7400737403587523,0.5412047003089644,0.7609557328780021,0.5557136833631283],"dir":"ltr"},{"str":"11","boundary":[0.7400737403587521,0.5610587927202823,0.7609557328780019,0.5755677757744462],"dir":"ltr"},{"str":"12","boundary":[0.7400737403587523,0.5809143360299056,0.7609557328780021,0.5954233190840695],"dir":"ltr"},{"str":"12","boundary":[0.7400737403587522,0.6007684284412235,0.760955732878002,0.6152774114953874],"dir":"ltr"},{"str":"13","boundary":[0.7400737403587521,0.6206225208525413,0.7609557328780019,0.6351315039067053],"dir":"ltr"},{"str":"14","boundary":[0.7400737403587521,0.6404766132638593,0.7609557328780019,0.6549855963180231],"dir":"ltr"},{"str":"15","boundary":[0.7400737403587521,0.6603321565734825,0.7609557328780019,0.6748411396276465],"dir":"ltr"},{"str":"17","boundary":[0.7389757899379635,0.6826888285009416,0.7609567650208817,0.6979613938319589],"dir":"ltr"},{"str":"18","boundary":[0.7389718216839087,0.7117067946092694,0.7609527967668268,0.7269793599402868],"dir":"ltr"},{"str":"19","boundary":[0.7400737403587522,0.7321118534073122,0.760955732878002,0.746620836461476],"dir":"ltr"},{"str":"20","boundary":[0.7400737403587521,0.7519673967169355,0.7609557328780019,0.7664763797710994],"dir":"ltr"},{"str":"20","boundary":[0.7400737403587521,0.7718214891282533,0.7609557328780019,0.7863304721824174],"dir":"ltr"},{"str":"21","boundary":[0.7400737403587521,0.7916755815395714,0.7609557328780019,0.8061845645937354],"dir":"ltr"},{"str":"21","boundary":[0.7400737403587522,0.8115296739508893,0.760955732878002,0.8260386570050533],"dir":"ltr"},{"str":"22","boundary":[0.7400737403587521,0.8313837663622072,0.7609557328780019,0.8458927494163712],"dir":"ltr"},{"str":"22","boundary":[0.7400737403587521,0.8512393096718305,0.7609557328780019,0.8657482927259945],"dir":"ltr"},{"str":"23","boundary":[0.7389757899379635,0.8735966616336156,0.7609567650208817,0.8888692269646329],"dir":"ltr"}],"boundary":[0.73897,0.40014,0.76096,0.88887],"dir":"ltr","type":"paragraph"},{"words":[{"str":"vii","boundary":[0.9050171501888663,0.9329336324576841,0.9269981252717845,0.9482061977887014],"dir":"ltr"}],"boundary":[0.90502,0.93293,0.927,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":8,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/0d8f9a5fedfb4ae49839e96b91357582.jpg","blurred":"/storage/books/4a8b03583f119702/pages/1a052eae8d0a1ab3fe6ca06c59b82d41.jpg"},"info":{"width":504.00001299999997,"height":652.3200069999999,"margin":[0.07306,0.05842,0.073,0.07749]},"elements":[{"words":[{"str":"viii","boundary":[0.07305950208378269,0.0584185359809148,0.10053571962903898,0.07369110142899557],"dir":"ltr"}],"boundary":[0.07306,0.05842,0.10054,0.07369],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Contents","boundary":[0.23910314859456164,0.059521148797142584,0.3112791086376421,0.0732665496798109],"dir":"ltr"},{"str":"1.4","boundary":[0.26224997339434597,0.09974284170621818,0.2924739230115853,0.11654272501870411],"dir":"ltr"},{"str":"Fundamental","boundary":[0.3043243205233806,0.09974284170621818,0.4396362906443021,0.11654272501870411],"dir":"ltr"},{"str":"Data","boundary":[0.44568108056774997,0.09974284170621818,0.49280000058253975,0.11654272501870411],"dir":"ltr"},{"str":"Structures","boundary":[0.4988447905059876,0.09974284170621818,0.6051504665338174,0.11654272501870411],"dir":"ltr"},{"str":"Linear","boundary":[0.30433528976912944,0.12125215714869242,0.35546987872795943,0.13576114031406697],"dir":"ltr"},{"str":"Data","boundary":[0.3606903766091768,0.12125215714869242,0.39928074763759974,0.13576114031406697],"dir":"ltr"},{"str":"Structures","boundary":[0.4045012455188171,0.12125215714869242,0.4910901510234683,0.13576114031406697],"dir":"ltr"},{"str":"Graphs","boundary":[0.30433528976912944,0.1411062497121909,0.3638076523224217,0.15561523287756546],"dir":"ltr"},{"str":"Trees","boundary":[0.30433528976912944,0.1609603422756894,0.34957334514989385,0.17546932544106394],"dir":"ltr"},{"str":"Sets","boundary":[0.30433528976912944,0.1808144348391879,0.3418928284829231,0.19532341800456243],"dir":"ltr"},{"str":"and","boundary":[0.3471133263641404,0.1808144348391879,0.37738470256745804,0.19532341800456243],"dir":"ltr"},{"str":"Dictionaries","boundary":[0.3826052004486754,0.1808144348391879,0.4806679340303906,0.19532341800456243],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.20372266835899777,0.38782569832989267,0.2182316515243723],"dir":"ltr"},{"str":"1.4","boundary":[0.39304619621111003,0.20372266835899777,0.4191486856171966,0.2182316515243723],"dir":"ltr"},{"str":"Summary","boundary":[0.30433631889608703,0.22608149101273867,0.39658920183400864,0.24135405646081945],"dir":"ltr"},{"str":"2","boundary":[0.2608313226372873,0.2700811542025877,0.292474516463951,0.3067354032573772],"dir":"ltr"},{"str":"Fundamentals","boundary":[0.30433528976912944,0.28331328277043033,0.4651374697484383,0.3016404839473214],"dir":"ltr"},{"str":"of","boundary":[0.4717318060862828,0.28331328277043033,0.4941240848737835,0.3016404839473214],"dir":"ltr"},{"str":"the","boundary":[0.500718421211628,0.28331328277043033,0.5376277281961103,0.3016404839473214],"dir":"ltr"},{"str":"Analysis","boundary":[0.5442220645339547,0.28331328277043033,0.6391283224034362,0.3016404839473214],"dir":"ltr"},{"str":"of","boundary":[0.6457226587412807,0.28331328277043033,0.6681149375287814,0.3016404839473214],"dir":"ltr"},{"str":"Algorithm","boundary":[0.6747092738666259,0.28331328277043033,0.7893510994810232,0.3016404839473214],"dir":"ltr"},{"str":"Efficiency","boundary":[0.30433528976912944,0.3031671398053564,0.4124064996799911,0.3214943409822475],"dir":"ltr"},{"str":"2.1","boundary":[0.26224997339434597,0.3333061210247383,0.2924739230115853,0.3501060043372242],"dir":"ltr"},{"str":"The","boundary":[0.3043243205233806,0.3333061210247383,0.34298488341507244,0.3501060043372242],"dir":"ltr"},{"str":"Analysis","boundary":[0.34902967333852036,0.3333061210247383,0.4360268117691497,0.3501060043372242],"dir":"ltr"},{"str":"Framework","boundary":[0.4420716016925975,0.3333061210247383,0.558053290367673,0.3501060043372242],"dir":"ltr"},{"str":"Measuring","boundary":[0.30433528976912944,0.35481390347728536,0.3930274174417531,0.3693228866426599],"dir":"ltr"},{"str":"an","boundary":[0.39824791532297044,0.35481390347728536,0.41807829576385347,0.3693228866426599],"dir":"ltr"},{"str":"Input’s","boundary":[0.4232987936450708,0.35481390347728536,0.479315862636694,0.3693228866426599],"dir":"ltr"},{"str":"Size","boundary":[0.4845363605179113,0.35481390347728536,0.5189578447491032,0.3693228866426599],"dir":"ltr"},{"str":"Units","boundary":[0.30433528976912944,0.3746694469391004,0.34814615867876975,0.38917843010447495],"dir":"ltr"},{"str":"for","boundary":[0.353366656559987,0.3746694469391004,0.3763143127141149,0.38917843010447495],"dir":"ltr"},{"str":"Measuring","boundary":[0.3815348105953323,0.3746694469391004,0.4702269382679559,0.38917843010447495],"dir":"ltr"},{"str":"Running","boundary":[0.4754474361491733,0.3746694469391004,0.5443467409196276,0.38917843010447495],"dir":"ltr"},{"str":"Time","boundary":[0.5495672388008451,0.3746694469391004,0.5899228141488163,0.38917843010447495],"dir":"ltr"},{"str":"Orders","boundary":[0.30433528976912944,0.39452353950259894,0.3617232089238061,0.40903252266797346],"dir":"ltr"},{"str":"of","boundary":[0.3669437068050234,0.39452353950259894,0.3836380327633047,0.40903252266797346],"dir":"ltr"},{"str":"Growth","boundary":[0.38885853064452197,0.39452353950259894,0.4514481689110591,0.40903252266797346],"dir":"ltr"},{"str":"Worst-Case,","boundary":[0.30433528976912944,0.41437763206609746,0.4072992821529947,0.4288866152314719],"dir":"ltr"},{"str":"Best-Case,","boundary":[0.412519780034212,0.41437763206609746,0.5033151298748082,0.4288866152314719],"dir":"ltr"},{"str":"and","boundary":[0.5085356277560255,0.41437763206609746,0.5388070039593432,0.4288866152314719],"dir":"ltr"},{"str":"Average-Case","boundary":[0.5440275018405605,0.41437763206609746,0.6591789155370518,0.4288866152314719],"dir":"ltr"},{"str":"Efficiencies","boundary":[0.6643994134182691,0.41437763206609746,0.7603964823707257,0.4288866152314719],"dir":"ltr"},{"str":"Recapitulation","boundary":[0.30433528976912944,0.4342317246295959,0.42224718256108457,0.44874070779497044],"dir":"ltr"},{"str":"of","boundary":[0.42746768044230193,0.4342317246295959,0.4441620064005832,0.44874070779497044],"dir":"ltr"},{"str":"the","boundary":[0.4493825042818005,0.4342317246295959,0.4765178260025164,0.44874070779497044],"dir":"ltr"},{"str":"Analysis","boundary":[0.48173832388373367,0.4342317246295959,0.5506000711154744,0.44874070779497044],"dir":"ltr"},{"str":"Framework","boundary":[0.5558205689966917,0.4342317246295959,0.650766026865162,0.44874070779497044],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.45714140904772227,0.38782569832989267,0.4716503922130968],"dir":"ltr"},{"str":"2.1","boundary":[0.39304619621111003,0.45714140904772227,0.4191486856171966,0.4716503922130968],"dir":"ltr"},{"str":"2.2","boundary":[0.26224997339434597,0.48452331341724447,0.2924739230115853,0.5013231967297304],"dir":"ltr"},{"str":"Asymptotic","boundary":[0.3043243205233806,0.48452331341724447,0.42148017702531293,0.5013231967297304],"dir":"ltr"},{"str":"Notations","boundary":[0.4275249669487608,0.48452331341724447,0.5277858530531427,0.5013231967297304],"dir":"ltr"},{"str":"and","boundary":[0.5338306429765907,0.48452331341724447,0.5724912058682825,0.5013231967297304],"dir":"ltr"},{"str":"Basic","boundary":[0.5785359957917303,0.48452331341724447,0.6329173612541157,0.5013231967297304],"dir":"ltr"},{"str":"Efficiency","boundary":[0.6389621511775636,0.48452331341724447,0.7380271256064431,0.5013231967297304],"dir":"ltr"},{"str":"Classes","boundary":[0.744071915529891,0.48452331341724447,0.8214147851619201,0.5013231967297304],"dir":"ltr"},{"str":"Informal","boundary":[0.30433528976912944,0.5060310958697916,0.3731970370008701,0.5205400790351661],"dir":"ltr"},{"str":"Introduction","boundary":[0.3784175348820874,0.5060310958697916,0.478602269401132,0.5205400790351661],"dir":"ltr"},{"str":"O","boundary":[0.30433528976912944,0.5265671106420627,0.3192080750997917,0.5410760938074373],"dir":"ltr"},{"str":"-notation","boundary":[0.3205225889547745,0.5258851884332901,0.39357200175310314,0.5403941715986647],"dir":"ltr"},{"str":"\u0002","boundary":[0.30433528976912944,0.5464226541038778,0.31894517232879516,0.5609316372692523],"dir":"ltr"},{"str":"-notation","boundary":[0.31894517232879516,0.5457407318951052,0.39199458512712376,0.5602497150604797],"dir":"ltr"},{"str":"\u0003","boundary":[0.30433528976912944,0.5662767466673763,0.3193958627933607,0.5807857298327508],"dir":"ltr"},{"str":"-notation","boundary":[0.31939398491642496,0.5655948244586037,0.3924433977147536,0.5801038076239782],"dir":"ltr"},{"str":"Useful","boundary":[0.30433528976912944,0.5854489170221021,0.35858715444120437,0.5999579001874766],"dir":"ltr"},{"str":"Property","boundary":[0.3638076523224217,0.5854489170221021,0.4347538429527779,0.5999579001874766],"dir":"ltr"},{"str":"Involving","boundary":[0.4399743408339952,0.5854489170221021,0.5140753647163101,0.5999579001874766],"dir":"ltr"},{"str":"the","boundary":[0.5192958625975274,0.5854489170221021,0.5464311843182432,0.5999579001874766],"dir":"ltr"},{"str":"Asymptotic","boundary":[0.5516516821994607,0.5854489170221021,0.646597140067931,0.5999579001874766],"dir":"ltr"},{"str":"Notations","boundary":[0.6518176379491483,0.5854489170221021,0.7321532132579529,0.5999579001874766],"dir":"ltr"},{"str":"Using","boundary":[0.30433528976912944,0.6053030095856007,0.3523338242453577,0.6198119927509752],"dir":"ltr"},{"str":"Limits","boundary":[0.357554322126575,0.6053030095856007,0.4086701323160482,0.6198119927509752],"dir":"ltr"},{"str":"for","boundary":[0.41389063019726546,0.6053030095856007,0.4368382863513934,0.6198119927509752],"dir":"ltr"},{"str":"Comparing","boundary":[0.4420587842326107,0.6053030095856007,0.5328541340732068,0.6198119927509752],"dir":"ltr"},{"str":"Orders","boundary":[0.5380746319544242,0.6053030095856007,0.595462551109101,0.6198119927509752],"dir":"ltr"},{"str":"of","boundary":[0.6006830489903182,0.6053030095856007,0.6173773749485996,0.6198119927509752],"dir":"ltr"},{"str":"Growth","boundary":[0.6225978728298168,0.6053030095856007,0.6851875110963539,0.6198119927509752],"dir":"ltr"},{"str":"Basic","boundary":[0.30433528976912944,0.6251585530474157,0.34919776976275596,0.6396675362127903],"dir":"ltr"},{"str":"Efficiency","boundary":[0.3544182676439732,0.6251585530474157,0.435805454036764,0.6396675362127903],"dir":"ltr"},{"str":"Classes","boundary":[0.44102595191798144,0.6251585530474157,0.5057188123524909,0.6396675362127903],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.648065335668909,0.38782569832989267,0.6625743188342835],"dir":"ltr"},{"str":"2.2","boundary":[0.39304619621111003,0.648065335668909,0.4191486856171966,0.6625743188342835],"dir":"ltr"},{"str":"2.3","boundary":[0.26224997339434597,0.6754480109024161,0.2924739230115853,0.6922478942149021],"dir":"ltr"},{"str":"Mathematical","boundary":[0.3043243205233806,0.6754480109024161,0.44446342504360214,0.6922478942149021],"dir":"ltr"},{"str":"Analysis","boundary":[0.45050821496705,0.6754480109024161,0.5375053533976794,0.6922478942149021],"dir":"ltr"},{"str":"of","boundary":[0.5435501433211273,0.6754480109024161,0.5640763364424755,0.6922478942149021],"dir":"ltr"},{"str":"Nonrecursive","boundary":[0.5701211263659234,0.6754480109024161,0.7078684075351402,0.6922478942149021],"dir":"ltr"},{"str":"Algorithms","boundary":[0.7139131974585882,0.6754480109024161,0.8286554867608704,0.6922478942149021],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.7000110422797443,0.38782569832989267,0.7145200254451188],"dir":"ltr"},{"str":"2.3","boundary":[0.39304619621111003,0.7000110422797443,0.4191486856171966,0.7145200254451188],"dir":"ltr"},{"str":"2.4","boundary":[0.26224997339434597,0.7273933745834047,0.2924739230115853,0.7441932578958906],"dir":"ltr"},{"str":"Mathematical","boundary":[0.3043243205233806,0.7273933745834047,0.44446342504360214,0.7441932578958906],"dir":"ltr"},{"str":"Analysis","boundary":[0.45050821496705,0.7273933745834047,0.5375053533976794,0.7441932578958906],"dir":"ltr"},{"str":"of","boundary":[0.5435501433211273,0.7273933745834047,0.5640763364424755,0.7441932578958906],"dir":"ltr"},{"str":"Recursive","boundary":[0.5701211263659234,0.7273933745834047,0.6704255001675963,0.7441932578958906],"dir":"ltr"},{"str":"Algorithms","boundary":[0.6764702900910442,0.7273933745834047,0.7912125793933263,0.7441932578958906],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.7519564059607329,0.38782569832989267,0.7664653891261074],"dir":"ltr"},{"str":"2.4","boundary":[0.39304619621111003,0.7519564059607329,0.4191486856171966,0.7664653891261074],"dir":"ltr"},{"str":"2.5","boundary":[0.26224997339434597,0.7793387382643931,0.2924739230115853,0.7961386215768792],"dir":"ltr"},{"str":"Example:","boundary":[0.3043243205233806,0.7793387382643931,0.39977981607710794,0.7961386215768792],"dir":"ltr"},{"str":"Computing","boundary":[0.40582460600055587,0.7793387382643931,0.5205668953028381,0.7961386215768792],"dir":"ltr"},{"str":"the","boundary":[0.526611685226286,0.7793387382643931,0.5592274581945299,0.7961386215768792],"dir":"ltr"},{"str":"nth","boundary":[0.5652809456574359,0.7793387382643931,0.5996144826686741,0.7961386215768792],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.605659272592122,0.7793387382643931,0.7035283353454993,0.7961386215768792],"dir":"ltr"},{"str":"Number","boundary":[0.7095731252689472,0.7793387382643931,0.794134952651281,0.7961386215768792],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.8039017696417216,0.38782569832989267,0.8184107528070962],"dir":"ltr"},{"str":"2.5","boundary":[0.39304619621111003,0.8039017696417216,0.4191486856171966,0.8184107528070962],"dir":"ltr"},{"str":"2.6","boundary":[0.26224997339434597,0.8312841019453818,0.2924739230115853,0.8480839852578678],"dir":"ltr"},{"str":"Empirical","boundary":[0.3043243205233806,0.8312841019453818,0.4009757277526102,0.8480839852578678],"dir":"ltr"},{"str":"Analysis","boundary":[0.4070205176760581,0.8312841019453818,0.49401765610668746,0.8480839852578678],"dir":"ltr"},{"str":"of","boundary":[0.5000624460301354,0.8312841019453818,0.5205886391514836,0.8480839852578678],"dir":"ltr"},{"str":"Algorithms","boundary":[0.5266334290749315,0.8312841019453818,0.6413757183772136,0.8480839852578678],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.855845600332783,0.38782569832989267,0.8703545834981575],"dir":"ltr"},{"str":"2.6","boundary":[0.39304619621111003,0.855845600332783,0.4191486856171966,0.8703545834981575],"dir":"ltr"},{"str":"2.7","boundary":[0.26224997339434597,0.8832279326364433,0.2924739230115853,0.9000278159489292],"dir":"ltr"},{"str":"Algorithm","boundary":[0.3043243205233806,0.8832279326364433,0.4081946855029149,0.9000278159489292],"dir":"ltr"},{"str":"Visualization","boundary":[0.41423947542636275,0.8832279326364433,0.5443329218723651,0.9000278159489292],"dir":"ltr"},{"str":"Summary","boundary":[0.3043363040548175,0.9072395043066648,0.39658918699273915,0.9225120697547455],"dir":"ltr"}],"boundary":[0.2391,0.05952,0.82866,0.92251],"dir":"ltr","type":"paragraph"},{"words":[{"str":"25","boundary":[0.9050178139578738,0.10084556520431873,0.926998787994079,0.11611813065239948],"dir":"ltr"},{"str":"25","boundary":[0.9061197325802449,0.12125215714869242,0.9270017241051142,0.13576114031406697],"dir":"ltr"},{"str":"28","boundary":[0.906119732580245,0.1411062497121909,0.9270017241051143,0.15561523287756546],"dir":"ltr"},{"str":"31","boundary":[0.9061197325802449,0.1609603422756894,0.9270017241051142,0.17546932544106394],"dir":"ltr"},{"str":"35","boundary":[0.906119732580245,0.1808144348391879,0.9270017241051143,0.19532341800456243],"dir":"ltr"},{"str":"37","boundary":[0.9050217822117398,0.20317264284061756,0.9270027562479448,0.21844520828869832],"dir":"ltr"},{"str":"38","boundary":[0.9050178287991434,0.22608149101273867,0.9269988028353484,0.24135405646081945],"dir":"ltr"}],"boundary":[0.90502,0.10085,0.927,0.24135],"dir":"ltr","type":"paragraph"},{"words":[{"str":"41","boundary":[0.9050178139578738,0.3053724823129641,0.926998787994079,0.3206450477610449],"dir":"ltr"},{"str":"42","boundary":[0.9050178139578738,0.33440884452283876,0.926998787994079,0.34968140997091957],"dir":"ltr"},{"str":"43","boundary":[0.906119732580245,0.35481390347728536,0.9270017241051143,0.3693228866426599],"dir":"ltr"},{"str":"44","boundary":[0.9061197325802451,0.3746694469391004,0.9270017241051144,0.38917843010447495],"dir":"ltr"},{"str":"45","boundary":[0.906119732580245,0.39452353950259894,0.9270017241051143,0.40903252266797346],"dir":"ltr"},{"str":"47","boundary":[0.9061197325802455,0.41437763206609746,0.9270017241051147,0.4288866152314719],"dir":"ltr"},{"str":"50","boundary":[0.9061197325802455,0.4342317246295959,0.9270017241051147,0.44874070779497044],"dir":"ltr"},{"str":"50","boundary":[0.9050217822117398,0.4565896747054704,0.9270027562479448,0.47186224015355116],"dir":"ltr"},{"str":"52","boundary":[0.9050178139578738,0.48562603691534506,0.926998787994079,0.5008986023634259],"dir":"ltr"},{"str":"52","boundary":[0.906119732580245,0.5060310958697916,0.9270017241051143,0.5205400790351661],"dir":"ltr"},{"str":"53","boundary":[0.906119732580245,0.5258851884332901,0.9270017241051143,0.5403941715986647],"dir":"ltr"},{"str":"54","boundary":[0.906119732580245,0.5457407318951052,0.9270017241051143,0.5602497150604797],"dir":"ltr"},{"str":"55","boundary":[0.9061178547033093,0.5655948244586037,0.9269998462281785,0.5801038076239782],"dir":"ltr"},{"str":"55","boundary":[0.9061197325802454,0.5854489170221021,0.9270017241051146,0.5999579001874766],"dir":"ltr"},{"str":"56","boundary":[0.9061197325802453,0.6053030095856007,0.9270017241051145,0.6198119927509752],"dir":"ltr"},{"str":"58","boundary":[0.906119732580245,0.6251585530474157,0.9270017241051143,0.6396675362127903],"dir":"ltr"},{"str":"58","boundary":[0.9050217822117398,0.647515905180569,0.9270027562479448,0.6627884706286499],"dir":"ltr"},{"str":"61","boundary":[0.9050178139578738,0.6765507344005167,0.926998787994079,0.6918232998485975],"dir":"ltr"},{"str":"67","boundary":[0.9050217822117398,0.6994597358716305,0.9270027562479448,0.7147323013197112],"dir":"ltr"},{"str":"70","boundary":[0.9050178139578738,0.7284960980815053,0.926998787994079,0.743768663529586],"dir":"ltr"},{"str":"76","boundary":[0.9050217822117398,0.751405099552619,0.9270027562479448,0.7666776650006998],"dir":"ltr"},{"str":"80","boundary":[0.9050178139578738,0.7804414617624937,0.926998787994079,0.7957140272105746],"dir":"ltr"},{"str":"83","boundary":[0.9050217822117398,0.8033504632336075,0.9270027562479448,0.8186230286816882],"dir":"ltr"},{"str":"84","boundary":[0.9050178139578738,0.8323868254434823,0.926998787994079,0.847659390891563],"dir":"ltr"},{"str":"89","boundary":[0.9050217822117398,0.8552942939246689,0.9270027562479448,0.8705668593727497],"dir":"ltr"},{"str":"91","boundary":[0.9050178139578738,0.8843306561345436,0.926998787994079,0.8996032215826244],"dir":"ltr"},{"str":"94","boundary":[0.9050178139578738,0.9072395043066648,0.926998787994079,0.9225120697547455],"dir":"ltr"}],"boundary":[0.90502,0.30537,0.927,0.92251],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":9,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/eda8881f3996c589201ed306a4ae9680.jpg","blurred":"/storage/books/4a8b03583f119702/pages/8a1ed5225d0f6139a05f273d9b17c62a.jpg"},"info":{"width":503.999989,"height":652.3200069999999,"margin":[0.26083,0.05842,0.073,0.07749]},"elements":[{"words":[{"str":"Contents","boundary":[0.6887773761439505,0.059521148797142584,0.7609533396239816,0.0732665496798109],"dir":"ltr"},{"str":"3","boundary":[0.2608289541053938,0.09757686368187712,0.2924721494388762,0.1342311127366666],"dir":"ltr"},{"str":"Brute","boundary":[0.3043329233088534,0.11080899224971974,0.3662912230738163,0.12913619342661084],"dir":"ltr"},{"str":"Force","boundary":[0.37288555972567683,0.11080899224971974,0.4348438594906397,0.12913619342661084],"dir":"ltr"},{"str":"and","boundary":[0.4414381961425003,0.11080899224971974,0.48361348595188164,0.12913619342661084],"dir":"ltr"},{"str":"Exhaustive","boundary":[0.4902078226037421,0.11080899224971974,0.6141244221336679,0.12913619342661084],"dir":"ltr"},{"str":"Search","boundary":[0.6207187587855284,0.11080899224971974,0.6984987223878689,0.12913619342661084],"dir":"ltr"},{"str":"3.1","boundary":[0.2622476049300072,0.1446395177022373,0.29247155598648233,0.16143940101472323],"dir":"ltr"},{"str":"Selection","boundary":[0.30432195406258233,0.1446395177022373,0.39977745416180954,0.16143940101472323],"dir":"ltr"},{"str":"Sort","boundary":[0.40582224437310455,0.1446395177022373,0.4493099437349392,0.16143940101472323],"dir":"ltr"},{"str":"and","boundary":[0.45535473394623427,0.1446395177022373,0.4940152986789053,0.16143940101472323],"dir":"ltr"},{"str":"Bubble","boundary":[0.5000600888902004,0.1446395177022373,0.5725540837263788,0.16143940101472323],"dir":"ltr"},{"str":"Sort","boundary":[0.5785988739376737,0.1446395177022373,0.6220865732995084,0.16143940101472323],"dir":"ltr"},{"str":"Selection","boundary":[0.3043329233088534,0.16614867984571885,0.3815512265814751,0.1806576630110934],"dir":"ltr"},{"str":"Sort","boundary":[0.38677172471128757,0.16614867984571885,0.42119321058159775,0.1806576630110934],"dir":"ltr"},{"str":"Bubble","boundary":[0.3043329233088534,0.18600277240921737,0.3627912351006023,0.2005117555745919],"dir":"ltr"},{"str":"Sort","boundary":[0.36801173323041475,0.18600277240921737,0.40243321910072494,0.2005117555745919],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.20890955503071068,0.3878233358453505,0.2234185381960852],"dir":"ltr"},{"str":"3.1","boundary":[0.39304383397516296,0.20890955503071068,0.41914632462422524,0.2234185381960852],"dir":"ltr"},{"str":"3.2","boundary":[0.2622476049300072,0.23998535921036085,0.29247155598648233,0.2567852425228468],"dir":"ltr"},{"str":"Sequential","boundary":[0.30432195406258233,0.23998535921036085,0.41428060189898136,0.2567852425228468],"dir":"ltr"},{"str":"Search","boundary":[0.4203253921102764,0.23998535921036085,0.4916234752140044,0.2567852425228468],"dir":"ltr"},{"str":"and","boundary":[0.4976682654252994,0.23998535921036085,0.5363288301579705,0.2567852425228468],"dir":"ltr"},{"str":"Brute-Force","boundary":[0.5423736203692655,0.23998535921036085,0.6619865374639919,0.2567852425228468],"dir":"ltr"},{"str":"String","boundary":[0.668031327675287,0.23998535921036085,0.7308493094034572,0.2567852425228468],"dir":"ltr"},{"str":"Matching","boundary":[0.7368940996147522,0.23998535921036085,0.8335237675967488,0.2567852425228468],"dir":"ltr"},{"str":"Sequential","boundary":[0.3043329233088534,0.261493141662908,0.3919922228411,0.2760021248282825],"dir":"ltr"},{"str":"Search","boundary":[0.3972127209709125,0.261493141662908,0.4546006428583473,0.2760021248282825],"dir":"ltr"},{"str":"Brute-Force","boundary":[0.3043329233088534,0.28134723422640645,0.40243321910072494,0.295856217391781],"dir":"ltr"},{"str":"String","boundary":[0.4076537172305374,0.28134723422640645,0.456685086356222,0.295856217391781],"dir":"ltr"},{"str":"Matching","boundary":[0.4619055844860345,0.28134723422640645,0.540156720122468,0.295856217391781],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.3042569186445328,0.3878233358453505,0.3187659018099073],"dir":"ltr"},{"str":"3.2","boundary":[0.39304383397516296,0.3042569186445328,0.41914632462422524,0.3187659018099073],"dir":"ltr"},{"str":"3.3","boundary":[0.2622476049300072,0.3353296677285572,0.29247155598648233,0.35212955104104315],"dir":"ltr"},{"str":"Closest-Pair","boundary":[0.30432195406258233,0.3353296677285572,0.4263484384718905,0.35212955104104315],"dir":"ltr"},{"str":"and","boundary":[0.43239322868318547,0.3353296677285572,0.4710537934158565,0.35212955104104315],"dir":"ltr"},{"str":"Convex-Hull","boundary":[0.47709858362715163,0.3353296677285572,0.6027562909331731,0.35212955104104315],"dir":"ltr"},{"str":"Problems","boundary":[0.6088010811444681,0.3353296677285572,0.7066484047085961,0.35212955104104315],"dir":"ltr"},{"str":"by","boundary":[0.712693194919891,0.3353296677285572,0.7380682674975216,0.35212955104104315],"dir":"ltr"},{"str":"Brute","boundary":[0.7441130577088167,0.3353296677285572,0.7996903374932415,0.35212955104104315],"dir":"ltr"},{"str":"Force","boundary":[0.8057351277045364,0.3353296677285572,0.8625300630710926,0.35212955104104315],"dir":"ltr"},{"str":"Closest-Pair","boundary":[0.3043329233088534,0.3568389831710314,0.40344727269428565,0.37134796633640593],"dir":"ltr"},{"str":"Problem","boundary":[0.4086677708240981,0.3568389831710314,0.4785811324690326,0.37134796633640593],"dir":"ltr"},{"str":"Convex-Hull","boundary":[0.3043329233088534,0.3766930757345299,0.4045176625985997,0.39120205889990445],"dir":"ltr"},{"str":"Problem","boundary":[0.4097381607284122,0.3766930757345299,0.4796515223733467,0.39120205889990445],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.39959985835602324,0.3878233358453505,0.41410884152139776],"dir":"ltr"},{"str":"3.3","boundary":[0.39304383397516296,0.39959985835602324,0.41914632462422524,0.41410884152139776],"dir":"ltr"},{"str":"3.4","boundary":[0.2622476049300072,0.4306755092366807,0.29247155598648233,0.4474753925491666],"dir":"ltr"},{"str":"Exhaustive","boundary":[0.30432195406258233,0.4306755092366807,0.4166941692135632,0.4474753925491666],"dir":"ltr"},{"str":"Search","boundary":[0.4227389594248583,0.4306755092366807,0.49403704252858627,0.4474753925491666],"dir":"ltr"},{"str":"Traveling","boundary":[0.3043329233088534,0.4521832916892278,0.377739136220497,0.4666922748546023],"dir":"ltr"},{"str":"Salesman","boundary":[0.3829596343503094,0.4521832916892278,0.4643468246186806,0.4666922748546023],"dir":"ltr"},{"str":"Problem","boundary":[0.4695673227484931,0.4521832916892278,0.5394806843934276,0.4666922748546023],"dir":"ltr"},{"str":"Knapsack","boundary":[0.3043329233088534,0.47203738425272623,0.38363567007934984,0.48654636741810076],"dir":"ltr"},{"str":"Problem","boundary":[0.38885616820916236,0.47203738425272623,0.4587695298540968,0.48654636741810076],"dir":"ltr"},{"str":"Assignment","boundary":[0.3043329233088534,0.49189147681622475,0.4045176625985997,0.5064004599815993],"dir":"ltr"},{"str":"Problem","boundary":[0.4097381607284122,0.49189147681622475,0.4796515223733467,0.5064004599815993],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.5147997103360347,0.3878233358453505,0.5293086935014092],"dir":"ltr"},{"str":"3.4","boundary":[0.39304383397516296,0.5147997103360347,0.41914632462422524,0.5293086935014092],"dir":"ltr"},{"str":"3.5","boundary":[0.2622476049300072,0.5458735703012096,0.29247155598648233,0.5626734536136956],"dir":"ltr"},{"str":"Depth-First","boundary":[0.30432195406258233,0.5458735703012096,0.41786833709633275,0.5626734536136956],"dir":"ltr"},{"str":"Search","boundary":[0.42391312730762776,0.5458735703012096,0.49521121041135574,0.5626734536136956],"dir":"ltr"},{"str":"and","boundary":[0.5012560006226507,0.5458735703012096,0.5399165653553218,0.5626734536136956],"dir":"ltr"},{"str":"Breadth-First","boundary":[0.5459613555666168,0.5458735703012096,0.6788597648163837,0.5626734536136956],"dir":"ltr"},{"str":"Search","boundary":[0.6849045550276788,0.5458735703012096,0.7562026381314068,0.5626734536136956],"dir":"ltr"},{"str":"Depth-First","boundary":[0.3043329233088534,0.567382885743684,0.39719394220066134,0.5818918689090585],"dir":"ltr"},{"str":"Search","boundary":[0.40241444033047385,0.567382885743684,0.4598023622179086,0.5818918689090585],"dir":"ltr"},{"str":"Breadth-First","boundary":[0.3043329233088534,0.5872369783071825,0.41180382545603583,0.601745961472557],"dir":"ltr"},{"str":"Search","boundary":[0.4170243235858483,0.5872369783071825,0.4744122454732831,0.601745961472557],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.6101452118269924,0.3878233358453505,0.624654194992367],"dir":"ltr"},{"str":"3.5","boundary":[0.39304383397516296,0.6101452118269924,0.41914632462422524,0.624654194992367],"dir":"ltr"},{"str":"Summary","boundary":[0.30433455878507965,0.6325031815251377,0.3965874461159958,0.6477757469732186],"dir":"ltr"},{"str":"4","boundary":[0.2608289541053938,0.6851841666723556,0.2924721494388762,0.721838415727145],"dir":"ltr"},{"str":"Decrease-and-Conquer","boundary":[0.3043329233088534,0.6984162952401982,0.5613460082833452,0.7167434964170893],"dir":"ltr"},{"str":"4.1","boundary":[0.2622476049300072,0.7322468206927157,0.29247155598648233,0.7490467040052017],"dir":"ltr"},{"str":"Insertion","boundary":[0.30432195406258233,0.7322468206927157,0.3949285756829649,0.7490467040052017],"dir":"ltr"},{"str":"Sort","boundary":[0.40097336589425997,0.7322468206927157,0.4444610652560947,0.7490467040052017],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.7568098520700441,0.3878233358453505,0.7713188352354187],"dir":"ltr"},{"str":"4.1","boundary":[0.39304383397516296,0.7568098520700441,0.41914632462422524,0.7713188352354187],"dir":"ltr"},{"str":"4.2","boundary":[0.2622476049300072,0.7878836241182469,0.29247155598648233,0.8046835074307327],"dir":"ltr"},{"str":"Topological","boundary":[0.30432195406258233,0.7878836241182469,0.42286942252294374,0.8046835074307327],"dir":"ltr"},{"str":"Sorting","boundary":[0.42891421273423874,0.7878836241182469,0.5050176866174495,0.8046835074307327],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.8124466554955753,0.3878233358453505,0.8269556386609499],"dir":"ltr"},{"str":"4.2","boundary":[0.39304383397516296,0.8124466554955753,0.41914632462422524,0.8269556386609499],"dir":"ltr"},{"str":"4.3","boundary":[0.2622476049300072,0.8435188945538508,0.29247155598648233,0.8603187778663366],"dir":"ltr"},{"str":"Algorithms","boundary":[0.30432195406258233,0.8435188945538508,0.4190642488287832,0.8603187778663366],"dir":"ltr"},{"str":"for","boundary":[0.42510903904007824,0.8435188945538508,0.45409359066474103,0.8603187778663366],"dir":"ltr"},{"str":"Generating","boundary":[0.46013838087603603,0.8435188945538508,0.5749241633415987,0.8603187778663366],"dir":"ltr"},{"str":"Combinatorial","boundary":[0.5809689535528938,0.8435188945538508,0.7271528549577012,0.8603187778663366],"dir":"ltr"},{"str":"Objects","boundary":[0.7331976451689961,0.8435188945538508,0.8105187746343382,0.8603187778663366],"dir":"ltr"},{"str":"Generating","boundary":[0.3043329233088534,0.865028209996325,0.39616110983684955,0.8795371931616996],"dir":"ltr"},{"str":"Permutations","boundary":[0.401381607966662,0.865028209996325,0.5130213971095939,0.8795371931616996],"dir":"ltr"},{"str":"Generating","boundary":[0.3043329233088534,0.8848823025598235,0.39616110983684955,0.8993912857251981],"dir":"ltr"},{"str":"Subsets","boundary":[0.401381607966662,0.8848823025598235,0.46921052611372166,0.8993912857251981],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.9077890851813168,0.3878233358453505,0.9222980683466915],"dir":"ltr"},{"str":"4.3","boundary":[0.39304383397516296,0.9077890851813168,0.41914632462422524,0.9222980683466915],"dir":"ltr"}],"boundary":[0.26083,0.05952,0.86253,0.9223],"dir":"ltr","type":"paragraph"},{"words":[{"str":"ix","boundary":[0.9105095238404856,0.0584185359809148,0.9269952551526741,0.07369110142899557],"dir":"ltr"}],"boundary":[0.91051,0.05842,0.927,0.07369],"dir":"ltr","type":"paragraph"},{"words":[{"str":"97","boundary":[0.9050097221331487,0.1130144392459208,0.9269906972160668,0.12828700469400156],"dir":"ltr"},{"str":"98","boundary":[0.9050156745142309,0.14574224120033785,0.926996649597149,0.1610148066484186],"dir":"ltr"},{"str":"98","boundary":[0.9061173947763715,0.16614867984571885,0.9269993872956214,0.1806576630110934],"dir":"ltr"},{"str":"100","boundary":[0.8956763985167467,0.18600277240921737,0.9269993872956215,0.2005117555745919],"dir":"ltr"},{"str":"102","boundary":[0.8940295631633436,0.20836028075404414,0.9270010257877208,0.22363284620212492],"dir":"ltr"},{"str":"104","boundary":[0.8940253964965859,0.24108808270846135,0.9269968591209631,0.25636064815654214],"dir":"ltr"},{"str":"104","boundary":[0.8956763985167466,0.261493141662908,0.9269993872956214,0.2760021248282825],"dir":"ltr"},{"str":"105","boundary":[0.8956763985167467,0.28134723422640645,0.9269993872956215,0.295856217391781],"dir":"ltr"},{"str":"106","boundary":[0.8940295631633436,0.3037045892722406,0.9270010257877208,0.31897715472032134],"dir":"ltr"},{"str":"108","boundary":[0.8940253964965859,0.3364323912266577,0.9269968591209631,0.3517049566747385],"dir":"ltr"},{"str":"108","boundary":[0.8956763985167467,0.3568389831710314,0.9269993872956215,0.37134796633640593],"dir":"ltr"},{"str":"109","boundary":[0.8956763985167467,0.3766930757345299,0.9269993872956215,0.39120205889990445],"dir":"ltr"},{"str":"113","boundary":[0.8940295631633436,0.3990504307803642,0.9270010257877208,0.41432299622844493],"dir":"ltr"},{"str":"115","boundary":[0.8940253964965859,0.4317782327347813,0.9269968591209631,0.4470507981828621],"dir":"ltr"},{"str":"116","boundary":[0.8956763985167467,0.4521832916892278,0.9269993872956215,0.4666922748546023],"dir":"ltr"},{"str":"116","boundary":[0.8956763985167465,0.47203738425272623,0.9269993872956213,0.48654636741810076],"dir":"ltr"},{"str":"119","boundary":[0.8956763985167466,0.49189147681622475,0.9269993872956214,0.5064004599815993],"dir":"ltr"},{"str":"120","boundary":[0.8940295631633436,0.5142500248348203,0.9270010257877208,0.529522590282901],"dir":"ltr"},{"str":"122","boundary":[0.8940253964965859,0.5469762937993102,0.9269968591209631,0.562248859247391],"dir":"ltr"},{"str":"122","boundary":[0.8956763985167466,0.567382885743684,0.9269993872956214,0.5818918689090585],"dir":"ltr"},{"str":"125","boundary":[0.8956763985167467,0.5872369783071825,0.9269993872956215,0.601745961472557],"dir":"ltr"},{"str":"128","boundary":[0.8940295631633436,0.6095943333530167,0.9270010257877208,0.6248668988010975],"dir":"ltr"},{"str":"130","boundary":[0.8940256097505589,0.6325031815251377,0.9269970723749361,0.6477757469732186],"dir":"ltr"}],"boundary":[0.89403,0.11301,0.927,0.64778],"dir":"ltr","type":"paragraph"},{"words":[{"str":"131","boundary":[0.8940214282425312,0.7006217422363993,0.9269928908669083,0.71589430768448],"dir":"ltr"},{"str":"134","boundary":[0.8940253964965859,0.7333495441908163,0.9269968591209631,0.7486221096388971],"dir":"ltr"},{"str":"136","boundary":[0.8940295631633436,0.7562585456619303,0.9270010257877208,0.771531111110011],"dir":"ltr"},{"str":"138","boundary":[0.8940253964965859,0.7889863476163472,0.9269968591209631,0.804258913064428],"dir":"ltr"},{"str":"142","boundary":[0.8940295631633436,0.8118953490874612,0.9270010257877208,0.827167914535542],"dir":"ltr"},{"str":"144","boundary":[0.8940253964965859,0.8446216180519511,0.9269968591209631,0.8598941835000319],"dir":"ltr"},{"str":"144","boundary":[0.8956763985167467,0.865028209996325,0.9269993872956215,0.8795371931616996],"dir":"ltr"},{"str":"146","boundary":[0.8956763985167466,0.8848823025598235,0.9269993872956214,0.8993912857251981],"dir":"ltr"},{"str":"148","boundary":[0.8940295631633436,0.9072396576056575,0.9270010257877208,0.9225122230537381],"dir":"ltr"}],"boundary":[0.89402,0.70062,0.927,0.92251],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":10,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/9923cd58ace886d0feded9a1ceec08a8.jpg","blurred":"/storage/books/4a8b03583f119702/pages/ae363fd896b62411bd4ad61fc7b1cc85.jpg"},"info":{"width":504.00001299999997,"height":652.3200069999999,"margin":[0.07306,0.05752,0.073,0.09734]},"elements":[{"words":[{"str":"x","boundary":[0.07305950208378269,0.057521583574547765,0.08404998910188521,0.07279414902262853],"dir":"ltr"}],"boundary":[0.07306,0.05752,0.08405,0.07279],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Contents","boundary":[0.23910314859456164,0.05862419639077555,0.3112791086376421,0.07236959727344386],"dir":"ltr"},{"str":"4.4","boundary":[0.26224997339434597,0.09974284170621818,0.2924739230115853,0.11654272501870411],"dir":"ltr"},{"str":"Decrease-by-a-Constant-Factor","boundary":[0.3043243205233806,0.09974284170621818,0.6208495252558655,0.11654272501870411],"dir":"ltr"},{"str":"Algorithms","boundary":[0.6268943151793134,0.09974284170621818,0.7416366044815955,0.11654272501870411],"dir":"ltr"},{"str":"Binary","boundary":[0.30433528976912944,0.12125215714869242,0.3565027110425888,0.13576114031406697],"dir":"ltr"},{"str":"Search","boundary":[0.3617232089238061,0.12125215714869242,0.4191111280784828,0.13576114031406697],"dir":"ltr"},{"str":"Fake-Coin","boundary":[0.30433528976912944,0.1411062497121909,0.38679286601526336,0.15561523287756546],"dir":"ltr"},{"str":"Problem","boundary":[0.3920133638964807,0.1411062497121909,0.4619267222122076,0.15561523287756546],"dir":"ltr"},{"str":"Russian","boundary":[0.30433528976912944,0.1609603422756894,0.3700797612876252,0.17546932544106394],"dir":"ltr"},{"str":"Peasant","boundary":[0.3753002591688425,0.1609603422756894,0.44207756300196765,0.17546932544106394],"dir":"ltr"},{"str":"Multiplication","boundary":[0.4472980608831849,0.1609603422756894,0.5589190659405797,0.17546932544106394],"dir":"ltr"},{"str":"Josephus","boundary":[0.30433528976912944,0.1808144348391879,0.38470842261664784,0.19532341800456243],"dir":"ltr"},{"str":"Problem","boundary":[0.38992892049786515,0.1808144348391879,0.459842278813592,0.19532341800456243],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.20372266835899777,0.38782569832989267,0.2182316515243723],"dir":"ltr"},{"str":"4.4","boundary":[0.39304619621111003,0.20372266835899777,0.4191486856171966,0.2182316515243723],"dir":"ltr"},{"str":"4.5","boundary":[0.26224997339434597,0.23961744162784832,0.2924739230115853,0.25641732494033426],"dir":"ltr"},{"str":"Variable-Size-Decrease","boundary":[0.3043243205233806,0.23961744162784832,0.5384403388894358,0.25641732494033426],"dir":"ltr"},{"str":"Algorithms","boundary":[0.5444851288128837,0.23961744162784832,0.6592274181151658,0.25641732494033426],"dir":"ltr"},{"str":"Computing","boundary":[0.30433528976912944,0.2611252240803954,0.3961822506937118,0.2756342072457699],"dir":"ltr"},{"str":"a","boundary":[0.4014027485749291,0.2611252240803954,0.4107921332533775,0.2756342072457699],"dir":"ltr"},{"str":"Median","boundary":[0.41601263113459486,0.2611252240803954,0.47862104817048884,0.2756342072457699],"dir":"ltr"},{"str":"and","boundary":[0.48384154605170615,0.2611252240803954,0.5141129222550238,0.2756342072457699],"dir":"ltr"},{"str":"the","boundary":[0.5193334201362412,0.2611252240803954,0.546468741856957,0.2756342072457699],"dir":"ltr"},{"str":"Selection","boundary":[0.5516892397381744,0.2611252240803954,0.6289075393337341,0.2756342072457699],"dir":"ltr"},{"str":"Problem","boundary":[0.6341280372149515,0.2611252240803954,0.7040413955306783,0.2756342072457699],"dir":"ltr"},{"str":"Interpolation","boundary":[0.30433528976912944,0.2809793166438939,0.40868891108540506,0.29548829980926844],"dir":"ltr"},{"str":"Search","boundary":[0.41390940896662237,0.2809793166438939,0.47129732812129904,0.29548829980926844],"dir":"ltr"},{"str":"Searching","boundary":[0.30433528976912944,0.30083340920739243,0.3867740872459065,0.31534239237276696],"dir":"ltr"},{"str":"and","boundary":[0.39199458512712376,0.30083340920739243,0.4222659613304415,0.31534239237276696],"dir":"ltr"},{"str":"Insertion","boundary":[0.42748645921165884,0.30083340920739243,0.5005358720099874,0.31534239237276696],"dir":"ltr"},{"str":"in","boundary":[0.5057563698912048,0.30083340920739243,0.5203662524508704,0.31534239237276696],"dir":"ltr"},{"str":"a","boundary":[0.5255867503320879,0.30083340920739243,0.5349761350105363,0.31534239237276696],"dir":"ltr"},{"str":"Binary","boundary":[0.5401966328917536,0.30083340920739243,0.5923640541652129,0.31534239237276696],"dir":"ltr"},{"str":"Search","boundary":[0.5975845520464304,0.30083340920739243,0.654972471201107,0.31534239237276696],"dir":"ltr"},{"str":"Tree","boundary":[0.6601929690823242,0.30083340920739243,0.6960416397846402,0.31534239237276696],"dir":"ltr"},{"str":"The","boundary":[0.30433528976912944,0.3206889526692075,0.33565827705643336,0.33519793583458196],"dir":"ltr"},{"str":"Game","boundary":[0.3408787749376506,0.3206889526692075,0.3909617528124944,0.33519793583458196],"dir":"ltr"},{"str":"of","boundary":[0.3961822506937118,0.3206889526692075,0.41287657665199307,0.33519793583458196],"dir":"ltr"},{"str":"Nim","boundary":[0.4180970745332104,0.3206889526692075,0.4525185587644022,0.33519793583458196],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.3435957352907008,0.38782569832989267,0.35810471845607533],"dir":"ltr"},{"str":"4.5","boundary":[0.39304619621111003,0.3435957352907008,0.4191486856171966,0.35810471845607533],"dir":"ltr"},{"str":"Summary","boundary":[0.30433672683258445,0.3659545579444417,0.3965896097705061,0.38122712339252246],"dir":"ltr"}],"boundary":[0.2391,0.05862,0.74164,0.38123],"dir":"ltr","type":"paragraph"},{"words":[{"str":"5","boundary":[0.2608313226372873,0.43068790989879924,0.292474516463951,0.4673421589535887],"dir":"ltr"},{"str":"Divide-and-Conquer","boundary":[0.30433528976912944,0.4439200384666419,0.5297050363369733,0.462247239643533],"dir":"ltr"},{"str":"5.1","boundary":[0.26224997339434597,0.48257028425007376,0.2924739230115853,0.49937016756255964],"dir":"ltr"},{"str":"Mergesort","boundary":[0.3043243205233806,0.48257028425007376,0.41062999655121046,0.49937016756255964],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.507133315627402,0.38782569832989267,0.5216422987927766],"dir":"ltr"},{"str":"5.1","boundary":[0.39304619621111003,0.507133315627402,0.4191486856171966,0.5216422987927766],"dir":"ltr"},{"str":"5.2","boundary":[0.26224997339434597,0.5430252750165919,0.2924739230115853,0.5598251583290778],"dir":"ltr"},{"str":"Quicksort","boundary":[0.3043243205233806,0.5430252750165919,0.40217163942811246,0.5598251583290778],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.5675883063939201,0.38782569832989267,0.5820972895592946],"dir":"ltr"},{"str":"5.2","boundary":[0.39304619621111003,0.5675883063939201,0.4191486856171966,0.5820972895592946],"dir":"ltr"},{"str":"5.3","boundary":[0.26224997339434597,0.603481798773037,0.2924739230115853,0.620281682085523],"dir":"ltr"},{"str":"Binary","boundary":[0.3043243205233806,0.603481798773037,0.3707952658326618,0.620281682085523],"dir":"ltr"},{"str":"Tree","boundary":[0.3768400557561097,0.603481798773037,0.4207626300200115,0.620281682085523],"dir":"ltr"},{"str":"Traversals","boundary":[0.42680741994345944,0.603481798773037,0.5311561495931946,0.620281682085523],"dir":"ltr"},{"str":"and","boundary":[0.5372009395166425,0.603481798773037,0.5758615024083343,0.620281682085523],"dir":"ltr"},{"str":"Related","boundary":[0.5819062923317823,0.603481798773037,0.6592491619638113,0.620281682085523],"dir":"ltr"},{"str":"Properties","boundary":[0.6652939518872593,0.603481798773037,0.7704037162395868,0.620281682085523],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.6280448301503654,0.38782569832989267,0.6425538133157399],"dir":"ltr"},{"str":"5.3","boundary":[0.39304619621111003,0.6280448301503654,0.4191486856171966,0.6425538133157399],"dir":"ltr"},{"str":"5.4","boundary":[0.26224997339434597,0.6639367895395551,0.2924739230115853,0.6807366728520411],"dir":"ltr"},{"str":"Multiplication","boundary":[0.3043243205233806,0.6639367895395551,0.4456593367191044,0.6807366728520411],"dir":"ltr"},{"str":"of","boundary":[0.4517041266425523,0.6639367895395551,0.47223031976390045,0.6807366728520411],"dir":"ltr"},{"str":"Large","boundary":[0.4782751096873484,0.6639367895395551,0.5362876978735317,0.6807366728520411],"dir":"ltr"},{"str":"Integers","boundary":[0.5423324877969795,0.6639367895395551,0.6256984035038111,0.6807366728520411],"dir":"ltr"},{"str":"and","boundary":[0.631743193427259,0.6639367895395551,0.6704037563189509,0.6807366728520411],"dir":"ltr"},{"str":"Strassen’s","boundary":[0.30433519244770335,0.682263782245146,0.40905356752441197,0.699063665557632],"dir":"ltr"},{"str":"Matrix","boundary":[0.4150983574478599,0.682263782245146,0.48154755890849554,0.699063665557632],"dir":"ltr"},{"str":"Multiplication","boundary":[0.48759234883194347,0.682263782245146,0.6289273650276672,0.699063665557632],"dir":"ltr"},{"str":"Multiplication","boundary":[0.30433528976912944,0.7037729995609351,0.41595629482652413,0.7182819827263095],"dir":"ltr"},{"str":"of","boundary":[0.4211767927077415,0.7037729995609351,0.43787111866602274,0.7182819827263095],"dir":"ltr"},{"str":"Large","boundary":[0.44309161654724005,0.7037729995609351,0.490057318708839,0.7182819827263095],"dir":"ltr"},{"str":"Integers","boundary":[0.4952778165900563,0.7037729995609351,0.5641583425911538,0.7182819827263095],"dir":"ltr"},{"str":"Strassen’s","boundary":[0.30433528976912944,0.7236270921244335,0.39058617742535656,0.7381360752898081],"dir":"ltr"},{"str":"Matrix","boundary":[0.3958066753065738,0.7236270921244335,0.44898815012530563,0.7381360752898081],"dir":"ltr"},{"str":"Multiplication","boundary":[0.45420864800652294,0.7236270921244335,0.5658296530639177,0.7381360752898081],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.7465367765425599,0.38782569832989267,0.7610457597079344],"dir":"ltr"},{"str":"5.4","boundary":[0.39304619621111003,0.7465367765425599,0.4191486856171966,0.7610457597079344],"dir":"ltr"},{"str":"5.5","boundary":[0.26224997339434597,0.7824292459574984,0.2924739230115853,0.7992291292699845],"dir":"ltr"},{"str":"The","boundary":[0.3043243205233806,0.7824292459574984,0.34298488341507244,0.7992291292699845],"dir":"ltr"},{"str":"Closest-Pair","boundary":[0.34902967333852036,0.7824292459574984,0.4710561519370437,0.7992291292699845],"dir":"ltr"},{"str":"and","boundary":[0.4771009418604916,0.7824292459574984,0.5157615047521835,0.7992291292699845],"dir":"ltr"},{"str":"Convex-Hull","boundary":[0.5218062946756313,0.7824292459574984,0.6474639959979526,0.7992291292699845],"dir":"ltr"},{"str":"Problems","boundary":[0.6535087859214004,0.7824292459574984,0.7513561048261322,0.7992291292699845],"dir":"ltr"},{"str":"by","boundary":[0.30433519244770335,0.8007562386630894,0.32971026381699714,0.8175561219755753],"dir":"ltr"},{"str":"Divide-and-Conquer","boundary":[0.33575505374044506,0.8007562386630894,0.5423433597213022,0.8175561219755753],"dir":"ltr"},{"str":"The","boundary":[0.30433528976912944,0.8222639229889515,0.33565827705643336,0.836772906154326],"dir":"ltr"},{"str":"Closest-Pair","boundary":[0.3408787749376506,0.8222639229889515,0.4399931196033521,0.836772906154326],"dir":"ltr"},{"str":"Problem","boundary":[0.44521361748456945,0.8222639229889515,0.5151269758002963,0.836772906154326],"dir":"ltr"},{"str":"Convex-Hull","boundary":[0.30433528976912944,0.8421194664507665,0.404520024288174,0.856628449616141],"dir":"ltr"},{"str":"Problem","boundary":[0.40974052216939133,0.8421194664507665,0.4796538804851182,0.856628449616141],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.8650262490722598,0.38782569832989267,0.8795352322376344],"dir":"ltr"},{"str":"5.5","boundary":[0.39304619621111003,0.8650262490722598,0.4191486856171966,0.8795352322376344],"dir":"ltr"},{"str":"Summary","boundary":[0.30433672683258445,0.8873857517603321,0.3965896097705061,0.9026583172084128],"dir":"ltr"}],"boundary":[0.26083,0.43069,0.7704,0.90266],"dir":"ltr","type":"paragraph"},{"words":[{"str":"150","boundary":[0.8940277348762689,0.10084556520431873,0.9269991959305763,0.11611813065239948],"dir":"ltr"},{"str":"150","boundary":[0.8956787368178104,0.12125215714869242,0.9270017241051144,0.13576114031406697],"dir":"ltr"},{"str":"152","boundary":[0.8956787368178103,0.1411062497121909,0.9270017241051143,0.15561523287756546],"dir":"ltr"},{"str":"153","boundary":[0.8956787368178104,0.1609603422756894,0.9270017241051144,0.17546932544106394],"dir":"ltr"},{"str":"154","boundary":[0.8956787368178102,0.1808144348391879,0.9270017241051142,0.19532341800456243],"dir":"ltr"},{"str":"156","boundary":[0.8940317031301347,0.20317264284061756,0.9270031641844423,0.21844520828869832],"dir":"ltr"},{"str":"157","boundary":[0.8940277348762689,0.24072016512594882,0.9269991959305763,0.2559927305740296],"dir":"ltr"},{"str":"158","boundary":[0.8956787368178105,0.2611252240803954,0.9270017241051145,0.2756342072457699],"dir":"ltr"},{"str":"161","boundary":[0.8956787368178102,0.2809793166438939,0.9270017241051142,0.29548829980926844],"dir":"ltr"},{"str":"163","boundary":[0.8956787368178105,0.30083340920739243,0.9270017241051145,0.31534239237276696],"dir":"ltr"},{"str":"164","boundary":[0.8956787368178104,0.3206889526692075,0.9270017241051144,0.33519793583458196],"dir":"ltr"},{"str":"166","boundary":[0.8940317031301347,0.3430457097723206,0.9270031641844423,0.3583182752204013],"dir":"ltr"},{"str":"167","boundary":[0.8940277497175384,0.3659545579444417,0.926999210771846,0.38122712339252246],"dir":"ltr"}],"boundary":[0.89403,0.10085,0.927,0.38123],"dir":"ltr","type":"paragraph"},{"words":[{"str":"169","boundary":[0.8940239650350963,0.446125485462843,0.9269954260894038,0.4613980509109238],"dir":"ltr"},{"str":"172","boundary":[0.8940277348762689,0.48367300774817434,0.9269991959305763,0.4989455731962551],"dir":"ltr"},{"str":"174","boundary":[0.8940317031301347,0.5065820092192882,0.9270031641844423,0.521854574667369],"dir":"ltr"},{"str":"176","boundary":[0.8940277348762689,0.5441279985146925,0.9269991959305763,0.5594005639627733],"dir":"ltr"},{"str":"181","boundary":[0.8940317031301347,0.5670369999858063,0.9270031641844423,0.582309565433887],"dir":"ltr"},{"str":"182","boundary":[0.8940277348762689,0.6045845222711376,0.9269991959305763,0.6198570877192183],"dir":"ltr"},{"str":"185","boundary":[0.8940317031301347,0.6274935237422515,0.9270031641844423,0.6427660891903323],"dir":"ltr"}],"boundary":[0.89402,0.44613,0.927,0.64277],"dir":"ltr","type":"paragraph"},{"words":[{"str":"186","boundary":[0.8940277348762689,0.6833679406064885,0.9269991959305763,0.6986405060545693],"dir":"ltr"},{"str":"187","boundary":[0.8956787368178105,0.7037729995609351,0.9270017241051145,0.7182819827263095],"dir":"ltr"},{"str":"189","boundary":[0.8956787368178105,0.7236270921244335,0.9270017241051145,0.7381360752898081],"dir":"ltr"},{"str":"191","boundary":[0.8940317031301347,0.7459844471702678,0.9270031641844423,0.7612570126183485],"dir":"ltr"}],"boundary":[0.89403,0.68337,0.927,0.76126],"dir":"ltr","type":"paragraph"},{"words":[{"str":"192","boundary":[0.8940277348762689,0.8018588640345047,0.9269991959305763,0.8171314294825853],"dir":"ltr"},{"str":"192","boundary":[0.8956787368178104,0.8222639229889515,0.9270017241051144,0.836772906154326],"dir":"ltr"},{"str":"195","boundary":[0.8956787368178103,0.8421194664507665,0.9270017241051143,0.856628449616141],"dir":"ltr"},{"str":"197","boundary":[0.8940317031301347,0.8644769035882109,0.9270031641844423,0.8797494690362917],"dir":"ltr"},{"str":"198","boundary":[0.8940277497175384,0.8873857517603321,0.926999210771846,0.9026583172084128],"dir":"ltr"}],"boundary":[0.89403,0.80186,0.927,0.90266],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":11,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/2c0eb3dcc5d013c7f2c09c62cd38ca0f.jpg","blurred":"/storage/books/4a8b03583f119702/pages/023ab373ed16c89e95d1bf6c7a347f92.jpg"},"info":{"width":503.999989,"height":652.3200069999999,"margin":[0.26083,0.05842,0.073,0.09755]},"elements":[{"words":[{"str":"Contents","boundary":[0.6887773761439505,0.059521148797142584,0.7609533396239816,0.0732665496798109],"dir":"ltr"},{"str":"6","boundary":[0.2608289541053938,0.09757686368187712,0.2924721494388762,0.1342311127366666],"dir":"ltr"},{"str":"Transform-and-Conquer","boundary":[0.3043329233088534,0.11080899224971974,0.5736095768049708,0.12913619342661084],"dir":"ltr"},{"str":"6.1","boundary":[0.2622476049300072,0.14114905293714242,0.29247155598648233,0.15794893624962833],"dir":"ltr"},{"str":"Presorting","boundary":[0.30432195406258233,0.14114905293714242,0.41062763515258727,0.15794893624962833],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.16571193101547796,0.3878233358453505,0.18022091418085248],"dir":"ltr"},{"str":"6.1","boundary":[0.39304383397516296,0.16571193101547796,0.41914632462422524,0.18022091418085248],"dir":"ltr"},{"str":"6.2","boundary":[0.2622476049300072,0.193295084999593,0.29247155598648233,0.21009496831207894],"dir":"ltr"},{"str":"Gaussian","boundary":[0.30432195406258233,0.193295084999593,0.39977745416180954,0.21009496831207894],"dir":"ltr"},{"str":"Elimination","boundary":[0.40582224437310455,0.193295084999593,0.5229998503035681,0.21009496831207894],"dir":"ltr"},{"str":"LU","boundary":[0.3043329233088534,0.21548478966091272,0.33062320166042697,0.22999377282628725],"dir":"ltr"},{"str":"Decomposition","boundary":[0.3379074866408379,0.21480286745214014,0.46417593780939537,0.22931185061751466],"dir":"ltr"},{"str":"Computing","boundary":[0.3043329233088534,0.23465841091395517,0.3961798886071006,0.2491673940793297],"dir":"ltr"},{"str":"a","boundary":[0.40140038673691314,0.23465841091395517,0.41078977186247506,0.2491673940793297],"dir":"ltr"},{"str":"Matrix","boundary":[0.4160102699922876,0.23465841091395517,0.4691917473434706,0.2491673940793297],"dir":"ltr"},{"str":"Inverse","boundary":[0.4744122454732831,0.23465841091395517,0.5359878331267185,0.2491673940793297],"dir":"ltr"},{"str":"Computing","boundary":[0.3043329233088534,0.25451395437577023,0.3961798886071006,0.26902293754114476],"dir":"ltr"},{"str":"a","boundary":[0.40140038673691314,0.25451395437577023,0.41078977186247506,0.26902293754114476],"dir":"ltr"},{"str":"Determinant","boundary":[0.4160102699922876,0.25451395437577023,0.5203451175075322,0.26902293754114476],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.27742073699726355,0.3878233358453505,0.2919297201626381],"dir":"ltr"},{"str":"6.2","boundary":[0.39304383397516296,0.27742073699726355,0.41914632462422524,0.2919297201626381],"dir":"ltr"},{"str":"6.3","boundary":[0.2622476049300072,0.3050040609899615,0.29247155598648233,0.32180394430244746],"dir":"ltr"},{"str":"Balanced","boundary":[0.30432195406258233,0.3050040609899615,0.398581542429359,0.32180394430244746],"dir":"ltr"},{"str":"Search","boundary":[0.40462633264065406,0.3050040609899615,0.47592441574438205,0.32180394430244746],"dir":"ltr"},{"str":"Trees","boundary":[0.4819692059556771,0.3050040609899615,0.5367637071515888,0.32180394430244746],"dir":"ltr"},{"str":"AVL","boundary":[0.3043329233088534,0.3265118434425086,0.3373835589508316,0.34102082660788313],"dir":"ltr"},{"str":"Trees","boundary":[0.34260405708064406,0.3265118434425086,0.3878421146156017,0.34102082660788313],"dir":"ltr"},{"str":"2-3","boundary":[0.3043329233088534,0.3463659360060071,0.3304354139579157,0.36087491917138165],"dir":"ltr"},{"str":"Trees","boundary":[0.3356559120877282,0.3463659360060071,0.3808939696226858,0.36087491917138165],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.369274169525817,0.3878233358453505,0.3837831526911915],"dir":"ltr"},{"str":"6.3","boundary":[0.39304383397516296,0.369274169525817,0.41914632462422524,0.3837831526911915],"dir":"ltr"},{"str":"6.4","boundary":[0.2622476049300072,0.39685775144407015,0.29247155598648233,0.41365763475655615],"dir":"ltr"},{"str":"Heaps","boundary":[0.30432195406258233,0.39685775144407015,0.36835759137288393,0.41365763475655615],"dir":"ltr"},{"str":"and","boundary":[0.37440238158417893,0.39685775144407015,0.41306294631685,0.41365763475655615],"dir":"ltr"},{"str":"Heapsort","boundary":[0.4191077365281451,0.39685775144407015,0.5121279254631096,0.41365763475655615],"dir":"ltr"},{"str":"Notion","boundary":[0.3043329233088534,0.4183670668865444,0.35963640169841343,0.4328760500519189],"dir":"ltr"},{"str":"of","boundary":[0.36485689982822594,0.4183670668865444,0.3815512265814751,0.4328760500519189],"dir":"ltr"},{"str":"the","boundary":[0.38677172471128757,0.4183670668865444,0.41390704772416165,0.4328760500519189],"dir":"ltr"},{"str":"Heap","boundary":[0.41912754585397416,0.4183670668865444,0.4629571956200975,0.4328760500519189],"dir":"ltr"},{"str":"Heapsort","boundary":[0.3043329233088534,0.4382211594500429,0.3804996154474122,0.45273014261541744],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.46112794207153623,0.3878233358453505,0.47563692523691076],"dir":"ltr"},{"str":"6.4","boundary":[0.39304383397516296,0.46112794207153623,0.41914632462422524,0.47563692523691076],"dir":"ltr"},{"str":"6.5","boundary":[0.2622476049300072,0.48871297488810594,0.29247155598648233,0.5055128582005919],"dir":"ltr"},{"str":"Horner’s","boundary":[0.30432195406258233,0.48871297488810594,0.39090596349199525,0.5055128582005919],"dir":"ltr"},{"str":"Rule","boundary":[0.39695075370329025,0.48871297488810594,0.4428737642293877,0.5055128582005919],"dir":"ltr"},{"str":"and","boundary":[0.44891855444068274,0.48871297488810594,0.4875791191733538,0.5055128582005919],"dir":"ltr"},{"str":"Binary","boundary":[0.4936239093846488,0.48871297488810594,0.5600948578592131,0.5055128582005919],"dir":"ltr"},{"str":"Exponentiation","boundary":[0.5661396480705082,0.48871297488810594,0.7219778187336428,0.5055128582005919],"dir":"ltr"},{"str":"Horner’s","boundary":[0.3043329233088534,0.5102207573406531,0.3749410994530795,0.5247297405060276],"dir":"ltr"},{"str":"Rule","boundary":[0.3801615975828919,0.5102207573406531,0.41773791685539097,0.5247297405060276],"dir":"ltr"},{"str":"Binary","boundary":[0.3043329233088534,0.5300748499041517,0.35650034706647576,0.5445838330695262],"dir":"ltr"},{"str":"Exponentiation","boundary":[0.3617208451962882,0.5300748499041517,0.4859048528669709,0.5445838330695262],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.552984534322278,0.3878233358453505,0.5674935174876525],"dir":"ltr"},{"str":"6.5","boundary":[0.39304383397516296,0.552984534322278,0.41914632462422524,0.5674935174876525],"dir":"ltr"},{"str":"6.6","boundary":[0.2622476049300072,0.5805666653422147,0.29247155598648233,0.5973665486547006],"dir":"ltr"},{"str":"Problem","boundary":[0.30432195406258233,0.5805666653422147,0.3912973527862517,0.5973665486547006],"dir":"ltr"},{"str":"Reduction","boundary":[0.3973421429975468,0.5805666653422147,0.5012342567729698,0.5973665486547006],"dir":"ltr"},{"str":"Computing","boundary":[0.3043329233088534,0.6020744477947618,0.3961798886071006,0.6165834309601363],"dir":"ltr"},{"str":"the","boundary":[0.40140038673691314,0.6020744477947618,0.4285357097497872,0.6165834309601363],"dir":"ltr"},{"str":"Least","boundary":[0.4337562078795997,0.6020744477947618,0.47967030114359777,0.6165834309601363],"dir":"ltr"},{"str":"Common","boundary":[0.4848907992734102,0.6020744477947618,0.562127881316283,0.6165834309601363],"dir":"ltr"},{"str":"Multiple","boundary":[0.5673483794460955,0.6020744477947618,0.6351585188229042,0.6165834309601363],"dir":"ltr"},{"str":"Counting","boundary":[0.3043329233088534,0.6219299912565769,0.3794855618538515,0.6364389744219514],"dir":"ltr"},{"str":"Paths","boundary":[0.3847060599836639,0.6219299912565769,0.4316529856114738,0.6364389744219514],"dir":"ltr"},{"str":"in","boundary":[0.4368734837412863,0.6219299912565769,0.45148336699666075,0.6364389744219514],"dir":"ltr"},{"str":"a","boundary":[0.4567038651264732,0.6219299912565769,0.4660932502520352,0.6364389744219514],"dir":"ltr"},{"str":"Graph","boundary":[0.47131374838184764,0.6219299912565769,0.5213967286415953,0.6364389744219514],"dir":"ltr"},{"str":"Reduction","boundary":[0.3043329233088534,0.6417840838200753,0.3888749469794135,0.6562930669854499],"dir":"ltr"},{"str":"of","boundary":[0.39409544510922595,0.6417840838200753,0.4107897718624751,0.6562930669854499],"dir":"ltr"},{"str":"Optimization","boundary":[0.4160102699922876,0.6417840838200753,0.5213779498713441,0.6562930669854499],"dir":"ltr"},{"str":"Problems","boundary":[0.5265984480011566,0.6417840838200753,0.6059011947716532,0.6562930669854499],"dir":"ltr"},{"str":"Linear","boundary":[0.3043329233088534,0.6616381763835738,0.35546751470266397,0.6761471595489483],"dir":"ltr"},{"str":"Programming","boundary":[0.36068801283247637,0.6616381763835738,0.47337941310947124,0.6761471595489483],"dir":"ltr"},{"str":"Reduction","boundary":[0.3043329233088534,0.6814922689470724,0.3888749469794135,0.6960012521124469],"dir":"ltr"},{"str":"to","boundary":[0.39409544510922595,0.6814922689470724,0.4107897718624751,0.6960012521124469],"dir":"ltr"},{"str":"Graph","boundary":[0.4160102699922876,0.6814922689470724,0.46609325025203513,0.6960012521124469],"dir":"ltr"},{"str":"Problems","boundary":[0.47131374838184764,0.6814922689470724,0.550616495152344,0.6960012521124469],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.7044019533651987,0.3878233358453505,0.7189109365305733],"dir":"ltr"},{"str":"6.6","boundary":[0.39304383397516296,0.7044019533651987,0.41914632462422524,0.7189109365305733],"dir":"ltr"},{"str":"Summary","boundary":[0.30433455878507965,0.7267590671950679,0.3965874461159958,0.7420316326431486],"dir":"ltr"},{"str":"7","boundary":[0.2608289541053938,0.7707112076971757,0.2924721494388762,0.8073654567519651],"dir":"ltr"},{"str":"Space","boundary":[0.3043329233088534,0.7839433362650183,0.37288555972567683,0.8022705374419095],"dir":"ltr"},{"str":"and","boundary":[0.3794798963775374,0.7839433362650183,0.42165518618691866,0.8022705374419095],"dir":"ltr"},{"str":"Time","boundary":[0.4282495228387792,0.7839433362650183,0.48316279387855293,0.8022705374419095],"dir":"ltr"},{"str":"Trade-Offs","boundary":[0.4897571305304135,0.7839433362650183,0.6061780092618215,0.8022705374419095],"dir":"ltr"},{"str":"7.1","boundary":[0.2622476049300072,0.8142832436534484,0.29247155598648233,0.8310831269659342],"dir":"ltr"},{"str":"Sorting","boundary":[0.30432195406258233,0.8142832436534484,0.3804254279457931,0.8310831269659342],"dir":"ltr"},{"str":"by","boundary":[0.3864702181570881,0.8142832436534484,0.4118452907347186,0.8310831269659342],"dir":"ltr"},{"str":"Counting","boundary":[0.41789008094601365,0.8142832436534484,0.5121061816134286,0.8310831269659342],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.8388447420408496,0.3878233358453505,0.8533537252062241],"dir":"ltr"},{"str":"7.1","boundary":[0.39304383397516296,0.8388447420408496,0.41914632462422524,0.8533537252062241],"dir":"ltr"},{"str":"7.2","boundary":[0.2622476049300072,0.8664278960249645,0.29247155598648233,0.8832277793374504],"dir":"ltr"},{"str":"Input","boundary":[0.30432195406258233,0.8664278960249645,0.35746392268274435,0.8832277793374504],"dir":"ltr"},{"str":"Enhancement","boundary":[0.36350871289403935,0.8664278960249645,0.5048437358200022,0.8832277793374504],"dir":"ltr"},{"str":"in","boundary":[0.5108885260312972,0.8664278960249645,0.5302188083976328,0.8832277793374504],"dir":"ltr"},{"str":"String","boundary":[0.5362635986089277,0.8664278960249645,0.5990815803370979,0.8832277793374504],"dir":"ltr"},{"str":"Matching","boundary":[0.605126370548393,0.8664278960249645,0.7017560385303897,0.8832277793374504],"dir":"ltr"},{"str":"Horspool’s","boundary":[0.3043329233088534,0.8879372114674388,0.3926870373403916,0.9024461946328134],"dir":"ltr"},{"str":"Algorithm","boundary":[0.3979075354702041,0.8879372114674388,0.4792947257385753,0.9024461946328134],"dir":"ltr"}],"boundary":[0.26083,0.05952,0.76095,0.90245],"dir":"ltr","type":"paragraph"},{"words":[{"str":"xi","boundary":[0.9105095238404856,0.0584185359809148,0.9269952551526741,0.07369110142899557],"dir":"ltr"}],"boundary":[0.91051,0.05842,0.927,0.07369],"dir":"ltr","type":"paragraph"},{"words":[{"str":"201","boundary":[0.8940214282425312,0.1130144392459208,0.9269928908669083,0.12828700469400156],"dir":"ltr"},{"str":"202","boundary":[0.8940253964965859,0.14225177643524295,0.9269968591209631,0.1575243418833237],"dir":"ltr"},{"str":"205","boundary":[0.8940295631633436,0.16516062460736408,0.9270010257877208,0.18043319005544484],"dir":"ltr"},{"str":"208","boundary":[0.8940253964965859,0.19439780849769353,0.9269968591209631,0.20967037394577429],"dir":"ltr"},{"str":"212","boundary":[0.8956745206397215,0.21480286745214014,0.9269975094185963,0.22931185061751466],"dir":"ltr"},{"str":"214","boundary":[0.8956763985167469,0.23465841091395517,0.9269993872956216,0.2491673940793297],"dir":"ltr"},{"str":"215","boundary":[0.8956763985167467,0.25451395437577023,0.9269993872956215,0.26902293754114476],"dir":"ltr"},{"str":"216","boundary":[0.8940295631633436,0.2768696005977326,0.9270010257877208,0.29214216604581333],"dir":"ltr"},{"str":"218","boundary":[0.8940253964965859,0.306106784488062,0.9269968591209631,0.3213793499361428],"dir":"ltr"},{"str":"218","boundary":[0.8956763985167467,0.3265118434425086,0.9269993872956215,0.34102082660788313],"dir":"ltr"},{"str":"223","boundary":[0.8956763985167467,0.3463659360060071,0.9269993872956215,0.36087491917138165],"dir":"ltr"},{"str":"225","boundary":[0.8940295631633436,0.3687248240417683,0.9270010257877208,0.38399738948984913],"dir":"ltr"},{"str":"226","boundary":[0.8940253964965859,0.39796047494217074,0.9269968591209631,0.41323304039025155],"dir":"ltr"},{"str":"227","boundary":[0.8956763985167467,0.4183670668865444,0.9269993872956215,0.4328760500519189],"dir":"ltr"},{"str":"231","boundary":[0.8956763985167467,0.4382211594500429,0.9269993872956215,0.45273014261541744],"dir":"ltr"},{"str":"233","boundary":[0.8940295631633436,0.46057851449587706,0.9270010257877208,0.47585107994395787],"dir":"ltr"},{"str":"234","boundary":[0.8940253964965859,0.48981569838620653,0.9269968591209631,0.5050882638342873],"dir":"ltr"},{"str":"234","boundary":[0.8956763985167467,0.5102207573406531,0.9269993872956215,0.5247297405060276],"dir":"ltr"},{"str":"236","boundary":[0.8956763985167467,0.5300748499041517,0.9269993872956215,0.5445838330695262],"dir":"ltr"},{"str":"239","boundary":[0.8940295631633436,0.5524322049499858,0.9270010257877208,0.5677047703980665],"dir":"ltr"},{"str":"240","boundary":[0.8940253964965859,0.5816693888403153,0.9269968591209631,0.596941954288396],"dir":"ltr"},{"str":"241","boundary":[0.895676398516747,0.6020744477947618,0.9269993872956217,0.6165834309601363],"dir":"ltr"},{"str":"242","boundary":[0.8956763985167467,0.6219299912565769,0.9269993872956215,0.6364389744219514],"dir":"ltr"},{"str":"243","boundary":[0.8956763985167469,0.6417840838200753,0.9269993872956216,0.6562930669854499],"dir":"ltr"},{"str":"244","boundary":[0.8956763985167466,0.6616381763835738,0.9269993872956214,0.6761471595489483],"dir":"ltr"},{"str":"246","boundary":[0.895676398516747,0.6814922689470724,0.9269993872956217,0.6960012521124469],"dir":"ltr"},{"str":"248","boundary":[0.8940295631633436,0.7038502190229468,0.9270010257877208,0.7191227844710276],"dir":"ltr"},{"str":"250","boundary":[0.8940256097505589,0.7267590671950679,0.9269970723749361,0.7420316326431486],"dir":"ltr"}],"boundary":[0.89402,0.11301,0.927,0.74203],"dir":"ltr","type":"paragraph"},{"words":[{"str":"253","boundary":[0.8940214282425312,0.7861487832612193,0.9269928908669083,0.8014213487093],"dir":"ltr"},{"str":"254","boundary":[0.8940253964965859,0.8153844341616218,0.9269968591209631,0.8306569996097024],"dir":"ltr"},{"str":"257","boundary":[0.8940295631633436,0.8382934356327355,0.9270010257877208,0.8535660010808162],"dir":"ltr"},{"str":"258","boundary":[0.8940253964965859,0.867530619523065,0.9269968591209631,0.8828031849711456],"dir":"ltr"},{"str":"259","boundary":[0.8956763985167467,0.8879372114674388,0.9269993872956215,0.9024461946328134],"dir":"ltr"}],"boundary":[0.89402,0.78615,0.927,0.90245],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":12,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/0e10a0c7e35eb9a9373b95464d36311b.jpg","blurred":"/storage/books/4a8b03583f119702/pages/c44ee1d2a22eb0fe60c96b9f3dddd96c.jpg"},"info":{"width":504.00001299999997,"height":652.3200069999999,"margin":[0.07306,0.05842,0.073,0.07749]},"elements":[{"words":[{"str":"xii","boundary":[0.07305950208378269,0.0584185359809148,0.09504047611998774,0.07369110142899557],"dir":"ltr"}],"boundary":[0.07306,0.05842,0.09504,0.07369],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Contents","boundary":[0.23910314859456164,0.059521148797142584,0.3112791086376421,0.0732665496798109],"dir":"ltr"}],"boundary":[0.2391,0.05952,0.31128,0.07327],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Boyer-Moore","boundary":[0.30433528976912944,0.1013968716124326,0.4132145945004172,0.11590585477780714],"dir":"ltr"},{"str":"Algorithm","boundary":[0.4184350923816345,0.1013968716124326,0.4998222787744254,0.11590585477780714],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.12430510513224248,0.38782569832989267,0.13881408829761702],"dir":"ltr"},{"str":"7.2","boundary":[0.39304619621111003,0.12430510513224248,0.4191486856171966,0.13881408829761702],"dir":"ltr"},{"str":"7.3","boundary":[0.26224997339434597,0.1539846242980557,0.2924739230115853,0.17078450761054162],"dir":"ltr"},{"str":"Hashing","boundary":[0.3043243205233806,0.1539846242980557,0.38888614790571446,0.17078450761054162],"dir":"ltr"},{"str":"Open","boundary":[0.30433528976912944,0.17549393974052993,0.3502681596160991,0.19000292290590448],"dir":"ltr"},{"str":"Hashing","boundary":[0.35548865749731634,0.17549393974052993,0.4233175724144277,0.19000292290590448],"dir":"ltr"},{"str":"(Separate","boundary":[0.42853807029564506,0.17549393974052993,0.5078408132898203,0.19000292290590448],"dir":"ltr"},{"str":"Chaining)","boundary":[0.5130613111710377,0.17549393974052993,0.5902983895359543,0.19000292290590448],"dir":"ltr"},{"str":"Closed","boundary":[0.30433528976912944,0.19534803230402842,0.361741987693163,0.20985701546940294],"dir":"ltr"},{"str":"Hashing","boundary":[0.3669624855743803,0.19534803230402842,0.4347914004914916,0.20985701546940294],"dir":"ltr"},{"str":"(Open","boundary":[0.44001189837270904,0.19534803230402842,0.49116526610089595,0.20985701546940294],"dir":"ltr"},{"str":"Addressing)","boundary":[0.49638576398211326,0.19534803230402842,0.5955376661865285,0.20985701546940294],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.2182562658238383,0.38782569832989267,0.23276524898921283],"dir":"ltr"},{"str":"7.3","boundary":[0.39304619621111003,0.2182562658238383,0.4191486856171966,0.23276524898921283],"dir":"ltr"},{"str":"7.4","boundary":[0.26224997339434597,0.24793559827147862,0.2924739230115853,0.26473548158396454],"dir":"ltr"},{"str":"B-Trees","boundary":[0.3043243205233806,0.24793559827147862,0.38086266775552646,0.26473548158396454],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.27249847634981417,0.38782569832989267,0.28700745951518863],"dir":"ltr"},{"str":"7.4","boundary":[0.39304619621111003,0.27249847634981417,0.4191486856171966,0.28700745951518863],"dir":"ltr"},{"str":"Summary","boundary":[0.30433672683258445,0.29485601811382134,0.3965896097705061,0.31012858356190215],"dir":"ltr"}],"boundary":[0.26225,0.1014,0.59554,0.31013],"dir":"ltr","type":"paragraph"},{"words":[{"str":"8","boundary":[0.2608313226372873,0.3445997945606475,0.292474516463951,0.38125404361543697],"dir":"ltr"},{"str":"Dynamic","boundary":[0.30433528976912944,0.3578319231284901,0.40317917293387057,0.3761591243053812],"dir":"ltr"},{"str":"Programming","boundary":[0.409773509271715,0.3578319231284901,0.5652622671658541,0.3761591243053812],"dir":"ltr"},{"str":"8.1","boundary":[0.26224997339434597,0.39026896073724154,0.2924739230115853,0.4070688440497275],"dir":"ltr"},{"str":"Three","boundary":[0.3043243205233806,0.39026896073724154,0.3635328203850662,0.4070688440497275],"dir":"ltr"},{"str":"Basic","boundary":[0.369577610308514,0.39026896073724154,0.4239589757708994,0.4070688440497275],"dir":"ltr"},{"str":"Examples","boundary":[0.43000376569434734,0.39026896073724154,0.5302863956473747,0.4070688440497275],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.41483199211456984,0.38782569832989267,0.42934097527994436],"dir":"ltr"},{"str":"8.1","boundary":[0.39304619621111003,0.41483199211456984,0.4191486856171966,0.42934097527994436],"dir":"ltr"},{"str":"8.2","boundary":[0.26224997339434597,0.44451074332907914,0.2924739230115853,0.461310626641565],"dir":"ltr"},{"str":"The","boundary":[0.3043243205233806,0.44451074332907914,0.34298488341507244,0.461310626641565],"dir":"ltr"},{"str":"Knapsack","boundary":[0.34902967333852036,0.44451074332907914,0.44689873609189773,0.461310626641565],"dir":"ltr"},{"str":"Problem","boundary":[0.4529435260153456,0.44451074332907914,0.5399189205973295,0.461310626641565],"dir":"ltr"},{"str":"and","boundary":[0.5459637105207774,0.44451074332907914,0.5846242734124693,0.461310626641565],"dir":"ltr"},{"str":"Memory","boundary":[0.5906690633359171,0.44451074332907914,0.677644457917901,0.461310626641565],"dir":"ltr"},{"str":"Functions","boundary":[0.6836892478413488,0.44451074332907914,0.7839501339457308,0.461310626641565],"dir":"ltr"},{"str":"Memory","boundary":[0.30433528976912944,0.4660185257816263,0.3752814803994856,0.4805275089470008],"dir":"ltr"},{"str":"Functions","boundary":[0.3805019782807029,0.4660185257816263,0.4619079434428507,0.4805275089470008],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.48892675930143614,0.38782569832989267,0.5034357424668107],"dir":"ltr"},{"str":"8.2","boundary":[0.39304619621111003,0.48892675930143614,0.4191486856171966,0.5034357424668107],"dir":"ltr"},{"str":"8.3","boundary":[0.26224997339434597,0.5186062784672495,0.2924739230115853,0.5354061617797354],"dir":"ltr"},{"str":"Optimal","boundary":[0.3043243205233806,0.5186062784672495,0.3864725807060644,0.5354061617797354],"dir":"ltr"},{"str":"Binary","boundary":[0.3925173706295122,0.5186062784672495,0.4589883159387934,0.5354061617797354],"dir":"ltr"},{"str":"Search","boundary":[0.46503310586224134,0.5186062784672495,0.5363311855708226,0.5354061617797354],"dir":"ltr"},{"str":"Trees","boundary":[0.5423759754942705,0.5186062784672495,0.5971704740809204,0.5354061617797354],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.5431693098445778,0.38782569832989267,0.5576782930099523],"dir":"ltr"},{"str":"8.3","boundary":[0.39304619621111003,0.5431693098445778,0.4191486856171966,0.5576782930099523],"dir":"ltr"},{"str":"8.4","boundary":[0.26224997339434597,0.572848061059087,0.2924739230115853,0.589647944371573],"dir":"ltr"},{"str":"Warshall’s","boundary":[0.3043243205233806,0.572848061059087,0.40945582872435365,0.589647944371573],"dir":"ltr"},{"str":"and","boundary":[0.4155006186478015,0.572848061059087,0.4541611815394933,0.589647944371573],"dir":"ltr"},{"str":"Floyd’s","boundary":[0.46020597146294123,0.572848061059087,0.5323085735714058,0.589647944371573],"dir":"ltr"},{"str":"Algorithms","boundary":[0.5383533634948537,0.572848061059087,0.653095652797136,0.589647944371573],"dir":"ltr"},{"str":"Warshall’s","boundary":[0.30433528976912944,0.5943573765015613,0.38919654849294616,0.6088663596669358],"dir":"ltr"},{"str":"Algorithm","boundary":[0.39441704637416347,0.5943573765015613,0.4758042327669543,0.6088663596669358],"dir":"ltr"},{"str":"Floyd’s","boundary":[0.30433528976912944,0.6142114690650597,0.3624368021593682,0.6287204522304343],"dir":"ltr"},{"str":"Algorithm","boundary":[0.36765730004058556,0.6142114690650597,0.44904448643337636,0.6287204522304343],"dir":"ltr"},{"str":"for","boundary":[0.45426498431459367,0.6142114690650597,0.4772126404687216,0.6287204522304343],"dir":"ltr"},{"str":"the","boundary":[0.4824331383499389,0.6142114690650597,0.5095684600706548,0.6287204522304343],"dir":"ltr"},{"str":"All-Pairs","boundary":[0.5147889579518722,0.6142114690650597,0.5815474830156404,0.6287204522304343],"dir":"ltr"},{"str":"Shortest-Paths","boundary":[0.5867679808968577,0.6142114690650597,0.7098815928006732,0.6287204522304343],"dir":"ltr"},{"str":"Problem","boundary":[0.7151020906818906,0.6142114690650597,0.7850154489976174,0.6287204522304343],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.6371211534831861,0.38782569832989267,0.6516301366485606],"dir":"ltr"},{"str":"8.4","boundary":[0.39304619621111003,0.6371211534831861,0.4191486856171966,0.6516301366485606],"dir":"ltr"},{"str":"Summary","boundary":[0.30433672683258445,0.6594776722830151,0.3965896097705061,0.674750237731096],"dir":"ltr"},{"str":"9","boundary":[0.2608313226372873,0.7092214487298412,0.292474516463951,0.7458756977846306],"dir":"ltr"},{"str":"Greedy","boundary":[0.30433528976912944,0.7224535772976838,0.3860765955972307,0.7407807784745748],"dir":"ltr"},{"str":"Technique","boundary":[0.39267093193507513,0.7224535772976838,0.5077871702356483,0.7407807784745748],"dir":"ltr"},{"str":"9.1","boundary":[0.26224997339434597,0.7548906149064353,0.2924739230115853,0.7716904982189212],"dir":"ltr"},{"str":"Prim’s","boundary":[0.3043243205233806,0.7548906149064353,0.36794682166010184,0.7716904982189212],"dir":"ltr"},{"str":"Algorithm","boundary":[0.37399161158354977,0.7548906149064353,0.477861976563084,0.7716904982189212],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.7794521132938365,0.38782569832989267,0.793961096459211],"dir":"ltr"},{"str":"9.1","boundary":[0.39304619621111003,0.7794521132938365,0.4191486856171966,0.793961096459211],"dir":"ltr"},{"str":"9.2","boundary":[0.26224997339434597,0.8091323974982729,0.2924739230115853,0.8259322808107588],"dir":"ltr"},{"str":"Kruskal’s","boundary":[0.3043243205233806,0.8091323974982729,0.39575720407769116,0.8259322808107588],"dir":"ltr"},{"str":"Algorithm","boundary":[0.4018019940011391,0.8091323974982729,0.5056723589806733,0.8259322808107588],"dir":"ltr"},{"str":"Disjoint","boundary":[0.30433528976912944,0.8306401799508201,0.3669249280356665,0.8451491631161946],"dir":"ltr"},{"str":"Subsets","boundary":[0.3721454259168839,0.8306401799508201,0.4399743408339952,0.8451491631161946],"dir":"ltr"},{"str":"and","boundary":[0.4451948387152125,0.8306401799508201,0.4754662149185302,0.8451491631161946],"dir":"ltr"},{"str":"Union-Find","boundary":[0.4806867127997475,0.8306401799508201,0.5704492303257144,0.8451491631161946],"dir":"ltr"},{"str":"Algorithms","boundary":[0.5756697282069316,0.8306401799508201,0.6664462992781709,0.8451491631161946],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.8535469625723133,0.38782569832989267,0.868055945737688],"dir":"ltr"},{"str":"9.2","boundary":[0.39304619621111003,0.8535469625723133,0.4191486856171966,0.868055945737688],"dir":"ltr"},{"str":"9.3","boundary":[0.26224997339434597,0.8832279326364433,0.2924739230115853,0.9000278159489292],"dir":"ltr"},{"str":"Dijkstra’s","boundary":[0.3043243205233806,0.8832279326364433,0.3969531157531934,0.9000278159489292],"dir":"ltr"},{"str":"Algorithm","boundary":[0.40299790567664134,0.8832279326364433,0.5068682706561756,0.9000278159489292],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.9077909640137716,0.38782569832989267,0.9222999471791461],"dir":"ltr"},{"str":"9.3","boundary":[0.39304619621111003,0.9077909640137716,0.4191486856171966,0.9222999471791461],"dir":"ltr"}],"boundary":[0.26083,0.3446,0.78502,0.9223],"dir":"ltr","type":"paragraph"},{"words":[{"str":"263","boundary":[0.8956787368178103,0.1013968716124326,0.9270017241051143,0.11590585477780714],"dir":"ltr"},{"str":"267","boundary":[0.8940317031301347,0.12375456667543253,0.9270031641844423,0.13902713212351328],"dir":"ltr"},{"str":"269","boundary":[0.8940277348762689,0.15508734779615624,0.9269991959305763,0.170359913244237],"dir":"ltr"},{"str":"270","boundary":[0.8956787368178104,0.17549393974052993,0.9270017241051144,0.19000292290590448],"dir":"ltr"},{"str":"272","boundary":[0.8956787368178105,0.19534803230402842,0.9270017241051145,0.20985701546940294],"dir":"ltr"},{"str":"274","boundary":[0.8940317031301347,0.21770538734986256,0.9270031641844423,0.2329779527979433],"dir":"ltr"},{"str":"276","boundary":[0.8940277348762689,0.24903832176957913,0.9269991959305763,0.2643108872176599],"dir":"ltr"},{"str":"279","boundary":[0.8940317031301347,0.27194716994170026,0.9270031641844423,0.287219735389781],"dir":"ltr"},{"str":"280","boundary":[0.8940277497175384,0.29485601811382134,0.926999210771846,0.31012858356190215],"dir":"ltr"}],"boundary":[0.89403,0.1014,0.927,0.31013],"dir":"ltr","type":"paragraph"},{"words":[{"str":"283","boundary":[0.8940239650350963,0.36003737012469117,0.9269954260894038,0.3753099355727719],"dir":"ltr"},{"str":"285","boundary":[0.8940277348762689,0.3913716842353421,0.9269991959305763,0.4066442496834228],"dir":"ltr"},{"str":"290","boundary":[0.8940317031301347,0.414280685706456,0.9270031641844423,0.42955325115453674],"dir":"ltr"},{"str":"292","boundary":[0.8940277348762689,0.4456134668271797,0.9269991959305763,0.4608860322752605],"dir":"ltr"},{"str":"294","boundary":[0.8956787368178102,0.4660185257816263,0.9270017241051142,0.4805275089470008],"dir":"ltr"},{"str":"296","boundary":[0.8940317031301347,0.48837622084462623,0.9270031641844423,0.503648786292707],"dir":"ltr"},{"str":"297","boundary":[0.8940277348762689,0.5197090019653501,0.9269991959305763,0.5349815674134308],"dir":"ltr"},{"str":"303","boundary":[0.8940317031301347,0.5426180034364639,0.9270031641844423,0.5578905688845447],"dir":"ltr"},{"str":"304","boundary":[0.8940277348762689,0.5739507845571876,0.9269991959305763,0.5892233500052684],"dir":"ltr"},{"str":"304","boundary":[0.8956787368178104,0.5943573765015613,0.9270017241051144,0.6088663596669358],"dir":"ltr"},{"str":"308","boundary":[0.8956787368178105,0.6142114690650597,0.9270017241051145,0.6287204522304343],"dir":"ltr"},{"str":"311","boundary":[0.8940317031301347,0.636568824110894,0.9270031641844423,0.6518413895589749],"dir":"ltr"},{"str":"312","boundary":[0.8940277497175384,0.6594776722830151,0.926999210771846,0.674750237731096],"dir":"ltr"}],"boundary":[0.89402,0.36004,0.927,0.67475],"dir":"ltr","type":"paragraph"},{"words":[{"str":"315","boundary":[0.8940257507493358,0.7246590242938848,0.9269972118036434,0.7399315897419656],"dir":"ltr"},{"str":"318","boundary":[0.8940277348762689,0.7559918054146086,0.9269991959305763,0.7712643708626894],"dir":"ltr"},{"str":"322","boundary":[0.8940317031301347,0.7789008068857226,0.9270031641844423,0.7941733723338034],"dir":"ltr"},{"str":"325","boundary":[0.8940277348762689,0.8102351209963733,0.9269991959305763,0.8255076864444539],"dir":"ltr"},{"str":"327","boundary":[0.8956787368178104,0.8306401799508201,0.9270017241051144,0.8451491631161946],"dir":"ltr"},{"str":"331","boundary":[0.8940317031301347,0.85299787501382,0.9270031641844423,0.8682704404619007],"dir":"ltr"},{"str":"333","boundary":[0.8940277348762689,0.8843306561345436,0.9269991959305763,0.8996032215826244],"dir":"ltr"},{"str":"337","boundary":[0.8940317031301347,0.9072396576056575,0.9270031641844423,0.9225122230537381],"dir":"ltr"}],"boundary":[0.89403,0.72466,0.927,0.92251],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":13,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/ee730f9682e7350fbf0bd5e50b0266b3.jpg","blurred":"/storage/books/4a8b03583f119702/pages/10b08d2c0ebb043e50abb82434572cb1.jpg"},"info":{"width":503.999989,"height":652.3200069999999,"margin":[0.23393,0.05842,0.073,0.07749]},"elements":[{"words":[{"str":"9.4","boundary":[0.2622476049300072,0.09974284170621818,0.29247155598648233,0.11654272501870411],"dir":"ltr"},{"str":"Huffman","boundary":[0.30432195406258233,0.09974284170621818,0.39368917625115263,0.11654272501870411],"dir":"ltr"},{"str":"Trees","boundary":[0.39973396646244763,0.09974284170621818,0.4545284676583593,0.11654272501870411],"dir":"ltr"},{"str":"and","boundary":[0.46057325786965436,0.09974284170621818,0.4992338226023254,0.11654272501870411],"dir":"ltr"},{"str":"Codes","boundary":[0.5052786128136205,0.09974284170621818,0.5693142501239221,0.11654272501870411],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.1243058730835464,0.3878233358453505,0.13881485624892095],"dir":"ltr"},{"str":"9.4","boundary":[0.39304383397516296,0.1243058730835464,0.41914632462422524,0.13881485624892095],"dir":"ltr"},{"str":"Summary","boundary":[0.30433455878507965,0.14666341484755366,0.3965874461159958,0.1619359802956344],"dir":"ltr"}],"boundary":[0.26225,0.09974,0.56931,0.16194],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Contents","boundary":[0.6887773761439505,0.059521148797142584,0.7609533396239816,0.0732665496798109],"dir":"ltr"}],"boundary":[0.68878,0.05952,0.76095,0.07327],"dir":"ltr","type":"paragraph"},{"words":[{"str":"10","boundary":[0.23392815986747964,0.1984416222266812,0.287735824256139,0.2350958712814707],"dir":"ltr"},{"str":"Iterative","boundary":[0.3043329233088534,0.21167375079452383,0.39795827138400985,0.2300009519714149],"dir":"ltr"},{"str":"Improvement","boundary":[0.40455260803587034,0.21167375079452383,0.557432103436018,0.2300009519714149],"dir":"ltr"},{"str":"10.1","boundary":[0.250158318951868,0.24492311976566453,0.2924718504309332,0.26172300307815044],"dir":"ltr"},{"str":"The","boundary":[0.30432224850703316,0.24492311976566453,0.3429828132397042,0.26172300307815044],"dir":"ltr"},{"str":"Simplex","boundary":[0.34902760345099926,0.24492311976566453,0.43361117870976773,0.26172300307815044],"dir":"ltr"},{"str":"Method","boundary":[0.4396559689210628,0.24492311976566453,0.5193689218513058,0.26172300307815044],"dir":"ltr"},{"str":"Geometric","boundary":[0.3043329233088534,0.26643090221821164,0.3919734440708489,0.28093988538358616],"dir":"ltr"},{"str":"Interpretation","boundary":[0.39719394220066134,0.26643090221821164,0.5098853424776562,0.28093988538358616],"dir":"ltr"},{"str":"of","boundary":[0.5151058406074687,0.26643090221821164,0.531800167360718,0.28093988538358616],"dir":"ltr"},{"str":"Linear","boundary":[0.5370206654905304,0.26643090221821164,0.5881552568843409,0.28093988538358616],"dir":"ltr"},{"str":"Programming","boundary":[0.5933757550141534,0.26643090221821164,0.7060671552911483,0.28093988538358616],"dir":"ltr"},{"str":"An","boundary":[0.3043329233088534,0.2862864456800267,0.32729935932597803,0.3007954288454012],"dir":"ltr"},{"str":"Outline","boundary":[0.33251985745579044,0.2862864456800267,0.39304383397516296,0.3007954288454012],"dir":"ltr"},{"str":"of","boundary":[0.3982643321049754,0.2862864456800267,0.41495865885822464,0.3007954288454012],"dir":"ltr"},{"str":"the","boundary":[0.4201791569880371,0.2862864456800267,0.4473144800009112,0.3007954288454012],"dir":"ltr"},{"str":"Simplex","boundary":[0.4525349781307237,0.2862864456800267,0.5193122851437205,0.3007954288454012],"dir":"ltr"},{"str":"Method","boundary":[0.5245327832735329,0.2862864456800267,0.5902772579227179,0.3007954288454012],"dir":"ltr"},{"str":"Further","boundary":[0.3043329233088534,0.30614053824352516,0.36485689982822594,0.3206495214088997],"dir":"ltr"},{"str":"Notes","boundary":[0.3700773979580384,0.30614053824352516,0.42016037821778596,0.3206495214088997],"dir":"ltr"},{"str":"on","boundary":[0.4253808763475984,0.30614053824352516,0.44626286886684824,0.3206495214088997],"dir":"ltr"},{"str":"the","boundary":[0.4514833669966607,0.30614053824352516,0.4786186900095348,0.3206495214088997],"dir":"ltr"},{"str":"Simplex","boundary":[0.4838391881393473,0.30614053824352516,0.550616495152344,0.3206495214088997],"dir":"ltr"},{"str":"Method","boundary":[0.5558369932821566,0.30614053824352516,0.6215814679313416,0.3206495214088997],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.3290473208650185,0.3878233358453505,0.343556304030393],"dir":"ltr"},{"str":"10.1","boundary":[0.39304383397516296,0.3290473208650185,0.42958732088385015,0.343556304030393],"dir":"ltr"},{"str":"10.2","boundary":[0.250158318951868,0.3595417106377364,0.2924718504309332,0.37634159395022226],"dir":"ltr"},{"str":"The","boundary":[0.30432224850703316,0.3595417106377364,0.3429828132397042,0.37634159395022226],"dir":"ltr"},{"str":"Maximum-Flow","boundary":[0.34902760345099926,0.3595417106377364,0.510888820475748,0.37634159395022226],"dir":"ltr"},{"str":"Problem","boundary":[0.516933610687043,0.3595417106377364,0.6039090094107125,0.37634159395022226],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.38410474201506456,0.3878233358453505,0.3986137251804391],"dir":"ltr"},{"str":"10.2","boundary":[0.39304383397516296,0.38410474201506456,0.42958732088385015,0.3986137251804391],"dir":"ltr"},{"str":"10.3","boundary":[0.250158318951868,0.4145975108808829,0.2924718504309332,0.43139739419336887],"dir":"ltr"},{"str":"Maximum","boundary":[0.30432224850703316,0.4145975108808829,0.4094102740149067,0.43139739419336887],"dir":"ltr"},{"str":"Matching","boundary":[0.41545506422620176,0.4145975108808829,0.5120847322081985,0.43139739419336887],"dir":"ltr"},{"str":"in","boundary":[0.5181295224194934,0.4145975108808829,0.537459804785829,0.43139739419336887],"dir":"ltr"},{"str":"Bipartite","boundary":[0.543504594997124,0.4145975108808829,0.6305017375704743,0.43139739419336887],"dir":"ltr"},{"str":"Graphs","boundary":[0.6365465277817693,0.4145975108808829,0.7114540899325296,0.43139739419336887],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.43916054225821116,0.3878233358453505,0.4536695254235857],"dir":"ltr"},{"str":"10.3","boundary":[0.39304383397516296,0.43916054225821116,0.42958732088385015,0.4536695254235857],"dir":"ltr"},{"str":"10.4","boundary":[0.250158318951868,0.4696517781341024,0.2924718504309332,0.48645166144658836],"dir":"ltr"},{"str":"The","boundary":[0.30432224850703316,0.4696517781341024,0.3429828132397042,0.48645166144658836],"dir":"ltr"},{"str":"Stable","boundary":[0.34902760345099926,0.4696517781341024,0.4142808963434322,0.48645166144658836],"dir":"ltr"},{"str":"Marriage","boundary":[0.42032568655472724,0.4696517781341024,0.5133676193393727,0.48645166144658836],"dir":"ltr"},{"str":"Problem","boundary":[0.5194124095506677,0.4696517781341024,0.6063878082743371,0.48645166144658836],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.49421480951143065,0.3878233358453505,0.5087237926768051],"dir":"ltr"},{"str":"10.4","boundary":[0.39304383397516296,0.49421480951143065,0.42958732088385015,0.5087237926768051],"dir":"ltr"},{"str":"Summary","boundary":[0.304336535491472,0.5165723512754379,0.3965894228223882,0.5318449167235187],"dir":"ltr"},{"str":"11","boundary":[0.2436106997613446,0.5678015949616583,0.2879301496572056,0.6044558440164478],"dir":"ltr"},{"str":"Limitations","boundary":[0.3043329233088534,0.581033723529501,0.43218714832154487,0.599360924706392],"dir":"ltr"},{"str":"of","boundary":[0.43878148497340536,0.581033723529501,0.4611737648272051,0.599360924706392],"dir":"ltr"},{"str":"Algorithm","boundary":[0.46776810147906567,0.581033723529501,0.5824099325525977,0.599360924706392],"dir":"ltr"},{"str":"Power","boundary":[0.5890042692044581,0.581033723529501,0.6614945311040472,0.599360924706392],"dir":"ltr"},{"str":"11.1","boundary":[0.250158318951868,0.6142817128097071,0.2924718504309332,0.631081596122193],"dir":"ltr"},{"str":"Lower-Bound","boundary":[0.30432224850703316,0.6142817128097071,0.4424391816802201,0.631081596122193],"dir":"ltr"},{"str":"Arguments","boundary":[0.4484839718915152,0.6142817128097071,0.563226266657716,0.631081596122193],"dir":"ltr"},{"str":"Trivial","boundary":[0.3043329233088534,0.6357910282521814,0.3505850344373717,0.6503000114175559],"dir":"ltr"},{"str":"Lower","boundary":[0.35580553256718417,0.6357910282521814,0.40902456745886945,0.6503000114175559],"dir":"ltr"},{"str":"Bounds","boundary":[0.41424506558868196,0.6357910282521814,0.4779238755102433,0.6503000114175559],"dir":"ltr"},{"str":"Information-Theoretic","boundary":[0.3043329233088534,0.6556451208156798,0.4838204093690961,0.6701541039810543],"dir":"ltr"},{"str":"Arguments","boundary":[0.48904090749890866,0.6556451208156798,0.5819207051609677,0.6701541039810543],"dir":"ltr"},{"str":"Adversary","boundary":[0.3043329233088534,0.6754992133791783,0.3878045570750994,0.6900081965445528],"dir":"ltr"},{"str":"Arguments","boundary":[0.3930250552049118,0.6754992133791783,0.4859048528669709,0.6900081965445528],"dir":"ltr"},{"str":"Problem","boundary":[0.3043329233088534,0.6953547568409933,0.3742462849537879,0.7098637400063679],"dir":"ltr"},{"str":"Reduction","boundary":[0.3794667830836003,0.6953547568409933,0.4640088067541604,0.7098637400063679],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.7182615394624867,0.3878233358453505,0.7327705226278612],"dir":"ltr"},{"str":"11.1","boundary":[0.39304383397516296,0.7182615394624867,0.42958732088385015,0.7327705226278612],"dir":"ltr"},{"str":"11.2","boundary":[0.250158318951868,0.7487555892180386,0.2924718504309332,0.7655554725305246],"dir":"ltr"},{"str":"Decision","boundary":[0.30432224850703316,0.7487555892180386,0.3925153028128339,0.7655554725305246],"dir":"ltr"},{"str":"Trees","boundary":[0.398560093024129,0.7487555892180386,0.45335459422004065,0.7655554725305246],"dir":"ltr"},{"str":"Decision","boundary":[0.3043329233088534,0.7702633716705858,0.37633072845166265,0.7847723548359603],"dir":"ltr"},{"str":"Trees","boundary":[0.3815512265814751,0.7702633716705858,0.42678928411643274,0.7847723548359603],"dir":"ltr"},{"str":"for","boundary":[0.43200978224624514,0.7702633716705858,0.4549574394931186,0.7847723548359603],"dir":"ltr"},{"str":"Sorting","boundary":[0.4601779376229311,0.7702633716705858,0.5196503030082407,0.7847723548359603],"dir":"ltr"},{"str":"Decision","boundary":[0.3043329233088534,0.7901174642340844,0.37633072845166265,0.804626447399459],"dir":"ltr"},{"str":"Trees","boundary":[0.3815512265814751,0.7901174642340844,0.42678928411643274,0.804626447399459],"dir":"ltr"},{"str":"for","boundary":[0.43200978224624514,0.7901174642340844,0.4549574394931186,0.804626447399459],"dir":"ltr"},{"str":"Searching","boundary":[0.4601779376229311,0.7901174642340844,0.5426167390253652,0.804626447399459],"dir":"ltr"},{"str":"a","boundary":[0.5478372371551777,0.7901174642340844,0.5572266222807398,0.804626447399459],"dir":"ltr"},{"str":"Sorted","boundary":[0.5624471204105522,0.7901174642340844,0.6177505988001122,0.804626447399459],"dir":"ltr"},{"str":"Array","boundary":[0.6229710969299248,0.7901174642340844,0.6667819679257969,0.804626447399459],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043329233088534,0.8130271486522108,0.3878233358453505,0.8275361318175855],"dir":"ltr"},{"str":"11.2","boundary":[0.39304383397516296,0.8130271486522108,0.42958732088385015,0.8275361318175855],"dir":"ltr"},{"str":"11.3","boundary":[0.250158318951868,0.8435188945538508,0.2924718504309332,0.8603187778663366],"dir":"ltr"},{"str":"P","boundary":[0.3043331204318736,0.8435188945538508,0.3176186125869141,0.8603187778663366],"dir":"ltr"},{"str":",","boundary":[0.3201430735348686,0.8435188945538508,0.32618786374616365,0.8603187778663366],"dir":"ltr"},{"str":"NP","boundary":[0.3322326539574586,0.8435188945538508,0.36243486116425283,0.8603187778663366],"dir":"ltr"},{"str":",","boundary":[0.36495714772723925,0.8435188945538508,0.37100193793853425,0.8603187778663366],"dir":"ltr"},{"str":"and","boundary":[0.37704672814982926,0.8435188945538508,0.4157072928825003,0.8603187778663366],"dir":"ltr"},{"str":"NP-Complete","boundary":[0.4217499087088273,0.8435188945538508,0.5582599713905945,0.8603187778663366],"dir":"ltr"},{"str":"Problems","boundary":[0.5643047616018896,0.8435188945538508,0.6621520851660176,0.8603187778663366],"dir":"ltr"},{"str":"P","boundary":[0.3043329233088534,0.865028209996325,0.31580675193229013,0.8795371931616996],"dir":"ltr"},{"str":"and","boundary":[0.3230929147897263,0.865028209996325,0.3533642924345381,0.8795371931616996],"dir":"ltr"},{"str":"NP","boundary":[0.3585847905643505,0.865028209996325,0.3836168913090987,0.8795371931616996],"dir":"ltr"},{"str":"Problems","boundary":[0.39090305416653487,0.865028209996325,0.4702058009370313,0.8795371931616996],"dir":"ltr"},{"str":"NP","boundary":[0.3043310454318283,0.8848823025598235,0.3293631461765765,0.8993912857251981],"dir":"ltr"},{"str":"-Complete","boundary":[0.3314288109042002,0.8848823025598235,0.418055278072635,0.8993912857251981],"dir":"ltr"},{"str":"Problems","boundary":[0.42327577620244744,0.8848823025598235,0.5025785229729439,0.8993912857251981],"dir":"ltr"},{"str":"Exercises","boundary":[0.3043310454318283,0.9077890851813168,0.3878214579683254,0.9222980683466915],"dir":"ltr"},{"str":"11.3","boundary":[0.39304195609813786,0.9077890851813168,0.42958544300682505,0.9222980683466915],"dir":"ltr"}],"boundary":[0.23393,0.19844,0.71145,0.9223],"dir":"ltr","type":"paragraph"},{"words":[{"str":"xiii","boundary":[0.8995194442355433,0.0584185359809148,0.9269956630891909,0.07369110142899557],"dir":"ltr"},{"str":"338","boundary":[0.8940253964965859,0.10084556520431873,0.9269968591209631,0.11611813065239948],"dir":"ltr"},{"str":"342","boundary":[0.8940295631633436,0.12375456667543253,0.9270010257877208,0.13902713212351328],"dir":"ltr"},{"str":"344","boundary":[0.8940256097505589,0.14666341484755366,0.9269970723749361,0.1619359802956344],"dir":"ltr"}],"boundary":[0.89403,0.05842,0.927,0.16194],"dir":"ltr","type":"paragraph"},{"words":[{"str":"345","boundary":[0.8940214282425312,0.2138791977907249,0.9269928908669083,0.22915176323880565],"dir":"ltr"},{"str":"346","boundary":[0.8940253964965859,0.246025843263765,0.9269968591209631,0.2612984087118458],"dir":"ltr"},{"str":"347","boundary":[0.8956763985167472,0.26643090221821164,0.9269993872956219,0.28093988538358616],"dir":"ltr"},{"str":"351","boundary":[0.895676398516747,0.2862864456800267,0.9269993872956217,0.3007954288454012],"dir":"ltr"},{"str":"357","boundary":[0.895676398516747,0.30614053824352516,0.9269993872956217,0.3206495214088997],"dir":"ltr"},{"str":"359","boundary":[0.8940295631633436,0.32849763536380405,0.9270010257877208,0.3437702008118848],"dir":"ltr"},{"str":"361","boundary":[0.8940253964965859,0.36064443413583686,0.9269968591209631,0.3759169995839176],"dir":"ltr"},{"str":"371","boundary":[0.8940295631633436,0.38355343560695065,0.9270010257877208,0.3988260010550314],"dir":"ltr"},{"str":"372","boundary":[0.8940253964965859,0.4157002343789835,0.9269968591209631,0.43097279982706427],"dir":"ltr"},{"str":"378","boundary":[0.8940295631633436,0.4386092358500973,0.9270010257877208,0.45388180129817807],"dir":"ltr"},{"str":"380","boundary":[0.8940253964965859,0.470754501632203,0.9269968591209631,0.48602706708028376],"dir":"ltr"},{"str":"383","boundary":[0.8940295631633436,0.4936635031033168,0.9270010257877208,0.5089360685513976],"dir":"ltr"},{"str":"384","boundary":[0.8940275864569515,0.5165723512754379,0.9269990490813286,0.5318449167235187],"dir":"ltr"}],"boundary":[0.89402,0.21388,0.927,0.53184],"dir":"ltr","type":"paragraph"},{"words":[{"str":"387","boundary":[0.8940214282425312,0.5832391705257021,0.9269928908669083,0.5985117359737828],"dir":"ltr"},{"str":"388","boundary":[0.8940253964965859,0.6153844363078077,0.9269968591209631,0.6306570017558885],"dir":"ltr"},{"str":"389","boundary":[0.8956763985167467,0.6357910282521814,0.9269993872956215,0.6503000114175559],"dir":"ltr"},{"str":"390","boundary":[0.895676398516747,0.6556451208156798,0.9269993872956217,0.6701541039810543],"dir":"ltr"},{"str":"390","boundary":[0.8956763985167467,0.6754992133791783,0.9269993872956215,0.6900081965445528],"dir":"ltr"},{"str":"391","boundary":[0.8956763985167466,0.6953547568409933,0.9269993872956214,0.7098637400063679],"dir":"ltr"},{"str":"393","boundary":[0.8940295631633436,0.7177115139441065,0.9270010257877208,0.7329840793921873],"dir":"ltr"},{"str":"394","boundary":[0.8940253964965859,0.7498583127161392,0.9269968591209631,0.76513087816422],"dir":"ltr"},{"str":"395","boundary":[0.8956763985167467,0.7702633716705858,0.9269993872956215,0.7847723548359603],"dir":"ltr"},{"str":"397","boundary":[0.895676398516747,0.7901174642340844,0.9269993872956217,0.804626447399459],"dir":"ltr"},{"str":"399","boundary":[0.8940295631633436,0.8124748192799184,0.9270010257877208,0.827747384727999],"dir":"ltr"},{"str":"401","boundary":[0.8940253964965859,0.8446216180519511,0.9269968591209631,0.8598941835000319],"dir":"ltr"},{"str":"402","boundary":[0.8956763985167467,0.865028209996325,0.9269993872956215,0.8795371931616996],"dir":"ltr"},{"str":"406","boundary":[0.8956745206397217,0.8848823025598235,0.9269975094185965,0.8993912857251981],"dir":"ltr"},{"str":"409","boundary":[0.8940295631633436,0.9072396576056575,0.9270010257877208,0.9225122230537381],"dir":"ltr"}],"boundary":[0.89402,0.58324,0.927,0.92251],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":14,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/edccc2285989ed6b287edab73ca787f4.jpg","blurred":"/storage/books/4a8b03583f119702/pages/e74cf3c663ec9da5f8e2b4876b606cfc.jpg"},"info":{"width":504.00001299999997,"height":652.3200069999999,"margin":[0.07306,0.05842,0.073,0.0777]},"elements":[{"words":[{"str":"xiv","boundary":[0.07305950208378269,0.0584185359809148,0.10053571962903898,0.07369110142899557],"dir":"ltr"}],"boundary":[0.07306,0.05842,0.10054,0.07369],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Contents","boundary":[0.23910314859456164,0.059521148797142584,0.3112791086376421,0.0732665496798109],"dir":"ltr"},{"str":"11.4","boundary":[0.250160687991887,0.09974284170621818,0.2924742174560222,0.11654272501870411],"dir":"ltr"},{"str":"Challenges","boundary":[0.3043246149678175,0.09974284170621818,0.4179144802918884,0.11654272501870411],"dir":"ltr"},{"str":"of","boundary":[0.4239592702153363,0.09974284170621818,0.4444854633366845,0.11654272501870411],"dir":"ltr"},{"str":"Numerical","boundary":[0.4505302532601324,0.09974284170621818,0.5568576731366076,0.11654272501870411],"dir":"ltr"},{"str":"Algorithms","boundary":[0.5629024630600555,0.09974284170621818,0.6776447523623378,0.11654272501870411],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.1243058730835464,0.38782569832989267,0.13881485624892095],"dir":"ltr"},{"str":"11.4","boundary":[0.39304619621111003,0.1243058730835464,0.4295896813796312,0.13881485624892095],"dir":"ltr"},{"str":"Summary","boundary":[0.30433672683258445,0.14666341484755366,0.3965896097705061,0.1619359802956344],"dir":"ltr"},{"str":"12","boundary":[0.22918846631061496,0.1938072403779577,0.29247485396394224,0.23046148943274716],"dir":"ltr"},{"str":"Coping","boundary":[0.30433528976912944,0.20703936894580033,0.38472451944162944,0.2253665701226914],"dir":"ltr"},{"str":"with","boundary":[0.3913188557794739,0.20703936894580033,0.4427214703266287,0.2253665701226914],"dir":"ltr"},{"str":"the","boundary":[0.44931580666447324,0.20703936894580033,0.4862251136489554,0.2253665701226914],"dir":"ltr"},{"str":"Limitations","boundary":[0.49281944998679994,0.20703936894580033,0.6206736689111951,0.2253665701226914],"dir":"ltr"},{"str":"of","boundary":[0.6272680052490396,0.20703936894580033,0.6496602840365403,0.2253665701226914],"dir":"ltr"},{"str":"Algorithm","boundary":[0.6562546203743849,0.20703936894580033,0.7708964459887822,0.2253665701226914],"dir":"ltr"},{"str":"Power","boundary":[0.7774907823266267,0.20703936894580033,0.8499810407742986,0.2253665701226914],"dir":"ltr"},{"str":"12.1","boundary":[0.250160687991887,0.23843550639402686,0.2924742174560222,0.25523538970651277],"dir":"ltr"},{"str":"Backtracking","boundary":[0.3043246149678175,0.23843550639402686,0.43480945068943877,0.25523538970651277],"dir":"ltr"},{"str":"n-Queens","boundary":[0.30433528976912944,0.25994328884657386,0.3862107241651995,0.2744522720119484],"dir":"ltr"},{"str":"Problem","boundary":[0.39143122204641684,0.25994328884657386,0.4613445803621437,0.2744522720119484],"dir":"ltr"},{"str":"Hamiltonian","boundary":[0.30433528976912944,0.2797988323083889,0.40344963443483084,0.29430781547376345],"dir":"ltr"},{"str":"Circuit","boundary":[0.4086701323160482,0.2797988323083889,0.46187038590413687,0.29430781547376345],"dir":"ltr"},{"str":"Problem","boundary":[0.46709088378535424,0.2797988323083889,0.5370042421010811,0.29430781547376345],"dir":"ltr"},{"str":"Subset-Sum","boundary":[0.30433528976912944,0.29965292487188744,0.40660446768678954,0.31416190803726196],"dir":"ltr"},{"str":"Problem","boundary":[0.4118249655680068,0.29965292487188744,0.48173832388373367,0.31416190803726196],"dir":"ltr"},{"str":"General","boundary":[0.30433528976912944,0.31950701743538595,0.36902815020363894,0.3340160006007604],"dir":"ltr"},{"str":"Remarks","boundary":[0.3742486480848563,0.31950701743538595,0.4483308931978143,0.3340160006007604],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.3424152509551958,0.38782569832989267,0.35692423412057034],"dir":"ltr"},{"str":"12.1","boundary":[0.39304619621111003,0.3424152509551958,0.4295896813796312,0.35692423412057034],"dir":"ltr"},{"str":"12.2","boundary":[0.250160687991887,0.3710544649905244,0.2924742174560222,0.38785434830301035],"dir":"ltr"},{"str":"Branch-and-Bound","boundary":[0.3043246149678175,0.3710544649905244,0.4976056855776312,0.38785434830301035],"dir":"ltr"},{"str":"Assignment","boundary":[0.30433528976912944,0.3925637804329986,0.404520024288174,0.40707276359837313],"dir":"ltr"},{"str":"Problem","boundary":[0.40974052216939133,0.3925637804329986,0.4796538804851182,0.40707276359837313],"dir":"ltr"},{"str":"Knapsack","boundary":[0.30433528976912944,0.4124178729964971,0.3836380327633047,0.42692685616187165],"dir":"ltr"},{"str":"Problem","boundary":[0.38885853064452197,0.4124178729964971,0.45877188896024884,0.42692685616187165],"dir":"ltr"},{"str":"Traveling","boundary":[0.30433528976912944,0.43227196555999564,0.3777414991852391,0.44678094872537016],"dir":"ltr"},{"str":"Salesman","boundary":[0.3829619970664564,0.43227196555999564,0.4643491834592472,0.44678094872537016],"dir":"ltr"},{"str":"Problem","boundary":[0.46956968134046456,0.43227196555999564,0.5394830396561914,0.44678094872537016],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.455181649978122,0.38782569832989267,0.4696906331434965],"dir":"ltr"},{"str":"12.2","boundary":[0.39304619621111003,0.455181649978122,0.4295896813796312,0.4696906331434965],"dir":"ltr"},{"str":"12.3","boundary":[0.250160687991887,0.48381967104068924,0.2924742174560222,0.5006195543531752],"dir":"ltr"},{"str":"Approximation","boundary":[0.3043246149678175,0.48381967104068924,0.4589451226859393,0.5006195543531752],"dir":"ltr"},{"str":"Algorithms","boundary":[0.46498991260938716,0.48381967104068924,0.5797322019116694,0.5006195543531752],"dir":"ltr"},{"str":"for","boundary":[0.5857769918351173,0.48381967104068924,0.6147615420795635,0.5006195543531752],"dir":"ltr"},{"str":"NP","boundary":[0.6208150295424695,0.48381967104068924,0.6510172353110634,0.5006195543531752],"dir":"ltr"},{"str":"-Hard","boundary":[0.6535395217539409,0.48381967104068924,0.7103127105673309,0.5006195543531752],"dir":"ltr"},{"str":"Problems","boundary":[0.7163575004907788,0.48381967104068924,0.8142048193955106,0.5006195543531752],"dir":"ltr"},{"str":"Approximation","boundary":[0.30433528976912944,0.5053289864831635,0.4253832370436863,0.519837969648538],"dir":"ltr"},{"str":"Algorithms","boundary":[0.43060373492490367,0.5053289864831635,0.5213803059961428,0.519837969648538],"dir":"ltr"},{"str":"for","boundary":[0.5266008038773603,0.5053289864831635,0.5495484600314883,0.519837969648538],"dir":"ltr"},{"str":"the","boundary":[0.5547689579127055,0.5053289864831635,0.5819042796334214,0.519837969648538],"dir":"ltr"},{"str":"Traveling","boundary":[0.5871247775146387,0.5053289864831635,0.6605309869307484,0.519837969648538],"dir":"ltr"},{"str":"Salesman","boundary":[0.6657514848119658,0.5053289864831635,0.7471386712047566,0.519837969648538],"dir":"ltr"},{"str":"Problem","boundary":[0.7523591690859739,0.5053289864831635,0.8222725274017008,0.519837969648538],"dir":"ltr"},{"str":"Approximation","boundary":[0.30433528976912944,0.525183079046662,0.4253832370436863,0.5396920622120365],"dir":"ltr"},{"str":"Algorithms","boundary":[0.43060373492490367,0.525183079046662,0.5213803059961428,0.5396920622120365],"dir":"ltr"},{"str":"for","boundary":[0.5266008038773603,0.525183079046662,0.5495484600314883,0.5396920622120365],"dir":"ltr"},{"str":"the","boundary":[0.5547689579127055,0.525183079046662,0.5819042796334214,0.5396920622120365],"dir":"ltr"},{"str":"Knapsack","boundary":[0.5871247775146387,0.525183079046662,0.6664275205088139,0.5396920622120365],"dir":"ltr"},{"str":"Problem","boundary":[0.6716480183900312,0.525183079046662,0.7415613767057581,0.5396920622120365],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.5480927634647883,0.38782569832989267,0.5626017466301628],"dir":"ltr"},{"str":"12.3","boundary":[0.39304619621111003,0.5480927634647883,0.4295896813796312,0.5626017466301628],"dir":"ltr"},{"str":"12.4","boundary":[0.250160687991887,0.5767311245445215,0.2924742174560222,0.5935310078570073],"dir":"ltr"},{"str":"Algorithms","boundary":[0.3043246149678175,0.5767311245445215,0.4190669042700997,0.5935310078570073],"dir":"ltr"},{"str":"for","boundary":[0.4251116941935476,0.5767311245445215,0.45409624443799373,0.5935310078570073],"dir":"ltr"},{"str":"Solving","boundary":[0.46014103436144166,0.5767311245445215,0.5386798156689732,0.5935310078570073],"dir":"ltr"},{"str":"Nonlinear","boundary":[0.544724605592421,0.5767311245445215,0.6462248910695961,0.5935310078570073],"dir":"ltr"},{"str":"Equations","boundary":[0.652269680993044,0.5767311245445215,0.7549441342970761,0.5935310078570073],"dir":"ltr"},{"str":"Bisection","boundary":[0.30433528976912944,0.5982404399869957,0.3815535893646892,0.6127494231523702],"dir":"ltr"},{"str":"Method","boundary":[0.3867740872459065,0.5982404399869957,0.45251855876440233,0.6127494231523702],"dir":"ltr"},{"str":"Method","boundary":[0.30433528976912944,0.6180945325504942,0.3700797612876252,0.6326035157158687],"dir":"ltr"},{"str":"of","boundary":[0.3753002591688425,0.6180945325504942,0.39199458512712376,0.6326035157158687],"dir":"ltr"},{"str":"False","boundary":[0.3972150830083411,0.6180945325504942,0.4410447306873383,0.6326035157158687],"dir":"ltr"},{"str":"Position","boundary":[0.44626522856855555,0.6180945325504942,0.5130425324016806,0.6326035157158687],"dir":"ltr"},{"str":"Newton’s","boundary":[0.30433528976912944,0.6379486251139928,0.3843328472295099,0.6524576082793672],"dir":"ltr"},{"str":"Method","boundary":[0.3895533451107272,0.6379486251139928,0.455297816629223,0.6524576082793672],"dir":"ltr"},{"str":"Exercises","boundary":[0.30433528976912944,0.660855407735486,0.38782569832989267,0.6753643909008605],"dir":"ltr"},{"str":"12.4","boundary":[0.39304619621111003,0.660855407735486,0.4295896813796312,0.6753643909008605],"dir":"ltr"},{"str":"Summary","boundary":[0.30433672683258445,0.6832144883147822,0.3965896097705061,0.698487053762863],"dir":"ltr"},{"str":"Epilogue","boundary":[0.30433528976912944,0.735991411344218,0.40317917293387057,0.754318612521109],"dir":"ltr"},{"str":"APPENDIX","boundary":[0.23910738085635716,0.8003317636093907,0.3596073967958409,0.8156043290574714],"dir":"ltr"},{"str":"A","boundary":[0.36618982876891315,0.8003317636093907,0.3834464747523727,0.8156043290574714],"dir":"ltr"},{"str":"Useful","boundary":[0.30433528976912944,0.8256161344442716,0.37682554821680136,0.8439433356211626],"dir":"ltr"},{"str":"Formulas","boundary":[0.3834198845546458,0.8256161344442716,0.48885810405723146,0.8439433356211626],"dir":"ltr"},{"str":"for","boundary":[0.4954524403950759,0.8256161344442716,0.5270720459286972,0.8439433356211626],"dir":"ltr"},{"str":"the","boundary":[0.5336663822665417,0.8256161344442716,0.570575689251024,0.8439433356211626],"dir":"ltr"},{"str":"Analysis","boundary":[0.5771700255888684,0.8256161344442716,0.6720762834583499,0.8439433356211626],"dir":"ltr"},{"str":"of","boundary":[0.6786706197961944,0.8256161344442716,0.7010628985836951,0.8439433356211626],"dir":"ltr"},{"str":"Algorithms","boundary":[0.7076572349215396,0.8256161344442716,0.8341593776903335,0.8439433356211626],"dir":"ltr"},{"str":"Properties","boundary":[0.30433528976912944,0.8482281733848465,0.38989136295915133,0.8627371565502211],"dir":"ltr"},{"str":"of","boundary":[0.3951118608403687,0.8482281733848465,0.41180618679864994,0.8627371565502211],"dir":"ltr"},{"str":"Logarithms","boundary":[0.4170266846798673,0.8482281733848465,0.5109393102337083,0.8627371565502211],"dir":"ltr"},{"str":"Combinatorics","boundary":[0.30433528976912944,0.8680822659483449,0.4243316259597001,0.8825912491137196],"dir":"ltr"},{"str":"Important","boundary":[0.30433528976912944,0.8879363585118435,0.38572247616192024,0.902445341677218],"dir":"ltr"},{"str":"Summation","boundary":[0.39094297404313755,0.8879363585118435,0.4869400429955941,0.902445341677218],"dir":"ltr"},{"str":"Formulas","boundary":[0.49216054087681144,0.8879363585118435,0.5693788404723711,0.902445341677218],"dir":"ltr"},{"str":"Sum","boundary":[0.30433528976912944,0.907790451075342,0.3429444395669093,0.9222994342407166],"dir":"ltr"},{"str":"Manipulation","boundary":[0.3481649374481266,0.907790451075342,0.4556358344776471,0.9222994342407166],"dir":"ltr"},{"str":"Rules","boundary":[0.4608563323588644,0.907790451075342,0.5078220345204634,0.9222994342407166],"dir":"ltr"}],"boundary":[0.22919,0.05952,0.84998,0.9223],"dir":"ltr","type":"paragraph"},{"words":[{"str":"412","boundary":[0.8940277348762689,0.10084556520431873,0.9269991959305763,0.11611813065239948],"dir":"ltr"},{"str":"419","boundary":[0.8940317031301347,0.12375456667543253,0.9270031641844423,0.13902713212351328],"dir":"ltr"},{"str":"420","boundary":[0.8940277497175384,0.14666341484755366,0.926999210771846,0.1619359802956344],"dir":"ltr"}],"boundary":[0.89403,0.10085,0.927,0.16194],"dir":"ltr","type":"paragraph"},{"words":[{"str":"423","boundary":[0.894019798368537,0.20924481594200137,0.9269912594228445,0.22451738139008215],"dir":"ltr"},{"str":"424","boundary":[0.8940277348762689,0.23953822989212736,0.9269991959305763,0.2548107953402081],"dir":"ltr"},{"str":"425","boundary":[0.8956787368178103,0.25994328884657386,0.9270017241051143,0.2744522720119484],"dir":"ltr"},{"str":"426","boundary":[0.8956787368178105,0.2797988323083889,0.9270017241051145,0.29430781547376345],"dir":"ltr"},{"str":"427","boundary":[0.8956787368178104,0.29965292487188744,0.9270017241051144,0.31416190803726196],"dir":"ltr"},{"str":"428","boundary":[0.8956787368178103,0.31950701743538595,0.9270017241051143,0.3340160006007604],"dir":"ltr"},{"str":"430","boundary":[0.8940317031301347,0.3418653075284262,0.9270031641844423,0.35713787297650695],"dir":"ltr"},{"str":"432","boundary":[0.8940277348762689,0.37215718848862495,0.9269991959305763,0.3874297539367057],"dir":"ltr"},{"str":"433","boundary":[0.8956787368178103,0.3925637804329986,0.9270017241051143,0.40707276359837313],"dir":"ltr"},{"str":"436","boundary":[0.8956787368178102,0.4124178729964971,0.9270017241051142,0.42692685616187165],"dir":"ltr"},{"str":"438","boundary":[0.8956787368178103,0.43227196555999564,0.9270017241051143,0.44678094872537016],"dir":"ltr"},{"str":"440","boundary":[0.8940317031301347,0.4546305135785911,0.9270031641844423,0.4699030790266719],"dir":"ltr"},{"str":"441","boundary":[0.8940277348762689,0.4849223945387898,0.9269991959305763,0.5001949599868706],"dir":"ltr"},{"str":"443","boundary":[0.8956787368178108,0.5053289864831635,0.9270017241051148,0.519837969648538],"dir":"ltr"},{"str":"453","boundary":[0.8956787368178108,0.525183079046662,0.9270017241051148,0.5396920622120365],"dir":"ltr"},{"str":"457","boundary":[0.8940317031301347,0.5475404340924962,0.9270031641844423,0.562812999540577],"dir":"ltr"},{"str":"459","boundary":[0.8940277348762689,0.5778338480426221,0.9269991959305763,0.5931064134907028],"dir":"ltr"},{"str":"460","boundary":[0.8956787368178103,0.5982404399869957,0.9270017241051143,0.6127494231523702],"dir":"ltr"},{"str":"464","boundary":[0.8956787368178102,0.6180945325504942,0.9270017241051142,0.6326035157158687],"dir":"ltr"},{"str":"464","boundary":[0.8956787368178102,0.6379486251139928,0.9270017241051142,0.6524576082793672],"dir":"ltr"},{"str":"467","boundary":[0.8940317031301347,0.660305640142661,0.9270031641844423,0.6755782055907419],"dir":"ltr"},{"str":"468","boundary":[0.8940277497175384,0.6832144883147822,0.926999210771846,0.698487053762863],"dir":"ltr"}],"boundary":[0.89402,0.20924,0.927,0.69849],"dir":"ltr","type":"paragraph"},{"words":[{"str":"471","boundary":[0.8940277348762689,0.738196858340419,0.9269991959305763,0.7534694237884998],"dir":"ltr"}],"boundary":[0.89403,0.7382,0.927,0.75347],"dir":"ltr","type":"paragraph"},{"words":[{"str":"475","boundary":[0.894019798368537,0.8278215814404726,0.9269912594228445,0.8430941468885533],"dir":"ltr"},{"str":"475","boundary":[0.8956787368178103,0.8482281733848465,0.9270017241051143,0.8627371565502211],"dir":"ltr"},{"str":"475","boundary":[0.8956787368178103,0.8680822659483449,0.9270017241051143,0.8825912491137196],"dir":"ltr"},{"str":"476","boundary":[0.8956787368178104,0.8879363585118435,0.9270017241051144,0.902445341677218],"dir":"ltr"},{"str":"476","boundary":[0.8956787368178104,0.907790451075342,0.9270017241051144,0.9222994342407166],"dir":"ltr"}],"boundary":[0.89402,0.82782,0.927,0.9223],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":15,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/1f162a7f6c4964e11b1895d150eb579e.jpg","blurred":"/storage/books/4a8b03583f119702/pages/7a128ea396e6b037ebb0dc2bda08dbda.jpg"},"info":{"width":503.999989,"height":652.3200069999999,"margin":[0.2391,0.05752,0.073,0.56994]},"elements":[{"words":[{"str":"Approximation","boundary":[0.3043329233088534,0.1013968716124326,0.4253808763475984,0.11590585477780714],"dir":"ltr"},{"str":"of","boundary":[0.43060137447741087,0.1013968716124326,0.44729570123066004,0.11590585477780714],"dir":"ltr"},{"str":"a","boundary":[0.45251619936047255,0.1013968716124326,0.4619055844860345,0.11590585477780714],"dir":"ltr"},{"str":"Sum","boundary":[0.467126082615847,0.1013968716124326,0.5057352342521578,0.11590585477780714],"dir":"ltr"},{"str":"by","boundary":[0.5109557323819703,0.1013968716124326,0.5307861137671572,0.11590585477780714],"dir":"ltr"},{"str":"a","boundary":[0.5360066118969696,0.1013968716124326,0.5453959970225316,0.11590585477780714],"dir":"ltr"},{"str":"Definite","boundary":[0.550616495152344,0.1013968716124326,0.616360969801529,0.11590585477780714],"dir":"ltr"},{"str":"Integral","boundary":[0.6215814679313416,0.1013968716124326,0.6841898879485888,0.11590585477780714],"dir":"ltr"},{"str":"Floor","boundary":[0.3043329233088534,0.12125241507424767,0.34607812957710193,0.1357613982396222],"dir":"ltr"},{"str":"and","boundary":[0.35129862770691445,0.12125241507424767,0.38157000535172625,0.1357613982396222],"dir":"ltr"},{"str":"Ceiling","boundary":[0.3867905034815387,0.12125241507424767,0.44314559300516165,0.1357613982396222],"dir":"ltr"},{"str":"Formulas","boundary":[0.4483660911349741,0.12125241507424767,0.5255843944075959,0.1357613982396222],"dir":"ltr"},{"str":"Miscellaneous","boundary":[0.3043329233088534,0.14110795853606273,0.42432926521353553,0.15561694170143725],"dir":"ltr"}],"boundary":[0.30433,0.1014,0.68419,0.15562],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Contents","boundary":[0.6887773761439505,0.05862419639077555,0.7609533396239816,0.07236959727344386],"dir":"ltr"}],"boundary":[0.68878,0.05862,0.76095,0.07237],"dir":"ltr","type":"paragraph"},{"words":[{"str":"APPENDIX","boundary":[0.23910077902799318,0.1985905359484093,0.359600800705573,0.2138631013964901],"dir":"ltr"},{"str":"B","boundary":[0.3661832329920943,0.1985905359484093,0.3812457357017918,0.2138631013964901],"dir":"ltr"},{"str":"Short","boundary":[0.3043329233088534,0.2238761973155303,0.36761957865836375,0.24220339849242137],"dir":"ltr"},{"str":"Tutorial","boundary":[0.37421391531022424,0.2238761973155303,0.4603814956035643,0.24220339849242137],"dir":"ltr"},{"str":"on","boundary":[0.4669758322554248,0.2238761973155303,0.4959719370152605,0.24220339849242137],"dir":"ltr"},{"str":"Recurrence","boundary":[0.502566273667121,0.2238761973155303,0.62916330500158,0.24220339849242137],"dir":"ltr"},{"str":"Relations","boundary":[0.6357576416534405,0.2238761973155303,0.7412622839561213,0.24220339849242137],"dir":"ltr"},{"str":"Sequences","boundary":[0.3043329233088534,0.2464867032661779,0.39723149974116356,0.2609956864315524],"dir":"ltr"},{"str":"and","boundary":[0.4024519978709761,0.2464867032661779,0.4327233755157879,0.2609956864315524],"dir":"ltr"},{"str":"Recurrence","boundary":[0.4379438736456004,0.2464867032661779,0.5339597259395971,0.2609956864315524],"dir":"ltr"},{"str":"Relations","boundary":[0.5391802240694096,0.2464867032661779,0.6163985273420313,0.2609956864315524],"dir":"ltr"},{"str":"Methods","boundary":[0.3043329233088534,0.26634224672799295,0.3794667830836003,0.28085122989336747],"dir":"ltr"},{"str":"for","boundary":[0.3846872812134128,0.26634224672799295,0.40763493846028626,0.28085122989336747],"dir":"ltr"},{"str":"Solving","boundary":[0.41285543659009877,0.26634224672799295,0.47337941310947124,0.28085122989336747],"dir":"ltr"},{"str":"Recurrence","boundary":[0.4785999112392837,0.26634224672799295,0.5746157635332804,0.28085122989336747],"dir":"ltr"},{"str":"Relations","boundary":[0.5798362616630929,0.26634224672799295,0.6570545649357147,0.28085122989336747],"dir":"ltr"},{"str":"Common","boundary":[0.3043329233088534,0.286197790189808,0.3815700053517262,0.3007067733551825],"dir":"ltr"},{"str":"Recurrence","boundary":[0.3867905034815387,0.286197790189808,0.48280635577553543,0.3007067733551825],"dir":"ltr"},{"str":"Types","boundary":[0.488026853905348,0.286197790189808,0.5367389839367634,0.3007067733551825],"dir":"ltr"},{"str":"in","boundary":[0.5419594820665758,0.286197790189808,0.5565693653219503,0.3007067733551825],"dir":"ltr"},{"str":"Algorithm","boundary":[0.5617898634517627,0.286197790189808,0.6431770537201339,0.3007067733551825],"dir":"ltr"},{"str":"Analysis","boundary":[0.6483975518499465,0.286197790189808,0.717259302360818,0.3007067733551825],"dir":"ltr"}],"boundary":[0.2391,0.19859,0.74126,0.30071],"dir":"ltr","type":"paragraph"},{"words":[{"str":"References","boundary":[0.3043329233088534,0.33842120467109954,0.4282495228387792,0.3567484058479906],"dir":"ltr"},{"str":"Hints","boundary":[0.3043329233088534,0.3750749938289109,0.36363451190472146,0.393402195005802],"dir":"ltr"},{"str":"to","boundary":[0.37022884855658195,0.3750749938289109,0.39394948399492913,0.393402195005802],"dir":"ltr"},{"str":"Exercises","boundary":[0.40054382064678967,0.3750749938289109,0.5060057658056814,0.393402195005802],"dir":"ltr"},{"str":"Index","boundary":[0.3043329233088534,0.4117287829867223,0.3662912230738163,0.43005598416361335],"dir":"ltr"}],"boundary":[0.30433,0.33842,0.50601,0.43006],"dir":"ltr","type":"paragraph"},{"words":[{"str":"xv","boundary":[0.9050156745142309,0.057521583574547765,0.926996649597149,0.07279414902262853],"dir":"ltr"},{"str":"477","boundary":[0.895676398516747,0.1013968716124326,0.9269993872956217,0.11590585477780714],"dir":"ltr"},{"str":"477","boundary":[0.8956763985167467,0.12125241507424767,0.9269993872956215,0.1357613982396222],"dir":"ltr"},{"str":"477","boundary":[0.8956763985167466,0.14110795853606273,0.9269993872956214,0.15561694170143725],"dir":"ltr"}],"boundary":[0.89568,0.05752,0.927,0.15562],"dir":"ltr","type":"paragraph"},{"words":[{"str":"479","boundary":[0.8940194441155036,0.22608164431173136,0.9269909067398808,0.24135420975981212],"dir":"ltr"},{"str":"479","boundary":[0.8956763985167467,0.2464867032661779,0.9269993872956215,0.2609956864315524],"dir":"ltr"},{"str":"480","boundary":[0.8956763985167471,0.26634224672799295,0.9269993872956218,0.28085122989336747],"dir":"ltr"},{"str":"485","boundary":[0.895676398516747,0.286197790189808,0.9269993872956217,0.3007067733551825],"dir":"ltr"}],"boundary":[0.89402,0.22608,0.927,0.30071],"dir":"ltr","type":"paragraph"},{"words":[{"str":"493","boundary":[0.8940236107822613,0.3406266516673006,0.9269950734066384,0.35589921711538136],"dir":"ltr"},{"str":"503","boundary":[0.8940236107822613,0.377280440825112,0.9269950734066384,0.3925530062731927],"dir":"ltr"},{"str":"547","boundary":[0.8940253964965859,0.41393422998292334,0.9269968591209631,0.42920679543100415],"dir":"ltr"}],"boundary":[0.89402,0.34063,0.927,0.42921],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":16,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/5cd8786053463fd92660cba7a9599696.jpg","blurred":"/storage/books/4a8b03583f119702/pages/e6182cfcf5faaed44ecf347a8b6be948.jpg"},"info":{"width":504.00001199999997,"height":652.3200059999999,"margin":[0.34119,0.23709,0.34383,0.74452]},"elements":[{"words":[{"str":"This","boundary":[0.3411914383049658,0.23708887693534894,0.382234294470612,0.2554847560891764],"dir":"ltr"},{"str":"page","boundary":[0.38818667528126966,0.23708887693534894,0.43449143608353724,0.2554847560891764],"dir":"ltr"},{"str":"intentionally","boundary":[0.4404438168941949,0.23708887693534894,0.560886671169365,0.2554847560891764],"dir":"ltr"},{"str":"left","boundary":[0.5668390519800225,0.23708887693534894,0.5972866703026982,0.2554847560891764],"dir":"ltr"},{"str":"blank","boundary":[0.6032390511133559,0.23708887693534894,0.6561676212817232,0.2554847560891764],"dir":"ltr"}],"boundary":[0.34119,0.23709,0.65617,0.25548],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":17,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/2d844bb4cc51a4280f8a9a226b19f06a.jpg","blurred":"/storage/books/4a8b03583f119702/pages/dc5394059f9192d433eb4c2673364836.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.16303,0.07295,0.05179]},"elements":[{"words":[{"str":"New","boundary":[0.14421784044919886,0.16302940802619442,0.2532374249714517,0.19968365680003092],"dir":"ltr"},{"str":"to","boundary":[0.2690353021019609,0.16302940802619442,0.31889586926161617,0.19968365680003092],"dir":"ltr"},{"str":"the","boundary":[0.3346937463921254,0.16302940802619442,0.4121175766533598,0.19968365680003092],"dir":"ltr"},{"str":"Third","boundary":[0.42791545378386897,0.16302940802619442,0.552590592219239,0.19968365680003092],"dir":"ltr"},{"str":"Edition","boundary":[0.5683884693497483,0.16302940802619442,0.7376582159012706,0.19968365680003092],"dir":"ltr"}],"boundary":[0.14422,0.16303,0.73766,0.19968],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Reordering","boundary":[0.27468212901091943,0.3251905799265899,0.37355698275620397,0.34046314525760724],"dir":"ltr"},{"str":"of","boundary":[0.3818591496040687,0.3251905799265899,0.3994320694320491,0.34046314525760724],"dir":"ltr"},{"str":"chapters","boundary":[0.40773423627991384,0.3251905799265899,0.48022005968734255,0.34046314525760724],"dir":"ltr"},{"str":"to","boundary":[0.4885222265352073,0.3251905799265899,0.5060951463631878,0.34046314525760724],"dir":"ltr"},{"str":"introduce","boundary":[0.5143973132110524,0.3251905799265899,0.5967864356441483,0.34046314525760724],"dir":"ltr"},{"str":"decrease-and-conquer","boundary":[0.6050886024920131,0.3251905799265899,0.7951093879884985,0.34046314525760724],"dir":"ltr"},{"str":"before","boundary":[0.8034115548363633,0.3251905799265899,0.8594314139955269,0.34046314525760724],"dir":"ltr"},{"str":"divide-","boundary":[0.8677335808433917,0.3251905799265899,0.9270545396777777,0.34046314525760724],"dir":"ltr"},{"str":"and-conquer","boundary":[0.27468212901091943,0.3435176583238107,0.3834405147179477,0.35879022365482804],"dir":"ltr"},{"str":"Restructuring","boundary":[0.27468212901091943,0.36489961770481466,0.393304279615768,0.380172183035832],"dir":"ltr"},{"str":"of","boundary":[0.3975344312953943,0.36489961770481466,0.4151073511233747,0.380172183035832],"dir":"ltr"},{"str":"chapter","boundary":[0.419337502803001,0.36489961770481466,0.48413393834419305,0.380172183035832],"dir":"ltr"},{"str":"8","boundary":[0.4883640900238194,0.36489961770481466,0.4982476219855632,0.380172183035832],"dir":"ltr"},{"str":"on","boundary":[0.5024777736651895,0.36489961770481466,0.5244587487481076,0.380172183035832],"dir":"ltr"},{"str":"dynamic","boundary":[0.528688900427734,0.36489961770481466,0.6011747238351626,0.380172183035832],"dir":"ltr"},{"str":"programming,","boundary":[0.6054048755147889,0.36489961770481466,0.7264188408543795,0.380172183035832],"dir":"ltr"},{"str":"including","boundary":[0.7307873619814701,0.36489961770481466,0.8098951518032672,0.380172183035832],"dir":"ltr"},{"str":"all","boundary":[0.8141253034828934,0.36489961770481466,0.8349993229860961,0.380172183035832],"dir":"ltr"},{"str":"new","boundary":[0.8392294746657225,0.36489961770481466,0.8743753143216834,0.380172183035832],"dir":"ltr"},{"str":"intro-","boundary":[0.8786054660013095,0.36489961770481466,0.9269359372942365,0.380172183035832],"dir":"ltr"},{"str":"ductory","boundary":[0.27468212901091943,0.38322669610203547,0.3405855201318268,0.39849926143305275],"dir":"ltr"},{"str":"material","boundary":[0.3455272861126987,0.38322669610203547,0.4169061539404121,0.39849926143305275],"dir":"ltr"},{"str":"and","boundary":[0.42184791992128395,0.38322669610203547,0.4537124269659458,0.39849926143305275],"dir":"ltr"},{"str":"new","boundary":[0.45865419294681764,0.38322669610203547,0.49380003260277844,0.39849926143305275],"dir":"ltr"},{"str":"exercises","boundary":[0.4987417985836503,0.38322669610203547,0.5756159101820932,0.39849926143305275],"dir":"ltr"},{"str":"focusing","boundary":[0.580557676162965,0.38322669610203547,0.651956311054602,0.39849926143305275],"dir":"ltr"},{"str":"on","boundary":[0.6568980770354738,0.38322669610203547,0.6788790521183918,0.39849926143305275],"dir":"ltr"},{"str":"well-known","boundary":[0.6838208180992639,0.38322669610203547,0.7837828603603403,0.39849926143305275],"dir":"ltr"},{"str":"applications","boundary":[0.788724626341212,0.38322669610203547,0.8919877682775107,0.39849926143305275],"dir":"ltr"},{"str":"More","boundary":[0.27468212901091943,0.40460865548303937,0.3219056447241311,0.4198812208140567],"dir":"ltr"},{"str":"coverage","boundary":[0.326847410705003,0.40460865548303937,0.4037215223034459,0.4198812208140567],"dir":"ltr"},{"str":"of","boundary":[0.40866328828431775,0.40460865548303937,0.4262362081122982,0.4198812208140567],"dir":"ltr"},{"str":"the","boundary":[0.43117797409317,0.40460865548303937,0.4586344258828942,0.4198812208140567],"dir":"ltr"},{"str":"applications","boundary":[0.46357619186376603,0.40460865548303937,0.5668393338000647,0.4198812208140567],"dir":"ltr"},{"str":"of","boundary":[0.5717810997809367,0.40460865548303937,0.5893540196089172,0.4198812208140567],"dir":"ltr"},{"str":"the","boundary":[0.5942957855897889,0.40460865548303937,0.621752237379513,0.4198812208140567],"dir":"ltr"},{"str":"algorithms","boundary":[0.6266940033603849,0.40460865548303937,0.7178597021755093,0.4198812208140567],"dir":"ltr"},{"str":"discussed","boundary":[0.7228014681563811,0.40460865548303937,0.80299644649397,0.4198812208140567],"dir":"ltr"},{"str":"Reordering","boundary":[0.27468212901091943,0.42598926583291774,0.37355698275620397,0.4412618311639351],"dir":"ltr"},{"str":"of","boundary":[0.37893362414339254,0.42598926583291774,0.39650654397137297,0.4412618311639351],"dir":"ltr"},{"str":"select","boundary":[0.4018831853585616,0.42598926583291774,0.45019388958756507,0.4412618311639351],"dir":"ltr"},{"str":"sections","boundary":[0.4555705309747536,0.42598926583291774,0.5236680661911681,0.4412618311639351],"dir":"ltr"},{"str":"throughout","boundary":[0.5290447075783568,0.42598926583291774,0.6257254172281341,0.4412618311639351],"dir":"ltr"},{"str":"the","boundary":[0.6311020586153226,0.42598926583291774,0.6585585104050468,0.4412618311639351],"dir":"ltr"},{"str":"book","boundary":[0.6639351517922354,0.42598926583291774,0.7078971019580717,0.4412618311639351],"dir":"ltr"},{"str":"to","boundary":[0.7132737433452602,0.42598926583291774,0.7308466631732405,0.4412618311639351],"dir":"ltr"},{"str":"achieve","boundary":[0.7362233045604292,0.42598926583291774,0.8010197401016212,0.4412618311639351],"dir":"ltr"},{"str":"a","boundary":[0.8063963814888098,0.42598926583291774,0.8162799134505535,0.4412618311639351],"dir":"ltr"},{"str":"better","boundary":[0.8216565548377421,0.42598926583291774,0.873268358741968,0.4412618311639351],"dir":"ltr"},{"str":"align-","boundary":[0.8786450001291565,0.42598926583291774,0.9269754714220835,0.4412618311639351],"dir":"ltr"},{"str":"ment","boundary":[0.27468212901091943,0.4443163442301386,0.31860454504890867,0.4595889095611559],"dir":"ltr"},{"str":"of","boundary":[0.3235463110297806,0.4443163442301386,0.34111923085776097,0.4595889095611559],"dir":"ltr"},{"str":"specific","boundary":[0.34606099683863284,0.4443163442301386,0.40866328828431775,0.4595889095611559],"dir":"ltr"},{"str":"algorithms","boundary":[0.4136050542651896,0.4443163442301386,0.504770753080314,0.4595889095611559],"dir":"ltr"},{"str":"and","boundary":[0.5097125190611859,0.4443163442301386,0.5415770261058477,0.4595889095611559],"dir":"ltr"},{"str":"general","boundary":[0.5465187920867196,0.4443163442301386,0.6102280391121199,0.4595889095611559],"dir":"ltr"},{"str":"algorithm","boundary":[0.6151698050929917,0.4443163442301386,0.6986461160418794,0.4595889095611559],"dir":"ltr"},{"str":"design","boundary":[0.7035878820227514,0.4443163442301386,0.7585205526661232,0.4595889095611559],"dir":"ltr"},{"str":"techniques","boundary":[0.763462318646995,0.4443163442301386,0.8557349730418347,0.4595889095611559],"dir":"ltr"},{"str":"Addition","boundary":[0.27468212901091943,0.46569830361114245,0.3527817985726186,0.48097086894215973],"dir":"ltr"},{"str":"of","boundary":[0.35772356455349047,0.46569830361114245,0.3752964843814709,0.48097086894215973],"dir":"ltr"},{"str":"the","boundary":[0.38023825036234277,0.46569830361114245,0.40769470215206693,0.48097086894215973],"dir":"ltr"},{"str":"Lomuto","boundary":[0.41263646813293875,0.46569830361114245,0.48184095892906853,0.48097086894215973],"dir":"ltr"},{"str":"partition","boundary":[0.48678272490994035,0.46569830361114245,0.5614824594767998,0.48097086894215973],"dir":"ltr"},{"str":"and","boundary":[0.5664242254576715,0.46569830361114245,0.5982887325023333,0.48097086894215973],"dir":"ltr"},{"str":"Gray","boundary":[0.6032304984832053,0.46569830361114245,0.6471529145211946,0.48097086894215973],"dir":"ltr"},{"str":"code","boundary":[0.6520946805020665,0.46569830361114245,0.6927357639287568,0.48097086894215973],"dir":"ltr"},{"str":"algorithms","boundary":[0.6976775299096287,0.46569830361114245,0.7888432287247531,0.48097086894215973],"dir":"ltr"},{"str":"Seventy","boundary":[0.27468212901091943,0.4870804469509363,0.3427796642273339,0.5023530122819536],"dir":"ltr"},{"str":"new","boundary":[0.34732608892973604,0.4870804469509363,0.38247192858569684,0.5023530122819536],"dir":"ltr"},{"str":"problems","boundary":[0.38701835328809897,0.4870804469509363,0.4672133316256878,0.5023530122819536],"dir":"ltr"},{"str":"added","boundary":[0.4717597563280899,0.4870804469509363,0.5244982828759546,0.5023530122819536],"dir":"ltr"},{"str":"to","boundary":[0.5290447075783568,0.4870804469509363,0.5466176274063371,0.5023530122819536],"dir":"ltr"},{"str":"the","boundary":[0.5511640521087392,0.4870804469509363,0.5786205038984633,0.5023530122819536],"dir":"ltr"},{"str":"end-of-chapter","boundary":[0.5831669286008655,0.4870804469509363,0.7105656555877424,0.5023530122819536],"dir":"ltr"},{"str":"exercises,","boundary":[0.7151120802901446,0.4870804469509363,0.7958407693536675,0.5023530122819536],"dir":"ltr"},{"str":"including","boundary":[0.8004662623117638,0.4870804469509363,0.8795740521335608,0.5023530122819536],"dir":"ltr"},{"str":"algo-","boundary":[0.8841204768359628,0.4870804469509363,0.9269557043581602,0.5023530122819536],"dir":"ltr"},{"str":"rithmic","boundary":[0.27468212901091943,0.5054075253481571,0.3361774648768891,0.5206800906791744],"dir":"ltr"},{"str":"puzzles","boundary":[0.34111923085776097,0.5054075253481571,0.4037215223034459,0.5206800906791744],"dir":"ltr"},{"str":"and","boundary":[0.40866328828431775,0.5054075253481571,0.4405277953289796,0.5206800906791744],"dir":"ltr"},{"str":"questions","boundary":[0.4454695613098515,0.5054075253481571,0.5267714952271556,0.5206800906791744],"dir":"ltr"},{"str":"asked","boundary":[0.5317132612080275,0.5054075253481571,0.5811506880806697,0.5206800906791744],"dir":"ltr"},{"str":"during","boundary":[0.5860924540615416,0.5054075253481571,0.6421320802846286,0.5206800906791744],"dir":"ltr"},{"str":"job","boundary":[0.6470738462655006,0.5054075253481571,0.6745500651191482,0.5206800906791744],"dir":"ltr"},{"str":"interviews","boundary":[0.6794918311000201,0.5054075253481571,0.7673564302399221,0.5206800906791744],"dir":"ltr"}],"boundary":[0.27468,0.32519,0.92705,0.52068],"dir":"ltr","type":"paragraph"},{"words":[{"str":"xvii","boundary":[0.89402377586163,0.932932446659325,0.9269952384860071,0.9482050119903421],"dir":"ltr"}],"boundary":[0.89402,0.93293,0.927,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":18,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/1578626ca1ffcb2727af0834ebed7b04.jpg","blurred":"/storage/books/4a8b03583f119702/pages/c47bb7dc57ee2b7909af7599b8872950.jpg"},"info":{"width":504.00001199999997,"height":652.3200059999999,"margin":[0.34119,0.23709,0.34383,0.74452]},"elements":[{"words":[{"str":"This","boundary":[0.3411914383049658,0.23708887693534894,0.382234294470612,0.2554847560891764],"dir":"ltr"},{"str":"page","boundary":[0.38818667528126966,0.23708887693534894,0.43449143608353724,0.2554847560891764],"dir":"ltr"},{"str":"intentionally","boundary":[0.4404438168941949,0.23708887693534894,0.560886671169365,0.2554847560891764],"dir":"ltr"},{"str":"left","boundary":[0.5668390519800225,0.23708887693534894,0.5972866703026982,0.2554847560891764],"dir":"ltr"},{"str":"blank","boundary":[0.6032390511133559,0.23708887693534894,0.6561676212817232,0.2554847560891764],"dir":"ltr"}],"boundary":[0.34119,0.23709,0.65617,0.25548],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":19,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/13ef3cf9a3afcacba60699375e64498d.jpg","blurred":"/storage/books/4a8b03583f119702/pages/06049eacda580e087f226c2f09cc66bb.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.16303,0.07291,0.05179]},"elements":[{"words":[{"str":"Preface","boundary":[0.14421784044919886,0.16302940802619442,0.3265813230007828,0.19968365680003092],"dir":"ltr"}],"boundary":[0.14422,0.16303,0.32658,0.19968],"dir":"ltr","type":"paragraph"},{"words":[{"str":"The","boundary":[0.23910077902799318,0.3251905799265899,0.27205247458844684,0.34046314525760724],"dir":"ltr"},{"str":"most","boundary":[0.2762233250763027,0.3251905799265899,0.31686440850299297,0.34046314525760724],"dir":"ltr"},{"str":"valuable","boundary":[0.32103525899084884,0.3251905799265899,0.39243389388248573,0.34046314525760724],"dir":"ltr"},{"str":"acquisitions","boundary":[0.3966047443703416,0.3251905799265899,0.49658655369534144,0.34046314525760724],"dir":"ltr"},{"str":"in","boundary":[0.5007574041831973,0.3251905799265899,0.5172431354953858,0.34046314525760724],"dir":"ltr"},{"str":"a","boundary":[0.5214139859832417,0.3251905799265899,0.5312975179449854,0.34046314525760724],"dir":"ltr"},{"str":"scientific","boundary":[0.5354683684328414,0.3251905799265899,0.60795419184027,0.34046314525760724],"dir":"ltr"},{"str":"or","boundary":[0.6121250423281258,0.3251905799265899,0.6308049177358215,0.34046314525760724],"dir":"ltr"},{"str":"technical","boundary":[0.6349757682236773,0.3251905799265899,0.7094185309595312,0.34046314525760724],"dir":"ltr"},{"str":"education","boundary":[0.7135893814473873,0.3251905799265899,0.7959785038804832,0.34046314525760724],"dir":"ltr"},{"str":"are","boundary":[0.8001493543683389,0.3251905799265899,0.8264988505783478,0.34046314525760724],"dir":"ltr"},{"str":"the","boundary":[0.8306697010662035,0.3251905799265899,0.8559320087604205,0.34046314525760724],"dir":"ltr"},{"str":"general-purpose","boundary":[0.23910077902799318,0.3435176583238107,0.3752958494608221,0.35879022365482804],"dir":"ltr"},{"str":"mental","boundary":[0.38023761544169393,0.3435176583238107,0.4373446631166493,0.35879022365482804],"dir":"ltr"},{"str":"tools","boundary":[0.44228642909752125,0.3435176583238107,0.48294727958813505,0.35879022365482804],"dir":"ltr"},{"str":"which","boundary":[0.4878890455690069,0.3435176583238107,0.5381764561903591,0.35879022365482804],"dir":"ltr"},{"str":"remain","boundary":[0.5431182221712311,0.3435176583238107,0.6024194139416935,0.35879022365482804],"dir":"ltr"},{"str":"serviceable","boundary":[0.6073611799225654,0.3435176583238107,0.699594300189558,0.35879022365482804],"dir":"ltr"},{"str":"for","boundary":[0.70453606617043,0.3435176583238107,0.729798373864647,0.35879022365482804],"dir":"ltr"},{"str":"a","boundary":[0.7347401398455189,0.3435176583238107,0.7446236718072626,0.35879022365482804],"dir":"ltr"},{"str":"life-time.","boundary":[0.7495654377881346,0.3435176583238107,0.8231779838392019,0.35879022365482804],"dir":"ltr"},{"str":"—George","boundary":[0.2547872873068654,0.3654455790327648,0.3351228664411737,0.3799545620869287],"dir":"ltr"},{"str":"Forsythe,","boundary":[0.33981755900395466,0.3654455790327648,0.4147824098464415,0.3799545620869287],"dir":"ltr"},{"str":"“What","boundary":[0.4194771024092224,0.3654455790327648,0.4733909518001993,0.3799545620869287],"dir":"ltr"},{"str":"to","boundary":[0.4780856443629803,0.3654455790327648,0.49477997111622946,0.3799545620869287],"dir":"ltr"},{"str":"do","boundary":[0.4994746636790104,0.3654455790327648,0.5203566561982602,0.3799545620869287],"dir":"ltr"},{"str":"till","boundary":[0.5250513487610412,0.3654455790327648,0.5469661736441029,0.3799545620869287],"dir":"ltr"},{"str":"the","boundary":[0.5516608662068839,0.3654455790327648,0.577744578085695,0.3799545620869287],"dir":"ltr"},{"str":"computer","boundary":[0.582439270648476,0.3654455790327648,0.6606904062849096,0.3799545620869287],"dir":"ltr"},{"str":"scientist","boundary":[0.6653850988476906,0.3654455790327648,0.7311107947266244,0.3799545620869287],"dir":"ltr"},{"str":"comes.”","boundary":[0.7358054872894053,0.3654455790327648,0.7989397128736841,0.3799545620869287],"dir":"ltr"},{"str":"(1968)","boundary":[0.8036344054364651,0.3654455790327648,0.8558018291940874,0.3799545620869287],"dir":"ltr"}],"boundary":[0.2391,0.32519,0.85593,0.37995],"dir":"ltr","type":"paragraph"},{"words":[{"str":"lgorithms","boundary":[0.2884995896299513,0.462644587699695,0.36978175648333195,0.47791715303071236],"dir":"ltr"},{"str":"play","boundary":[0.3732805267977892,0.462644587699695,0.4095333220334653,0.47791715303071236],"dir":"ltr"},{"str":"the","boundary":[0.41303209234792265,0.462644587699695,0.4404885441376468,0.47791715303071236],"dir":"ltr"},{"str":"central","boundary":[0.44398731445210404,0.462644587699695,0.5032885062225666,0.47791715303071236],"dir":"ltr"},{"str":"role","boundary":[0.5067872765370238,0.462644587699695,0.5408459276771928,0.47791715303071236],"dir":"ltr"},{"str":"both","boundary":[0.5443446979916501,0.462644587699695,0.5838985929025486,0.47791715303071236],"dir":"ltr"},{"str":"in","boundary":[0.5873973632170059,0.462644587699695,0.6038830945291944,0.47791715303071236],"dir":"ltr"},{"str":"the","boundary":[0.6073818648436516,0.462644587699695,0.6348383166333758,0.47791715303071236],"dir":"ltr"},{"str":"science","boundary":[0.6383370869478332,0.462644587699695,0.6998324228138028,0.47791715303071236],"dir":"ltr"},{"str":"and","boundary":[0.70333119312826,0.462644587699695,0.7351957001729218,0.47791715303071236],"dir":"ltr"},{"str":"practice","boundary":[0.7386944704873792,0.462644587699695,0.8067722386398702,0.47791715303071236],"dir":"ltr"},{"str":"of","boundary":[0.8102710089543276,0.462644587699695,0.827843928782308,0.47791715303071236],"dir":"ltr"},{"str":"computing.","boundary":[0.8313426990967651,0.462644587699695,0.9270943567421386,0.47791715303071236],"dir":"ltr"},{"str":"Recognition","boundary":[0.2884995896299513,0.48097166609691583,0.3939568756617572,0.49624423142793317],"dir":"ltr"},{"str":"of","boundary":[0.3981870273413835,0.48097166609691583,0.4157599471693639,0.49624423142793317],"dir":"ltr"},{"str":"this","boundary":[0.4199900988489902,0.48097166609691583,0.45074765031393677,0.49624423142793317],"dir":"ltr"},{"str":"fact","boundary":[0.45497780199356314,0.48097166609691583,0.48680277491037804,0.49624423142793317],"dir":"ltr"},{"str":"has","boundary":[0.49103292659000436,0.48097166609691583,0.5195963339594438,0.49624423142793317],"dir":"ltr"},{"str":"led","boundary":[0.5238264856390702,0.48097166609691583,0.5501957489130025,0.49624423142793317],"dir":"ltr"},{"str":"to","boundary":[0.5544259005926289,0.48097166609691583,0.5719988204206092,0.49624423142793317],"dir":"ltr"},{"str":"the","boundary":[0.5762289721002355,0.48097166609691583,0.6036854238899596,0.49624423142793317],"dir":"ltr"},{"str":"appearance","boundary":[0.607915575569586,0.48097166609691583,0.706770662250947,0.49624423142793317],"dir":"ltr"},{"str":"of","boundary":[0.7110008139305733,0.48097166609691583,0.7285737337585537,0.49624423142793317],"dir":"ltr"},{"str":"a","boundary":[0.73280388543818,0.48097166609691583,0.7426874173999236,0.49624423142793317],"dir":"ltr"},{"str":"considerable","boundary":[0.74691756907955,0.48097166609691583,0.8556759547865782,0.49624423142793317],"dir":"ltr"},{"str":"number","boundary":[0.8599061064662047,0.48097166609691583,0.9269164531668272,0.49624423142793317],"dir":"ltr"},{"str":"ofAtextbooks","boundary":[0.23910077902799318,0.4613464444809952,0.3485519298295064,0.514571309825154],"dir":"ltr"},{"str":"on","boundary":[0.3558459764172732,0.49929874449413664,0.37782695150019135,0.514571309825154],"dir":"ltr"},{"str":"the","boundary":[0.38512099808795824,0.49929874449413664,0.4125774498776824,0.514571309825154],"dir":"ltr"},{"str":"subject.","boundary":[0.41987149646544925,0.49929874449413664,0.48522140979649897,0.514571309825154],"dir":"ltr"},{"str":"By","boundary":[0.4925154563842659,0.49929874449413664,0.5166708084987677,0.514571309825154],"dir":"ltr"},{"str":"and","boundary":[0.5239648550865345,0.49929874449413664,0.5558293621311963,0.514571309825154],"dir":"ltr"},{"str":"large,","boundary":[0.5631234087189633,0.49929874449413664,0.6101690208568635,0.514571309825154],"dir":"ltr"},{"str":"they","boundary":[0.618056079362335,0.49929874449413664,0.6553960631138029,0.514571309825154],"dir":"ltr"},{"str":"follow","boundary":[0.6626901097015698,0.49929874449413664,0.7165158247652264,0.514571309825154],"dir":"ltr"},{"str":"one","boundary":[0.7238098713529931,0.49929874449413664,0.7556743783976549,0.514571309825154],"dir":"ltr"},{"str":"of","boundary":[0.7629684249854218,0.49929874449413664,0.7805413448134022,0.514571309825154],"dir":"ltr"},{"str":"two","boundary":[0.787835391401169,0.49929874449413664,0.8196801313819074,0.514571309825154],"dir":"ltr"},{"str":"alternatives","boundary":[0.8269741779696743,0.49929874449413664,0.9269164531668271,0.514571309825154],"dir":"ltr"},{"str":"in","boundary":[0.23910169688515603,0.5176258228913575,0.25558742819734465,0.5328983882223748],"dir":"ltr"},{"str":"presenting","boundary":[0.26151754737439087,0.5176258228913575,0.35159605767372343,0.5328983882223748],"dir":"ltr"},{"str":"algorithms.","boundary":[0.3575261768507697,0.5176258228913575,0.45254645313097414,0.5328983882223748],"dir":"ltr"},{"str":"One","boundary":[0.4584765723080204,0.5176258228913575,0.4958165560594883,0.5328983882223748],"dir":"ltr"},{"str":"classifies","boundary":[0.5017466752365347,0.5176258228913575,0.5753394542236786,0.5328983882223748],"dir":"ltr"},{"str":"algorithms","boundary":[0.5812695734007248,0.5176258228913575,0.6724352722158492,0.5328983882223748],"dir":"ltr"},{"str":"according","boundary":[0.6783653913928955,0.5176258228913575,0.7618417023417832,0.5328983882223748],"dir":"ltr"},{"str":"to","boundary":[0.7677718215188295,0.5176258228913575,0.7853447413468099,0.5328983882223748],"dir":"ltr"},{"str":"a","boundary":[0.7912748605238562,0.5176258228913575,0.8011583924855998,0.5328983882223748],"dir":"ltr"},{"str":"problem","boundary":[0.8070885116626463,0.5176258228913575,0.8795941021339985,0.5328983882223748],"dir":"ltr"},{"str":"type.","boundary":[0.8855242213110445,0.5176258228913575,0.9270745896782152,0.5328983882223748],"dir":"ltr"},{"str":"Such","boundary":[0.23910169688515603,0.5359529012885783,0.28084973589156165,0.5512254666195956],"dir":"ltr"},{"str":"a","boundary":[0.2867996221325314,0.5359529012885783,0.29668315409427515,0.5512254666195956],"dir":"ltr"},{"str":"book","boundary":[0.30263304033524485,0.5359529012885783,0.3465949905010811,0.5512254666195956],"dir":"ltr"},{"str":"would","boundary":[0.35254487674205087,0.5359529012885783,0.4052834032899156,0.5512254666195956],"dir":"ltr"},{"str":"have","boundary":[0.4112332895308852,0.5359529012885783,0.4518743729575755,0.5512254666195956],"dir":"ltr"},{"str":"separate","boundary":[0.45782425919854525,0.5359529012885783,0.530310082605974,0.5512254666195956],"dir":"ltr"},{"str":"chapters","boundary":[0.5362599688469438,0.5359529012885783,0.6087457922543725,0.5512254666195956],"dir":"ltr"},{"str":"on","boundary":[0.614695678495342,0.5359529012885783,0.6366766535782602,0.5512254666195956],"dir":"ltr"},{"str":"algorithms","boundary":[0.6426265398192299,0.5359529012885783,0.7337922386343544,0.5512254666195956],"dir":"ltr"},{"str":"for","boundary":[0.739742124875324,0.5359529012885783,0.765004432569541,0.5512254666195956],"dir":"ltr"},{"str":"sorting,","boundary":[0.7709543188105108,0.5359529012885783,0.8348612364751459,0.5512254666195956],"dir":"ltr"},{"str":"searching,","boundary":[0.8410680945471208,0.5359529012885783,0.9269362202307505,0.5512254666195956],"dir":"ltr"},{"str":"graphs,","boundary":[0.23910169688515603,0.5542799796857991,0.300083089089115,0.5695525450168164],"dir":"ltr"},{"str":"and","boundary":[0.30549926460415056,0.5542799796857991,0.3373637716488124,0.5695525450168164],"dir":"ltr"},{"str":"so","boundary":[0.34268111184423056,0.5542799796857991,0.3613609872519263,0.5695525450168164],"dir":"ltr"},{"str":"on.","boundary":[0.3666783274473444,0.5542799796857991,0.39360106851113436,0.5695525450168164],"dir":"ltr"},{"str":"The","boundary":[0.39891840870655254,0.5542799796857991,0.43218637728978204,0.5695525450168164],"dir":"ltr"},{"str":"advantage","boundary":[0.43750371748520017,0.5542799796857991,0.5253683166251021,0.5695525450168164],"dir":"ltr"},{"str":"of","boundary":[0.5306856568205203,0.5542799796857991,0.5482585766485006,0.5695525450168164],"dir":"ltr"},{"str":"this","boundary":[0.5535759168439187,0.5542799796857991,0.5843334683088653,0.5695525450168164],"dir":"ltr"},{"str":"approach","boundary":[0.5896508085042834,0.5542799796857991,0.6698457868418722,0.5695525450168164],"dir":"ltr"},{"str":"is","boundary":[0.6751631270372903,0.5542799796857991,0.6883477586742565,0.5695525450168164],"dir":"ltr"},{"str":"that","boundary":[0.6936650988696746,0.5542799796857991,0.7277039829459201,0.5695525450168164],"dir":"ltr"},{"str":"it","boundary":[0.7330213231413382,0.5542799796857991,0.745098999198589,0.5695525450168164],"dir":"ltr"},{"str":"allows","boundary":[0.7504163393940073,0.5542799796857991,0.8042420544576637,0.5695525450168164],"dir":"ltr"},{"str":"an","boundary":[0.8095593946530817,0.5542799796857991,0.8304334141562845,0.5695525450168164],"dir":"ltr"},{"str":"immediate","boundary":[0.8357507543517028,0.5542799796857991,0.9268966861029037,0.5695525450168164],"dir":"ltr"},{"str":"comparison","boundary":[0.23910169688515603,0.5726070580830199,0.3390637391462324,0.5878796234140372],"dir":"ltr"},{"str":"of,","boundary":[0.34536943253782487,0.5726070580830199,0.36689576515050276,0.5878796234140372],"dir":"ltr"},{"str":"say,","boundary":[0.3735374986287946,0.5726070580830199,0.4041171465184298,0.5878796234140372],"dir":"ltr"},{"str":"the","boundary":[0.41075887999672156,0.5726070580830199,0.4382153317864457,0.5878796234140372],"dir":"ltr"},{"str":"efficiency","boundary":[0.4445210251780382,0.5726070580830199,0.5254276178168726,0.5878796234140372],"dir":"ltr"},{"str":"of","boundary":[0.5317333112084651,0.5726070580830199,0.5493062310364455,0.5878796234140372],"dir":"ltr"},{"str":"different","boundary":[0.555611924428038,0.5726070580830199,0.6302918919309738,0.5878796234140372],"dir":"ltr"},{"str":"algorithms","boundary":[0.6365975853225663,0.5726070580830199,0.7277632841376906,0.5878796234140372],"dir":"ltr"},{"str":"for","boundary":[0.7340689775292831,0.5726070580830199,0.7593312852235001,0.5878796234140372],"dir":"ltr"},{"str":"the","boundary":[0.7656369786150927,0.5726070580830199,0.7930934304048168,0.5878796234140372],"dir":"ltr"},{"str":"same","boundary":[0.7993991237964092,0.5726070580830199,0.8433215398343985,0.5878796234140372],"dir":"ltr"},{"str":"problem.","boundary":[0.8496272332259911,0.5726070580830199,0.9270745896782151,0.5878796234140372],"dir":"ltr"},{"str":"The","boundary":[0.23910169688515603,0.5909341364802406,0.27236966546838554,0.606206701811258],"dir":"ltr"},{"str":"drawback","boundary":[0.27659981714801185,0.5909341364802406,0.3600761280968996,0.606206701811258],"dir":"ltr"},{"str":"of","boundary":[0.3643062797765259,0.5909341364802406,0.3818791996045063,0.606206701811258],"dir":"ltr"},{"str":"this","boundary":[0.38610935128413265,0.5909341364802406,0.4168669027490792,0.606206701811258],"dir":"ltr"},{"str":"approach","boundary":[0.42109705442870554,0.5909341364802406,0.5012920327662944,0.606206701811258],"dir":"ltr"},{"str":"is","boundary":[0.5055221844459207,0.5909341364802406,0.5187068160828868,0.606206701811258],"dir":"ltr"},{"str":"that","boundary":[0.5229369677625133,0.5909341364802406,0.5569758518387588,0.606206701811258],"dir":"ltr"},{"str":"it","boundary":[0.5612060035183849,0.5909341364802406,0.5732836795756358,0.606206701811258],"dir":"ltr"},{"str":"emphasizes","boundary":[0.5775138312552621,0.5909341364802406,0.6752619623569079,0.606206701811258],"dir":"ltr"},{"str":"problem","boundary":[0.6794921140365342,0.5909341364802406,0.7519977045078864,0.606206701811258],"dir":"ltr"},{"str":"types","boundary":[0.7562278561875125,0.5909341364802406,0.801257227805217,0.606206701811258],"dir":"ltr"},{"str":"at","boundary":[0.8054873794848434,0.5909341364802406,0.8219533437331084,0.606206701811258],"dir":"ltr"},{"str":"the","boundary":[0.8261834954127348,0.5909341364802406,0.853639947202459,0.606206701811258],"dir":"ltr"},{"str":"expense","boundary":[0.8578700988820852,0.5909341364802406,0.927074589678215,0.606206701811258],"dir":"ltr"},{"str":"of","boundary":[0.23910169688515603,0.6092612148774614,0.25667461671313646,0.6245337802084788],"dir":"ltr"},{"str":"algorithm","boundary":[0.2616163826940083,0.6092612148774614,0.345092693642896,0.6245337802084788],"dir":"ltr"},{"str":"design","boundary":[0.3500344596237679,0.6092612148774614,0.40496713026713965,0.6245337802084788],"dir":"ltr"},{"str":"techniques.","boundary":[0.4099088962480116,0.6092612148774614,0.5060361281079313,0.6245337802084788],"dir":"ltr"},{"str":"The","boundary":[0.27468241194743354,0.6275882932746822,0.30795038053066304,0.6428608586056996],"dir":"ltr"},{"str":"second","boundary":[0.3143351421779495,0.6275882932746822,0.37365610101233554,0.6428608586056996],"dir":"ltr"},{"str":"alternative","boundary":[0.380040862659622,0.6275882932746822,0.4722937499905382,0.6428608586056996],"dir":"ltr"},{"str":"organizes","boundary":[0.4786785116378246,0.6275882932746822,0.5599606784912052,0.6428608586056996],"dir":"ltr"},{"str":"the","boundary":[0.5663454401384918,0.6275882932746822,0.5938018919282159,0.6428608586056996],"dir":"ltr"},{"str":"presentation","boundary":[0.6001866535755024,0.6275882932746822,0.7078380837028153,0.6428608586056996],"dir":"ltr"},{"str":"around","boundary":[0.7142228453501018,0.6275882932746822,0.7757577153439185,0.6428608586056996],"dir":"ltr"},{"str":"algorithm","boundary":[0.7821424769912049,0.6275882932746822,0.8656187879400926,0.6428608586056996],"dir":"ltr"},{"str":"design","boundary":[0.8720035495873789,0.6275882932746822,0.9269362202307507,0.6428608586056996],"dir":"ltr"},{"str":"techniques.","boundary":[0.23910169688515603,0.645915371671903,0.33522892874507576,0.6611879370029203],"dir":"ltr"},{"str":"In","boundary":[0.3393009439133142,0.645915371671903,0.3579808193210099,0.6611879370029203],"dir":"ltr"},{"str":"this","boundary":[0.36205283448924835,0.645915371671903,0.39281038595419493,0.6611879370029203],"dir":"ltr"},{"str":"organization,","boundary":[0.3968824011224334,0.645915371671903,0.5094755972306182,0.6611879370029203],"dir":"ltr"},{"str":"algorithms","boundary":[0.5137255159741679,0.645915371671903,0.6048912147892924,0.6611879370029203],"dir":"ltr"},{"str":"from","boundary":[0.6089632299575308,0.645915371671903,0.650691501900013,0.6611879370029203],"dir":"ltr"},{"str":"different","boundary":[0.6547635170682513,0.645915371671903,0.7294434845711871,0.6611879370029203],"dir":"ltr"},{"str":"areas","boundary":[0.7335154997394255,0.645915371671903,0.77854487135713,0.6611879370029203],"dir":"ltr"},{"str":"of","boundary":[0.7826168865253685,0.645915371671903,0.800189806353349,0.6611879370029203],"dir":"ltr"},{"str":"computing","boundary":[0.8042618215215873,0.645915371671903,0.8954275203367118,0.6611879370029203],"dir":"ltr"},{"str":"are","boundary":[0.8994995355049501,0.645915371671903,0.9269559872946742,0.6611879370029203],"dir":"ltr"},{"str":"grouped","boundary":[0.23910169688515603,0.6642424500691237,0.31052009884071646,0.679515015400141],"dir":"ltr"},{"str":"together","boundary":[0.31395956796340324,0.6642424500691237,0.38644539137083195,0.679515015400141],"dir":"ltr"},{"str":"if","boundary":[0.3898848604935188,0.6642424500691237,0.4019625365507697,0.679515015400141],"dir":"ltr"},{"str":"they","boundary":[0.4054020056734564,0.6642424500691237,0.4427419894249244,0.679515015400141],"dir":"ltr"},{"str":"have","boundary":[0.44618145854761115,0.6642424500691237,0.4868225419743014,0.679515015400141],"dir":"ltr"},{"str":"the","boundary":[0.49026201109698825,0.6642424500691237,0.5177184628867123,0.679515015400141],"dir":"ltr"},{"str":"same","boundary":[0.5211579320093993,0.6642424500691237,0.5650803480473886,0.679515015400141],"dir":"ltr"},{"str":"design","boundary":[0.5685198171700753,0.6642424500691237,0.6234524878134471,0.679515015400141],"dir":"ltr"},{"str":"approach.","boundary":[0.6268919569361339,0.6642424500691237,0.7120287012545946,0.679515015400141],"dir":"ltr"},{"str":"I","boundary":[0.7154681703772814,0.6642424500691237,0.723157558243518,0.679515015400141],"dir":"ltr"},{"str":"share","boundary":[0.7265970273662048,0.6642424500691237,0.7727333545636247,0.679515015400141],"dir":"ltr"},{"str":"the","boundary":[0.7761728236863115,0.6642424500691237,0.8036292754760356,0.679515015400141],"dir":"ltr"},{"str":"belief","boundary":[0.8070687445987224,0.6642424500691237,0.8553992158916494,0.679515015400141],"dir":"ltr"},{"str":"of","boundary":[0.8588386850143362,0.6642424500691237,0.8764116048423166,0.679515015400141],"dir":"ltr"},{"str":"many","boundary":[0.8798510739650034,0.6642424500691237,0.927074589678215,0.679515015400141],"dir":"ltr"},{"str":"(e.g.,","boundary":[0.23910169688515603,0.6825695284663446,0.280296258101704,0.697842093797362],"dir":"ltr"},{"str":"[BaY95])","boundary":[0.28442757446171285,0.6825695284663446,0.3645830186714547,0.697842093797362],"dir":"ltr"},{"str":"that","boundary":[0.3685166643922288,0.6825695284663446,0.40255554846847424,0.697842093797362],"dir":"ltr"},{"str":"this","boundary":[0.4064891941892482,0.6825695284663446,0.4372467456541948,0.697842093797362],"dir":"ltr"},{"str":"organization","boundary":[0.44118039137496884,0.6825695284663446,0.5488318215022817,0.697842093797362],"dir":"ltr"},{"str":"is","boundary":[0.5527654672230558,0.6825695284663446,0.565950098860022,0.697842093797362],"dir":"ltr"},{"str":"more","boundary":[0.569883744580796,0.6825695284663446,0.6149131161985005,0.697842093797362],"dir":"ltr"},{"str":"appropriate","boundary":[0.6188467619192746,0.6825695284663446,0.7199157597600663,0.697842093797362],"dir":"ltr"},{"str":"for","boundary":[0.7238494054808402,0.6825695284663446,0.7491117131750572,0.697842093797362],"dir":"ltr"},{"str":"a","boundary":[0.7530453588958312,0.6825695284663446,0.762928890857575,0.697842093797362],"dir":"ltr"},{"str":"basic","boundary":[0.7668625365783491,0.6825695284663446,0.8096977641005465,0.697842093797362],"dir":"ltr"},{"str":"course","boundary":[0.8136314098213205,0.6825695284663446,0.8696512689804842,0.697842093797362],"dir":"ltr"},{"str":"on","boundary":[0.8735849147012582,0.6825695284663446,0.8955658897841763,0.697842093797362],"dir":"ltr"},{"str":"the","boundary":[0.8994995355049503,0.6825695284663446,0.9269559872946744,0.697842093797362],"dir":"ltr"},{"str":"design","boundary":[0.23910169688515603,0.7008966068635654,0.2940343675285278,0.7161691721945828],"dir":"ltr"},{"str":"and","boundary":[0.29887729818978226,0.7008966068635654,0.33074180523444413,0.7161691721945828],"dir":"ltr"},{"str":"analysis","boundary":[0.33558473589569854,0.7008966068635654,0.4025950825963212,0.7161691721945828],"dir":"ltr"},{"str":"of","boundary":[0.4074380132575756,0.7008966068635654,0.42501093308555604,0.7161691721945828],"dir":"ltr"},{"str":"algorithms.","boundary":[0.42985386374681045,0.7008966068635654,0.5248741400270148,0.7161691721945828],"dir":"ltr"},{"str":"There","boundary":[0.5297170706882692,0.7008966068635654,0.5805579590994792,0.7161691721945828],"dir":"ltr"},{"str":"are","boundary":[0.5854008897607337,0.7008966068635654,0.6128573415504578,0.7161691721945828],"dir":"ltr"},{"str":"three","boundary":[0.6177002722117122,0.7008966068635654,0.6627296438294167,0.7161691721945828],"dir":"ltr"},{"str":"principal","boundary":[0.6675725744906712,0.7008966068635654,0.7433792646372458,0.7161691721945828],"dir":"ltr"},{"str":"reasons","boundary":[0.7482221952985003,0.7008966068635654,0.8130383979036159,0.7161691721945828],"dir":"ltr"},{"str":"for","boundary":[0.8178813285648703,0.7008966068635654,0.8431436362590873,0.7161691721945828],"dir":"ltr"},{"str":"emphasis","boundary":[0.8479865669203417,0.7008966068635654,0.9270745896782152,0.7161691721945828],"dir":"ltr"},{"str":"on","boundary":[0.23910169688515603,0.7192236852607861,0.26108267196807416,0.7344962505918035],"dir":"ltr"},{"str":"algorithm","boundary":[0.26837671855584105,0.7192236852607861,0.3518530295047288,0.7344962505918035],"dir":"ltr"},{"str":"design","boundary":[0.3591470760924957,0.7192236852607861,0.41407974673586745,0.7344962505918035],"dir":"ltr"},{"str":"techniques.","boundary":[0.42137379332363434,0.7192236852607861,0.5175010251835541,0.7344962505918035],"dir":"ltr"},{"str":"First,","boundary":[0.5247950717713209,0.7192236852607861,0.5685395842339989,0.7344962505918035],"dir":"ltr"},{"str":"these","boundary":[0.5764068756755468,0.7192236852607861,0.6214362472932513,0.7344962505918035],"dir":"ltr"},{"str":"techniques","boundary":[0.6287302938810183,0.7192236852607861,0.7210029482758579,0.7344962505918035],"dir":"ltr"},{"str":"provide","boundary":[0.7282969948636249,0.7192236852607861,0.7942201530484557,0.7344962505918035],"dir":"ltr"},{"str":"a","boundary":[0.8015141996362226,0.7192236852607861,0.8113977315979662,0.7344962505918035],"dir":"ltr"},{"str":"student","boundary":[0.8186917781857332,0.7192236852607861,0.8824010252111335,0.7344962505918035],"dir":"ltr"},{"str":"with","boundary":[0.8896950717989002,0.7192236852607861,0.9270350555503681,0.7344962505918035],"dir":"ltr"},{"str":"tools","boundary":[0.23910169688515603,0.7375507636580069,0.28084973589156165,0.7528233289890242],"dir":"ltr"},{"str":"for","boundary":[0.2867205538768374,0.7375507636580069,0.3119828615710545,0.7528233289890242],"dir":"ltr"},{"str":"designing","boundary":[0.3178536795563303,0.7375507636580069,0.3991556134736344,0.7528233289890242],"dir":"ltr"},{"str":"algorithms","boundary":[0.40502643145891015,0.7375507636580069,0.4961921302740345,0.7528233289890242],"dir":"ltr"},{"str":"for","boundary":[0.5020629482593103,0.7375507636580069,0.5273252559535273,0.7528233289890242],"dir":"ltr"},{"str":"new","boundary":[0.5331960739388031,0.7375507636580069,0.5683419135947639,0.7528233289890242],"dir":"ltr"},{"str":"problems.","boundary":[0.5742127315800398,0.7375507636580069,0.6582622873827086,0.7528233289890242],"dir":"ltr"},{"str":"This","boundary":[0.6641331053679845,0.7375507636580069,0.7007021736264364,0.7528233289890242],"dir":"ltr"},{"str":"makes","boundary":[0.7065729916117122,0.7375507636580069,0.7614858951911605,0.7528233289890242],"dir":"ltr"},{"str":"learning","boundary":[0.7673567131764363,0.7375507636580069,0.8376681595522814,0.7528233289890242],"dir":"ltr"},{"str":"algorithm","boundary":[0.8435389775375572,0.7375507636580069,0.9270152884864449,0.7528233289890242],"dir":"ltr"},{"str":"design","boundary":[0.23910169688515603,0.7558793693117608,0.2940343675285278,0.7711519346427781],"dir":"ltr"},{"str":"techniques","boundary":[0.29921333827648156,0.7558793693117608,0.39148599267132117,0.7711519346427781],"dir":"ltr"},{"str":"a","boundary":[0.396664963419275,0.7558793693117608,0.4065484953810187,0.7711519346427781],"dir":"ltr"},{"str":"very","boundary":[0.4117274661289725,0.7558793693117608,0.44906744988044034,0.7711519346427781],"dir":"ltr"},{"str":"valuable","boundary":[0.4542464206283941,0.7558793693117608,0.5267520110997462,0.7711519346427781],"dir":"ltr"},{"str":"endeavor","boundary":[0.5319309818476999,0.7558793693117608,0.6121259601852888,0.7711519346427781],"dir":"ltr"},{"str":"from","boundary":[0.6173049309332426,0.7558793693117608,0.6590332028757246,0.7711519346427781],"dir":"ltr"},{"str":"a","boundary":[0.6642121736236785,0.7558793693117608,0.6740957055854221,0.7711519346427781],"dir":"ltr"},{"str":"practical","boundary":[0.679274676333376,0.7558793693117608,0.7528476882565965,0.7711519346427781],"dir":"ltr"},{"str":"standpoint.","boundary":[0.7580266590045502,0.7558793693117608,0.85415389086447,0.7711519346427781],"dir":"ltr"},{"str":"Second,","boundary":[0.8593328616124236,0.7558793693117608,0.926896686102904,0.7711519346427781],"dir":"ltr"},{"str":"they","boundary":[0.23910169688515603,0.7742064477089815,0.27644168063662394,0.7894790130399989],"dir":"ltr"},{"str":"seek","boundary":[0.281956691471277,0.7742064477089815,0.3204036308024602,0.7894790130399989],"dir":"ltr"},{"str":"to","boundary":[0.32591864163711315,0.7742064477089815,0.3434915614650936,0.7894790130399989],"dir":"ltr"},{"str":"classify","boundary":[0.3490065722997466,0.7742064477089815,0.4105019081657162,0.7894790130399989],"dir":"ltr"},{"str":"multitudes","boundary":[0.4160169190003692,0.7742064477089815,0.5071826178154936,0.7894790130399989],"dir":"ltr"},{"str":"of","boundary":[0.5126976286501467,0.7742064477089815,0.530270548478127,0.7894790130399989],"dir":"ltr"},{"str":"known","boundary":[0.53578555931278,0.7742064477089815,0.5940193296313742,0.7894790130399989],"dir":"ltr"},{"str":"algorithms","boundary":[0.5995343404660273,0.7742064477089815,0.6907000392811516,0.7894790130399989],"dir":"ltr"},{"str":"according","boundary":[0.6962150501158046,0.7742064477089815,0.7796913610646925,0.7894790130399989],"dir":"ltr"},{"str":"to","boundary":[0.7852063718993455,0.7742064477089815,0.802779291727326,0.7894790130399989],"dir":"ltr"},{"str":"an","boundary":[0.8082943025619788,0.7742064477089815,0.8291683220651815,0.7894790130399989],"dir":"ltr"},{"str":"underlying","boundary":[0.8346833328998347,0.7742064477089815,0.9269757543585978,0.7894790130399989],"dir":"ltr"},{"str":"design","boundary":[0.23910169688515603,0.7925335261062023,0.2940343675285278,0.8078060914372196],"dir":"ltr"},{"str":"idea.","boundary":[0.299272639468252,0.7925335261062023,0.34046720068479996,0.8078060914372196],"dir":"ltr"},{"str":"Learning","boundary":[0.34570547262452417,0.7925335261062023,0.4237063068666058,0.8078060914372196],"dir":"ltr"},{"str":"to","boundary":[0.4289445788063301,0.7925335261062023,0.44651749863431045,0.8078060914372196],"dir":"ltr"},{"str":"see","boundary":[0.45175577057403465,0.7925335261062023,0.47921222236375877,0.8078060914372196],"dir":"ltr"},{"str":"such","boundary":[0.48445049430348297,0.7925335261062023,0.5228974336346662,0.8078060914372196],"dir":"ltr"},{"str":"commonality","boundary":[0.5281357055743904,0.7925335261062023,0.640155656828794,0.8078060914372196],"dir":"ltr"},{"str":"among","boundary":[0.6453939287685183,0.7925335261062023,0.703607932023189,0.8078060914372196],"dir":"ltr"},{"str":"algorithms","boundary":[0.7088462039629132,0.7925335261062023,0.8000119027780376,0.8078060914372196],"dir":"ltr"},{"str":"from","boundary":[0.8052501747177618,0.7925335261062023,0.846978446660244,0.8078060914372196],"dir":"ltr"},{"str":"different","boundary":[0.8522167185999681,0.7925335261062023,0.926896686102904,0.8078060914372196],"dir":"ltr"},{"str":"application","boundary":[0.23910169688515603,0.8108606045034232,0.33467545095521817,0.8261331698344405],"dir":"ltr"},{"str":"areas","boundary":[0.33872769905953304,0.8108606045034232,0.3837570706772376,0.8261331698344405],"dir":"ltr"},{"str":"should","boundary":[0.38780931878155256,0.8108606045034232,0.44495590058435497,0.8261331698344405],"dir":"ltr"},{"str":"be","boundary":[0.44900814868866984,0.8108606045034232,0.4698821681918727,0.8261331698344405],"dir":"ltr"},{"str":"a","boundary":[0.47393441629618765,0.8108606045034232,0.4838179482579314,0.8261331698344405],"dir":"ltr"},{"str":"major","boundary":[0.4878701963622463,0.8108606045034232,0.5383948117506804,0.8261331698344405],"dir":"ltr"},{"str":"goal","boundary":[0.5424470598549953,0.8108606045034232,0.5786998550906713,0.8261331698344405],"dir":"ltr"},{"str":"of","boundary":[0.5827521031949864,0.8108606045034232,0.6003250230229668,0.8261331698344405],"dir":"ltr"},{"str":"computer","boundary":[0.6043772711272817,0.8108606045034232,0.6867466264964541,0.8261331698344405],"dir":"ltr"},{"str":"science","boundary":[0.690798874600769,0.8108606045034232,0.7522942104667386,0.8261331698344405],"dir":"ltr"},{"str":"education.","boundary":[0.7563464585710536,0.8108606045034232,0.8458714910805285,0.8261331698344405],"dir":"ltr"},{"str":"After","boundary":[0.8499237391848434,0.8108606045034232,0.897226323153749,0.8261331698344405],"dir":"ltr"},{"str":"all,","boundary":[0.9012785712580639,0.8108606045034232,0.9270943567421386,0.8261331698344405],"dir":"ltr"},{"str":"every","boundary":[0.23910169688515603,0.8291876829006439,0.2863252125983677,0.8444602482316612],"dir":"ltr"},{"str":"science","boundary":[0.29176115517732676,0.8291876829006439,0.35325649104329643,0.8444602482316612],"dir":"ltr"},{"str":"considers","boundary":[0.35869243362225545,0.8291876829006439,0.43888741195984426,0.8444602482316612],"dir":"ltr"},{"str":"classification","boundary":[0.44432335453880334,0.8291876829006439,0.5530619731819082,0.8444602482316612],"dir":"ltr"},{"str":"of","boundary":[0.5584979157608672,0.8291876829006439,0.5760708355888476,0.8444602482316612],"dir":"ltr"},{"str":"its","boundary":[0.5815067781678066,0.8291876829006439,0.6012738420912942,0.8444602482316612],"dir":"ltr"},{"str":"principal","boundary":[0.6067097846702532,0.8291876829006439,0.6825164748168278,0.8444602482316612],"dir":"ltr"},{"str":"subject","boundary":[0.6879524173957868,0.8291876829006439,0.7483605647459647,0.8444602482316612],"dir":"ltr"},{"str":"as","boundary":[0.7537965073249235,0.8291876829006439,0.771369427152904,0.8444602482316612],"dir":"ltr"},{"str":"a","boundary":[0.7768053697318631,0.8291876829006439,0.7866889016936068,0.8444602482316612],"dir":"ltr"},{"str":"major","boundary":[0.7921248442725659,0.8291876829006439,0.842649459661,0.8444602482316612],"dir":"ltr"},{"str":"if","boundary":[0.848085402239959,0.8291876829006439,0.8601630782972098,0.8444602482316612],"dir":"ltr"},{"str":"not","boundary":[0.8655990208761688,0.8291876829006439,0.8941624282456082,0.8444602482316612],"dir":"ltr"},{"str":"the","boundary":[0.8995983708245673,0.8291876829006439,0.9270548226142914,0.8444602482316612],"dir":"ltr"},{"str":"central","boundary":[0.23910169688515603,0.8475147612978647,0.29840288865561854,0.8627873266288819],"dir":"ltr"},{"str":"point","boundary":[0.3041551042573534,0.8475147612978647,0.3492042429389815,0.8627873266288819],"dir":"ltr"},{"str":"of","boundary":[0.35495645854071634,0.8475147612978647,0.37252937836869676,0.8627873266288819],"dir":"ltr"},{"str":"its","boundary":[0.37828159397043165,0.8475147612978647,0.39804865789391913,0.8627873266288819],"dir":"ltr"},{"str":"discipline.","boundary":[0.4038008734956539,0.8475147612978647,0.4893131920286609,0.8627873266288819],"dir":"ltr"},{"str":"Third,","boundary":[0.4950654076303958,0.8475147612978647,0.5475667294111787,0.8627873266288819],"dir":"ltr"},{"str":"in","boundary":[0.5535363827160719,0.8475147612978647,0.5700221140282603,0.8627873266288819],"dir":"ltr"},{"str":"my","boundary":[0.5757743296299952,0.8475147612978647,0.6021238258400041,0.8627873266288819],"dir":"ltr"},{"str":"opinion,","boundary":[0.607876041441739,0.8475147612978647,0.6787607326713652,0.8627873266288819],"dir":"ltr"},{"str":"algorithm","boundary":[0.6847303859762583,0.8475147612978647,0.7682066969251461,0.8627873266288819],"dir":"ltr"},{"str":"design","boundary":[0.773958912526881,0.8475147612978647,0.8288915831702528,0.8627873266288819],"dir":"ltr"},{"str":"techniques","boundary":[0.8346437987719875,0.8475147612978647,0.926916453166827,0.8627873266288819],"dir":"ltr"},{"str":"have","boundary":[0.23910169688515603,0.8658418396950854,0.2797427803118464,0.8811144050261027],"dir":"ltr"},{"str":"utility","boundary":[0.28454617684525385,0.8658418396950854,0.3350707922336879,0.8811144050261027],"dir":"ltr"},{"str":"as","boundary":[0.33987418876709535,0.8658418396950854,0.3574471085950758,0.8811144050261027],"dir":"ltr"},{"str":"general","boundary":[0.3622505051284832,0.8658418396950854,0.42595975215388343,0.8811144050261027],"dir":"ltr"},{"str":"problem","boundary":[0.43076314868729093,0.8658418396950854,0.5032687391586431,0.8811144050261027],"dir":"ltr"},{"str":"solving","boundary":[0.5080721356920505,0.8658418396950854,0.5685000501061518,0.8811144050261027],"dir":"ltr"},{"str":"strategies,","boundary":[0.5733034466395592,0.8658418396950854,0.6584204238940965,0.8811144050261027],"dir":"ltr"},{"str":"applicable","boundary":[0.6632435874914274,0.8658418396950854,0.7511279536952528,0.8811144050261027],"dir":"ltr"},{"str":"to","boundary":[0.7559313502286604,0.8658418396950854,0.7735042700566408,0.8811144050261027],"dir":"ltr"},{"str":"problems","boundary":[0.778307666590048,0.8658418396950854,0.8585026449276368,0.8811144050261027],"dir":"ltr"},{"str":"beyond","boundary":[0.8633060414610444,0.8658418396950854,0.9270350555503681,0.8811144050261027],"dir":"ltr"},{"str":"computing.","boundary":[0.23910169688515603,0.8841689180923064,0.33485335453052956,0.8994414834233235],"dir":"ltr"},{"str":"xix","boundary":[0.8995212792752659,0.9329342191942445,0.9269974981289135,0.9482067845252617],"dir":"ltr"}],"boundary":[0.2391,0.46135,0.92709,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":24,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/c329c31d5a53ac050c914bbd22b6fdfa.jpg","blurred":"/storage/books/4a8b03583f119702/pages/780fc37d1a61e5b741ca3525c313906b.jpg"},"info":{"width":504.00001199999997,"height":652.3200059999999,"margin":[0.07306,0.05842,0.07294,0.17518]},"elements":[{"words":[{"str":"xxiv","boundary":[0.07305950024461508,0.058418536070469824,0.11152620488429672,0.07369110154196327],"dir":"ltr"}],"boundary":[0.07306,0.05842,0.11153,0.07369],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Preface","boundary":[0.2391031470848457,0.05952114888838791,0.29939506945884753,0.07326654979212778],"dir":"ltr"}],"boundary":[0.2391,0.05952,0.2994,0.07327],"dir":"ltr","type":"paragraph"},{"words":[{"str":"28–30","boundary":[0.24119708608260906,0.10204529566428787,0.2856732754998426,0.11579069656802773],"dir":"ltr"},{"str":"31–33","boundary":[0.24119708608260906,0.13869878171420058,0.2856732754998426,0.15244418261794046],"dir":"ltr"},{"str":"34","boundary":[0.24119708608260906,0.15855263877956244,0.2589875618495025,0.1722980396833023],"dir":"ltr"},{"str":"35","boundary":[0.24119708608260906,0.17840649584492427,0.2589875618495025,0.19215189674866415],"dir":"ltr"},{"str":"36","boundary":[0.24119708608260906,0.1982603529102861,0.2589875618495025,0.21200575381402598],"dir":"ltr"},{"str":"37","boundary":[0.24119708608260906,0.21811420997564795,0.2589875618495025,0.2318596108793878],"dir":"ltr"},{"str":"38","boundary":[0.24119708608260906,0.23796944158110017,0.2589875618495025,0.25171484248484005],"dir":"ltr"},{"str":"39","boundary":[0.24119708608260906,0.25782329864646203,0.2589875618495025,0.2715686995502019],"dir":"ltr"},{"str":"40","boundary":[0.24119708608260906,0.2776771557118239,0.2589875618495025,0.2914225566155637],"dir":"ltr"}],"boundary":[0.2412,0.10205,0.28567,0.29142],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Greedy","boundary":[0.34358127412108075,0.10204529566428787,0.40189845368495747,0.11579069656802773],"dir":"ltr"},{"str":"algorithms:","boundary":[0.40855209162177564,0.10204529566428787,0.4950493848004115,0.11579069656802773],"dir":"ltr"},{"str":"Prim’s,","boundary":[0.5017030227372297,0.10204529566428787,0.5542738786283997,0.11579069656802773],"dir":"ltr"},{"str":"Kruskal’s,","boundary":[0.5614790213139915,0.10204529566428787,0.6378001623539644,0.11579069656802773],"dir":"ltr"},{"str":"Dijkstra’s,","boundary":[0.6450053050395562,0.10204529566428787,0.7232833984138873,0.11579069656802773],"dir":"ltr"},{"str":"Huffman’s","boundary":[0.343574157930774,0.11884355010874845,0.4252858131281156,0.1325889510124883],"dir":"ltr"},{"str":"Iterative","boundary":[0.34358127412108075,0.13869878171420058,0.4097974249254582,0.15244418261794046],"dir":"ltr"},{"str":"improvement","boundary":[0.4142450438671815,0.13869878171420058,0.5180346794912378,0.15244418261794046],"dir":"ltr"},{"str":"algorithms","boundary":[0.5224822984329612,0.13869878171420058,0.6045319726698737,0.15244418261794046],"dir":"ltr"},{"str":"Lower-bound","boundary":[0.34358127412108075,0.15855263877956244,0.44840275733961693,0.1722980396833023],"dir":"ltr"},{"str":"arguments","boundary":[0.4528503762813403,0.15855263877956244,0.5339037838753067,0.1722980396833023],"dir":"ltr"},{"str":"Decision","boundary":[0.34358127412108075,0.17840649584492427,0.41178995821135017,0.19215189674866415],"dir":"ltr"},{"str":"trees","boundary":[0.4162375771530735,0.17840649584492427,0.45379327149698556,0.19215189674866415],"dir":"ltr"},{"str":"P,","boundary":[0.343574157930774,0.1982603529102861,0.35529808146115677,0.21200575381402598],"dir":"ltr"},{"str":"N","boundary":[0.36054627181239035,0.1982603529102861,0.3720922905851042,0.21200575381402598],"dir":"ltr"},{"str":"P","boundary":[0.37438726195903343,0.1982603529102861,0.3839585379216221,0.21200575381402598],"dir":"ltr"},{"str":",","boundary":[0.3868761759473926,0.1982603529102861,0.391323794889116,0.21200575381402598],"dir":"ltr"},{"str":"and","boundary":[0.39577141383083936,0.1982603529102861,0.4244496607670716,0.21200575381402598],"dir":"ltr"},{"str":"NP-complete","boundary":[0.42889550066121823,0.1982603529102861,0.5316906486899052,0.21200575381402598],"dir":"ltr"},{"str":"problems","boundary":[0.5361382676316286,0.1982603529102861,0.6083142278179153,0.21200575381402598],"dir":"ltr"},{"str":"Numerical","boundary":[0.34358127412108075,0.21811420997564795,0.42463468171504726,0.2318596108793878],"dir":"ltr"},{"str":"algorithms","boundary":[0.42908230065677067,0.21811420997564795,0.5111319748936831,0.2318596108793878],"dir":"ltr"},{"str":"Backtracking","boundary":[0.34358127412108075,0.23796944158110017,0.44637464310219105,0.25171484248484005],"dir":"ltr"},{"str":"Branch-and-bound","boundary":[0.34358127412108075,0.25782329864646203,0.4899079373037793,0.2715686995502019],"dir":"ltr"},{"str":"Approximation","boundary":[0.34358127412108075,0.2776771557118239,0.46329338555650673,0.2914225566155637],"dir":"ltr"},{"str":"algorithms","boundary":[0.4677410044982301,0.2776771557118239,0.5497906787351425,0.2914225566155637],"dir":"ltr"},{"str":"for","boundary":[0.5542382976768659,0.2776771557118239,0.5769745257069558,0.2914225566155637],"dir":"ltr"},{"str":"NP-hard","boundary":[0.581411470363219,0.2776771557118239,0.6492661239857273,0.2914225566155637],"dir":"ltr"},{"str":"problems","boundary":[0.6537137429274507,0.2776771557118239,0.7258897031137374,0.2914225566155637],"dir":"ltr"}],"boundary":[0.34357,0.10205,0.72589,0.29142],"dir":"ltr","type":"paragraph"},{"words":[{"str":"9.1–9.4","boundary":[0.7824082655775809,0.10204529566428787,0.8357796928782613,0.11579069656802773],"dir":"ltr"},{"str":"3","boundary":[0.7824189398630413,0.13869878171420058,0.791314177746488,0.15244418261794046],"dir":"ltr"},{"str":"from","boundary":[0.7957617966882115,0.13869878171420058,0.8333174910321235,0.15244418261794046],"dir":"ltr"},{"str":"10.1–10.4","boundary":[0.8377651099738468,0.13869878171420058,0.9089270130414205,0.15244418261794046],"dir":"ltr"},{"str":"11.1","boundary":[0.7824189398630413,0.15855263877956244,0.8135522724551048,0.1722980396833023],"dir":"ltr"},{"str":"11.2","boundary":[0.7824189398630413,0.17840649584492427,0.8135522724551048,0.19215189674866415],"dir":"ltr"},{"str":"11.3","boundary":[0.7824118236727343,0.1982603529102861,0.8135451562647978,0.21200575381402598],"dir":"ltr"},{"str":"11.4","boundary":[0.7824189398630413,0.21811420997564795,0.8135522724551048,0.2318596108793878],"dir":"ltr"},{"str":"(+","boundary":[0.8179998913968282,0.21811420997564795,0.8355946719302857,0.2318596108793878],"dir":"ltr"},{"str":"12.4)","boundary":[0.8400422908720092,0.21811420997564795,0.8780961185373942,0.2318596108793878],"dir":"ltr"},{"str":"12.1","boundary":[0.7824189398630413,0.23796944158110017,0.8135522724551048,0.25171484248484005],"dir":"ltr"},{"str":"12.2","boundary":[0.7824189398630415,0.25782329864646203,0.8135522724551049,0.2715686995502019],"dir":"ltr"},{"str":"12.3","boundary":[0.7824100446251574,0.2776771557118239,0.8135433772172209,0.2914225566155637],"dir":"ltr"}],"boundary":[0.78241,0.10205,0.90893,0.29142],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Acknowledgments","boundary":[0.2391031470848457,0.32156751390513094,0.45128422139799473,0.33989471511011743],"dir":"ltr"},{"str":"I","boundary":[0.2391031470848457,0.35137097726847905,0.24679253460017775,0.3666435427399725],"dir":"ltr"},{"str":"would","boundary":[0.25475866099780964,0.35137097726847905,0.30749718513895596,0.3666435427399725],"dir":"ltr"},{"str":"like","boundary":[0.3154633115365878,0.35137097726847905,0.34732781712711547,0.3666435427399725],"dir":"ltr"},{"str":"to","boundary":[0.3552939435247474,0.35137097726847905,0.37286686255078905,0.3666435427399725],"dir":"ltr"},{"str":"express","boundary":[0.38083298894842094,0.35137097726847905,0.4445422330664548,0.3666435427399725],"dir":"ltr"},{"str":"my","boundary":[0.45250835946408674,0.35137097726847905,0.4788578544716384,0.3666435427399725],"dir":"ltr"},{"str":"gratitude","boundary":[0.48682398086927037,0.35137097726847905,0.5648050444887689,0.3666435427399725],"dir":"ltr"},{"str":"to","boundary":[0.5727711708864008,0.35137097726847905,0.5903440899124425,0.3666435427399725],"dir":"ltr"},{"str":"the","boundary":[0.5983102163100743,0.35137097726847905,0.6257666668468254,0.3666435427399725],"dir":"ltr"},{"str":"reviewers","boundary":[0.6337327932444573,0.35137097726847905,0.7161021448547109,0.3666435427399725],"dir":"ltr"},{"str":"and","boundary":[0.7240682712523429,0.35137097726847905,0.7559327768428704,0.3666435427399725],"dir":"ltr"},{"str":"many","boundary":[0.7638989032405024,0.35137097726847905,0.8111224167986727,0.3666435427399725],"dir":"ltr"},{"str":"readers","boundary":[0.8190885431963045,0.35137097726847905,0.8827977873143386,0.3666435427399725],"dir":"ltr"},{"str":"who","boundary":[0.8907639137119703,0.35137097726847905,0.927016707293253,0.3666435427399725],"dir":"ltr"},{"str":"have","boundary":[0.2391031470848457,0.36969805583427123,0.2797442286568835,0.3849706213057647],"dir":"ltr"},{"str":"shared","boundary":[0.2855557451851807,0.36969805583427123,0.34268255731708197,0.3849706213057647],"dir":"ltr"},{"str":"with","boundary":[0.3484940738453792,0.36969805583427123,0.38583405589284,0.3849706213057647],"dir":"ltr"},{"str":"me","boundary":[0.3916455724211372,0.36969805583427123,0.41799506742868886,0.3849706213057647],"dir":"ltr"},{"str":"their","boundary":[0.42380658395698606,0.36969805583427123,0.4644476655290238,0.3849706213057647],"dir":"ltr"},{"str":"opinions","boundary":[0.4702591820573211,0.36969805583427123,0.5438914918121074,0.3849706213057647],"dir":"ltr"},{"str":"about","boundary":[0.5497030083404046,0.36969805583427123,0.5991404329569738,0.3849706213057647],"dir":"ltr"},{"str":"the","boundary":[0.6049519494852712,0.36969805583427123,0.6324084000220224,0.3849706213057647],"dir":"ltr"},{"str":"first","boundary":[0.6382199165503195,0.36969805583427123,0.6711716106070252,0.3849706213057647],"dir":"ltr"},{"str":"two","boundary":[0.6769831271353225,0.36969805583427123,0.7088278656628286,0.3849706213057647],"dir":"ltr"},{"str":"editions","boundary":[0.714639382191126,0.36969805583427123,0.7827566813629364,0.3849706213057647],"dir":"ltr"},{"str":"of","boundary":[0.7885681978912337,0.36969805583427123,0.8061411169172752,0.3849706213057647],"dir":"ltr"},{"str":"the","boundary":[0.8119526334455724,0.36969805583427123,0.8394090839823236,0.3849706213057647],"dir":"ltr"},{"str":"book","boundary":[0.8452206005106209,0.36969805583427123,0.889182548670257,0.3849706213057647],"dir":"ltr"},{"str":"and","boundary":[0.8949940651985542,0.36969805583427123,0.9268585707890818,0.3849706213057647],"dir":"ltr"},{"str":"suggested","boundary":[0.2391031470848457,0.3880251344000634,0.3225794542242987,0.40329769987155684],"dir":"ltr"},{"str":"improvements","boundary":[0.3306839500630806,0.3880251344000634,0.45369438324537187,0.40329769987155684],"dir":"ltr"},{"str":"and","boundary":[0.4617988790841538,0.3880251344000634,0.49366338467468146,0.40329769987155684],"dir":"ltr"},{"str":"corrections.","boundary":[0.5017678805134633,0.3880251344000634,0.6011764404481801,0.40329769987155684],"dir":"ltr"},{"str":"The","boundary":[0.6092809362869619,0.3880251344000634,0.6425489033520102,0.40329769987155684],"dir":"ltr"},{"str":"third","boundary":[0.6506533991907922,0.3880251344000634,0.6924014362920295,0.40329769987155684],"dir":"ltr"},{"str":"edition","boundary":[0.7005059321308114,0.3880251344000634,0.7609338437872897,0.40329769987155684],"dir":"ltr"},{"str":"has","boundary":[0.7690383396260715,0.3880251344000634,0.7976017456920221,0.40329769987155684],"dir":"ltr"},{"str":"certainly","boundary":[0.8057062415308041,0.3880251344000634,0.8803862056257254,0.40329769987155684],"dir":"ltr"},{"str":"ben-","boundary":[0.8884907014645073,0.3880251344000634,0.9269376390411674,0.40329769987155684],"dir":"ltr"},{"str":"efited","boundary":[0.2391031470848457,0.40635221296585555,0.2874336161722155,0.421624778437349],"dir":"ltr"},{"str":"from","boundary":[0.29593345327142573,0.40635221296585555,0.3376617233096415,0.421624778437349],"dir":"ltr"},{"str":"the","boundary":[0.34616156040885177,0.40635221296585555,0.37361801094560293,0.421624778437349],"dir":"ltr"},{"str":"reviews","boundary":[0.3821178480448132,0.40635221296585555,0.4469142806290251,0.421624778437349],"dir":"ltr"},{"str":"by","boundary":[0.45541411772823526,0.40635221296585555,0.4762881362788539,0.421624778437349],"dir":"ltr"},{"str":"Andrew","boundary":[0.4847879733780641,0.40635221296585555,0.5551784847973377,0.421624778437349],"dir":"ltr"},{"str":"Harrington","boundary":[0.5636783218965479,0.40635221296585555,0.6603392600712874,0.421624778437349],"dir":"ltr"},{"str":"(Loyola","boundary":[0.6688390971704976,0.40635221296585555,0.736956396342308,0.421624778437349],"dir":"ltr"},{"str":"University","boundary":[0.7454562334415183,0.40635221296585555,0.8355149725671038,0.421624778437349],"dir":"ltr"},{"str":"Chicago),","boundary":[0.8440148096663141,0.40635221296585555,0.9269376390411674,0.421624778437349],"dir":"ltr"},{"str":"David","boundary":[0.2391031470848457,0.42467929153164774,0.29182190416297055,0.4399518570031412],"dir":"ltr"},{"str":"Levine","boundary":[0.29482649774222625,0.42467929153164774,0.3541474538695051,0.4399518570031412],"dir":"ltr"},{"str":"(Saint","boundary":[0.3571520474487608,0.42467929153164774,0.40878361606070757,0.4399518570031412],"dir":"ltr"},{"str":"Bonaventure","boundary":[0.41178820963996327,0.42467929153164774,0.5238279228453668,0.4399518570031412],"dir":"ltr"},{"str":"University),","boundary":[0.5268325164246226,0.42467929153164774,0.6295224088208949,0.4399518570031412],"dir":"ltr"},{"str":"Stefano","boundary":[0.6329223436605792,0.42467929153164774,0.6988257317739907,0.4399518570031412],"dir":"ltr"},{"str":"Lombardi","boundary":[0.7018303253532462,0.42467929153164774,0.7875205435510982,0.4399518570031412],"dir":"ltr"},{"str":"(UC","boundary":[0.7905251371303539,0.42467929153164774,0.8289523076439927,0.4399518570031412],"dir":"ltr"},{"str":"Riverside),","boundary":[0.8319569012232485,0.42467929153164774,0.9269771731672103,0.4399518570031412],"dir":"ltr"},{"str":"Daniel","boundary":[0.2391031470848457,0.44300637009743987,0.29731714768292505,0.45827893556893334],"dir":"ltr"},{"str":"McKee","boundary":[0.30243681700547265,0.44300637009743987,0.3648216679010714,0.45827893556893334],"dir":"ltr"},{"str":"(Mansfield","boundary":[0.369941337223619,0.44300637009743987,0.4622139874076035,0.45827893556893334],"dir":"ltr"},{"str":"University),","boundary":[0.46733365673015104,0.44300637009743987,0.5700235491264235,0.45827893556893334],"dir":"ltr"},{"str":"Susan","boundary":[0.5751827525750138,0.44300637009743987,0.6257271327207826,0.45827893556893334],"dir":"ltr"},{"str":"Brilliant","boundary":[0.6308468020433301,0.44300637009743987,0.702245433676696,0.45827893556893334],"dir":"ltr"},{"str":"(Virginia","boundary":[0.7073651029992436,0.44300637009743987,0.7846345523499709,0.45827893556893334],"dir":"ltr"},{"str":"Commonwealth","boundary":[0.7897542216725186,0.44300637009743987,0.9270364743562746,0.45827893556893334],"dir":"ltr"},{"str":"University),","boundary":[0.2391031470848457,0.46133344866323206,0.3417930394811181,0.47660601413472553],"dir":"ltr"},{"str":"David","boundary":[0.348059198458908,0.46133344866323206,0.4007779555370328,0.47660601413472553],"dir":"ltr"},{"str":"Akers","boundary":[0.4067871426955442,0.46133344866323206,0.45960473508877614,0.47660601413472553],"dir":"ltr"},{"str":"(University","boundary":[0.46561392224728765,0.46133344866323206,0.5633620488882053,0.47660601413472553],"dir":"ltr"},{"str":"of","boundary":[0.5693712360467167,0.46133344866323206,0.5869441550727583,0.47660601413472553],"dir":"ltr"},{"str":"Puget","boundary":[0.5929533422312696,0.46133344866323206,0.6423709997848175,0.47660601413472553],"dir":"ltr"},{"str":"Sound),","boundary":[0.6483801869433289,0.46133344866323206,0.7159637754135609,0.47660601413472553],"dir":"ltr"},{"str":"and","boundary":[0.7222299343913507,0.46133344866323206,0.7540944399818783,0.47660601413472553],"dir":"ltr"},{"str":"two","boundary":[0.7601036271403898,0.46133344866323206,0.791948365667896,0.47660601413472553],"dir":"ltr"},{"str":"anonymous","boundary":[0.7979575528264075,0.46133344866323206,0.8968324020595461,0.47660601413472553],"dir":"ltr"},{"str":"re-","boundary":[0.9028415892180573,0.46133344866323206,0.9269969402302316,0.47660601413472553],"dir":"ltr"},{"str":"viewers.","boundary":[0.2391031470848457,0.47966052722902425,0.3077541569582344,0.4949330927005177],"dir":"ltr"},{"str":"My","boundary":[0.27468386052340016,0.49798760579481643,0.3032274995263293,0.5132601712663099],"dir":"ltr"},{"str":"thanks","boundary":[0.30921691962181935,0.49798760579481643,0.3663437317537207,0.5132601712663099],"dir":"ltr"},{"str":"go","boundary":[0.3723331518492107,0.49798760579481643,0.39320717039982933,0.5132601712663099],"dir":"ltr"},{"str":"to","boundary":[0.39919659049531925,0.49798760579481643,0.4167695095213609,0.5132601712663099],"dir":"ltr"},{"str":"all","boundary":[0.4227589296168509,0.49798760579481643,0.4436329481674695,0.5132601712663099],"dir":"ltr"},{"str":"the","boundary":[0.44962236826295954,0.49798760579481643,0.4770788187997107,0.5132601712663099],"dir":"ltr"},{"str":"people","boundary":[0.48306823889520073,0.49798760579481643,0.5413020065563015,0.5132601712663099],"dir":"ltr"},{"str":"at","boundary":[0.5472914266517914,0.49798760579481643,0.5637573901486336,0.5132601712663099],"dir":"ltr"},{"str":"Pearson","boundary":[0.5697468102441235,0.49798760579481643,0.638951297882112,0.5132601712663099],"dir":"ltr"},{"str":"and","boundary":[0.6449407179776021,0.49798760579481643,0.6768052235681297,0.5132601712663099],"dir":"ltr"},{"str":"their","boundary":[0.6827946436636197,0.49798760579481643,0.7234357252356575,0.5132601712663099],"dir":"ltr"},{"str":"associates","boundary":[0.7294251453311476,0.49798760579481643,0.8139886409367786,0.5132601712663099],"dir":"ltr"},{"str":"who","boundary":[0.8199780610322686,0.49798760579481643,0.8562308546135512,0.5132601712663099],"dir":"ltr"},{"str":"worked","boundary":[0.8622202747090413,0.49798760579481643,0.9270364743562746,0.5132601712663099],"dir":"ltr"},{"str":"on","boundary":[0.23910314708484567,0.5163162116171557,0.2610841211646638,0.5315887770886492],"dir":"ltr"},{"str":"my","boundary":[0.2667968023778539,0.5163162116171557,0.29314629738540565,0.5315887770886492],"dir":"ltr"},{"str":"book.","boundary":[0.2988589785985957,0.5163162116171557,0.3477626925135867,0.5315887770886492],"dir":"ltr"},{"str":"I","boundary":[0.3534753737267768,0.5163162116171557,0.36116476124210883,0.5315887770886492],"dir":"ltr"},{"str":"am","boundary":[0.3668774424552989,0.5163162116171557,0.39322693746285065,0.5315887770886492],"dir":"ltr"},{"str":"especially","boundary":[0.39893961867604083,0.5163162116171557,0.48241592581549386,0.5315887770886492],"dir":"ltr"},{"str":"grateful","boundary":[0.488128607028684,0.5163162116171557,0.5551191836082734,0.5315887770886492],"dir":"ltr"},{"str":"to","boundary":[0.5608318648214636,0.5163162116171557,0.5784047838475053,0.5315887770886492],"dir":"ltr"},{"str":"my","boundary":[0.5841174650606953,0.5163162116171557,0.6104669600682471,0.5315887770886492],"dir":"ltr"},{"str":"editor,","boundary":[0.6161796412814372,0.5163162116171557,0.6723971685143533,0.5315887770886492],"dir":"ltr"},{"str":"Matt","boundary":[0.6783075203577575,0.5163162116171557,0.7200160233329519,0.5315887770886492],"dir":"ltr"},{"str":"Goldstein;","boundary":[0.725728704546142,0.5163162116171557,0.8152537329701492,0.5315887770886492],"dir":"ltr"},{"str":"the","boundary":[0.8213419883807463,0.5163162116171557,0.8487984389174975,0.5315887770886492],"dir":"ltr"},{"str":"editorial","boundary":[0.8545111201306876,0.5163162116171557,0.9270167072932531,0.5315887770886492],"dir":"ltr"},{"str":"assistant,","boundary":[0.23910314708484567,0.534644817439495,0.3165307329397445,0.5499173829109885],"dir":"ltr"},{"str":"Chelsea","boundary":[0.3219666752706347,0.534644817439495,0.39006420737942366,0.5499173829109885],"dir":"ltr"},{"str":"Bell;","boundary":[0.39540131439520676,0.534644817439495,0.4354889182026448,0.5499173829109885],"dir":"ltr"},{"str":"the","boundary":[0.44102369584864215,0.534644817439495,0.4684801463853933,0.5499173829109885],"dir":"ltr"},{"str":"marketing","boundary":[0.4738172534011765,0.534644817439495,0.5616818485313845,0.5499173829109885],"dir":"ltr"},{"str":"manager,","boundary":[0.5670189555471677,0.534644817439495,0.6462848782630584,0.5499173829109885],"dir":"ltr"},{"str":"Yez","boundary":[0.6517208205939486,0.534644817439495,0.6839411333188619,0.5499173829109885],"dir":"ltr"},{"str":"Alayan;","boundary":[0.6892782403346449,0.534644817439495,0.7569211299939411,0.5499173829109885],"dir":"ltr"},{"str":"and","boundary":[0.7624559076399385,0.534644817439495,0.7943204132304662,0.5499173829109885],"dir":"ltr"},{"str":"the","boundary":[0.7996575202462494,0.534644817439495,0.8271139707830005,0.5499173829109885],"dir":"ltr"},{"str":"production","boundary":[0.8324510777987837,0.534644817439495,0.9269376390411671,0.5499173829109885],"dir":"ltr"},{"str":"supervisor,","boundary":[0.23910314708484567,0.5529718960052872,0.3326804234282439,0.5682444614767806],"dir":"ltr"},{"str":"Kayla","boundary":[0.3367129042846134,0.5529718960052872,0.38723751736736073,0.5682444614767806],"dir":"ltr"},{"str":"Smith-Tarbox.","boundary":[0.39105256053049453,0.5529718960052872,0.5137467207044432,0.5682444614767806],"dir":"ltr"},{"str":"I","boundary":[0.517561763867577,0.5529718960052872,0.525251151382909,0.5682444614767806],"dir":"ltr"},{"str":"am","boundary":[0.529066194546043,0.5529718960052872,0.5554156895535947,0.5682444614767806],"dir":"ltr"},{"str":"also","boundary":[0.5592307327167286,0.5529718960052872,0.5932893823026338,0.5682444614767806],"dir":"ltr"},{"str":"grateful","boundary":[0.5971044254657677,0.5529718960052872,0.6640950020453571,0.5682444614767806],"dir":"ltr"},{"str":"to","boundary":[0.6679100452084911,0.5529718960052872,0.6854829642345327,0.5682444614767806],"dir":"ltr"},{"str":"Richard","boundary":[0.6892980073976666,0.5529718960052872,0.7585024950356549,0.5682444614767806],"dir":"ltr"},{"str":"Camp","boundary":[0.7623175381987889,0.5529718960052872,0.8139293397477143,0.5682444614767806],"dir":"ltr"},{"str":"for","boundary":[0.8177443829108483,0.5529718960052872,0.8430066894522219,0.5682444614767806],"dir":"ltr"},{"str":"copyedit-","boundary":[0.8468217326153556,0.5529718960052872,0.9269969402302317,0.5682444614767806],"dir":"ltr"},{"str":"ing","boundary":[0.23910314708484567,0.5712989745710794,0.2654724091554188,0.5865715400425728],"dir":"ltr"},{"str":"the","boundary":[0.2699199983352381,0.5712989745710794,0.29737644887198933,0.5865715400425728],"dir":"ltr"},{"str":"book,","boundary":[0.3018240380518086,0.5712989745710794,0.3507277519667995,0.5865715400425728],"dir":"ltr"},{"str":"Paul","boundary":[0.35527417646172593,0.5712989745710794,0.3937211140383862,0.5865715400425728],"dir":"ltr"},{"str":"Anagnostopoulos","boundary":[0.39816870321820547,0.5712989745710794,0.5498809119075974,0.5865715400425728],"dir":"ltr"},{"str":"of","boundary":[0.5543285010874167,0.5712989745710794,0.5719014201134583,0.5865715400425728],"dir":"ltr"},{"str":"Windfall","boundary":[0.5763490092932777,0.5712989745710794,0.6503173591194281,0.5865715400425728],"dir":"ltr"},{"str":"Software","boundary":[0.6547649482992474,0.5712989745710794,0.7316390563895464,0.5865715400425728],"dir":"ltr"},{"str":"and","boundary":[0.7360866455693658,0.5712989745710794,0.7679511511598933,0.5865715400425728],"dir":"ltr"},{"str":"Jacqui","boundary":[0.7723987403397127,0.5712989745710794,0.82584887874963,0.5865715400425728],"dir":"ltr"},{"str":"Scarlott","boundary":[0.8302964679294493,0.5712989745710794,0.8972870445090388,0.5865715400425728],"dir":"ltr"},{"str":"for","boundary":[0.901734633688858,0.5712989745710794,0.9269969402302316,0.5865715400425728],"dir":"ltr"},{"str":"its","boundary":[0.23910314708484567,0.5896260531368714,0.2588702101062648,0.6048986186083649],"dir":"ltr"},{"str":"project","boundary":[0.2643654536262194,0.5896260531368714,0.3247735982196762,0.6048986186083649],"dir":"ltr"},{"str":"management","boundary":[0.3302688417396307,0.5896260531368714,0.4411818323528135,0.6048986186083649],"dir":"ltr"},{"str":"and","boundary":[0.4466770758727681,0.5896260531368714,0.47854158146329573,0.6048986186083649],"dir":"ltr"},{"str":"typesetting,","boundary":[0.48403682498325024,0.5896260531368714,0.5830698107205601,0.6048986186083649],"dir":"ltr"},{"str":"and","boundary":[0.5887034236816646,0.5896260531368714,0.6205679292721923,0.6048986186083649],"dir":"ltr"},{"str":"MaryEllen","boundary":[0.6260631727921467,0.5896260531368714,0.7183160559131098,0.6048986186083649],"dir":"ltr"},{"str":"Oliver","boundary":[0.7238112994330643,0.5896260531368714,0.7787242005065667,0.6048986186083649],"dir":"ltr"},{"str":"for","boundary":[0.7842194440265211,0.5896260531368714,0.8094817505678947,0.6048986186083649],"dir":"ltr"},{"str":"proofreading","boundary":[0.8149769940878494,0.5896260531368714,0.9270364743562745,0.6048986186083649],"dir":"ltr"},{"str":"the","boundary":[0.23910314708484567,0.6079531317026636,0.26655959762159687,0.6232256971741571],"dir":"ltr"},{"str":"book.","boundary":[0.27150136337695163,0.6079531317026636,0.32040507729194256,0.6232256971741571],"dir":"ltr"},{"str":"Finally,","boundary":[0.27468386052340016,0.6262802102684557,0.3363966312762707,0.6415527757399492],"dir":"ltr"},{"str":"I","boundary":[0.3438685810983671,0.6262802102684557,0.35155796861369915,0.6415527757399492],"dir":"ltr"},{"str":"am","boundary":[0.35851597479723873,0.6262802102684557,0.38486546980479047,0.6415527757399492],"dir":"ltr"},{"str":"indebted","boundary":[0.39182347598832995,0.6262802102684557,0.46763016267547236,0.6415527757399492],"dir":"ltr"},{"str":"to","boundary":[0.47458816885901184,0.6262802102684557,0.49216108788505347,0.6415527757399492],"dir":"ltr"},{"str":"two","boundary":[0.499119094068593,0.6262802102684557,0.5309638325960992,0.6415527757399492],"dir":"ltr"},{"str":"members","boundary":[0.5379218387796388,0.6262802102684557,0.6169900908653153,0.6415527757399492],"dir":"ltr"},{"str":"of","boundary":[0.6239480970488549,0.6262802102684557,0.6415210160748964,0.6415527757399492],"dir":"ltr"},{"str":"my","boundary":[0.648479022258436,0.6262802102684557,0.6748285172659878,0.6415527757399492],"dir":"ltr"},{"str":"family.","boundary":[0.6817865234495272,0.6262802102684557,0.7387156649512143,0.6415527757399492],"dir":"ltr"},{"str":"Living","boundary":[0.7456736711347539,0.6262802102684557,0.8006063392712778,0.6415527757399492],"dir":"ltr"},{"str":"with","boundary":[0.8075643454548173,0.6262802102684557,0.8449043275022781,0.6415527757399492],"dir":"ltr"},{"str":"a","boundary":[0.8518623336858174,0.6262802102684557,0.861745865196527,0.6415527757399492],"dir":"ltr"},{"str":"spouse","boundary":[0.8687038713800667,0.6262802102684557,0.9269376390411674,0.6415527757399492],"dir":"ltr"},{"str":"writing","boundary":[0.23910314708484567,0.6446072888342479,0.29951129167830254,0.6598798543057414],"dir":"ltr"},{"str":"a","boundary":[0.3062913942946493,0.6446072888342479,0.3161749258053589,0.6598798543057414],"dir":"ltr"},{"str":"book","boundary":[0.3229550284217057,0.6446072888342479,0.36691697658134187,0.6598798543057414],"dir":"ltr"},{"str":"is","boundary":[0.3736970791976886,0.6446072888342479,0.38688171023297513,0.6598798543057414],"dir":"ltr"},{"str":"probably","boundary":[0.3936618128493219,0.6446072888342479,0.4705754550656638,0.6598798543057414],"dir":"ltr"},{"str":"more","boundary":[0.47735555768201055,0.6446072888342479,0.5223849272448033,0.6598798543057414],"dir":"ltr"},{"str":"trying","boundary":[0.5291650298611501,0.6446072888342479,0.5796896429438975,0.6598798543057414],"dir":"ltr"},{"str":"than","boundary":[0.5864697455602442,0.6446072888342479,0.6249166831369044,0.6598798543057414],"dir":"ltr"},{"str":"doing","boundary":[0.6316967857532512,0.6446072888342479,0.6800470219036424,0.6598798543057414],"dir":"ltr"},{"str":"the","boundary":[0.6868271245199892,0.6446072888342479,0.7142835750567403,0.6598798543057414],"dir":"ltr"},{"str":"actual","boundary":[0.7210636776730871,0.6446072888342479,0.7726754792220124,0.6598798543057414],"dir":"ltr"},{"str":"writing.","boundary":[0.7794555818383592,0.6446072888342479,0.8444496850527853,0.6598798543057414],"dir":"ltr"},{"str":"My","boundary":[0.8512297876691322,0.6446072888342479,0.8797734266720614,0.6598798543057414],"dir":"ltr"},{"str":"wife,","boundary":[0.886553529288408,0.6446072888342479,0.9269969402302316,0.6598798543057414],"dir":"ltr"},{"str":"Maria,","boundary":[0.23910314708484567,0.6629343674000401,0.2956567143891258,0.6782069328715336],"dir":"ltr"},{"str":"lived","boundary":[0.29961012699340966,0.6629343674000401,0.34135816409464687,0.6782069328715336],"dir":"ltr"},{"str":"through","boundary":[0.3450546048796523,0.6629343674000401,0.4131719040514626,0.6782069328715336],"dir":"ltr"},{"str":"several","boundary":[0.416868344836468,0.6629343674000401,0.47727648942992484,0.6782069328715336],"dir":"ltr"},{"str":"years","boundary":[0.4809729302149302,0.6629343674000401,0.5260022997777231,0.6782069328715336],"dir":"ltr"},{"str":"of","boundary":[0.5296987405627285,0.6629343674000401,0.5472716595887701,0.6782069328715336],"dir":"ltr"},{"str":"this,","boundary":[0.5509681003737754,0.6629343674000401,0.5855802277242803,0.6782069328715336],"dir":"ltr"},{"str":"helping","boundary":[0.589533640328564,0.6629343674000401,0.6532626515096194,0.6782069328715336],"dir":"ltr"},{"str":"me","boundary":[0.6569590922946248,0.6629343674000401,0.6833085873021766,0.6782069328715336],"dir":"ltr"},{"str":"any","boundary":[0.6870050280871819,0.6629343674000401,0.7177625781485101,0.6782069328715336],"dir":"ltr"},{"str":"way","boundary":[0.7214590189335154,0.6629343674000401,0.7554979014563991,0.6782069328715336],"dir":"ltr"},{"str":"she","boundary":[0.7591943422414047,0.6629343674000401,0.7877577483073553,0.6782069328715336],"dir":"ltr"},{"str":"could.","boundary":[0.7914541890923608,0.6629343674000401,0.8436392354689073,0.6782069328715336],"dir":"ltr"},{"str":"And","boundary":[0.8473356762539127,0.6629343674000401,0.8858814491456801,0.6782069328715336],"dir":"ltr"},{"str":"help","boundary":[0.8895778899306853,0.6629343674000401,0.9269376390411674,0.6782069328715336],"dir":"ltr"},{"str":"she","boundary":[0.23910314708484567,0.6812614459658322,0.26766655315079635,0.6965340114373256],"dir":"ltr"},{"str":"did:","boundary":[0.27416991688484327,0.6812614459658322,0.3065879002399706,0.6965340114373256],"dir":"ltr"},{"str":"over","boundary":[0.3130912639740175,0.6812614459658322,0.3515382015506778,0.6965340114373256],"dir":"ltr"},{"str":"400","boundary":[0.3580415652847246,0.6812614459658322,0.3876921598168533,0.6965340114373256],"dir":"ltr"},{"str":"figures","boundary":[0.3941955235509002,0.6812614459658322,0.45132233568280156,0.6965340114373256],"dir":"ltr"},{"str":"in","boundary":[0.4578256994168485,0.6812614459658322,0.474311429976712,0.6965340114373256],"dir":"ltr"},{"str":"the","boundary":[0.4808147937107589,0.6812614459658322,0.5082712442475101,0.6965340114373256],"dir":"ltr"},{"str":"book","boundary":[0.5147746079815569,0.6812614459658322,0.5587365561411931,0.6965340114373256],"dir":"ltr"},{"str":"and","boundary":[0.56523991987524,0.6812614459658322,0.5971044254657677,0.6965340114373256],"dir":"ltr"},{"str":"the","boundary":[0.6036077891998146,0.6812614459658322,0.6310642397365658,0.6965340114373256],"dir":"ltr"},{"str":"Instructor’s","boundary":[0.6375676034706127,0.6812614459658322,0.7360668785063443,0.6965340114373256],"dir":"ltr"},{"str":"Manual","boundary":[0.742570242240391,0.6812614459658322,0.8084736303538025,0.6965340114373256],"dir":"ltr"},{"str":"were","boundary":[0.8149769940878494,0.6812614459658322,0.8567052641260652,0.6965340114373256],"dir":"ltr"},{"str":"created","boundary":[0.8632086278601121,0.6812614459658322,0.9268981049151246,0.6965340114373256],"dir":"ltr"},{"str":"by","boundary":[0.23910314708484567,0.6995885245316242,0.2599771656354643,0.7148610900031177],"dir":"ltr"},{"str":"her.","boundary":[0.266282858739297,0.6995885245316242,0.29943222342621684,0.7148610900031177],"dir":"ltr"},{"str":"My","boundary":[0.3057379165300496,0.6995885245316242,0.33428155553297884,0.7148610900031177],"dir":"ltr"},{"str":"daughter","boundary":[0.3405872486368115,0.6995885245316242,0.41748112379013197,0.7148610900031177],"dir":"ltr"},{"str":"Miriam","boundary":[0.4237868168939647,0.6995885245316242,0.4874762939489771,0.7148610900031177],"dir":"ltr"},{"str":"has","boundary":[0.4937819870528099,0.6995885245316242,0.5223453931187605,0.7148610900031177],"dir":"ltr"},{"str":"been","boundary":[0.5286510862225933,0.6995885245316242,0.5703991233238305,0.7148610900031177],"dir":"ltr"},{"str":"my","boundary":[0.5767048164276632,0.6995885245316242,0.603054311435215,0.7148610900031177],"dir":"ltr"},{"str":"English","boundary":[0.6093600045390475,0.6995885245316242,0.6741762041862809,0.7148610900031177],"dir":"ltr"},{"str":"prose","boundary":[0.6804818972901137,0.6995885245316242,0.7277251779113053,0.7148610900031177],"dir":"ltr"},{"str":"guru","boundary":[0.7340308710151381,0.6995885245316242,0.7735847641209977,0.7148610900031177],"dir":"ltr"},{"str":"over","boundary":[0.7798904572248303,0.6995885245316242,0.8183373948014905,0.7148610900031177],"dir":"ltr"},{"str":"many","boundary":[0.8246430879053233,0.6995885245316242,0.8718666014634936,0.7148610900031177],"dir":"ltr"},{"str":"years.","boundary":[0.8781722945673266,0.6995885245316242,0.927056241419296,0.7148610900031177],"dir":"ltr"},{"str":"She","boundary":[0.23910314708484567,0.7179156030974164,0.27096765267537337,0.7331881685689099],"dir":"ltr"},{"str":"read","boundary":[0.2766407997625206,0.7179156030974164,0.31508773733918083,0.7331881685689099],"dir":"ltr"},{"str":"large","boundary":[0.32076088442632816,0.7179156030974164,0.3635961099937434,0.7331881685689099],"dir":"ltr"},{"str":"portions","boundary":[0.3692692570808907,0.7179156030974164,0.4406876557772781,0.7331881685689099],"dir":"ltr"},{"str":"of","boundary":[0.4463608028644253,0.7179156030974164,0.46393372189046694,0.7331881685689099],"dir":"ltr"},{"str":"the","boundary":[0.4696068689776142,0.7179156030974164,0.4970633195143654,0.7331881685689099],"dir":"ltr"},{"str":"book","boundary":[0.5027364666015127,0.7179156030974164,0.5466984147611489,0.7331881685689099],"dir":"ltr"},{"str":"and","boundary":[0.5523715618482963,0.7179156030974164,0.5842360674388238,0.7331881685689099],"dir":"ltr"},{"str":"was","boundary":[0.589909214525971,0.7179156030974164,0.6217539530534772,0.7331881685689099],"dir":"ltr"},{"str":"instrumental","boundary":[0.6274271001406245,0.7179156030974164,0.7361657138214512,0.7331881685689099],"dir":"ltr"},{"str":"in","boundary":[0.7418388609085985,0.7179156030974164,0.758324591468462,0.7331881685689099],"dir":"ltr"},{"str":"finding","boundary":[0.7639977385556093,0.7179156030974164,0.8233384617459095,0.7331881685689099],"dir":"ltr"},{"str":"the","boundary":[0.8290116088330569,0.7179156030974164,0.8564680593698081,0.7331881685689099],"dir":"ltr"},{"str":"chapter","boundary":[0.8621412064569555,0.7179156030974164,0.9269376390411673,0.7331881685689099],"dir":"ltr"},{"str":"epigraphs.","boundary":[0.23910314708484567,0.7362426816632086,0.32645379857649687,0.7515152471347021],"dir":"ltr"},{"str":"Anany","boundary":[0.23910314708484567,0.7728968387947929,0.29622995921674694,0.7881694042662862],"dir":"ltr"},{"str":"Levitin","boundary":[0.30117172497210176,0.7728968387947929,0.36157986956555865,0.7881694042662862],"dir":"ltr"},{"str":"[email protected]","boundary":[0.23910314708484567,0.791223917360585,0.4801229465050093,0.8064964828320784],"dir":"ltr"},{"str":"June","boundary":[0.23910314708484567,0.8095509959263772,0.2787558755058125,0.8248235613978706],"dir":"ltr"},{"str":"2011","boundary":[0.28369764126116725,0.8095509959263772,0.3232317673040055,0.8248235613978706],"dir":"ltr"}],"boundary":[0.2391,0.32157,0.92706,0.82482],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":27,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/95f208ae1292e7eddc77aa847ac23838.jpg","blurred":"/storage/books/4a8b03583f119702/pages/621cbe7ceb1be417ccc77fef29864a35.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07291,0.05179]},"elements":[{"words":[{"str":"1","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Introduction","boundary":[0.14421784044919886,0.17005356781848974,0.44077198442161075,0.20670781659232623],"dir":"ltr"},{"str":"Two","boundary":[0.23910077902799318,0.27356867751590624,0.2753535742636693,0.2888412428469236],"dir":"ltr"},{"str":"ideas","boundary":[0.2805523120755465,0.27356867751590624,0.3233875395977439,0.2888412428469236],"dir":"ltr"},{"str":"lie","boundary":[0.3285862774096211,0.27356867751590624,0.34835334133310863,0.2888412428469236],"dir":"ltr"},{"str":"gleaming","boundary":[0.35355207914498576,0.27356867751590624,0.4304261907434287,0.2888412428469236],"dir":"ltr"},{"str":"on","boundary":[0.43562492855530593,0.27356867751590624,0.45760590363822407,0.2888412428469236],"dir":"ltr"},{"str":"the","boundary":[0.46280464145010125,0.27356867751590624,0.4880669491443183,0.2888412428469236],"dir":"ltr"},{"str":"jeweler’s","boundary":[0.4932656869561955,0.27356867751590624,0.5635375992041936,0.2888412428469236],"dir":"ltr"},{"str":"velvet.","boundary":[0.5687363370160708,0.27356867751590624,0.6219888072259462,0.2888412428469236],"dir":"ltr"},{"str":"The","boundary":[0.6271875450378234,0.27356867751590624,0.660139240598277,0.2888412428469236],"dir":"ltr"},{"str":"first","boundary":[0.6653379784101544,0.27356867751590624,0.6972024854548162,0.2888412428469236],"dir":"ltr"},{"str":"is","boundary":[0.7024012232666934,0.27356867751590624,0.7155858549036596,0.2888412428469236],"dir":"ltr"},{"str":"the","boundary":[0.720784592715537,0.27356867751590624,0.7460469004097539,0.2888412428469236],"dir":"ltr"},{"str":"calculus,","boundary":[0.7512456382216312,0.27356867751590624,0.8231977509031256,0.2888412428469236],"dir":"ltr"},{"str":"the","boundary":[0.8284557899067733,0.27356867751590624,0.8537180976009903,0.2888412428469236],"dir":"ltr"},{"str":"second,","boundary":[0.23910077902799318,0.29189575591312705,0.30225654826353576,0.3071683212441444],"dir":"ltr"},{"str":"the","boundary":[0.30905641825321545,0.29189575591312705,0.3343187259474325,0.3071683212441444],"dir":"ltr"},{"str":"algorithm.","boundary":[0.34074302172256593,0.29189575591312705,0.4280739101365338,0.3071683212441444],"dir":"ltr"},{"str":"The","boundary":[0.43449820591166716,0.29189575591312705,0.4674499014721208,0.3071683212441444],"dir":"ltr"},{"str":"calculus","boundary":[0.4738741972472542,0.29189575591312705,0.5419717324636687,0.3071683212441444],"dir":"ltr"},{"str":"and","boundary":[0.5483960282388022,0.29189575591312705,0.580260535283464,0.3071683212441444],"dir":"ltr"},{"str":"the","boundary":[0.5866848310585975,0.29189575591312705,0.6119471387528145,0.3071683212441444],"dir":"ltr"},{"str":"rich","boundary":[0.618371434527948,0.29189575591312705,0.6510859253213198,0.3071683212441444],"dir":"ltr"},{"str":"body","boundary":[0.6575102210964532,0.29189575591312705,0.7003652156825741,0.3071683212441444],"dir":"ltr"},{"str":"of","boundary":[0.7067895114577075,0.29189575591312705,0.7243624312856879,0.3071683212441444],"dir":"ltr"},{"str":"mathematical","boundary":[0.7307867270608214,0.29189575591312705,0.843893866831017,0.3071683212441444],"dir":"ltr"},{"str":"analysis","boundary":[0.23910077902799318,0.31022436156688094,0.3061111257286158,0.3254969268978983],"dir":"ltr"},{"str":"to","boundary":[0.31016337383293074,0.31022436156688094,0.32664910514511936,0.3254969268978983],"dir":"ltr"},{"str":"which","boundary":[0.3307013532494343,0.31022436156688094,0.3809887638707865,0.3254969268978983],"dir":"ltr"},{"str":"it","boundary":[0.38504101197510143,0.31022436156688094,0.3960314995165605,0.3254969268978983],"dir":"ltr"},{"str":"gave","boundary":[0.4000837476208754,0.31022436156688094,0.4385109198881351,0.3254969268978983],"dir":"ltr"},{"str":"rise","boundary":[0.4425631679924501,0.31022436156688094,0.4722137638776813,0.3254969268978983],"dir":"ltr"},{"str":"made","boundary":[0.47626601198199625,0.31022436156688094,0.5223825721154927,0.3254969268978983],"dir":"ltr"},{"str":"modern","boundary":[0.5264348202198075,0.31022436156688094,0.592338211340715,0.3254969268978983],"dir":"ltr"},{"str":"science","boundary":[0.5963904594450298,0.31022436156688094,0.6556718841515689,0.3254969268978983],"dir":"ltr"},{"str":"possible;","boundary":[0.6597241322558837,0.31022436156688094,0.7327832005170934,0.3254969268978983],"dir":"ltr"},{"str":"but","boundary":[0.7371319545802609,0.31022436156688094,0.7646081734339085,0.3254969268978983],"dir":"ltr"},{"str":"it","boundary":[0.7686604215382232,0.31022436156688094,0.7796509090796824,0.3254969268978983],"dir":"ltr"},{"str":"has","boundary":[0.7837031571839973,0.31022436156688094,0.8122665645534368,0.3254969268978983],"dir":"ltr"},{"str":"been","boundary":[0.8163188126577516,0.31022436156688094,0.8558529405047266,0.3254969268978983],"dir":"ltr"},{"str":"the","boundary":[0.23910077902799318,0.32855143996410174,0.2643630867222102,0.3438240052951191],"dir":"ltr"},{"str":"algorithm","boundary":[0.2693048527030821,0.32855143996410174,0.351693975136178,0.3438240052951191],"dir":"ltr"},{"str":"that","boundary":[0.3566357411170499,0.32855143996410174,0.38850024816171175,0.3438240052951191],"dir":"ltr"},{"str":"has","boundary":[0.39344201414258356,0.32855143996410174,0.422005421512023,0.3438240052951191],"dir":"ltr"},{"str":"made","boundary":[0.42694718749289495,0.32855143996410174,0.4730637476263913,0.3438240052951191],"dir":"ltr"},{"str":"possible","boundary":[0.4780055136072631,0.32855143996410174,0.5461228158876011,0.3438240052951191],"dir":"ltr"},{"str":"the","boundary":[0.5510645818684731,0.32855143996410174,0.5763268895626901,0.3438240052951191],"dir":"ltr"},{"str":"modern","boundary":[0.5812686555435619,0.32855143996410174,0.6471720466644693,0.3438240052951191],"dir":"ltr"},{"str":"world.","boundary":[0.6521138126453411,0.32855143996410174,0.7064930054988552,0.3438240052951191],"dir":"ltr"},{"str":"—David","boundary":[0.4203706242541207,0.350477465498943,0.48923237476499226,0.36498644855310686],"dir":"ltr"},{"str":"Berlinski,","boundary":[0.49394584609802433,0.350477465498943,0.5727415660717404,0.36498644855310686],"dir":"ltr"},{"str":"The","boundary":[0.5774700604209735,0.350477465498943,0.6087742704295972,0.36498644855310686],"dir":"ltr"},{"str":"Advent","boundary":[0.6134877417626293,0.350477465498943,0.6719272747841271,0.36498644855310686],"dir":"ltr"},{"str":"of","boundary":[0.6766407461171592,0.350477465498943,0.6933350728704084,0.36498644855310686],"dir":"ltr"},{"str":"the","boundary":[0.6980485442034404,0.350477465498943,0.7220478125843769,0.36498644855310686],"dir":"ltr"},{"str":"Algorithm,","boundary":[0.7267612839174089,0.350477465498943,0.814946389016687,0.36498644855310686],"dir":"ltr"},{"str":"2000","boundary":[0.8181068560499511,0.350477465498943,0.855664396552199,0.36498644855310686],"dir":"ltr"},{"str":"hy","boundary":[0.2984023676238612,0.4426681961123095,0.319276387127064,0.45794076144332685],"dir":"ltr"},{"str":"do","boundary":[0.32611579124459067,0.4426681961123095,0.34809676632750874,0.45794076144332685],"dir":"ltr"},{"str":"you","boundary":[0.3549361704450355,0.4426681961123095,0.3868006774896974,0.45794076144332685],"dir":"ltr"},{"str":"need","boundary":[0.393640081607224,0.4426681961123095,0.4353881206136296,0.45794076144332685],"dir":"ltr"},{"str":"to","boundary":[0.44222752473115623,0.4426681961123095,0.45980044455913666,0.45794076144332685],"dir":"ltr"},{"str":"study","boundary":[0.46663984867666336,0.4426681961123095,0.5127761758740832,0.45794076144332685],"dir":"ltr"},{"str":"algorithms?","boundary":[0.5196155799916098,0.4426681961123095,0.6206648107684779,0.45794076144332685],"dir":"ltr"},{"str":"If","boundary":[0.6275042148860047,0.4426681961123095,0.6417760350387627,0.45794076144332685],"dir":"ltr"},{"str":"you","boundary":[0.6486154391562893,0.4426681961123095,0.6804799462009511,0.45794076144332685],"dir":"ltr"},{"str":"are","boundary":[0.6873193503184779,0.4426681961123095,0.714775802108202,0.45794076144332685],"dir":"ltr"},{"str":"going","boundary":[0.7216152062257287,0.4426681961123095,0.7688584890028639,0.45794076144332685],"dir":"ltr"},{"str":"to","boundary":[0.7756978931203905,0.4426681961123095,0.793270812948371,0.45794076144332685],"dir":"ltr"},{"str":"be","boundary":[0.8001102170658976,0.4426681961123095,0.8209842365691004,0.45794076144332685],"dir":"ltr"},{"str":"a","boundary":[0.8278236406866271,0.4426681961123095,0.8377071726483708,0.45794076144332685],"dir":"ltr"},{"str":"computer","boundary":[0.8445465767658975,0.4426681961123095,0.92691593213507,0.45794076144332685],"dir":"ltr"},{"str":"professional,","boundary":[0.2984023676238612,0.4609952745095303,0.4077142311207471,0.47626783984054766],"dir":"ltr"},{"str":"there","boundary":[0.41174671216113856,0.4609952745095303,0.4567760837788431,0.47626783984054766],"dir":"ltr"},{"str":"are","boundary":[0.4605713600521527,0.4609952745095303,0.4880278118418769,0.47626783984054766],"dir":"ltr"},{"str":"both","boundary":[0.4918230881151864,0.4609952745095303,0.5313769830260849,0.47626783984054766],"dir":"ltr"},{"str":"practical","boundary":[0.5351722592993945,0.4609952745095303,0.608745271222615,0.47626783984054766],"dir":"ltr"},{"str":"and","boundary":[0.6125405474959247,0.4609952745095303,0.6444050545405865,0.47626783984054766],"dir":"ltr"},{"str":"theoretical","boundary":[0.648200330813896,0.4609952745095303,0.7404532181448122,0.47626783984054766],"dir":"ltr"},{"str":"reasons","boundary":[0.7442484944181218,0.4609952745095303,0.8090646970232374,0.47626783984054766],"dir":"ltr"},{"str":"to","boundary":[0.8128599732965469,0.4609952745095303,0.8304328931245274,0.47626783984054766],"dir":"ltr"},{"str":"study","boundary":[0.834228169397837,0.4609952745095303,0.8803644965952568,0.47626783984054766],"dir":"ltr"},{"str":"algo-","boundary":[0.8841597728685664,0.4609952745095303,0.9269950003907639,0.47626783984054766],"dir":"ltr"},{"str":"rithms.W","boundary":[0.23910077902799318,0.44136851990369436,0.2984021692111584,0.49459491823776847],"dir":"ltr"},{"str":"From","boundary":[0.30198020619401245,0.4793223529067512,0.34847234054205506,0.49459491823776847],"dir":"ltr"},{"str":"a","boundary":[0.35258388983814043,0.4793223529067512,0.3624674217998842,0.49459491823776847],"dir":"ltr"},{"str":"practical","boundary":[0.3665789710959696,0.4793223529067512,0.4401519830191901,0.49459491823776847],"dir":"ltr"},{"str":"standpoint,","boundary":[0.44426353231527554,0.4793223529067512,0.5403907641751954,0.49459491823776847],"dir":"ltr"},{"str":"you","boundary":[0.5446802170465921,0.4793223529067512,0.5765447240912539,0.49459491823776847],"dir":"ltr"},{"str":"have","boundary":[0.5806562733873393,0.4793223529067512,0.6212973568140295,0.49459491823776847],"dir":"ltr"},{"str":"to","boundary":[0.625408906110115,0.4793223529067512,0.6429818259380954,0.49459491823776847],"dir":"ltr"},{"str":"know","boundary":[0.6470933752341808,0.4793223529067512,0.6943366580113158,0.49459491823776847],"dir":"ltr"},{"str":"a","boundary":[0.6984482073074012,0.4793223529067512,0.7083317392691448,0.49459491823776847],"dir":"ltr"},{"str":"standard","boundary":[0.7124432885652303,0.4793223529067512,0.7871430231320896,0.49459491823776847],"dir":"ltr"},{"str":"set","boundary":[0.791254572428175,0.4793223529067512,0.8154099245426767,0.49459491823776847],"dir":"ltr"},{"str":"of","boundary":[0.8195214738387622,0.4793223529067512,0.8370943936667427,0.49459491823776847],"dir":"ltr"},{"str":"important","boundary":[0.8412059429628279,0.4793223529067512,0.9268763980072228,0.49459491823776847],"dir":"ltr"},{"str":"algorithms","boundary":[0.23910117585339866,0.497649431303972,0.33026687466852306,0.5129219966349893],"dir":"ltr"},{"str":"from","boundary":[0.33566328311963517,0.497649431303972,0.37739155506211725,0.5129219966349893],"dir":"ltr"},{"str":"different","boundary":[0.38278796351322936,0.497649431303972,0.4574679310161652,0.5129219966349893],"dir":"ltr"},{"str":"areas","boundary":[0.46286433946727723,0.497649431303972,0.5078937110849817,0.5129219966349893],"dir":"ltr"},{"str":"of","boundary":[0.5132901195360939,0.497649431303972,0.5308630393640743,0.5129219966349893],"dir":"ltr"},{"str":"computing;","boundary":[0.5362594478151863,0.497649431303972,0.6323669126111826,0.5129219966349893],"dir":"ltr"},{"str":"in","boundary":[0.637980758765453,0.497649431303972,0.6544664900776416,0.5129219966349893],"dir":"ltr"},{"str":"addition,","boundary":[0.6598628985287537,0.497649431303972,0.7362230664651859,0.5129219966349893],"dir":"ltr"},{"str":"you","boundary":[0.7417183102359154,0.497649431303972,0.7735828172805772,0.5129219966349893],"dir":"ltr"},{"str":"should","boundary":[0.7789792257316894,0.497649431303972,0.8361258075344918,0.5129219966349893],"dir":"ltr"},{"str":"be","boundary":[0.8415222159856038,0.497649431303972,0.8623962354888065,0.5129219966349893],"dir":"ltr"},{"str":"able","boundary":[0.8677926439399187,0.497649431303972,0.9040454391755948,0.5129219966349893],"dir":"ltr"},{"str":"to","boundary":[0.9094418476267069,0.497649431303972,0.9270147674546874,0.5129219966349893],"dir":"ltr"},{"str":"design","boundary":[0.23910117585339866,0.5159765097011928,0.29403384649677045,0.5312490750322101],"dir":"ltr"},{"str":"new","boundary":[0.3006755799750623,0.5159765097011928,0.335821419631023,0.5312490750322101],"dir":"ltr"},{"str":"algorithms","boundary":[0.34246315310931486,0.5159765097011928,0.43362885192443923,0.5312490750322101],"dir":"ltr"},{"str":"and","boundary":[0.44027058540273106,0.5159765097011928,0.47213509244739293,0.5312490750322101],"dir":"ltr"},{"str":"analyze","boundary":[0.47877682592568466,0.5159765097011928,0.5435732614668767,0.5312490750322101],"dir":"ltr"},{"str":"their","boundary":[0.5502149949451685,0.5159765097011928,0.5908560783718588,0.5312490750322101],"dir":"ltr"},{"str":"efficiency.","boundary":[0.5974978118501506,0.5159765097011928,0.6815276005888959,0.5312490750322101],"dir":"ltr"},{"str":"From","boundary":[0.6881693340671878,0.5159765097011928,0.7346614684152305,0.5312490750322101],"dir":"ltr"},{"str":"the","boundary":[0.7413032018935223,0.5159765097011928,0.7687596536832464,0.5312490750322101],"dir":"ltr"},{"str":"theoretical","boundary":[0.7754013871615382,0.5159765097011928,0.8676542744924544,0.5312490750322101],"dir":"ltr"},{"str":"stand-","boundary":[0.8742960079707461,0.5159765097011928,0.9270147674546874,0.5312490750322101],"dir":"ltr"},{"str":"point,","boundary":[0.23910117585339866,0.5343035880984136,0.2890920805158986,0.5495761534294309],"dir":"ltr"},{"str":"the","boundary":[0.2969593719574466,0.5343035880984136,0.32441582374717076,0.5495761534294309],"dir":"ltr"},{"str":"study","boundary":[0.33169010327101417,0.5343035880984136,0.37782643046843395,0.5495761534294309],"dir":"ltr"},{"str":"of","boundary":[0.3851007099922774,0.5343035880984136,0.40267362982025784,0.5495761534294309],"dir":"ltr"},{"str":"algorithms,","boundary":[0.4099479093441012,0.5343035880984136,0.5049681856243057,0.5495761534294309],"dir":"ltr"},{"str":"sometimes","boundary":[0.5128354770658538,0.5343035880984136,0.6039814088170546,0.5495761534294309],"dir":"ltr"},{"str":"called","boundary":[0.611255688340898,0.5343035880984136,0.661780303729332,0.5495761534294309],"dir":"ltr"},{"str":"algorithmics","boundary":[0.6690980707938071,0.5343035880984136,0.7786273719938513,0.5495761534294309],"dir":"ltr"},{"str":",","boundary":[0.779220383911556,0.5343035880984136,0.7841621498924279,0.5495761534294309],"dir":"ltr"},{"str":"has","boundary":[0.7920294413339759,0.5343035880984136,0.8205928487034154,0.5495761534294309],"dir":"ltr"},{"str":"come","boundary":[0.8278671282272587,0.5343035880984136,0.8739836883607551,0.5495761534294309],"dir":"ltr"},{"str":"to","boundary":[0.8812579678845985,0.5343035880984136,0.8988308877125789,0.5495761534294309],"dir":"ltr"},{"str":"be","boundary":[0.9061051672364224,0.5343035880984136,0.9269791867396251,0.5495761534294309],"dir":"ltr"},{"str":"recognized","boundary":[0.23910117585339874,0.5526306664956344,0.3324610187640302,0.5679032318266518],"dir":"ltr"},{"str":"as","boundary":[0.3371458129138967,0.5526306664956344,0.35471873274187715,0.5679032318266518],"dir":"ltr"},{"str":"the","boundary":[0.35940352689174365,0.5526306664956344,0.3868599786814678,0.5679032318266518],"dir":"ltr"},{"str":"cornerstone","boundary":[0.3915447728313344,0.5526306664956344,0.49370095918791784,0.5679032318266518],"dir":"ltr"},{"str":"of","boundary":[0.4983857533377844,0.5526306664956344,0.5159586731657648,0.5679032318266518],"dir":"ltr"},{"str":"computer","boundary":[0.5206434673156313,0.5526306664956344,0.6030128226848037,0.5679032318266518],"dir":"ltr"},{"str":"science.","boundary":[0.6076976168346703,0.5526306664956344,0.6734033373163426,0.5679032318266518],"dir":"ltr"},{"str":"David","boundary":[0.6780881314662093,0.5526306664956344,0.7308068909501505,0.5679032318266518],"dir":"ltr"},{"str":"Harel,","boundary":[0.735491685100017,0.5526306664956344,0.7898511108896076,0.5679032318266518],"dir":"ltr"},{"str":"in","boundary":[0.7945952062312446,0.5526306664956344,0.811080937543433,0.5679032318266518],"dir":"ltr"},{"str":"his","boundary":[0.8157657316932997,0.5526306664956344,0.8399408508717249,0.5679032318266518],"dir":"ltr"},{"str":"delightful","boundary":[0.8446256450215913,0.5526306664956344,0.9270147674546871,0.5679032318266518],"dir":"ltr"},{"str":"book","boundary":[0.23910117585339874,0.5709577448928552,0.28306312601923495,0.5862303102238726],"dir":"ltr"},{"str":"pointedly","boundary":[0.2880048920001068,0.5709577448928552,0.36930682591741093,0.5862303102238726],"dir":"ltr"},{"str":"titled","boundary":[0.3742485918982828,0.5709577448928552,0.41927796351598734,0.5862303102238726],"dir":"ltr"},{"str":"Algorithmics:","boundary":[0.42422170620325156,0.5709577448928552,0.5390090464069435,0.5862303102238726],"dir":"ltr"},{"str":"the","boundary":[0.5439508123878154,0.5709577448928552,0.5692131200820324,0.5862303102238726],"dir":"ltr"},{"str":"Spirit","boundary":[0.5741548860629043,0.5709577448928552,0.6203109803242476,0.5862303102238726],"dir":"ltr"},{"str":"of","boundary":[0.6252527463051194,0.5709577448928552,0.6428256661330999,0.5862303102238726],"dir":"ltr"},{"str":"Computing","boundary":[0.6477674321139717,0.5709577448928552,0.7433411861840339,0.5862303102238726],"dir":"ltr"},{"str":",","boundary":[0.7439776856423702,0.5709577448928552,0.7489194516232421,0.5862303102238726],"dir":"ltr"},{"str":"put","boundary":[0.753861217604114,0.5709577448928552,0.7824246249735534,0.5862303102238726],"dir":"ltr"},{"str":"it","boundary":[0.7873663909544253,0.5709577448928552,0.7994440670116761,0.5862303102238726],"dir":"ltr"},{"str":"as","boundary":[0.8043858329925481,0.5709577448928552,0.8219587528205284,0.5862303102238726],"dir":"ltr"},{"str":"follows:","boundary":[0.8269005188014004,0.5709577448928552,0.8933573877121653,0.5862303102238726],"dir":"ltr"},{"str":"Algorithmics","boundary":[0.2746818909156763,0.5992730810165613,0.38680067748969743,0.6145456463475787],"dir":"ltr"},{"str":"is","boundary":[0.3931656720730604,0.5992730810165613,0.40635030371002656,0.6145456463475787],"dir":"ltr"},{"str":"more","boundary":[0.4127152982933896,0.5992730810165613,0.4577446699110941,0.6145456463475787],"dir":"ltr"},{"str":"than","boundary":[0.4641096644944571,0.5992730810165613,0.5025566038256403,0.6145456463475787],"dir":"ltr"},{"str":"a","boundary":[0.5089215984090033,0.5992730810165613,0.5188051303707469,0.6145456463475787],"dir":"ltr"},{"str":"branch","boundary":[0.52517012495411,0.5992730810165613,0.584491083788496,0.6145456463475787],"dir":"ltr"},{"str":"of","boundary":[0.5908560783718589,0.5992730810165613,0.6084289981998393,0.6145456463475787],"dir":"ltr"},{"str":"computer","boundary":[0.6147939927832023,0.5992730810165613,0.6971633481523748,0.6145456463475787],"dir":"ltr"},{"str":"science.","boundary":[0.7035283427357377,0.5992730810165613,0.7692340632174102,0.6145456463475787],"dir":"ltr"},{"str":"It","boundary":[0.7755990578007731,0.5992730810165613,0.7898708779535311,0.6145456463475787],"dir":"ltr"},{"str":"is","boundary":[0.7962358725368942,0.5992730810165613,0.8094205041738604,0.6145456463475787],"dir":"ltr"},{"str":"the","boundary":[0.8157854987572234,0.5992730810165613,0.8432419505469475,0.6145456463475787],"dir":"ltr"},{"str":"core","boundary":[0.8496069451303103,0.5992730810165613,0.8869469288817783,0.6145456463475787],"dir":"ltr"},{"str":"of","boundary":[0.8933119234651412,0.5992730810165613,0.9108848432931216,0.6145456463475787],"dir":"ltr"},{"str":"computer","boundary":[0.2746818909156763,0.6176001594137821,0.35705124628484874,0.6328727247447995],"dir":"ltr"},{"str":"science,","boundary":[0.36280346188658363,0.6176001594137821,0.4285091823682561,0.6328727247447995],"dir":"ltr"},{"str":"and,","boundary":[0.43445906860922584,0.6176001594137821,0.4712653416347595,0.6328727247447995],"dir":"ltr"},{"str":"in","boundary":[0.47721522787572923,0.6176001594137821,0.49370095918791784,0.6328727247447995],"dir":"ltr"},{"str":"all","boundary":[0.4994531747896528,0.6176001594137821,0.5203271942928556,0.6328727247447995],"dir":"ltr"},{"str":"fairness,","boundary":[0.5260794098945903,0.6176001594137821,0.5958373784805777,0.6328727247447995],"dir":"ltr"},{"str":"can","boundary":[0.6017872647215475,0.6176001594137821,0.6314378606067788,0.6328727247447995],"dir":"ltr"},{"str":"be","boundary":[0.6371900762085136,0.6176001594137821,0.6580640957117164,0.6328727247447995],"dir":"ltr"},{"str":"said","boundary":[0.6638163113134514,0.6176001594137821,0.6978749624536204,0.6328727247447995],"dir":"ltr"},{"str":"to","boundary":[0.7036271780553551,0.6176001594137821,0.7212000978833355,0.6328727247447995],"dir":"ltr"},{"str":"be","boundary":[0.7269523134850704,0.6176001594137821,0.7478263329882732,0.6328727247447995],"dir":"ltr"},{"str":"relevant","boundary":[0.7535785485900081,0.6176001594137821,0.8238702279019297,0.6328727247447995],"dir":"ltr"},{"str":"to","boundary":[0.8296224435036644,0.6176001594137821,0.8471953633316449,0.6328727247447995],"dir":"ltr"},{"str":"most","boundary":[0.8529475789333799,0.6176001594137821,0.8946758508758621,0.6328727247447995],"dir":"ltr"},{"str":"of","boundary":[0.9004280664775968,0.6176001594137821,0.9180009863055771,0.6328727247447995],"dir":"ltr"},{"str":"science,","boundary":[0.2746818909156763,0.6359272378110029,0.34038761139734874,0.6511998031420202],"dir":"ltr"},{"str":"business,","boundary":[0.34532937737822067,0.6359272378110029,0.4206023567988611,0.6511998031420202],"dir":"ltr"},{"str":"and","boundary":[0.42554412277973297,0.6359272378110029,0.45740862982439484,0.6511998031420202],"dir":"ltr"},{"str":"technology.","boundary":[0.4623503958052667,0.6359272378110029,0.5599403903955245,0.6511998031420202],"dir":"ltr"},{"str":"[Har92,","boundary":[0.5648821563763963,0.6359272378110029,0.6302123026435226,0.6511998031420202],"dir":"ltr"},{"str":"p.","boundary":[0.6351540686243945,0.6359272378110029,0.6502956395897859,0.6511998031420202],"dir":"ltr"},{"str":"6]","boundary":[0.6552374055706577,0.6359272378110029,0.6717033698189228,0.6511998031420202],"dir":"ltr"},{"str":"But","boundary":[0.2746818909156763,0.664242573934709,0.3065266308964147,0.6795151392657263],"dir":"ltr"},{"str":"even","boundary":[0.31196257347537376,0.664242573934709,0.352603656902064,0.6795151392657263],"dir":"ltr"},{"str":"if","boundary":[0.35803959948102315,0.664242573934709,0.370117275538274,0.6795151392657263],"dir":"ltr"},{"str":"you","boundary":[0.3755532181172331,0.664242573934709,0.40741772516189495,0.6795151392657263],"dir":"ltr"},{"str":"are","boundary":[0.41285366774085397,0.664242573934709,0.44031011953057814,0.6795151392657263],"dir":"ltr"},{"str":"not","boundary":[0.4457460621095372,0.664242573934709,0.4743094694789767,0.6795151392657263],"dir":"ltr"},{"str":"a","boundary":[0.4797454120579357,0.664242573934709,0.48962894401967944,0.6795151392657263],"dir":"ltr"},{"str":"student","boundary":[0.49506488659863856,0.664242573934709,0.5587741336240388,0.6795151392657263],"dir":"ltr"},{"str":"in","boundary":[0.5642100762029979,0.664242573934709,0.5806958075151865,0.6795151392657263],"dir":"ltr"},{"str":"a","boundary":[0.5861317500941455,0.664242573934709,0.5960152820558893,0.6795151392657263],"dir":"ltr"},{"str":"computing-related","boundary":[0.6014512246348483,0.664242573934709,0.7596075030866719,0.6795151392657263],"dir":"ltr"},{"str":"program,","boundary":[0.7650434456656309,0.664242573934709,0.8435779906336468,0.6795151392657263],"dir":"ltr"},{"str":"there","boundary":[0.8491325355961467,0.664242573934709,0.8941619072138512,0.6795151392657263],"dir":"ltr"},{"str":"are","boundary":[0.8995978497928102,0.664242573934709,0.9270543015825343,0.6795151392657263],"dir":"ltr"},{"str":"compelling","boundary":[0.2391011758533988,0.6825696523319298,0.3335679743437456,0.6978422176629471],"dir":"ltr"},{"str":"reasons","boundary":[0.34147479991314056,0.6825696523319298,0.4062910025182561,0.6978422176629471],"dir":"ltr"},{"str":"to","boundary":[0.4141978280876511,0.6825696523319298,0.4317707479156315,0.6978422176629471],"dir":"ltr"},{"str":"study","boundary":[0.4396775734850265,0.6825696523319298,0.48581390068244634,0.6978422176629471],"dir":"ltr"},{"str":"algorithms.","boundary":[0.49372072625184127,0.6825696523319298,0.5887410025320456,0.6978422176629471],"dir":"ltr"},{"str":"To","boundary":[0.5966478281014409,0.6825696523319298,0.6188462408875173,0.6978422176629471],"dir":"ltr"},{"str":"put","boundary":[0.6267530664569123,0.6825696523319298,0.6553164738263517,0.6978422176629471],"dir":"ltr"},{"str":"it","boundary":[0.6632232993957466,0.6825696523319298,0.6753009754529975,0.6978422176629471],"dir":"ltr"},{"str":"bluntly,","boundary":[0.6832078010223925,0.6825696523319298,0.746758911536405,0.6978422176629471],"dir":"ltr"},{"str":"computer","boundary":[0.7554168855348925,0.6825696523319298,0.837786240904065,0.6978422176629471],"dir":"ltr"},{"str":"programs","boundary":[0.8456930664734598,0.6825696523319298,0.9269752333268405,0.6978422176629471],"dir":"ltr"},{"str":"would","boundary":[0.2391011758533988,0.7008967307291505,0.29183970240126345,0.7161692960601679],"dir":"ltr"},{"str":"not","boundary":[0.29863957239094313,0.7008967307291505,0.3272029797603826,0.7161692960601679],"dir":"ltr"},{"str":"exist","boundary":[0.3340028497500623,0.7008967307291505,0.3735369775970373,0.7161692960601679],"dir":"ltr"},{"str":"without","boundary":[0.38033684758671704,0.7008967307291505,0.44624023870762436,0.7161692960601679],"dir":"ltr"},{"str":"algorithms.","boundary":[0.45304010869730404,0.7008967307291505,0.5480603849775084,0.7161692960601679],"dir":"ltr"},{"str":"And","boundary":[0.5548602549671882,0.7008967307291505,0.5934060296179888,0.7161692960601679],"dir":"ltr"},{"str":"with","boundary":[0.6002058996076686,0.7008967307291505,0.6375458833591365,0.7161692960601679],"dir":"ltr"},{"str":"computer","boundary":[0.6443457533488162,0.7008967307291505,0.7267151087179886,0.7161692960601679],"dir":"ltr"},{"str":"applications","boundary":[0.7335149787076682,0.7008967307291505,0.836778120643967,0.7161692960601679],"dir":"ltr"},{"str":"becoming","boundary":[0.8435779906336469,0.7008967307291505,0.9270543015825347,0.7161692960601679],"dir":"ltr"},{"str":"indispensable","boundary":[0.2391011758533988,0.7192238091263712,0.3555687164905872,0.7344963744573886],"dir":"ltr"},{"str":"in","boundary":[0.3595023622113612,0.7192238091263712,0.37598809352354984,0.7344963744573886],"dir":"ltr"},{"str":"almost","boundary":[0.3799217392443238,0.7192238091263712,0.4370287869192792,0.7344963744573886],"dir":"ltr"},{"str":"all","boundary":[0.4409624326400532,0.7192238091263712,0.461836452143256,0.7344963744573886],"dir":"ltr"},{"str":"aspects","boundary":[0.46577009786403,0.7192238091263712,0.5272654337299997,0.7344963744573886],"dir":"ltr"},{"str":"of","boundary":[0.5311990794507736,0.7192238091263712,0.5487719992787541,0.7344963744573886],"dir":"ltr"},{"str":"our","boundary":[0.5527056449995281,0.7192238091263712,0.5823760079486828,0.7344963744573886],"dir":"ltr"},{"str":"professional","boundary":[0.5863096536694569,0.7192238091263712,0.6906797511854709,0.7344963744573886],"dir":"ltr"},{"str":"and","boundary":[0.6946133969062449,0.7192238091263712,0.7264779039509067,0.7344963744573886],"dir":"ltr"},{"str":"personal","boundary":[0.7304115496716809,0.7192238091263712,0.8040240957227484,0.7344963744573886],"dir":"ltr"},{"str":"lives,","boundary":[0.8079577414435224,0.7192238091263712,0.8502592582397858,0.7344963744573886],"dir":"ltr"},{"str":"studying","boundary":[0.854410341663718,0.7192238091263712,0.9269159321350703,0.7344963744573886],"dir":"ltr"},{"str":"algorithms","boundary":[0.2391011758533988,0.7375508875235921,0.33026687466852317,0.7528234528546094],"dir":"ltr"},{"str":"becomes","boundary":[0.33520864064939504,0.7375508875235921,0.4098886081523308,0.7528234528546094],"dir":"ltr"},{"str":"a","boundary":[0.4148303741332027,0.7375508875235921,0.42471390609494647,0.7528234528546094],"dir":"ltr"},{"str":"necessity","boundary":[0.42965567207581834,0.7375508875235921,0.5065297836742613,0.7528234528546094],"dir":"ltr"},{"str":"for","boundary":[0.5114715496551332,0.7375508875235921,0.5367338573493502,0.7528234528546094],"dir":"ltr"},{"str":"more","boundary":[0.5416756233302221,0.7375508875235921,0.5867049949479266,0.7528234528546094],"dir":"ltr"},{"str":"and","boundary":[0.5916467609287984,0.7375508875235921,0.6235112679734602,0.7528234528546094],"dir":"ltr"},{"str":"more","boundary":[0.6284530339543323,0.7375508875235921,0.6734824055720368,0.7528234528546094],"dir":"ltr"},{"str":"people.","boundary":[0.6784241715529086,0.7375508875235921,0.7408683264872056,0.7528234528546094],"dir":"ltr"},{"str":"Another","boundary":[0.2746818909156763,0.7558779659208129,0.3483735052224377,0.7711505312518302],"dir":"ltr"},{"str":"reason","boundary":[0.35361177716216197,0.7558779659208129,0.41073859190104084,0.7711505312518302],"dir":"ltr"},{"str":"for","boundary":[0.415976863840765,0.7558779659208129,0.44123917153498204,0.7711505312518302],"dir":"ltr"},{"str":"studying","boundary":[0.44647744347470625,0.7558779659208129,0.5189830339460585,0.7711505312518302],"dir":"ltr"},{"str":"algorithms","boundary":[0.5242213058857826,0.7558779659208129,0.615387004700907,0.7711505312518302],"dir":"ltr"},{"str":"is","boundary":[0.6206252766406312,0.7558779659208129,0.6338099082775974,0.7711505312518302],"dir":"ltr"},{"str":"their","boundary":[0.6390481802173216,0.7558779659208129,0.6796892636440118,0.7711505312518302],"dir":"ltr"},{"str":"usefulness","boundary":[0.6849275355837361,0.7558779659208129,0.7728119017875617,0.7711505312518302],"dir":"ltr"},{"str":"in","boundary":[0.7780501737272858,0.7558779659208129,0.7945359050394744,0.7711505312518302],"dir":"ltr"},{"str":"developing","boundary":[0.7997741769791987,0.7558779659208129,0.894260742533469,0.7711505312518302],"dir":"ltr"},{"str":"an-","boundary":[0.8994990144731931,0.7558779659208129,0.9269554662629172,0.7711505312518302],"dir":"ltr"},{"str":"alytical","boundary":[0.2391011758533988,0.7742065715745666,0.3005965117193684,0.789479136905584],"dir":"ltr"},{"str":"skills.","boundary":[0.30767312060397695,0.7742065715745666,0.3543826926551779,0.789479136905584],"dir":"ltr"},{"str":"After","boundary":[0.36145930153978645,0.7742065715745666,0.4087618855086921,0.789479136905584],"dir":"ltr"},{"str":"all,","boundary":[0.4158384943933006,0.7742065715745666,0.44165427987737527,0.789479136905584],"dir":"ltr"},{"str":"algorithms","boundary":[0.44924483242399443,0.7742065715745666,0.5404105312391189,0.789479136905584],"dir":"ltr"},{"str":"can","boundary":[0.5474871401237275,0.7742065715745666,0.5771377360089587,0.789479136905584],"dir":"ltr"},{"str":"be","boundary":[0.5842143448935672,0.7742065715745666,0.6050883643967698,0.789479136905584],"dir":"ltr"},{"str":"seen","boundary":[0.6121649732813784,0.7742065715745666,0.6506119126125617,0.789479136905584],"dir":"ltr"},{"str":"as","boundary":[0.6576885214971703,0.7742065715745666,0.6752614413251506,0.789479136905584],"dir":"ltr"},{"str":"special","boundary":[0.6823380502097591,0.7742065715745666,0.7405520534644299,0.789479136905584],"dir":"ltr"},{"str":"kinds","boundary":[0.7476286623490384,0.7742065715745666,0.7937847566103816,0.789479136905584],"dir":"ltr"},{"str":"of","boundary":[0.8008613654949903,0.7742065715745666,0.8184342853229708,0.789479136905584],"dir":"ltr"},{"str":"solutions","boundary":[0.8255108942075792,0.7742065715745666,0.902424539933869,0.789479136905584],"dir":"ltr"},{"str":"to","boundary":[0.9095011488184775,0.7742065715745666,0.9270740686464579,0.789479136905584],"dir":"ltr"},{"str":"problems—not","boundary":[0.2391011758533988,0.7925336499717874,0.3676266254839145,0.8078062153028047],"dir":"ltr"},{"str":"just","boundary":[0.37211374899454625,0.7925336499717874,0.4028713004594928,0.8078062153028047],"dir":"ltr"},{"str":"answers","boundary":[0.40735842397012445,0.7925336499717874,0.4754559591865389,0.8078062153028047],"dir":"ltr"},{"str":"but","boundary":[0.47994308269717056,0.7925336499717874,0.5085064900666101,0.8078062153028047],"dir":"ltr"},{"str":"precisely","boundary":[0.5129936135772417,0.7925336499717874,0.5887805366598928,0.8078062153028047],"dir":"ltr"},{"str":"defined","boundary":[0.5932676601705245,0.7925336499717874,0.6569966742598482,0.8078062153028047],"dir":"ltr"},{"str":"procedures","boundary":[0.6614837977704798,0.7925336499717874,0.7570575518405419,0.8078062153028047],"dir":"ltr"},{"str":"for","boundary":[0.7615446753511735,0.7925336499717874,0.7868069830453905,0.8078062153028047],"dir":"ltr"},{"str":"getting","boundary":[0.7912941065560224,0.7925336499717874,0.8505952983264848,0.8078062153028047],"dir":"ltr"},{"str":"answers.","boundary":[0.8550824218371165,0.7925336499717874,0.927034534518611,0.8078062153028047],"dir":"ltr"},{"str":"Consequently,","boundary":[0.2391011758533988,0.8108607283690084,0.36086628962208184,0.8261332937000256],"dir":"ltr"},{"str":"specific","boundary":[0.3644045940643861,0.8108607283690084,0.427006885510071,0.8261332937000256],"dir":"ltr"},{"str":"algorithm","boundary":[0.4301893828017525,0.8108607283690084,0.5136656937506402,0.8261332937000256],"dir":"ltr"},{"str":"design","boundary":[0.5168481910423217,0.8108607283690084,0.5717808616856935,0.8261332937000256],"dir":"ltr"},{"str":"techniques","boundary":[0.5749633589773749,0.8108607283690084,0.6672360133722146,0.8261332937000256],"dir":"ltr"},{"str":"can","boundary":[0.6704185106638961,0.8108607283690084,0.7000691065491274,0.8261332937000256],"dir":"ltr"},{"str":"be","boundary":[0.7032516038408089,0.8108607283690084,0.7241256233440116,0.8261332937000256],"dir":"ltr"},{"str":"interpreted","boundary":[0.7273081206356933,0.8108607283690084,0.8239690632215473,0.8261332937000256],"dir":"ltr"},{"str":"as","boundary":[0.8271515605132288,0.8108607283690084,0.8447244803412092,0.8261332937000256],"dir":"ltr"},{"str":"problem-","boundary":[0.8479069776328905,0.8108607283690084,0.9269950003907641,0.8261332937000256],"dir":"ltr"},{"str":"solving","boundary":[0.2391011758533988,0.829187806766229,0.29952909026750013,0.8444603720972463],"dir":"ltr"},{"str":"strategies","boundary":[0.30381854313889683,0.829187806766229,0.38508094292835393,0.8444603720972463],"dir":"ltr"},{"str":"that","boundary":[0.3893703957997508,0.829187806766229,0.42340927987599625,0.8444603720972463],"dir":"ltr"},{"str":"can","boundary":[0.4276987327473931,0.829187806766229,0.45734932863262434,0.8444603720972463],"dir":"ltr"},{"str":"be","boundary":[0.46163878150402116,0.829187806766229,0.48251280100722393,0.8444603720972463],"dir":"ltr"},{"str":"useful","boundary":[0.4868022538786207,0.829187806766229,0.53843382484677,0.8444603720972463],"dir":"ltr"},{"str":"regardless","boundary":[0.5427232777181669,0.829187806766229,0.629500688342277,0.8444603720972463],"dir":"ltr"},{"str":"of","boundary":[0.6337901412136738,0.829187806766229,0.6513630610416542,0.8444603720972463],"dir":"ltr"},{"str":"whether","boundary":[0.6556525139130509,0.829187806766229,0.7259441932249726,0.8444603720972463],"dir":"ltr"},{"str":"a","boundary":[0.7302336460963693,0.829187806766229,0.7401171780581131,0.8444603720972463],"dir":"ltr"},{"str":"computer","boundary":[0.7444066309295099,0.829187806766229,0.8267759862986823,0.8444603720972463],"dir":"ltr"},{"str":"is","boundary":[0.8310654391700789,0.829187806766229,0.8442500708070451,0.8444603720972463],"dir":"ltr"},{"str":"involved.","boundary":[0.848539523678442,0.829187806766229,0.9270938357103813,0.8444603720972463],"dir":"ltr"},{"str":"Of","boundary":[0.2391011758533988,0.8475148851634499,0.26214957238818526,0.862787450494467],"dir":"ltr"},{"str":"course,","boundary":[0.26950292016772254,0.8475148851634499,0.32973316394258895,0.862787450494467],"dir":"ltr"},{"str":"the","boundary":[0.337679523639831,0.8475148851634499,0.36513597542955517,0.862787450494467],"dir":"ltr"},{"str":"precision","boundary":[0.37248932320909245,0.8475148851634499,0.45049015745117416,0.862787450494467],"dir":"ltr"},{"str":"inherently","boundary":[0.45784350523071154,0.8475148851634499,0.545727871434537,0.862787450494467],"dir":"ltr"},{"str":"imposed","boundary":[0.5530812192140744,0.8475148851634499,0.6255868096854266,0.862787450494467],"dir":"ltr"},{"str":"by","boundary":[0.6329401574649639,0.8475148851634499,0.6538141769681666,0.862787450494467],"dir":"ltr"},{"str":"algorithmic","boundary":[0.661167524747704,0.8475148851634499,0.7589156558493497,0.862787450494467],"dir":"ltr"},{"str":"thinking","boundary":[0.7662690036288872,0.8475148851634499,0.8376874055844474,0.862787450494467],"dir":"ltr"},{"str":"limits","boundary":[0.8450407533639849,0.8475148851634499,0.8922642690771965,0.862787450494467],"dir":"ltr"},{"str":"the","boundary":[0.8996176168567337,0.8475148851634499,0.9270740686464578,0.862787450494467],"dir":"ltr"},{"str":"kinds","boundary":[0.2391011758533988,0.8658419635606708,0.2852572701147421,0.881114528891688],"dir":"ltr"},{"str":"of","boundary":[0.29235364606327413,0.8658419635606708,0.30992656589125456,0.881114528891688],"dir":"ltr"},{"str":"problems","boundary":[0.3170229418397865,0.8658419635606708,0.39721792017737534,0.881114528891688],"dir":"ltr"},{"str":"that","boundary":[0.4043142961259074,0.8658419635606708,0.43835318020215286,0.881114528891688],"dir":"ltr"},{"str":"can","boundary":[0.4454495561506848,0.8658419635606708,0.47510015203591605,0.881114528891688],"dir":"ltr"},{"str":"be","boundary":[0.4821965279844481,0.8658419635606708,0.5030705474876509,0.881114528891688],"dir":"ltr"},{"str":"solved","boundary":[0.510166923436183,0.8658419635606708,0.5650995940795548,0.881114528891688],"dir":"ltr"},{"str":"with","boundary":[0.5721959700280868,0.8658419635606708,0.6095359537795546,0.881114528891688],"dir":"ltr"},{"str":"an","boundary":[0.6166323297280865,0.8658419635606708,0.6375063492312892,0.881114528891688],"dir":"ltr"},{"str":"algorithm.","boundary":[0.6446027251798213,0.8658419635606708,0.733020802109581,0.881114528891688],"dir":"ltr"},{"str":"You","boundary":[0.7401171780581131,0.8658419635606708,0.7756583589925435,0.881114528891688],"dir":"ltr"},{"str":"will","boundary":[0.7827547349410756,0.8658419635606708,0.8135122864060222,0.881114528891688],"dir":"ltr"},{"str":"not","boundary":[0.8206086623545543,0.8658419635606708,0.8491720697239937,0.881114528891688],"dir":"ltr"},{"str":"find,","boundary":[0.8562684456725257,0.8658419635606708,0.8941816742777748,0.881114528891688],"dir":"ltr"},{"str":"for","boundary":[0.9018117609522409,0.8658419635606708,0.9270740686464579,0.881114528891688],"dir":"ltr"},{"str":"example,","boundary":[0.2391011758533988,0.8841690419578915,0.3157973838765303,0.8994416072889088],"dir":"ltr"},{"str":"an","boundary":[0.3225379526744396,0.8841690419578915,0.3434119721776424,0.8994416072889088],"dir":"ltr"},{"str":"algorithm","boundary":[0.3497967338249288,0.8841690419578915,0.43327304477381656,0.8994416072889088],"dir":"ltr"},{"str":"for","boundary":[0.439657806421103,0.8841690419578915,0.4649201141153201,0.8994416072889088],"dir":"ltr"},{"str":"living","boundary":[0.47130487576260655,0.8841690419578915,0.5185481585397417,0.8994416072889088],"dir":"ltr"},{"str":"a","boundary":[0.5249329201870281,0.8841690419578915,0.5348164521487718,0.8994416072889088],"dir":"ltr"},{"str":"happy","boundary":[0.5412012137960583,0.8841690419578915,0.593939740343923,0.8994416072889088],"dir":"ltr"},{"str":"life","boundary":[0.6003245019912095,0.8841690419578915,0.6277809537809336,0.8994416072889088],"dir":"ltr"},{"str":"or","boundary":[0.6341657154282202,0.8841690419578915,0.6528455908359159,0.8994416072889088],"dir":"ltr"},{"str":"becoming","boundary":[0.6592303524832023,0.8841690419578915,0.74270666343209,0.8994416072889088],"dir":"ltr"},{"str":"rich","boundary":[0.7490914250793764,0.8841690419578915,0.7820431206398302,0.8994416072889088],"dir":"ltr"},{"str":"and","boundary":[0.7884278822871167,0.8841690419578915,0.8202923893317786,0.8994416072889088],"dir":"ltr"},{"str":"famous.","boundary":[0.8266771509790651,0.8841690419578915,0.8931340198898301,0.8994416072889088],"dir":"ltr"},{"str":"On","boundary":[0.8995187815371166,0.8841690419578915,0.9269752333268407,0.8994416072889088],"dir":"ltr"},{"str":"1","boundary":[0.9160064895556974,0.9329343430598296,0.9269969770971564,0.9482069083908469],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92709,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":67,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/8d9a74132be2e72ec3362b00e5d5c253.jpg","blurred":"/storage/books/4a8b03583f119702/pages/31068029d48b1f4284725318a74ed8a7.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.0729,0.05179]},"elements":[{"words":[{"str":"2","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Fundamentals","boundary":[0.14421784044919886,0.17005356781848974,0.48033783885657977,0.20670781659232623],"dir":"ltr"},{"str":"of","boundary":[0.49613571598708894,0.17005356781848974,0.5459962831467442,0.20670781659232623],"dir":"ltr"},{"str":"the","boundary":[0.5617941602772535,0.17005356781848974,0.6392179905384878,0.20670781659232623],"dir":"ltr"},{"str":"Analysis","boundary":[0.6550158676689971,0.17005356781848974,0.8571148363656017,0.20670781659232623],"dir":"ltr"},{"str":"of","boundary":[0.14421784044919886,0.20976111551518684,0.1940784076088541,0.24641536428902333],"dir":"ltr"},{"str":"Algorithm","boundary":[0.20987628473936334,0.20976111551518684,0.4526796936100726,0.24641536428902333],"dir":"ltr"},{"str":"Efficiency","boundary":[0.46847757074058183,0.20976111551518684,0.7072010473793878,0.24641536428902333],"dir":"ltr"},{"str":"I","boundary":[0.23910077902799318,0.3142741587391314,0.2467901668942298,0.32954672407014873],"dir":"ltr"},{"str":"often","boundary":[0.2523249447928063,0.3142741587391314,0.2951601723150037,0.32954672407014873],"dir":"ltr"},{"str":"say","boundary":[0.3006949502135802,0.3142741587391314,0.3277955948526816,0.32954672407014873],"dir":"ltr"},{"str":"that","boundary":[0.33333037275125815,0.3142741587391314,0.36519487979592,0.32954672407014873],"dir":"ltr"},{"str":"when","boundary":[0.3707296576944965,0.3142741587391314,0.41575902931220104,0.32954672407014873],"dir":"ltr"},{"str":"you","boundary":[0.4212938072107776,0.3142741587391314,0.45315831425543945,0.32954672407014873],"dir":"ltr"},{"str":"can","boundary":[0.4586930921540159,0.3142741587391314,0.48834368803924716,0.32954672407014873],"dir":"ltr"},{"str":"measure","boundary":[0.4938784659378237,0.3142741587391314,0.5641503781858217,0.32954672407014873],"dir":"ltr"},{"str":"what","boundary":[0.5696851560843982,0.3142741587391314,0.6103262395110884,0.32954672407014873],"dir":"ltr"},{"str":"you","boundary":[0.615861017409665,0.3142741587391314,0.6477255244543269,0.32954672407014873],"dir":"ltr"},{"str":"are","boundary":[0.6532603023529036,0.3142741587391314,0.6796097985629125,0.32954672407014873],"dir":"ltr"},{"str":"speaking","boundary":[0.6851445764614889,0.3142741587391314,0.759844311028348,0.32954672407014873],"dir":"ltr"},{"str":"about","boundary":[0.7653790889269246,0.3142741587391314,0.8137293272837751,0.32954672407014873],"dir":"ltr"},{"str":"and","boundary":[0.8192641051823516,0.3142741587391314,0.8511286122270134,0.32954672407014873],"dir":"ltr"},{"str":"express","boundary":[0.23910077902799318,0.3326012371363522,0.3005961148939628,0.34787380246736954],"dir":"ltr"},{"str":"it","boundary":[0.30571578445014613,0.3326012371363522,0.31670627199160517,0.34787380246736954],"dir":"ltr"},{"str":"in","boundary":[0.3218259415477884,0.3326012371363522,0.33831167285997693,0.34787380246736954],"dir":"ltr"},{"str":"numbers","boundary":[0.3434313424161602,0.3326012371363522,0.4170241214033042,0.34787380246736954],"dir":"ltr"},{"str":"you","boundary":[0.4221437909594875,0.3326012371363522,0.4540082980041494,0.34787380246736954],"dir":"ltr"},{"str":"know","boundary":[0.45912796756033264,0.3326012371363522,0.506015443186845,0.34787380246736954],"dir":"ltr"},{"str":"something","boundary":[0.5111351127430283,0.3326012371363522,0.5979125233671384,0.34787380246736954],"dir":"ltr"},{"str":"about","boundary":[0.6030321929233217,0.3326012371363522,0.6513824312801721,0.34787380246736954],"dir":"ltr"},{"str":"it;","boundary":[0.6565021008363554,0.3326012371363522,0.6724343543586864,0.34787380246736954],"dir":"ltr"},{"str":"but","boundary":[0.6776330921705637,0.3326012371363522,0.7051093110242113,0.34787380246736954],"dir":"ltr"},{"str":"when","boundary":[0.7102289805803944,0.3326012371363522,0.755258352198099,0.34787380246736954],"dir":"ltr"},{"str":"you","boundary":[0.7603780217542824,0.3326012371363522,0.7922425287989442,0.34787380246736954],"dir":"ltr"},{"str":"cannot","boundary":[0.7973621983551274,0.3326012371363522,0.8544890130940064,0.34787380246736954],"dir":"ltr"},{"str":"express","boundary":[0.23910077902799318,0.350928315533573,0.3005961148939628,0.36620088086459035],"dir":"ltr"},{"str":"it","boundary":[0.30779132616211224,0.350928315533573,0.31878181370357134,0.36620088086459035],"dir":"ltr"},{"str":"in","boundary":[0.32597702497172076,0.350928315533573,0.3424627562839094,0.36620088086459035],"dir":"ltr"},{"str":"numbers","boundary":[0.3496579675520588,0.350928315533573,0.4232507465392028,0.36620088086459035],"dir":"ltr"},{"str":"your","boundary":[0.4304459578073523,0.350928315533573,0.46999985271825084,0.36620088086459035],"dir":"ltr"},{"str":"knowledge","boundary":[0.47719506398640027,0.350928315533573,0.5680049556509019,0.36620088086459035],"dir":"ltr"},{"str":"is","boundary":[0.5752001669190513,0.350928315533573,0.5883847985560174,0.36620088086459035],"dir":"ltr"},{"str":"a","boundary":[0.5955800098241669,0.350928315533573,0.6054635417859107,0.36620088086459035],"dir":"ltr"},{"str":"meagre","boundary":[0.6126587530540601,0.350928315533573,0.6741343218561062,0.36620088086459035],"dir":"ltr"},{"str":"and","boundary":[0.6813295331242558,0.350928315533573,0.7131940401689176,0.36620088086459035],"dir":"ltr"},{"str":"unsatisfactory","boundary":[0.7203892514370671,0.350928315533573,0.8379242135261239,0.36620088086459035],"dir":"ltr"},{"str":"kind:","boundary":[0.23910077902799318,0.3692553939307939,0.2825092514039717,0.38452795926181116],"dir":"ltr"},{"str":"it","boundary":[0.2874114832569966,0.3692553939307939,0.2984019707984557,0.38452795926181116],"dir":"ltr"},{"str":"may","boundary":[0.30330420265148056,0.3692553939307939,0.3391814236726104,0.38452795926181116],"dir":"ltr"},{"str":"be","boundary":[0.3440836555256353,0.3692553939307939,0.36385071944912284,0.38452795926181116],"dir":"ltr"},{"str":"the","boundary":[0.36875295130214775,0.3692553939307939,0.3940152589963648,0.38452795926181116],"dir":"ltr"},{"str":"beginning","boundary":[0.3989174908493897,0.3692553939307939,0.48241356886220094,0.38452795926181116],"dir":"ltr"},{"str":"of","boundary":[0.4873158007152258,0.3692553939307939,0.5048887205432062,0.38452795926181116],"dir":"ltr"},{"str":"knowledge","boundary":[0.5097909523962311,0.3692553939307939,0.6006008440607327,0.38452795926181116],"dir":"ltr"},{"str":"but","boundary":[0.6055030759137576,0.3692553939307939,0.6329792947674052,0.38452795926181116],"dir":"ltr"},{"str":"you","boundary":[0.6378815266204302,0.3692553939307939,0.669746033665092,0.38452795926181116],"dir":"ltr"},{"str":"have","boundary":[0.674648265518117,0.3692553939307939,0.7141823933650919,0.38452795926181116],"dir":"ltr"},{"str":"scarcely,","boundary":[0.7190846252181168,0.3692553939307939,0.7899100152559725,0.38452795926181116],"dir":"ltr"},{"str":"in","boundary":[0.7948320141729208,0.3692553939307939,0.8113177454851094,0.38452795926181116],"dir":"ltr"},{"str":"your","boundary":[0.8162199773381345,0.3692553939307939,0.855773872249033,0.38452795926181116],"dir":"ltr"},{"str":"thoughts,","boundary":[0.23910077902799318,0.3875824723280147,0.3154807140283489,0.40285503765903197],"dir":"ltr"},{"str":"advanced","boundary":[0.32042248000922074,0.3875824723280147,0.4005976912828861,0.40285503765903197],"dir":"ltr"},{"str":"to","boundary":[0.405539457263758,0.3875824723280147,0.42202518857594656,0.40285503765903197],"dir":"ltr"},{"str":"the","boundary":[0.42696695455681843,0.3875824723280147,0.4522292622510355,0.40285503765903197],"dir":"ltr"},{"str":"stage","boundary":[0.45717102823190736,0.3875824723280147,0.49889930017438944,0.40285503765903197],"dir":"ltr"},{"str":"of","boundary":[0.5038410661552614,0.3875824723280147,0.5214139859832418,0.40285503765903197],"dir":"ltr"},{"str":"science,","boundary":[0.5263557519641137,0.3875824723280147,0.5900847660534374,0.40285503765903197],"dir":"ltr"},{"str":"whatever","boundary":[0.5950265320343092,0.3875824723280147,0.6707936880530369,0.40285503765903197],"dir":"ltr"},{"str":"the","boundary":[0.6757354540339088,0.3875824723280147,0.7009977617281258,0.40285503765903197],"dir":"ltr"},{"str":"matter","boundary":[0.7059395277089976,0.3875824723280147,0.7597454757087306,0.40285503765903197],"dir":"ltr"},{"str":"may","boundary":[0.7646872416896024,0.3875824723280147,0.8005644627107322,0.40285503765903197],"dir":"ltr"},{"str":"be.","boundary":[0.8055062286916042,0.3875824723280147,0.8297208819978764,0.40285503765903197],"dir":"ltr"},{"str":"—Lord","boundary":[0.6332714225515588,0.4095098411605992,0.6927625667071196,0.42401882421476306],"dir":"ltr"},{"str":"Kelvin","boundary":[0.6974948168104027,0.4095098411605992,0.7515776751336397,0.42401882421476306],"dir":"ltr"},{"str":"(1824–1907)","boundary":[0.756309925236923,0.4095098411605992,0.8554242746223552,0.42401882421476306],"dir":"ltr"},{"str":"Not","boundary":[0.23910077902799318,0.4669998120493046,0.270965286072655,0.4822723773803219],"dir":"ltr"},{"str":"everything","boundary":[0.2759861203092209,0.4669998120493046,0.36385071944912284,0.4822723773803219],"dir":"ltr"},{"str":"that","boundary":[0.3688715536856886,0.4669998120493046,0.40073606073035045,0.4822723773803219],"dir":"ltr"},{"str":"can","boundary":[0.40575689496691636,0.4669998120493046,0.4354074908521476,0.4822723773803219],"dir":"ltr"},{"str":"be","boundary":[0.4404283250887134,0.4669998120493046,0.4601953890122009,0.4822723773803219],"dir":"ltr"},{"str":"counted","boundary":[0.4652162232487667,0.4669998120493046,0.5322265699493893,0.4822723773803219],"dir":"ltr"},{"str":"counts,","boundary":[0.5372474041859552,0.4669998120493046,0.596034652294407,0.4822723773803219],"dir":"ltr"},{"str":"and","boundary":[0.6010752535948963,0.4669998120493046,0.6329397606395581,0.4822723773803219],"dir":"ltr"},{"str":"not","boundary":[0.6379605948761241,0.4669998120493046,0.6654368137297716,0.4822723773803219],"dir":"ltr"},{"str":"everything","boundary":[0.6704576479663376,0.4669998120493046,0.7583222471062395,0.4822723773803219],"dir":"ltr"},{"str":"that","boundary":[0.7633430813428054,0.4669998120493046,0.7952075883874672,0.4822723773803219],"dir":"ltr"},{"str":"counts","boundary":[0.800228422624033,0.4669998120493046,0.8551610932674049,0.4822723773803219],"dir":"ltr"},{"str":"can","boundary":[0.23910077902799318,0.48532689044652544,0.26875137491322443,0.5005994557775427],"dir":"ltr"},{"str":"be","boundary":[0.2736931408940963,0.48532689044652544,0.29346020481758384,0.5005994557775427],"dir":"ltr"},{"str":"counted.","boundary":[0.2984019707984557,0.48532689044652544,0.37035408347995025,0.5005994557775427],"dir":"ltr"},{"str":"—Albert","boundary":[0.6059241997324726,0.5072548111554795,0.6790487310903492,0.5217637942096434],"dir":"ltr"},{"str":"Einstein","boundary":[0.6837809811936325,0.5072548111554795,0.7516098993406922,0.5217637942096434],"dir":"ltr"},{"str":"(1879–1955)","boundary":[0.7563421494439754,0.5072548111554795,0.8554564988294076,0.5217637942096434],"dir":"ltr"},{"str":"his","boundary":[0.278654351319837,0.6275881706354889,0.30282947049826225,0.6428607359665062],"dir":"ltr"},{"str":"chapter","boundary":[0.30767240115951666,0.6275881706354889,0.3724688367007087,0.6428607359665062],"dir":"ltr"},{"str":"is","boundary":[0.37731176736196315,0.6275881706354889,0.39049639899892935,0.6428607359665062],"dir":"ltr"},{"str":"devoted","boundary":[0.39533932966018376,0.6275881706354889,0.4645438204563135,0.6428607359665062],"dir":"ltr"},{"str":"to","boundary":[0.46938675111756795,0.6275881706354889,0.4869596709455483,0.6428607359665062],"dir":"ltr"},{"str":"analysis","boundary":[0.4918026016068027,0.6275881706354889,0.5588129483074253,0.6428607359665062],"dir":"ltr"},{"str":"of","boundary":[0.5636558789686797,0.6275881706354889,0.5812287987966602,0.6428607359665062],"dir":"ltr"},{"str":"algorithms.","boundary":[0.5860717294579146,0.6275881706354889,0.681092005738119,0.6428607359665062],"dir":"ltr"},{"str":"The","boundary":[0.6859349363993734,0.6275881706354889,0.7192029049826029,0.6428607359665062],"dir":"ltr"},{"str":"American","boundary":[0.7240695561205657,0.6275881706354889,0.8075261000055299,0.6428607359665062],"dir":"ltr"},{"str":"Heritage","boundary":[0.8123690306667843,0.6275881706354889,0.8848350870102895,0.6428607359665062],"dir":"ltr"},{"str":"Dic-","boundary":[0.889678017671544,0.6275881706354889,0.9269982343590885,0.6428607359665062],"dir":"ltr"},{"str":"tionary","boundary":[0.278654351319837,0.6459152490327096,0.33908226573393835,0.6611878143637269],"dir":"ltr"},{"str":"defines","boundary":[0.34398252088057085,0.6459152490327096,0.4044104352946722,0.6611878143637269],"dir":"ltr"},{"str":"“analysis”","boundary":[0.4095103377869319,0.6459152490327096,0.49628774841104206,0.6611878143637269],"dir":"ltr"},{"str":"as","boundary":[0.501387650903302,0.6459152490327096,0.5189605707312823,0.6611878143637269],"dir":"ltr"},{"str":"“the","boundary":[0.524060473223542,0.6459152490327096,0.56140045697501,0.6611878143637269],"dir":"ltr"},{"str":"separation","boundary":[0.5665003594672697,0.6459152490327096,0.6565788697666023,0.6611878143637269],"dir":"ltr"},{"str":"of","boundary":[0.6616787722588621,0.6459152490327096,0.6792516920868424,0.6611878143637269],"dir":"ltr"},{"str":"an","boundary":[0.6843515945791021,0.6459152490327096,0.7052256140823049,0.6611878143637269],"dir":"ltr"},{"str":"intellectual","boundary":[0.7103255165745648,0.6459152490327096,0.8058795035807034,0.6611878143637269],"dir":"ltr"},{"str":"or","boundary":[0.8109794060729631,0.6459152490327096,0.8296592814806587,0.6611878143637269],"dir":"ltr"},{"str":"substantial","boundary":[0.8347591839729186,0.6459152490327096,0.9270318383677584,0.6611878143637269],"dir":"ltr"},{"str":"Twhole","boundary":[0.23910077902799318,0.6262900274167891,0.2907340040834802,0.6795148927609477],"dir":"ltr"},{"str":"into","boundary":[0.2940351037587026,0.6642423274299303,0.32809375489887166,0.6795148927609477],"dir":"ltr"},{"str":"its","boundary":[0.33139485457409407,0.6642423274299303,0.35116191849758155,0.6795148927609477],"dir":"ltr"},{"str":"constituent","boundary":[0.3544630181728039,0.6642423274299303,0.45001700517894255,0.6795148927609477],"dir":"ltr"},{"str":"parts","boundary":[0.45331810485416496,0.6642423274299303,0.4961533323763624,0.6795148927609477],"dir":"ltr"},{"str":"for","boundary":[0.4994544320515849,0.6642423274299303,0.5247167397458019,0.6795148927609477],"dir":"ltr"},{"str":"individual","boundary":[0.5280178394210242,0.6642423274299303,0.6137278285932661,0.6795148927609477],"dir":"ltr"},{"str":"study.”","boundary":[0.6170289282684885,0.6642423274299303,0.6750847950117713,0.6795148927609477],"dir":"ltr"},{"str":"Accordingly,","boundary":[0.6783858946869937,0.6642423274299303,0.7870454450744045,0.6795148927609477],"dir":"ltr"},{"str":"each","boundary":[0.7906825848363263,0.6642423274299303,0.8302167126833013,0.6795148927609477],"dir":"ltr"},{"str":"of","boundary":[0.833517812358524,0.6642423274299303,0.8510907321865043,0.6795148927609477],"dir":"ltr"},{"str":"the","boundary":[0.8543918318617266,0.6642423274299303,0.8818482836514507,0.6795148927609477],"dir":"ltr"},{"str":"prin-","boundary":[0.8851493833266733,0.6642423274299303,0.9268974223330789,0.6795148927609477],"dir":"ltr"},{"str":"cipal","boundary":[0.2391024331153309,0.6825694058271511,0.27974351654202123,0.6978419711581685],"dir":"ltr"},{"str":"dimensions","boundary":[0.28324228685647845,0.6825694058271511,0.37992299650625583,0.6978419711581685],"dir":"ltr"},{"str":"of","boundary":[0.38342176682071316,0.6825694058271511,0.40099468664869353,0.6978419711581685],"dir":"ltr"},{"str":"an","boundary":[0.40449345696315075,0.6825694058271511,0.4253674764663536,0.6978419711581685],"dir":"ltr"},{"str":"algorithm","boundary":[0.42886624678081087,0.6825694058271511,0.5123425577296986,0.6978419711581685],"dir":"ltr"},{"str":"pointed","boundary":[0.5158413280441558,0.6825694058271511,0.5817644862289867,0.6978419711581685],"dir":"ltr"},{"str":"out","boundary":[0.585263256543444,0.6825694058271511,0.6138266639128835,0.6978419711581685],"dir":"ltr"},{"str":"in","boundary":[0.6173254342273408,0.6825694058271511,0.6338111655395292,0.6978419711581685],"dir":"ltr"},{"str":"Section","boundary":[0.6373099358539867,0.6825694058271511,0.7010191828793868,0.6978419711581685],"dir":"ltr"},{"str":"1.2","boundary":[0.7045179531938441,0.6825694058271511,0.7292267830982035,0.6978419711581685],"dir":"ltr"},{"str":"is","boundary":[0.7327255534126608,0.6825694058271511,0.7459101850496269,0.6978419711581685],"dir":"ltr"},{"str":"both","boundary":[0.7494089553640841,0.6825694058271511,0.7889628502749827,0.6978419711581685],"dir":"ltr"},{"str":"a","boundary":[0.79246162058944,0.6825694058271511,0.8023451525511838,0.6978419711581685],"dir":"ltr"},{"str":"legitimate","boundary":[0.805843922865641,0.6825694058271511,0.8914946108461124,0.6978419711581685],"dir":"ltr"},{"str":"and","boundary":[0.8949933811605697,0.6825694058271511,0.9268578882052315,0.6978419711581685],"dir":"ltr"},{"str":"desirable","boundary":[0.2391024331153309,0.7008964842243719,0.31710326735741257,0.7161690495553893],"dir":"ltr"},{"str":"subject","boundary":[0.32153108967627375,0.7008964842243719,0.38193923702645155,0.7161690495553893],"dir":"ltr"},{"str":"of","boundary":[0.3863670593453128,0.7008964842243719,0.4039399791732932,0.7161690495553893],"dir":"ltr"},{"str":"study.","boundary":[0.4083678014921544,0.7008964842243719,0.4576273247894853,0.7161690495553893],"dir":"ltr"},{"str":"But","boundary":[0.46205514710834644,0.7008964842243719,0.4938998870890848,0.7161690495553893],"dir":"ltr"},{"str":"the","boundary":[0.4983277094079461,0.7008964842243719,0.5257841611976701,0.7161690495553893],"dir":"ltr"},{"str":"term","boundary":[0.5302119835165313,0.7008964842243719,0.5708332998792982,0.7161690495553893],"dir":"ltr"},{"str":"“analysis","boundary":[0.5752611221981594,0.7008964842243719,0.6521550008605257,0.7161690495553893],"dir":"ltr"},{"str":"of","boundary":[0.6565828231793871,0.7008964842243719,0.6741557430073675,0.7161690495553893],"dir":"ltr"},{"str":"algorithms”","boundary":[0.6785835653262285,0.7008964842243719,0.7796327961030967,0.7161690495553893],"dir":"ltr"},{"str":"is","boundary":[0.7840606184219578,0.7008964842243719,0.797245250058924,0.7161690495553893],"dir":"ltr"},{"str":"usually","boundary":[0.8016730723777852,0.7008964842243719,0.8621009867918865,0.7161690495553893],"dir":"ltr"},{"str":"used","boundary":[0.8665288091107479,0.7008964842243719,0.9060827040216465,0.7161690495553893],"dir":"ltr"},{"str":"in","boundary":[0.9105105263405077,0.7008964842243719,0.9269962576526961,0.7161690495553893],"dir":"ltr"},{"str":"a","boundary":[0.2391024331153309,0.7192235626215927,0.24898596507707466,0.73449612795261],"dir":"ltr"},{"str":"narrower,","boundary":[0.25444167471995716,0.7192235626215927,0.33811565630807977,0.73449612795261],"dir":"ltr"},{"str":"technical","boundary":[0.3437097353984268,0.7192235626215927,0.42058384699686974,0.73449612795261],"dir":"ltr"},{"str":"sense","boundary":[0.42603955663975224,0.7192235626215927,0.47217588383717213,0.73449612795261],"dir":"ltr"},{"str":"to","boundary":[0.4776315934800546,0.7192235626215927,0.495204513308035,0.73449612795261],"dir":"ltr"},{"str":"mean","boundary":[0.5006602229509176,0.7192235626215927,0.5478837386641292,0.73449612795261],"dir":"ltr"},{"str":"an","boundary":[0.5533394483070116,0.7192235626215927,0.5742134678102144,0.73449612795261],"dir":"ltr"},{"str":"investigation","boundary":[0.5796691774530971,0.7192235626215927,0.6895147516759171,0.73449612795261],"dir":"ltr"},{"str":"of","boundary":[0.6949704613187997,0.7192235626215927,0.7125433811467802,0.73449612795261],"dir":"ltr"},{"str":"an","boundary":[0.7179990907896626,0.7192235626215927,0.7388731102928654,0.73449612795261],"dir":"ltr"},{"str":"algorithm’s","boundary":[0.7443288199357481,0.7192235626215927,0.8406339553709792,0.73449612795261],"dir":"ltr"},{"str":"efficiency","boundary":[0.8460896650138616,0.7192235626215927,0.9269962576526959,0.73449612795261],"dir":"ltr"},{"str":"with","boundary":[0.2391024331153309,0.7375506410188134,0.27644241686679877,0.7528232063498307],"dir":"ltr"},{"str":"respect","boundary":[0.28108767688881836,0.7375506410188134,0.342583012754788,0.7528232063498307],"dir":"ltr"},{"str":"to","boundary":[0.3472282727768075,0.7375506410188134,0.36480119260478794,0.7528232063498307],"dir":"ltr"},{"str":"two","boundary":[0.36944645262680753,0.7375506410188134,0.4012911926075459,0.7528232063498307],"dir":"ltr"},{"str":"resources:","boundary":[0.40593645262956546,0.7375506410188134,0.49216038546381796,0.7528232063498307],"dir":"ltr"},{"str":"running","boundary":[0.4968056454858375,0.7375506410188134,0.5638357592503835,0.7528232063498307],"dir":"ltr"},{"str":"time","boundary":[0.5684810192724031,0.7375506410188134,0.6069081915396628,0.7528232063498307],"dir":"ltr"},{"str":"and","boundary":[0.6115534515616825,0.7375506410188134,0.6434179586063443,0.7528232063498307],"dir":"ltr"},{"str":"memory","boundary":[0.6480632186283638,0.7375506410188134,0.7194420864560772,0.7528232063498307],"dir":"ltr"},{"str":"space.","boundary":[0.7240873464780968,0.7375506410188134,0.7755212468070112,0.7528232063498307],"dir":"ltr"},{"str":"This","boundary":[0.780166506829031,0.7375506410188134,0.8167355750874828,0.7528232063498307],"dir":"ltr"},{"str":"emphasis","boundary":[0.8213808351095024,0.7375506410188134,0.900468857867376,0.7528232063498307],"dir":"ltr"},{"str":"on","boundary":[0.9051141178893954,0.7375506410188134,0.9270950929723135,0.7528232063498307],"dir":"ltr"},{"str":"efficiency","boundary":[0.2391024331153309,0.7558777194160342,0.32000902575416523,0.7711502847470515],"dir":"ltr"},{"str":"is","boundary":[0.3257810084198236,0.7558777194160342,0.33896564005678975,0.7711502847470515],"dir":"ltr"},{"str":"easy","boundary":[0.34473762272244807,0.7558777194160342,0.382077606473916,0.7711502847470515],"dir":"ltr"},{"str":"to","boundary":[0.38784958913957435,0.7558777194160342,0.4054225089675547,0.7711502847470515],"dir":"ltr"},{"str":"explain.","boundary":[0.4111944916332131,0.7558777194160342,0.4787583161236934,0.7711502847470515],"dir":"ltr"},{"str":"First,","boundary":[0.4845302987893517,0.7558777194160342,0.5282748112520296,0.7711502847470515],"dir":"ltr"},{"str":"unlike","boundary":[0.5342444645569228,0.7558777194160342,0.5880899466845028,0.7711502847470515],"dir":"ltr"},{"str":"such","boundary":[0.5938619293501612,0.7558777194160342,0.6323088686813444,0.7711502847470515],"dir":"ltr"},{"str":"dimensions","boundary":[0.6380808513470027,0.7558777194160342,0.73476156099678,0.7711502847470515],"dir":"ltr"},{"str":"as","boundary":[0.7405335436624385,0.7558777194160342,0.758106463490419,0.7711502847470515],"dir":"ltr"},{"str":"simplicity","boundary":[0.7638784461560773,0.7558777194160342,0.8462478015252497,0.7711502847470515],"dir":"ltr"},{"str":"and","boundary":[0.8520197841909082,0.7558777194160342,0.88388429123557,0.7711502847470515],"dir":"ltr"},{"str":"gen-","boundary":[0.8896562739012284,0.7558777194160342,0.9269962576526962,0.7711502847470515],"dir":"ltr"},{"str":"erality,","boundary":[0.2391024331153309,0.774204797813255,0.29713853279469016,0.7894773631442724],"dir":"ltr"},{"str":"efficiency","boundary":[0.30425467580714566,0.774204797813255,0.38516126844598003,0.7894773631442724],"dir":"ltr"},{"str":"can","boundary":[0.39184253605211883,0.774204797813255,0.42149313193735005,0.7894773631442724],"dir":"ltr"},{"str":"be","boundary":[0.4281743995434889,0.774204797813255,0.4490484190466917,0.7894773631442724],"dir":"ltr"},{"str":"studied","boundary":[0.45572968665283037,0.774204797813255,0.5183517451624388,0.7894773631442724],"dir":"ltr"},{"str":"in","boundary":[0.5250330127685776,0.774204797813255,0.5415187440807662,0.7894773631442724],"dir":"ltr"},{"str":"precise","boundary":[0.5482000116869049,0.774204797813255,0.6086081590370827,0.7894773631442724],"dir":"ltr"},{"str":"quantitative","boundary":[0.6152894266432215,0.774204797813255,0.7185328015155967,0.7894773631442724],"dir":"ltr"},{"str":"terms.","boundary":[0.7252140691217356,0.774204797813255,0.7773793508158191,0.7894773631442724],"dir":"ltr"},{"str":"Second,","boundary":[0.7840606184219578,0.774204797813255,0.8516244429124382,0.7894773631442724],"dir":"ltr"},{"str":"one","boundary":[0.8587405859248938,0.774204797813255,0.8906050929695556,0.7894773631442724],"dir":"ltr"},{"str":"can","boundary":[0.8972863605756942,0.774204797813255,0.9269369564609256,0.7894773631442724],"dir":"ltr"},{"str":"argue—although","boundary":[0.2391024331153309,0.7925318762104758,0.38300665847831994,0.8078044415414931],"dir":"ltr"},{"str":"this","boundary":[0.38933211893383596,0.7925318762104758,0.42008967039878253,0.8078044415414931],"dir":"ltr"},{"str":"is","boundary":[0.42641513085429855,0.7925318762104758,0.4395997624912647,0.8078044415414931],"dir":"ltr"},{"str":"hardly","boundary":[0.44592522294678066,0.7925318762104758,0.5008578935901525,0.8078044415414931],"dir":"ltr"},{"str":"always","boundary":[0.5071833540456684,0.7925318762104758,0.5642904017206238,0.8078044415414931],"dir":"ltr"},{"str":"the","boundary":[0.5706158621761399,0.7925318762104758,0.598072313965864,0.8078044415414931],"dir":"ltr"},{"str":"case,","boundary":[0.6043977744213801,0.7925318762104758,0.6448411872088355,0.8078044415414931],"dir":"ltr"},{"str":"given","boundary":[0.6515224548149742,0.7925318762104758,0.6976587820123941,0.8078044415414931],"dir":"ltr"},{"str":"the","boundary":[0.7039842424679101,0.7925318762104758,0.7314406942576342,0.8078044415414931],"dir":"ltr"},{"str":"speed","boundary":[0.7377661547131503,0.7925318762104758,0.7872035815857925,0.8078044415414931],"dir":"ltr"},{"str":"and","boundary":[0.7935290420413085,0.7925318762104758,0.8253935490859703,0.8078044415414931],"dir":"ltr"},{"str":"memory","boundary":[0.8317190095414865,0.7925318762104758,0.9030978773691998,0.8078044415414931],"dir":"ltr"},{"str":"of","boundary":[0.9094233378247157,0.7925318762104758,0.9269962576526961,0.8078044415414931],"dir":"ltr"},{"str":"today’s","boundary":[0.2391024331153309,0.8108589546076965,0.30026172889460123,0.8261315199387138],"dir":"ltr"},{"str":"computers—that","boundary":[0.3052034948754731,0.8108589546076965,0.44906818611061516,0.8261315199387138],"dir":"ltr"},{"str":"the","boundary":[0.4540099520914871,0.8108589546076965,0.48146640388121126,0.8261315199387138],"dir":"ltr"},{"str":"efficiency","boundary":[0.4864081698620831,0.8108589546076965,0.5673147625009174,0.8261315199387138],"dir":"ltr"},{"str":"considerations","boundary":[0.5722565284817893,0.8108589546076965,0.6963936899212909,0.8261315199387138],"dir":"ltr"},{"str":"are","boundary":[0.7013354559021627,0.8108589546076965,0.7287919076918868,0.8261315199387138],"dir":"ltr"},{"str":"of","boundary":[0.7337336736727588,0.8108589546076965,0.7513065935007391,0.8261315199387138],"dir":"ltr"},{"str":"primary","boundary":[0.7562483594816111,0.8108589546076965,0.8243458946980255,0.8261315199387138],"dir":"ltr"},{"str":"importance","boundary":[0.8292876606788973,0.8108589546076965,0.927035791780543,0.8261315199387138],"dir":"ltr"},{"str":"from","boundary":[0.2391024331153309,0.8291860330049174,0.280830705057813,0.8444585983359347],"dir":"ltr"},{"str":"a","boundary":[0.286385250020313,0.8291860330049174,0.29626878198205675,0.8444585983359347],"dir":"ltr"},{"str":"practical","boundary":[0.3018233269445567,0.8291860330049174,0.37539633886777724,0.8444585983359347],"dir":"ltr"},{"str":"point","boundary":[0.38095088383027725,0.8291860330049174,0.4260000225119053,0.8444585983359347],"dir":"ltr"},{"str":"of","boundary":[0.43155456747440524,0.8291860330049174,0.44912748730238566,0.8444585983359347],"dir":"ltr"},{"str":"view.","boundary":[0.4546820322648856,0.8291860330049174,0.49769516336239444,0.8444585983359347],"dir":"ltr"},{"str":"In","boundary":[0.5032497083248944,0.8291860330049174,0.52192958373259,0.8444585983359347],"dir":"ltr"},{"str":"this","boundary":[0.5274841286950902,0.8291860330049174,0.5582416801600367,0.8444585983359347],"dir":"ltr"},{"str":"chapter,","boundary":[0.5637962251225368,0.8291860330049174,0.6331786194939779,0.8444585983359347],"dir":"ltr"},{"str":"we","boundary":[0.6388715339039421,0.8291860330049174,0.6630268860184438,0.8444585983359347],"dir":"ltr"},{"str":"too","boundary":[0.6685814309809439,0.8291860330049174,0.6971448383503833,0.8444585983359347],"dir":"ltr"},{"str":"will","boundary":[0.7026993833128834,0.8291860330049174,0.7334569347778299,0.8444585983359347],"dir":"ltr"},{"str":"limit","boundary":[0.7390114797403299,0.8291860330049174,0.778545607587305,0.8444585983359347],"dir":"ltr"},{"str":"the","boundary":[0.7841001525498048,0.8291860330049174,0.8115566043395289,0.8444585983359347],"dir":"ltr"},{"str":"discussion","boundary":[0.8171111493020291,0.8291860330049174,0.9039083269900627,0.8444585983359347],"dir":"ltr"},{"str":"to","boundary":[0.9094628719525627,0.8291860330049174,0.9270357917805431,0.8444585983359347],"dir":"ltr"},{"str":"an","boundary":[0.2391024331153309,0.8475146386586713,0.2599764526185337,0.8627872039896886],"dir":"ltr"},{"str":"algorithm’s","boundary":[0.26491821859940556,0.8475146386586713,0.3612233540346367,0.8627872039896886],"dir":"ltr"},{"str":"efficiency.","boundary":[0.3661651200155086,0.8475146386586713,0.45019490875425394,0.8627872039896886],"dir":"ltr"},{"str":"41","boundary":[0.905015282569778,0.9329356238115841,0.9269962576526961,0.9482081891426013],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.9271,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":123,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/09340b65385d87eaf14b5d71ee8ad7bc.jpg","blurred":"/storage/books/4a8b03583f119702/pages/c072ee29cda604bbc91c08fa712fc49e.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07291,0.05179]},"elements":[{"words":[{"str":"3","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Brute","boundary":[0.14421784044919886,0.17005356781848974,0.27411149685560804,0.20670781659232623],"dir":"ltr"},{"str":"Force","boundary":[0.2899093739861172,0.17005356781848974,0.42245973045050994,0.20670781659232623],"dir":"ltr"},{"str":"and","boundary":[0.4382576075810192,0.17005356781848974,0.5262607970017238,0.20670781659232623],"dir":"ltr"},{"str":"Exhaustive","boundary":[0.14421784044919886,0.20976111551518684,0.4041000354069451,0.24641536428902333],"dir":"ltr"},{"str":"Search","boundary":[0.4198979125374544,0.20976111551518684,0.5852774911469293,0.24641536428902333],"dir":"ltr"},{"str":"Science","boundary":[0.23910077902799318,0.313277715294131,0.30168330340975463,0.32855028062514835],"dir":"ltr"},{"str":"is","boundary":[0.30662506939062645,0.313277715294131,0.31980970102759265,0.32855028062514835],"dir":"ltr"},{"str":"as","boundary":[0.3247514670084646,0.313277715294131,0.34232438683644495,0.32855028062514835],"dir":"ltr"},{"str":"far","boundary":[0.3472661528173168,0.313277715294131,0.3714215049318186,0.32855028062514835],"dir":"ltr"},{"str":"removed","boundary":[0.3763632709126904,0.313277715294131,0.44958047568528814,0.32855028062514835],"dir":"ltr"},{"str":"from","boundary":[0.45452224166616007,0.313277715294131,0.49625051360864214,0.32855028062514835],"dir":"ltr"},{"str":"brute","boundary":[0.501192279589514,0.313277715294131,0.5451344626914267,0.32855028062514835],"dir":"ltr"},{"str":"force","boundary":[0.5500762286722986,0.313277715294131,0.5928916891305724,0.32855028062514835],"dir":"ltr"},{"str":"as","boundary":[0.5978334551114445,0.313277715294131,0.6154063749394248,0.32855028062514835],"dir":"ltr"},{"str":"this","boundary":[0.6203481409202967,0.313277715294131,0.6500185038694514,0.32855028062514835],"dir":"ltr"},{"str":"sword","boundary":[0.6549602698503233,0.313277715294131,0.706038363028615,0.32855028062514835],"dir":"ltr"},{"str":"from","boundary":[0.7109801290094869,0.313277715294131,0.752708400951969,0.32855028062514835],"dir":"ltr"},{"str":"a","boundary":[0.7576501669328408,0.313277715294131,0.7675336988945846,0.32855028062514835],"dir":"ltr"},{"str":"crowbar.","boundary":[0.7724754648754565,0.313277715294131,0.845890340287289,0.32855028062514835],"dir":"ltr"},{"str":"—Edward","boundary":[0.39650574278087924,0.33520581996187493,0.47997737654712525,0.3497148030160388],"dir":"ltr"},{"str":"Lytton","boundary":[0.4846908478801573,0.33520581996187493,0.5389614939059055,0.3497148030160388],"dir":"ltr"},{"str":"(1803–1873),","boundary":[0.5436749652389378,0.33520581996187493,0.6474840071871509,0.3497148030160388],"dir":"ltr"},{"str":"Leila","boundary":[0.6522068679053086,0.33520581996187493,0.6939332954033061,0.3497148030160388],"dir":"ltr"},{"str":",","boundary":[0.6938600581993266,0.33520581996187493,0.6985547507621076,0.3497148030160388],"dir":"ltr"},{"str":"Book","boundary":[0.7032682220951397,0.33520581996187493,0.748149482995326,0.3497148030160388],"dir":"ltr"},{"str":"II,","boundary":[0.7528629543283581,0.33520581996187493,0.7721675301465135,0.3497148030160388],"dir":"ltr"},{"str":"Chapter","boundary":[0.7768810014795456,0.33520581996187493,0.8436583084925424,0.3497148030160388],"dir":"ltr"},{"str":"I","boundary":[0.8483717798255744,0.33520581996187493,0.8556767214532617,0.3497148030160388],"dir":"ltr"},{"str":"Doing","boundary":[0.23910077902799318,0.3926957908505804,0.2929264940916496,0.4079683561815977],"dir":"ltr"},{"str":"a","boundary":[0.29786826007252154,0.3926957908505804,0.3077517920342653,0.4079683561815977],"dir":"ltr"},{"str":"thing","boundary":[0.31269355801513715,0.3926957908505804,0.35554855260125806,0.4079683561815977],"dir":"ltr"},{"str":"well","boundary":[0.36049031858212993,0.3926957908505804,0.3945292026583754,0.4079683561815977],"dir":"ltr"},{"str":"is","boundary":[0.39947096863924725,0.3926957908505804,0.41265560027621345,0.4079683561815977],"dir":"ltr"},{"str":"often","boundary":[0.4175973662570853,0.3926957908505804,0.46043259377928275,0.4079683561815977],"dir":"ltr"},{"str":"a","boundary":[0.4653743597601547,0.3926957908505804,0.4752578917218984,0.4079683561815977],"dir":"ltr"},{"str":"waste","boundary":[0.4801996577027703,0.3926957908505804,0.5263162178362667,0.4079683561815977],"dir":"ltr"},{"str":"of","boundary":[0.5312579838171384,0.3926957908505804,0.5488309036451189,0.4079683561815977],"dir":"ltr"},{"str":"time.","boundary":[0.5537726696259908,0.3926957908505804,0.594453287180528,0.4079683561815977],"dir":"ltr"},{"str":"—Robert","boundary":[0.34028530504590937,0.414622362528409,0.41750360831853106,0.42913134558257293],"dir":"ltr"},{"str":"Byrne,","boundary":[0.4222170796515632,0.414622362528409,0.47629993797480014,0.42913134558257293],"dir":"ltr"},{"str":"a","boundary":[0.48101340930783226,0.414622362528409,0.49040279443339424,0.42913134558257293],"dir":"ltr"},{"str":"master","boundary":[0.49511626576642637,0.414622362528409,0.5504009653857354,0.42913134558257293],"dir":"ltr"},{"str":"pool","boundary":[0.5551144367187674,0.414622362528409,0.5916579236274545,0.42913134558257293],"dir":"ltr"},{"str":"and","boundary":[0.5963713949604867,0.414622362528409,0.6266427726052985,0.42913134558257293],"dir":"ltr"},{"str":"billiards","boundary":[0.6313562439383307,0.414622362528409,0.6971194973577667,0.42913134558257293],"dir":"ltr"},{"str":"player","boundary":[0.7018329686907988,0.414622362528409,0.7529675600846094,0.42913134558257293],"dir":"ltr"},{"str":"and","boundary":[0.7576810314176414,0.414622362528409,0.7879524090624532,0.42913134558257293],"dir":"ltr"},{"str":"a","boundary":[0.7926658803954854,0.414622362528409,0.8020552655210473,0.42913134558257293],"dir":"ltr"},{"str":"writer","boundary":[0.8067687368540795,0.414622362528409,0.8558001059797642,0.42913134558257293],"dir":"ltr"},{"str":"fter","boundary":[0.2884995896299513,0.5069571941938217,0.31923737403097435,0.5222297595248391],"dir":"ltr"},{"str":"introducing","boundary":[0.32542446503902595,0.5069571941938217,0.4242993187843105,0.5222297595248391],"dir":"ltr"},{"str":"the","boundary":[0.4304864097923621,0.5069571941938217,0.45794286158208625,0.5222297595248391],"dir":"ltr"},{"str":"framework","boundary":[0.46412995259013784,0.5069571941938217,0.5585769840165611,0.5222297595248391],"dir":"ltr"},{"str":"and","boundary":[0.5647640750246127,0.5069571941938217,0.5966285820692745,0.5222297595248391],"dir":"ltr"},{"str":"methods","boundary":[0.6028156730773261,0.5069571941938217,0.6764084520644701,0.5222297595248391],"dir":"ltr"},{"str":"for","boundary":[0.6825955430725218,0.5069571941938217,0.7078578507667388,0.5222297595248391],"dir":"ltr"},{"str":"algorithm","boundary":[0.7140449417747903,0.5069571941938217,0.797521252723678,0.5222297595248391],"dir":"ltr"},{"str":"analysis","boundary":[0.8037083437317296,0.5069571941938217,0.8707186904323522,0.5222297595248391],"dir":"ltr"},{"str":"in","boundary":[0.8769057814404038,0.5069571941938217,0.8933915127525923,0.5222297595248391],"dir":"ltr"},{"str":"the","boundary":[0.899578603760644,0.5069571941938217,0.9270350555503681,0.5222297595248391],"dir":"ltr"},{"str":"preceding","boundary":[0.2884995896299513,0.5252842725910426,0.37308285615855435,0.5405568379220599],"dir":"ltr"},{"str":"chapter,","boundary":[0.3804362039380917,0.5252842725910426,0.44981859830953286,0.5405568379220599],"dir":"ltr"},{"str":"we","boundary":[0.45776495800677486,0.5252842725910426,0.4819203101212766,0.5405568379220599],"dir":"ltr"},{"str":"are","boundary":[0.4892736579008139,0.5252842725910426,0.5167301096905381,0.5405568379220599],"dir":"ltr"},{"str":"ready","boundary":[0.5240834574700753,0.5252842725910426,0.5724139287630023,0.5405568379220599],"dir":"ltr"},{"str":"to","boundary":[0.5797672765425397,0.5252842725910426,0.5973401963705202,0.5405568379220599],"dir":"ltr"},{"str":"embark","boundary":[0.6046935441500575,0.5252842725910426,0.6705969352709649,0.5405568379220599],"dir":"ltr"},{"str":"on","boundary":[0.6779502830505022,0.5252842725910426,0.6999312581334203,0.5405568379220599],"dir":"ltr"},{"str":"a","boundary":[0.7072846059129575,0.5252842725910426,0.7171681378747012,0.5405568379220599],"dir":"ltr"},{"str":"discussion","boundary":[0.7245214856542387,0.5252842725910426,0.8113186633422723,0.5405568379220599],"dir":"ltr"},{"str":"of","boundary":[0.8186720111218098,0.5252842725910426,0.8362449309497901,0.5405568379220599],"dir":"ltr"},{"str":"algorithm","boundary":[0.8435982787293275,0.5252842725910426,0.9270745896782151,0.5405568379220599],"dir":"ltr"},{"str":"Adesign","boundary":[0.23910077902799318,0.505659050975122,0.2940343675285278,0.5588839163192807],"dir":"ltr"},{"str":"strategies.","boundary":[0.298501723975236,0.5436113509882634,0.3836187012297732,0.5588839163192807],"dir":"ltr"},{"str":"Each","boundary":[0.38808605767648136,0.5436113509882634,0.4320084737144706,0.5588839163192807],"dir":"ltr"},{"str":"of","boundary":[0.43647583016117886,0.5436113509882634,0.45404874998915923,0.5588839163192807],"dir":"ltr"},{"str":"the","boundary":[0.4585161064358674,0.5436113509882634,0.48597255822559154,0.5588839163192807],"dir":"ltr"},{"str":"next","boundary":[0.4904399146722997,0.5436113509882634,0.5277798984237676,0.5588839163192807],"dir":"ltr"},{"str":"eight","boundary":[0.5322472548704759,0.5436113509882634,0.5750824823926732,0.5588839163192807],"dir":"ltr"},{"str":"chapters","boundary":[0.5795498388393814,0.5436113509882634,0.6520356622468101,0.5588839163192807],"dir":"ltr"},{"str":"is","boundary":[0.6565030186935182,0.5436113509882634,0.6696876503304844,0.5588839163192807],"dir":"ltr"},{"str":"devoted","boundary":[0.6741550067771926,0.5436113509882634,0.7433594975733224,0.5588839163192807],"dir":"ltr"},{"str":"to","boundary":[0.7478268540200306,0.5436113509882634,0.765399773848011,0.5588839163192807],"dir":"ltr"},{"str":"a","boundary":[0.7698671302947191,0.5436113509882634,0.7797506622564628,0.5588839163192807],"dir":"ltr"},{"str":"particular","boundary":[0.7842180187031711,0.5436113509882634,0.8676943296520587,0.5588839163192807],"dir":"ltr"},{"str":"design","boundary":[0.872161686098767,0.5436113509882634,0.9270943567421388,0.5588839163192807],"dir":"ltr"},{"str":"strategy.","boundary":[0.23910169688515603,0.5619399566420172,0.31030266113755806,0.5772125219730345],"dir":"ltr"},{"str":"The","boundary":[0.3157386037165171,0.5619399566420172,0.3490065722997466,0.5772125219730345],"dir":"ltr"},{"str":"subject","boundary":[0.3544425148787056,0.5619399566420172,0.4148506622288834,0.5772125219730345],"dir":"ltr"},{"str":"of","boundary":[0.4202866048078425,0.5619399566420172,0.43785952463582295,0.5772125219730345],"dir":"ltr"},{"str":"this","boundary":[0.44329546721478197,0.5619399566420172,0.47405301867972854,0.5772125219730345],"dir":"ltr"},{"str":"chapter","boundary":[0.4794889612586876,0.5619399566420172,0.5442853967998796,0.5772125219730345],"dir":"ltr"},{"str":"is","boundary":[0.5497213393788387,0.5619399566420172,0.5629059710158049,0.5772125219730345],"dir":"ltr"},{"str":"brute","boundary":[0.5683419135947639,0.5619399566420172,0.6144782407921838,0.5772125219730345],"dir":"ltr"},{"str":"force","boundary":[0.6199141833711428,0.5619399566420172,0.663836599409132,0.5772125219730345],"dir":"ltr"},{"str":"and","boundary":[0.669272541988091,0.5619399566420172,0.7011370490327529,0.5772125219730345],"dir":"ltr"},{"str":"its","boundary":[0.7065729916117119,0.5619399566420172,0.7263400555351994,0.5772125219730345],"dir":"ltr"},{"str":"important","boundary":[0.7317759981141585,0.5619399566420172,0.8174464531585534,0.5772125219730345],"dir":"ltr"},{"str":"special","boundary":[0.8228823957375124,0.5619399566420172,0.8810963989921832,0.5772125219730345],"dir":"ltr"},{"str":"case,","boundary":[0.886532341571142,0.5619399566420172,0.9269757543585974,0.5772125219730345],"dir":"ltr"},{"str":"exhaustive","boundary":[0.23910169688515603,0.580267035039238,0.3302673957002804,0.5955396003702553],"dir":"ltr"},{"str":"search.","boundary":[0.3352091616811523,0.580267035039238,0.3950638312414725,0.5955396003702553],"dir":"ltr"},{"str":"Brute","boundary":[0.4000055972223443,0.580267035039238,0.44942325703106306,0.5955396003702553],"dir":"ltr"},{"str":"force","boundary":[0.454365023011935,0.580267035039238,0.49828743904992423,0.5955396003702553],"dir":"ltr"},{"str":"can","boundary":[0.503229205030796,0.580267035039238,0.5328798009160273,0.5955396003702553],"dir":"ltr"},{"str":"be","boundary":[0.5378215668968992,0.580267035039238,0.558695586400102,0.5955396003702553],"dir":"ltr"},{"str":"described","boundary":[0.5636373523809739,0.580267035039238,0.6460264748140698,0.5955396003702553],"dir":"ltr"},{"str":"as","boundary":[0.6509682407949416,0.580267035039238,0.668541160622922,0.5955396003702553],"dir":"ltr"},{"str":"follows:","boundary":[0.6734829266037939,0.580267035039238,0.7399397955145589,0.5955396003702553],"dir":"ltr"},{"str":"Brute","boundary":[0.27468241194743354,0.6086908063767944,0.322993116176437,0.6239633717078118],"dir":"ltr"},{"str":"force","boundary":[0.33099877706544945,0.6086908063767944,0.3738142375237234,0.6239633717078118],"dir":"ltr"},{"str":"is","boundary":[0.38173490003786487,0.6086908063767944,0.394919531674831,0.6239633717078118],"dir":"ltr"},{"str":"a","boundary":[0.4021147429429805,0.6086908063767944,0.41199827490472424,0.6239633717078118],"dir":"ltr"},{"str":"straightforward","boundary":[0.41919348617287366,0.6086908063767944,0.5520874569304802,0.6239633717078118],"dir":"ltr"},{"str":"approach","boundary":[0.5592826681986296,0.6086908063767944,0.6394776465362184,0.6239633717078118],"dir":"ltr"},{"str":"to","boundary":[0.6466728578043679,0.6086908063767944,0.6642457776323483,0.6239633717078118],"dir":"ltr"},{"str":"solving","boundary":[0.6714409889004977,0.6086908063767944,0.7318689033145991,0.6239633717078118],"dir":"ltr"},{"str":"a","boundary":[0.7390641145827485,0.6086908063767944,0.7489476465444922,0.6239633717078118],"dir":"ltr"},{"str":"problem,","boundary":[0.7561428578126418,0.6086908063767944,0.8335902142648658,0.6239633717078118],"dir":"ltr"},{"str":"usually","boundary":[0.8413389033228729,0.6086908063767944,0.9017668177369742,0.6239633717078118],"dir":"ltr"},{"str":"directly","boundary":[0.27468241194743354,0.6270178847740151,0.3394788474886256,0.6422904501050325],"dir":"ltr"},{"str":"based","boundary":[0.3463380186700758,0.6270178847740151,0.39577544554271804,0.6422904501050325],"dir":"ltr"},{"str":"on","boundary":[0.4026346167241682,0.6270178847740151,0.4246155918070863,0.6422904501050325],"dir":"ltr"},{"str":"the","boundary":[0.43147476298853643,0.6270178847740151,0.4589312147782606,0.6422904501050325],"dir":"ltr"},{"str":"problem","boundary":[0.46579038595971073,0.6270178847740151,0.538295976431063,0.6422904501050325],"dir":"ltr"},{"str":"statement","boundary":[0.545155147612513,0.6270178847740151,0.6296988800132692,0.6422904501050325],"dir":"ltr"},{"str":"and","boundary":[0.6365580511947193,0.6270178847740151,0.6684225582393811,0.6422904501050325],"dir":"ltr"},{"str":"definitions","boundary":[0.6752817294208313,0.6270178847740151,0.7653800067840874,0.6422904501050325],"dir":"ltr"},{"str":"of","boundary":[0.7722391779655376,0.6270178847740151,0.789812097793518,0.6422904501050325],"dir":"ltr"},{"str":"the","boundary":[0.7966712689749682,0.6270178847740151,0.8241277207646923,0.6422904501050325],"dir":"ltr"},{"str":"concepts","boundary":[0.8309868919461425,0.6270178847740151,0.9056668594490783,0.6422904501050325],"dir":"ltr"},{"str":"involved.","boundary":[0.27468241194743354,0.6453449631712359,0.35323672397937295,0.6606175285022532],"dir":"ltr"},{"str":"The","boundary":[0.27468241194743354,0.6737702617653254,0.30795038053066304,0.6890428270963427],"dir":"ltr"},{"str":"“force”","boundary":[0.3154420977576648,0.6737702617653254,0.3791315777191416,0.6890428270963427],"dir":"ltr"},{"str":"implied","boundary":[0.3866232949461433,0.6737702617653254,0.4514394975512588,0.6890428270963427],"dir":"ltr"},{"str":"by","boundary":[0.4589312147782606,0.6737702617653254,0.47980523428146343,0.6890428270963427],"dir":"ltr"},{"str":"the","boundary":[0.48729695150846514,0.6737702617653254,0.5147534032981893,0.6890428270963427],"dir":"ltr"},{"str":"strategy’s","boundary":[0.522245120525191,0.6737702617653254,0.6031517131640255,0.6890428270963427],"dir":"ltr"},{"str":"definition","boundary":[0.6106434303910272,0.6737702617653254,0.6930523198880466,0.6890428270963427],"dir":"ltr"},{"str":"is","boundary":[0.7005440371150484,0.6737702617653254,0.7137286687520146,0.6890428270963427],"dir":"ltr"},{"str":"that","boundary":[0.7212203859790164,0.6737702617653254,0.7552592700552618,0.6890428270963427],"dir":"ltr"},{"str":"of","boundary":[0.7627509872822636,0.6737702617653254,0.780323907110244,0.6890428270963427],"dir":"ltr"},{"str":"a","boundary":[0.7878156243372458,0.6737702617653254,0.7976991562989895,0.6890428270963427],"dir":"ltr"},{"str":"computer","boundary":[0.8051908735259914,0.6737702617653254,0.8875602288951638,0.6890428270963427],"dir":"ltr"},{"str":"and","boundary":[0.8950519461221657,0.6737702617653254,0.9269164531668275,0.6890428270963427],"dir":"ltr"},{"str":"not","boundary":[0.23910169688515603,0.6920973401625461,0.2676651042545955,0.7073699054935635],"dir":"ltr"},{"str":"that","boundary":[0.2751172873537503,0.6920973401625461,0.3091561714299958,0.7073699054935635],"dir":"ltr"},{"str":"of","boundary":[0.31660835452915054,0.6920973401625461,0.33418127435713096,0.7073699054935635],"dir":"ltr"},{"str":"one’s","boundary":[0.3416334574562857,0.6920973401625461,0.38632678898729095,0.7073699054935635],"dir":"ltr"},{"str":"intellect.","boundary":[0.3937789720864458,0.6920973401625461,0.4679054617995239,0.7073699054935635],"dir":"ltr"},{"str":"“Just","boundary":[0.4753576448986787,0.6920973401625461,0.5182917077404936,0.7073699054935635],"dir":"ltr"},{"str":"do","boundary":[0.5257438908396483,0.6920973401625461,0.5477248659225665,0.7073699054935635],"dir":"ltr"},{"str":"it!”","boundary":[0.5551770490217213,0.6920973401625461,0.5837206893272372,0.7073699054935635],"dir":"ltr"},{"str":"would","boundary":[0.591172872426392,0.6920973401625461,0.6439113989742566,0.7073699054935635],"dir":"ltr"},{"str":"be","boundary":[0.6513635820734114,0.6920973401625461,0.6722376015766142,0.7073699054935635],"dir":"ltr"},{"str":"another","boundary":[0.679689784675769,0.6920973401625461,0.7467001313763916,0.7073699054935635],"dir":"ltr"},{"str":"way","boundary":[0.7541523144755464,0.6920973401625461,0.7881911985517919,0.7073699054935635],"dir":"ltr"},{"str":"to","boundary":[0.7956433816509467,0.6920973401625461,0.8132163014789271,0.7073699054935635],"dir":"ltr"},{"str":"describe","boundary":[0.8206684845780817,0.6920973401625461,0.8920671194697186,0.7073699054935635],"dir":"ltr"},{"str":"the","boundary":[0.8995193025688736,0.6920973401625461,0.9269757543585977,0.7073699054935635],"dir":"ltr"},{"str":"prescription","boundary":[0.23910169688515603,0.7104244185597668,0.3423648388214548,0.7256969838907842],"dir":"ltr"},{"str":"of","boundary":[0.3487298334048178,0.7104244185597668,0.3663027532327982,0.7256969838907842],"dir":"ltr"},{"str":"the","boundary":[0.37266774781616113,0.7104244185597668,0.4001241996058853,0.7256969838907842],"dir":"ltr"},{"str":"brute-force","boundary":[0.4064891941892482,0.7104244185597668,0.5031303697111786,0.7256969838907842],"dir":"ltr"},{"str":"approach.","boundary":[0.5094953642945417,0.7104244185597668,0.5946321086130024,0.7256969838907842],"dir":"ltr"},{"str":"And","boundary":[0.6009971031963651,0.7104244185597668,0.6395428778471658,0.7256969838907842],"dir":"ltr"},{"str":"often,","boundary":[0.6459078724305288,0.7104244185597668,0.6958790100291052,0.7256969838907842],"dir":"ltr"},{"str":"the","boundary":[0.7025998117630909,0.7104244185597668,0.730056263552815,0.7256969838907842],"dir":"ltr"},{"str":"brute-force","boundary":[0.7364212581361781,0.7104244185597668,0.8330624336581084,0.7256969838907842],"dir":"ltr"},{"str":"strategy","boundary":[0.8394274282414714,0.7104244185597668,0.9075051963939623,0.7256969838907842],"dir":"ltr"},{"str":"is","boundary":[0.9138701909773254,0.7104244185597668,0.9270548226142915,0.7256969838907842],"dir":"ltr"},{"str":"indeed","boundary":[0.23910169688515603,0.7287514969569877,0.29733546720375026,0.744024062288005],"dir":"ltr"},{"str":"the","boundary":[0.30227723318462213,0.7287514969569877,0.3297336849743463,0.744024062288005],"dir":"ltr"},{"str":"one","boundary":[0.33467545095521817,0.7287514969569877,0.36653995799988004,0.744024062288005],"dir":"ltr"},{"str":"that","boundary":[0.37148172398075185,0.7287514969569877,0.40552060805699736,0.744024062288005],"dir":"ltr"},{"str":"is","boundary":[0.4104623740378692,0.7287514969569877,0.42364700567483543,0.744024062288005],"dir":"ltr"},{"str":"easiest","boundary":[0.42858877165570725,0.7287514969569877,0.4856958193306627,0.744024062288005],"dir":"ltr"},{"str":"to","boundary":[0.49063758531153456,0.7287514969569877,0.5082105051395149,0.744024062288005],"dir":"ltr"},{"str":"apply.","boundary":[0.5131522711203869,0.7287514969569877,0.563518749997433,0.744024062288005],"dir":"ltr"},{"str":"As","boundary":[0.27468241194743354,0.7470785753542085,0.29893659938155276,0.7623511406852258],"dir":"ltr"},{"str":"an","boundary":[0.30824688648951537,0.7470785753542085,0.3291209059927182,0.7623511406852258],"dir":"ltr"},{"str":"example,","boundary":[0.33843119310068076,0.7470785753542085,0.41512740112381225,0.7623511406852258],"dir":"ltr"},{"str":"consider","boundary":[0.4255446438114902,0.7470785753542085,0.4980502342828424,0.7623511406852258],"dir":"ltr"},{"str":"the","boundary":[0.507360521390805,0.7470785753542085,0.5348169731805291,0.7623511406852258],"dir":"ltr"},{"str":"exponentiation","boundary":[0.5441272602884918,0.7470785753542085,0.6737596654987229,0.7623511406852258],"dir":"ltr"},{"str":"problem:","boundary":[0.6830699526066855,0.7470785753542085,0.7605173090589095,0.7623511406852258],"dir":"ltr"},{"str":"compute","boundary":[0.7698275961668721,0.7470785753542085,0.8445075636698081,0.7623511406852258],"dir":"ltr"},{"str":"a","boundary":[0.8538731985567563,0.7476894779674492,0.8637567305184999,0.7629620432984665],"dir":"ltr"},{"str":"n","boundary":[0.8646484117284374,0.7447218743306009,0.8727282531746245,0.7561763749783597],"dir":"ltr"},{"str":"for","boundary":[0.882541467674516,0.7470770695901939,0.907803775368733,0.7623496349212112],"dir":"ltr"},{"str":"a","boundary":[0.9171140624766957,0.7470770695901939,0.9269975944384394,0.7623496349212112],"dir":"ltr"},{"str":"nonzero","boundary":[0.23910179319468194,0.7654041479874147,0.30941323957052697,0.780676713318432],"dir":"ltr"},{"str":"number","boundary":[0.31676658735006435,0.7654041479874147,0.383776934050687,0.780676713318432],"dir":"ltr"},{"str":"a","boundary":[0.39112039829826256,0.7660150506006554,0.40100393026000636,0.7812876159316727],"dir":"ltr"},{"str":"and","boundary":[0.4092369123841389,0.7654041479874147,0.44110141942880077,0.780676713318432],"dir":"ltr"},{"str":"a","boundary":[0.4484547672083381,0.7654041479874147,0.45833829917008184,0.780676713318432],"dir":"ltr"},{"str":"nonnegative","boundary":[0.46569164694961923,0.7654041479874147,0.571148932981425,0.780676713318432],"dir":"ltr"},{"str":"integer","boundary":[0.5785022807609624,0.7654041479874147,0.6389104281111402,0.780676713318432],"dir":"ltr"},{"str":"n.","boundary":[0.646238078707577,0.7660150506006554,0.6624470711248368,0.7812876159316727],"dir":"ltr"},{"str":"Although","boundary":[0.6697944887851971,0.7654041479874147,0.7522824465379104,0.780676713318432],"dir":"ltr"},{"str":"this","boundary":[0.7596357943174478,0.7654041479874147,0.7903933457823944,0.780676713318432],"dir":"ltr"},{"str":"problem","boundary":[0.7977466935619317,0.7654041479874147,0.8702522840332839,0.780676713318432],"dir":"ltr"},{"str":"might","boundary":[0.8776056318128213,0.7654041479874147,0.92702329162154,0.780676713318432],"dir":"ltr"},{"str":"seem","boundary":[0.23910179319468194,0.7837312263846354,0.2830242092326712,0.7990037917156528],"dir":"ltr"},{"str":"trivial,","boundary":[0.2888752601540235,0.7837312263846354,0.34434164152332947,0.7990037917156528],"dir":"ltr"},{"str":"it","boundary":[0.35041013014784006,0.7837312263846354,0.36248780620509097,0.7990037917156528],"dir":"ltr"},{"str":"provides","boundary":[0.3683388571264432,0.7837312263846354,0.4419514031775107,0.7990037917156528],"dir":"ltr"},{"str":"a","boundary":[0.447802454098863,0.7837312263846354,0.4576859860606068,0.7990037917156528],"dir":"ltr"},{"str":"useful","boundary":[0.463537036981959,0.7837312263846354,0.5151686079501084,0.7990037917156528],"dir":"ltr"},{"str":"vehicle","boundary":[0.5210196588714607,0.7837312263846354,0.5814278062216386,0.7990037917156528],"dir":"ltr"},{"str":"for","boundary":[0.5872788571429908,0.7837312263846354,0.6125411648372078,0.7990037917156528],"dir":"ltr"},{"str":"illustrating","boundary":[0.6183922157585602,0.7837312263846354,0.7106648701533999,0.7990037917156528],"dir":"ltr"},{"str":"several","boundary":[0.716515921074752,0.7837312263846354,0.7769240684249299,0.7990037917156528],"dir":"ltr"},{"str":"algorithm","boundary":[0.7827751193462822,0.7837312263846354,0.8662514302951699,0.7990037917156528],"dir":"ltr"},{"str":"design","boundary":[0.8721024812165223,0.7837312263846354,0.9270351518598942,0.7990037917156528],"dir":"ltr"},{"str":"strategies,","boundary":[0.23910179319468194,0.8020583047818562,0.32421877044921915,0.8173308701128735],"dir":"ltr"},{"str":"including","boundary":[0.3280338137864522,0.8020583047818562,0.4071416036082492,0.8173308701128735],"dir":"ltr"},{"str":"the","boundary":[0.4106799080505535,0.8020583047818562,0.43813635984027766,0.8173308701128735],"dir":"ltr"},{"str":"brute","boundary":[0.4416746642825819,0.8020583047818562,0.48781099148000173,0.8173308701128735],"dir":"ltr"},{"str":"force.","boundary":[0.49134929592230603,0.8020583047818562,0.5394820965759981,0.8173308701128735],"dir":"ltr"},{"str":"(Also","boundary":[0.5430204010183024,0.8020583047818562,0.5914497076308467,0.8173308701128735],"dir":"ltr"},{"str":"note","boundary":[0.5949880120731509,0.8020583047818562,0.6334349514043341,0.8173308701128735],"dir":"ltr"},{"str":"that","boundary":[0.6369732558466384,0.8020583047818562,0.6710121399228839,0.8173308701128735],"dir":"ltr"},{"str":"computing","boundary":[0.6745504443651882,0.8020583047818562,0.7657161431803126,0.8173308701128735],"dir":"ltr"},{"str":"a","boundary":[0.7693078186952104,0.802669207395097,0.779191350656954,0.8179417727261142],"dir":"ltr"},{"str":"n","boundary":[0.7800809495652588,0.7997025576458938,0.7881607910114458,0.8111570582936526],"dir":"ltr"},{"str":"mod","boundary":[0.792198013321782,0.8020577529054868,0.8306449526529651,0.817330318236504],"dir":"ltr"},{"str":"m","boundary":[0.8341891872144465,0.8026686555187275,0.8496272641386903,0.8179412208497446],"dir":"ltr"},{"str":"for","boundary":[0.8531714987001716,0.8020577529054868,0.8784338063943886,0.817330318236504],"dir":"ltr"},{"str":"some","boundary":[0.8819721108366929,0.8020577529054868,0.9270014824543974,0.817330318236504],"dir":"ltr"},{"str":"large","boundary":[0.2391037045042475,0.8203863585592407,0.28193893202644493,0.835658923890258],"dir":"ltr"},{"str":"integers","boundary":[0.2862086178339182,0.8203863585592407,0.3543061530503327,0.835658923890258],"dir":"ltr"},{"str":"is","boundary":[0.35857583885780603,0.8203863585592407,0.3717604704947722,0.835658923890258],"dir":"ltr"},{"str":"a","boundary":[0.3760301563022455,0.8203863585592407,0.38591368826398925,0.835658923890258],"dir":"ltr"},{"str":"principal","boundary":[0.39018337407146253,0.8203863585592407,0.4659900642180371,0.835658923890258],"dir":"ltr"},{"str":"component","boundary":[0.4702597500255104,0.8203863585592407,0.5669206926113642,0.835658923890258],"dir":"ltr"},{"str":"of","boundary":[0.5711903784188377,0.8203863585592407,0.5887632982468181,0.835658923890258],"dir":"ltr"},{"str":"a","boundary":[0.5930329840542914,0.8203863585592407,0.6029165160160351,0.835658923890258],"dir":"ltr"},{"str":"leading","boundary":[0.6071862018235084,0.8203863585592407,0.6698082603331168,0.835658923890258],"dir":"ltr"},{"str":"encryption","boundary":[0.6740779461405901,0.8203863585592407,0.7663506005354298,0.835658923890258],"dir":"ltr"},{"str":"algorithm.)","boundary":[0.7706202863429031,0.8203863585592407,0.8667277511388994,0.835658923890258],"dir":"ltr"},{"str":"By","boundary":[0.8709974369463728,0.8203863585592407,0.8951527890608745,0.835658923890258],"dir":"ltr"},{"str":"the","boundary":[0.8994224748683478,0.8203863585592407,0.9268789266580719,0.835658923890258],"dir":"ltr"},{"str":"definition","boundary":[0.2391037045042475,0.8387134369564614,0.3215125940012669,0.8539860022874787],"dir":"ltr"},{"str":"of","boundary":[0.32645435998213884,0.8387134369564614,0.3440272798101192,0.8539860022874787],"dir":"ltr"},{"str":"exponentiation,","boundary":[0.3489690457909911,0.8387134369564614,0.48354321698209407,0.8539860022874787],"dir":"ltr"},{"str":"a","boundary":[0.5139587982411643,0.8689638071076075,0.5238423302029079,0.8842363724386246],"dir":"ltr"},{"str":"n","boundary":[0.5247297535159271,0.8652332775588681,0.5328095949621141,0.8766877782066269],"dir":"ltr"},{"str":"a","boundary":[0.5575065751043101,0.8689628044095635,0.5673901070660538,0.8842353697405808],"dir":"ltr"},{"str":"∗","boundary":[0.5726718665464097,0.8716355033424915,0.5829705068505466,0.8869080686735087],"dir":"ltr"},{"str":"...∗","boundary":[0.5873627484543457,0.8658319285167051,0.6271459413067565,0.8869080686735087],"dir":"ltr"},{"str":"a","boundary":[0.6315401596169479,0.8689628044095635,0.6414236915786915,0.8842353697405808],"dir":"ltr"},{"str":".","boundary":[0.6467059466542965,0.8689628044095635,0.6521418892332554,0.8842353697405808],"dir":"ltr"},{"str":"=","boundary":[0.537696023640191,0.8716355033424915,0.5531143335005112,0.8869080686735087],"dir":"ltr"},{"str":"\u0017","boundary":[0.5575065751043101,0.8780056903420588,0.5664017538698795,0.8932782556730761],"dir":"ltr"},{"str":"\u0018\u0019","boundary":[0.5910154692483535,0.8780050764409174,0.6088058267794921,0.8932776417719347],"dir":"ltr"},{"str":"\u001a","boundary":[0.6334184463642915,0.8780050764409174,0.6423136251298608,0.8932776417719347],"dir":"ltr"},{"str":"n","boundary":[0.5761583260669475,0.8932931249700802,0.5842381675131346,0.904747625617839],"dir":"ltr"},{"str":"times","boundary":[0.5891794723828853,0.8928349449441697,0.6237671239314253,0.9042894455919285],"dir":"ltr"},{"str":"97","boundary":[0.9050160078872541,0.9329349988115958,0.9269969829701723,0.9482075641426131],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92709,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":157,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/e820d737f8508e886c5baf3e9edc7169.jpg","blurred":"/storage/books/4a8b03583f119702/pages/3ab58479a49b3b52cebee2ae915bd1eb.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07295,0.05179]},"elements":[{"words":[{"str":"4","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Decrease-and-Conquer","boundary":[0.14421784044919886,0.17005356781848974,0.6878925308865432,0.20670781659232623],"dir":"ltr"},{"str":"Plutarch","boundary":[0.23910077902799318,0.27434437041309123,0.3113691647322635,0.2896169357441086],"dir":"ltr"},{"str":"says","boundary":[0.31555978228404286,0.27434437041309123,0.3503498147893809,0.2896169357441086],"dir":"ltr"},{"str":"that","boundary":[0.3545404323411602,0.27434437041309123,0.3864049393858221,0.2896169357441086],"dir":"ltr"},{"str":"Sertorius,","boundary":[0.3905955569376014,0.27434437041309123,0.470256824549256,0.2896169357441086],"dir":"ltr"},{"str":"in","boundary":[0.4745858115484998,0.27434437041309123,0.4910715428606884,0.2896169357441086],"dir":"ltr"},{"str":"order","boundary":[0.49526216041246773,0.27434437041309123,0.5410426804592647,0.2896169357441086],"dir":"ltr"},{"str":"to","boundary":[0.5452332980110441,0.27434437041309123,0.5617190293232327,0.2896169357441086],"dir":"ltr"},{"str":"teach","boundary":[0.5659096468750121,0.27434437041309123,0.6095948581459195,0.2896169357441086],"dir":"ltr"},{"str":"his","boundary":[0.6137854756976988,0.27434437041309123,0.6379605948761241,0.2896169357441086],"dir":"ltr"},{"str":"soldiers","boundary":[0.6421512124279033,0.27434437041309123,0.7069674150330189,0.2896169357441086],"dir":"ltr"},{"str":"that","boundary":[0.7111580325847983,0.27434437041309123,0.7430225396294601,0.2896169357441086],"dir":"ltr"},{"str":"perseverance","boundary":[0.7472131571812395,0.27434437041309123,0.8559122416964973,0.2896169357441086],"dir":"ltr"},{"str":"and","boundary":[0.23910077902799318,0.2926729760668451,0.270965286072655,0.30794554139786245],"dir":"ltr"},{"str":"wit","boundary":[0.27659889929084897,0.2926729760668451,0.301861206985066,0.30794554139786245],"dir":"ltr"},{"str":"are","boundary":[0.30749482020325997,0.2926729760668451,0.3338443164132688,0.30794554139786245],"dir":"ltr"},{"str":"better","boundary":[0.3394779296314627,0.2926729760668451,0.3867014453446744,0.30794554139786245],"dir":"ltr"},{"str":"than","boundary":[0.3923350585628683,0.2926729760668451,0.42969480937825977,0.30794554139786245],"dir":"ltr"},{"str":"brute","boundary":[0.43532842259645366,0.2926729760668451,0.47927060569836644,0.30794554139786245],"dir":"ltr"},{"str":"force,","boundary":[0.4849042189165603,0.2926729760668451,0.5321672687576189,0.30794554139786245],"dir":"ltr"},{"str":"had","boundary":[0.5379787855511242,0.2926729760668451,0.569843292595786,0.30794554139786245],"dir":"ltr"},{"str":"two","boundary":[0.5754769058139801,0.2926729760668451,0.6062344572789267,0.30794554139786245],"dir":"ltr"},{"str":"horses","boundary":[0.6118680704971206,0.2926729760668451,0.6656937855607771,0.30794554139786245],"dir":"ltr"},{"str":"brought","boundary":[0.6713273987789711,0.2926729760668451,0.7383575125435172,0.30794554139786245],"dir":"ltr"},{"str":"before","boundary":[0.7439911257617111,0.2926729760668451,0.7977970737614442,0.30794554139786245],"dir":"ltr"},{"str":"them,","boundary":[0.803430686979638,0.2926729760668451,0.850100724902992,0.30794554139786245],"dir":"ltr"},{"str":"and","boundary":[0.23910077902799318,0.3110000544640659,0.270965286072655,0.32627261979508326],"dir":"ltr"},{"str":"set","boundary":[0.27483963060165856,0.3110000544640659,0.2968008386206532,0.32627261979508326],"dir":"ltr"},{"str":"two","boundary":[0.30067518314965674,0.3110000544640659,0.3314327346146033,0.32627261979508326],"dir":"ltr"},{"str":"men","boundary":[0.33530707914360686,0.3110000544640659,0.3715401073153594,0.32627261979508326],"dir":"ltr"},{"str":"to","boundary":[0.375414451844363,0.3110000544640659,0.39190018315655156,0.32627261979508326],"dir":"ltr"},{"str":"pull","boundary":[0.39577452768555516,0.3110000544640659,0.4287459903099323,0.32627261979508326],"dir":"ltr"},{"str":"out","boundary":[0.4326203348389358,0.3110000544640659,0.46009655369258345,0.32627261979508326],"dir":"ltr"},{"str":"their","boundary":[0.46397089822158705,0.3110000544640659,0.5024178375527703,0.32627261979508326],"dir":"ltr"},{"str":"tails.","boundary":[0.5062921820817738,0.3110000544640659,0.5442054106870229,0.32627261979508326],"dir":"ltr"},{"str":"One","boundary":[0.5480797552160265,0.3110000544640659,0.584312783387779,0.32627261979508326],"dir":"ltr"},{"str":"of","boundary":[0.5881871279167826,0.3110000544640659,0.605760047744763,0.32627261979508326],"dir":"ltr"},{"str":"the","boundary":[0.6096343922737666,0.3110000544640659,0.6348966999679835,0.32627261979508326],"dir":"ltr"},{"str":"men","boundary":[0.6387710444969872,0.3110000544640659,0.6750040726687397,0.32627261979508326],"dir":"ltr"},{"str":"was","boundary":[0.6788784171977433,0.3110000544640659,0.7107231571784817,0.32627261979508326],"dir":"ltr"},{"str":"a","boundary":[0.7145975017074851,0.3110000544640659,0.7244810336692289,0.32627261979508326],"dir":"ltr"},{"str":"burly","boundary":[0.7283553781982326,0.3110000544640659,0.7734045168798607,0.32627261979508326],"dir":"ltr"},{"str":"Hercules,","boundary":[0.7772788614088642,0.3110000544640659,0.8557936393129566,0.32627261979508326],"dir":"ltr"},{"str":"who","boundary":[0.23910077902799318,0.32932713286128673,0.2753535742636693,0.34459969819230407],"dir":"ltr"},{"str":"tugged","boundary":[0.2787139751306621,0.32932713286128673,0.33473383428982567,0.34459969819230407],"dir":"ltr"},{"str":"and","boundary":[0.3380942351568186,0.32932713286128673,0.36995874220148045,0.34459969819230407],"dir":"ltr"},{"str":"tugged,","boundary":[0.37331914306847336,0.32932713286128673,0.43428076820850886,0.34459969819230407],"dir":"ltr"},{"str":"but","boundary":[0.43795744209827747,0.32932713286128673,0.4654336609519251,0.34459969819230407],"dir":"ltr"},{"str":"all","boundary":[0.468794061818918,0.32932713286128673,0.4896680813221208,0.34459969819230407],"dir":"ltr"},{"str":"to","boundary":[0.49302848218911377,0.32932713286128673,0.5095142135013023,0.34459969819230407],"dir":"ltr"},{"str":"no","boundary":[0.5128746143682951,0.32932713286128673,0.5348555894512131,0.34459969819230407],"dir":"ltr"},{"str":"purpose;","boundary":[0.5382159903182062,0.32932713286128673,0.611275058579416,0.34459969819230407],"dir":"ltr"},{"str":"the","boundary":[0.615169170172343,0.32932713286128673,0.64043147786656,0.34459969819230407],"dir":"ltr"},{"str":"other","boundary":[0.6437918787335529,0.32932713286128673,0.6877340618354657,0.34459969819230407],"dir":"ltr"},{"str":"was","boundary":[0.6910944627024586,0.32932713286128673,0.7229392026831969,0.34459969819230407],"dir":"ltr"},{"str":"a","boundary":[0.7262996035501897,0.32932713286128673,0.7361831355119335,0.34459969819230407],"dir":"ltr"},{"str":"sharp,","boundary":[0.7395435363789264,0.32932713286128673,0.7906413966211416,0.34459969819230407],"dir":"ltr"},{"str":"weasel-","boundary":[0.7943180705109105,0.32932713286128673,0.8557936393129566,0.34459969819230407],"dir":"ltr"},{"str":"faced","boundary":[0.23910077902799318,0.34765421125850754,0.2841103835817742,0.3629267765895249],"dir":"ltr"},{"str":"tailor,","boundary":[0.2891905190101105,0.34765421125850754,0.3377186609422723,0.3629267765895249],"dir":"ltr"},{"str":"who","boundary":[0.34283833049845563,0.34765421125850754,0.37909112573413173,0.3629267765895249],"dir":"ltr"},{"str":"plucked","boundary":[0.38417126116246797,0.34765421125850754,0.4509444030960088,0.3629267765895249],"dir":"ltr"},{"str":"one","boundary":[0.45602453852434505,0.34765421125850754,0.4867820899892916,0.3629267765895249],"dir":"ltr"},{"str":"hair","boundary":[0.49186222541762786,0.34765421125850754,0.5259208765577968,0.3629267765895249],"dir":"ltr"},{"str":"at","boundary":[0.531001011986133,0.34765421125850754,0.5463797877186063,0.3629267765895249],"dir":"ltr"},{"str":"a","boundary":[0.5514599231469427,0.34765421125850754,0.5613434551086864,0.3629267765895249],"dir":"ltr"},{"str":"time,","boundary":[0.5664235905370227,0.34765421125850754,0.60710420809156,0.3629267765895249],"dir":"ltr"},{"str":"amidst","boundary":[0.6122238776477434,0.34765421125850754,0.668243736806907,0.3629267765895249],"dir":"ltr"},{"str":"roars","boundary":[0.6733238722352433,0.34765421125850754,0.7172660553371559,0.3629267765895249],"dir":"ltr"},{"str":"of","boundary":[0.7223461907654922,0.34765421125850754,0.7399191105934726,0.3629267765895249],"dir":"ltr"},{"str":"laughter,","boundary":[0.744999246021809,0.34765421125850754,0.8176827400684726,0.3629267765895249],"dir":"ltr"},{"str":"and","boundary":[0.8228024096246557,0.34765421125850754,0.8546669166693175,0.3629267765895249],"dir":"ltr"},{"str":"soon","boundary":[0.23910077902799318,0.3659812896557284,0.279761629518607,0.3812538549867457],"dir":"ltr"},{"str":"left","boundary":[0.2847033954994788,0.3659812896557284,0.31105289170948763,0.3812538549867457],"dir":"ltr"},{"str":"the","boundary":[0.31599465769035956,0.3659812896557284,0.3412569653845766,0.3812538549867457],"dir":"ltr"},{"str":"tail","boundary":[0.3461987313654485,0.3659812896557284,0.37256799463938084,0.3812538549867457],"dir":"ltr"},{"str":"quite","boundary":[0.3775097606202527,0.3659812896557284,0.4192577996266584,0.3812538549867457],"dir":"ltr"},{"str":"bare.","boundary":[0.42419956560753014,0.3659812896557284,0.46598713874178277,0.3812538549867457],"dir":"ltr"},{"str":"—E.","boundary":[0.3711543533386863,0.38790848026290525,0.4081860882739027,0.4024174633170692],"dir":"ltr"},{"str":"Cobham","boundary":[0.4128995596069348,0.38790848026290525,0.48281292125186925,0.4024174633170692],"dir":"ltr"},{"str":"Brewer,","boundary":[0.48752639258490144,0.38790848026290525,0.5523882650322836,0.4024174633170692],"dir":"ltr"},{"str":"Dictionary","boundary":[0.5570979806112654,0.38790848026290525,0.6437056690094489,0.4024174633170692],"dir":"ltr"},{"str":"of","boundary":[0.6484191403424812,0.38790848026290525,0.6651134670957304,0.4024174633170692],"dir":"ltr"},{"str":"Phrase","boundary":[0.6698269384287625,0.38790848026290525,0.7251304168183226,0.4024174633170692],"dir":"ltr"},{"str":"and","boundary":[0.7298438881513545,0.38790848026290525,0.7601152657961664,0.4024174633170692],"dir":"ltr"},{"str":"Fable","boundary":[0.7648287371291984,0.38790848026290525,0.8086583868953218,0.4024174633170692],"dir":"ltr"},{"str":",","boundary":[0.8087447692384769,0.38790848026290525,0.8134394618012579,0.4024174633170692],"dir":"ltr"},{"str":"1898","boundary":[0.81815293313429,0.38790848026290525,0.8557104736365378,0.4024174633170692],"dir":"ltr"},{"str":"he","boundary":[0.278654351319837,0.4845126888426659,0.29952837082303985,0.49978525417368325],"dir":"ltr"},{"str":"decrease-and-conquer","boundary":[0.3059645268365273,0.4845126888426659,0.49598531233301274,0.49978525417368325],"dir":"ltr"},{"str":"technique","boundary":[0.503882254370446,0.4845126888426659,0.588465520899049,0.49978525417368325],"dir":"ltr"},{"str":"is","boundary":[0.5948898166741824,0.4845126888426659,0.6080744483111487,0.49978525417368325],"dir":"ltr"},{"str":"based","boundary":[0.614498744086282,0.4845126888426659,0.6639361709589242,0.49978525417368325],"dir":"ltr"},{"str":"on","boundary":[0.6703604667340578,0.4845126888426659,0.6923414418169759,0.49978525417368325],"dir":"ltr"},{"str":"exploiting","boundary":[0.6987657375921094,0.4845126888426659,0.7844559597004277,0.49978525417368325],"dir":"ltr"},{"str":"the","boundary":[0.7908802554755611,0.4845126888426659,0.8183367072652852,0.49978525417368325],"dir":"ltr"},{"str":"relationship","boundary":[0.8247610030404187,0.4845126888426659,0.9269369564609257,0.49978525417368325],"dir":"ltr"},{"str":"between","boundary":[0.27865435131983696,0.5028397672398868,0.35114017472726566,0.518112332570904],"dir":"ltr"},{"str":"a","boundary":[0.35861212489034394,0.5028397672398868,0.3684956568520877,0.518112332570904],"dir":"ltr"},{"str":"solution","boundary":[0.3759676070151659,0.5028397672398868,0.4451918648752192,0.518112332570904],"dir":"ltr"},{"str":"to","boundary":[0.45266381503829745,0.5028397672398868,0.4702367348662779,0.518112332570904],"dir":"ltr"},{"str":"a","boundary":[0.47770868502935615,0.5028397672398868,0.4875922169910999,0.518112332570904],"dir":"ltr"},{"str":"given","boundary":[0.49506416715417817,0.5028397672398868,0.541200494351598,0.518112332570904],"dir":"ltr"},{"str":"instance","boundary":[0.5486724445146762,0.5028397672398868,0.6189641238265979,0.518112332570904],"dir":"ltr"},{"str":"of","boundary":[0.6264360739896763,0.5028397672398868,0.6440089938176566,0.518112332570904],"dir":"ltr"},{"str":"a","boundary":[0.6514809439807348,0.5028397672398868,0.6613644759424785,0.518112332570904],"dir":"ltr"},{"str":"problem","boundary":[0.6688364261055568,0.5028397672398868,0.741342016576909,0.518112332570904],"dir":"ltr"},{"str":"and","boundary":[0.7488139667399872,0.5028397672398868,0.780678473784649,0.518112332570904],"dir":"ltr"},{"str":"a","boundary":[0.7881504239477273,0.5028397672398868,0.798033955909471,0.518112332570904],"dir":"ltr"},{"str":"solution","boundary":[0.8055059060725493,0.5028397672398868,0.8747301639326026,0.518112332570904],"dir":"ltr"},{"str":"to","boundary":[0.882202114095681,0.5028397672398868,0.8997750339236613,0.518112332570904],"dir":"ltr"},{"str":"its","boundary":[0.9072469840867396,0.5028397672398868,0.9270140480102271,0.518112332570904],"dir":"ltr"},{"str":"Tsmaller","boundary":[0.23910045640893843,0.4832145456239661,0.30170274785462337,0.5364394109681249],"dir":"ltr"},{"str":"instance.","boundary":[0.30561662651147387,0.5211668456371076,0.3801186904390983,0.5364394109681249],"dir":"ltr"},{"str":"Once","boundary":[0.38403256909594885,0.5211668456371076,0.4301491292294452,0.5364394109681249],"dir":"ltr"},{"str":"such","boundary":[0.4340630078862957,0.5211668456371076,0.47250994721747896,0.5364394109681249],"dir":"ltr"},{"str":"a","boundary":[0.47642382587432947,0.5211668456371076,0.4863073578360732,0.5364394109681249],"dir":"ltr"},{"str":"relationship","boundary":[0.49022123649292376,0.5211668456371076,0.5923971899134307,0.5364394109681249],"dir":"ltr"},{"str":"is","boundary":[0.5963110685702812,0.5211668456371076,0.6094957002072473,0.5364394109681249],"dir":"ltr"},{"str":"established,","boundary":[0.6134095788640979,0.5211668456371076,0.7139250989150319,0.5364394109681249],"dir":"ltr"},{"str":"it","boundary":[0.7180366482111173,0.5211668456371076,0.7301143242683682,0.5364394109681249],"dir":"ltr"},{"str":"can","boundary":[0.7340282029252188,0.5211668456371076,0.76367879881045,0.5364394109681249],"dir":"ltr"},{"str":"be","boundary":[0.7675926774673004,0.5211668456371076,0.7884666969705032,0.5364394109681249],"dir":"ltr"},{"str":"exploited","boundary":[0.7923805756273539,0.5211668456371076,0.8725755539649427,0.5364394109681249],"dir":"ltr"},{"str":"either","boundary":[0.8764894326217931,0.5211668456371076,0.9270140480102272,0.5364394109681249],"dir":"ltr"},{"str":"top","boundary":[0.23910045640893843,0.5394939240343284,0.2676638637783779,0.5547664893653457],"dir":"ltr"},{"str":"down","boundary":[0.27408815955351135,0.5394939240343284,0.3213314423306464,0.5547664893653457],"dir":"ltr"},{"str":"or","boundary":[0.3277557381057799,0.5394939240343284,0.3464356135134756,0.5547664893653457],"dir":"ltr"},{"str":"bottom","boundary":[0.35285990928860905,0.5394939240343284,0.41546220073429396,0.5547664893653457],"dir":"ltr"},{"str":"up.","boundary":[0.4218864965094274,0.5394939240343284,0.44801855501627785,0.5547664893653457],"dir":"ltr"},{"str":"The","boundary":[0.45444285079141133,0.5394939240343284,0.48771081937464084,0.5547664893653457],"dir":"ltr"},{"str":"former","boundary":[0.4941351151497743,0.5394939240343284,0.5534363069202368,0.5547664893653457],"dir":"ltr"},{"str":"leads","boundary":[0.5598606026953702,0.5394939240343284,0.603802785797283,0.5547664893653457],"dir":"ltr"},{"str":"naturally","boundary":[0.6102270815724163,0.5394939240343284,0.6871209602347828,0.5547664893653457],"dir":"ltr"},{"str":"to","boundary":[0.6935452560099161,0.5394939240343284,0.7111181758378965,0.5547664893653457],"dir":"ltr"},{"str":"a","boundary":[0.71754247161303,0.5394939240343284,0.7274260035747737,0.5547664893653457],"dir":"ltr"},{"str":"recursive","boundary":[0.7338502993499072,0.5394939240343284,0.8118313665280654,0.5547664893653457],"dir":"ltr"},{"str":"implementa-","boundary":[0.8182556623031988,0.5394939240343284,0.9269745138823801,0.5547664893653457],"dir":"ltr"},{"str":"tion,","boundary":[0.23910045640893843,0.5578210024315492,0.27810087352997925,0.5730935677625665],"dir":"ltr"},{"str":"although,","boundary":[0.2835961173007088,0.5578210024315492,0.36434457342815524,0.5730935677625665],"dir":"ltr"},{"str":"as","boundary":[0.3698398171988848,0.5578210024315492,0.38741273702686524,0.5730935677625665],"dir":"ltr"},{"str":"one","boundary":[0.3928091454779773,0.5578210024315492,0.4246736525226392,0.5730935677625665],"dir":"ltr"},{"str":"can","boundary":[0.4300700609737512,0.5578210024315492,0.45972065685898245,0.5730935677625665],"dir":"ltr"},{"str":"see","boundary":[0.46511706531009456,0.5578210024315492,0.49257351709981867,0.5730935677625665],"dir":"ltr"},{"str":"from","boundary":[0.4979699255509307,0.5578210024315492,0.539698197493413,0.5730935677625665],"dir":"ltr"},{"str":"several","boundary":[0.545094605944525,0.5578210024315492,0.6055027532947028,0.5730935677625665],"dir":"ltr"},{"str":"examples","boundary":[0.610899161745815,0.5578210024315492,0.6910743730194804,0.5730935677625665],"dir":"ltr"},{"str":"in","boundary":[0.6964707814705925,0.5578210024315492,0.7129565127827809,0.5730935677625665],"dir":"ltr"},{"str":"this","boundary":[0.7183529212338929,0.5578210024315492,0.7491104726988396,0.5730935677625665],"dir":"ltr"},{"str":"chapter,","boundary":[0.7545068811499517,0.5578210024315492,0.8238892755213929,0.5730935677625665],"dir":"ltr"},{"str":"an","boundary":[0.8293845192921223,0.5578210024315492,0.8502585387953251,0.5730935677625665],"dir":"ltr"},{"str":"ultimate","boundary":[0.8556549472464372,0.5578210024315492,0.9270338150741506,0.5730935677625665],"dir":"ltr"},{"str":"implementation","boundary":[0.23910045640893843,0.57614808082877,0.37529552684176737,0.5914206461597873],"dir":"ltr"},{"str":"may","boundary":[0.38300468177192754,0.57614808082877,0.4192377099436801,0.5914206461597873],"dir":"ltr"},{"str":"well","boundary":[0.42694686487384015,0.57614808082877,0.462092704529801,0.5914206461597873],"dir":"ltr"},{"str":"be","boundary":[0.46980185945996117,0.57614808082877,0.49067587896316395,0.5914206461597873],"dir":"ltr"},{"str":"nonrecursive.","boundary":[0.498385033893324,0.57614808082877,0.6135479483115622,0.5914206461597873],"dir":"ltr"},{"str":"The","boundary":[0.6212571032417225,0.57614808082877,0.6545250718249519,0.5914206461597873],"dir":"ltr"},{"str":"bottom-up","boundary":[0.6622342267551122,0.57614808082877,0.7533999255702366,0.5914206461597873],"dir":"ltr"},{"str":"variation","boundary":[0.7611090805003967,0.57614808082877,0.838002959162763,0.5914206461597873],"dir":"ltr"},{"str":"is","boundary":[0.8457121140929232,0.57614808082877,0.8588967457298894,0.5914206461597873],"dir":"ltr"},{"str":"usually","boundary":[0.8666059006600495,0.57614808082877,0.9270338150741508,0.5914206461597873],"dir":"ltr"},{"str":"implemented","boundary":[0.23910045640893843,0.5944751592259908,0.3522273632430575,0.6097477245570081],"dir":"ltr"},{"str":"iteratively,","boundary":[0.3589283979131197,0.5944751592259908,0.44880923757321745,0.6097477245570081],"dir":"ltr"},{"str":"starting","boundary":[0.45594514764959637,0.5944751592259908,0.5207415831907883,0.6097477245570081],"dir":"ltr"},{"str":"with","boundary":[0.5274426178608507,0.5944751592259908,0.5647826016123186,0.6097477245570081],"dir":"ltr"},{"str":"a","boundary":[0.5714836362823809,0.5944751592259908,0.5813671682441245,0.6097477245570081],"dir":"ltr"},{"str":"solution","boundary":[0.5880682029141868,0.5944751592259908,0.6572924607742401,0.6097477245570081],"dir":"ltr"},{"str":"to","boundary":[0.6639934954443023,0.5944751592259908,0.6815664152722827,0.6097477245570081],"dir":"ltr"},{"str":"the","boundary":[0.6882674499423449,0.5944751592259908,0.715723901732069,0.6097477245570081],"dir":"ltr"},{"str":"smallest","boundary":[0.7224249364021313,0.5944751592259908,0.7916096601343376,0.6097477245570081],"dir":"ltr"},{"str":"instance","boundary":[0.7983106948043999,0.5944751592259908,0.8686023741163214,0.6097477245570081],"dir":"ltr"},{"str":"of","boundary":[0.8753034087863837,0.5944751592259908,0.8928763286143641,0.6097477245570081],"dir":"ltr"},{"str":"the","boundary":[0.8995773632844264,0.5944751592259908,0.9270338150741505,0.6097477245570081],"dir":"ltr"},{"str":"problem;","boundary":[0.23910045640893843,0.6128022376232115,0.31654781286116246,0.6280748029542289],"dir":"ltr"},{"str":"it","boundary":[0.3214895788420344,0.6128022376232115,0.33356725489928524,0.6280748029542289],"dir":"ltr"},{"str":"is","boundary":[0.3385090208801571,0.6128022376232115,0.35169365251712326,0.6280748029542289],"dir":"ltr"},{"str":"called","boundary":[0.3566354184979951,0.6128022376232115,0.4071600338864292,0.6280748029542289],"dir":"ltr"},{"str":"sometimes","boundary":[0.41210179986730106,0.6128022376232115,0.503247731618502,0.6280748029542289],"dir":"ltr"},{"str":"the","boundary":[0.5081894975993739,0.6128022376232115,0.535645949389098,0.6280748029542289],"dir":"ltr"},{"str":"incremental","boundary":[0.5405916687827546,0.6128022376232115,0.6437955095272828,0.6280748029542289],"dir":"ltr"},{"str":"approach","boundary":[0.6492907532980124,0.6128022376232115,0.7318973134342667,0.6280748029542289],"dir":"ltr"},{"str":".","boundary":[0.7317609206931946,0.6128022376232115,0.7367026866740666,0.6280748029542289],"dir":"ltr"},{"str":"There","boundary":[0.274681171471216,0.6311308432769654,0.3255220598824259,0.6464034086079827],"dir":"ltr"},{"str":"are","boundary":[0.33046382586329776,0.6311308432769654,0.3579202776530219,0.6464034086079827],"dir":"ltr"},{"str":"three","boundary":[0.3628620436338938,0.6311308432769654,0.4078914152515983,0.6464034086079827],"dir":"ltr"},{"str":"major","boundary":[0.4128331812324702,0.6311308432769654,0.46335779662090426,0.6464034086079827],"dir":"ltr"},{"str":"variations","boundary":[0.4682995626017762,0.6311308432769654,0.5528828291303792,0.6464034086079827],"dir":"ltr"},{"str":"of","boundary":[0.557824595111251,0.6311308432769654,0.5753975149392314,0.6464034086079827],"dir":"ltr"},{"str":"decrease-and-conquer:","boundary":[0.5803392809201033,0.6311308432769654,0.7753018323974606,0.6464034086079827],"dir":"ltr"},{"str":"decrease","boundary":[0.27468212901091943,0.6627564922843423,0.34936209651385525,0.6780290576153597],"dir":"ltr"},{"str":"by","boundary":[0.3543038624947272,0.6627564922843423,0.37517788199792995,0.6780290576153597],"dir":"ltr"},{"str":"a","boundary":[0.3801196479788018,0.6627564922843423,0.39000317994054556,0.6780290576153597],"dir":"ltr"},{"str":"constant","boundary":[0.39494494592141743,0.6627564922843423,0.46743076932884614,0.6780290576153597],"dir":"ltr"},{"str":"decrease","boundary":[0.27468212901091943,0.6841386356241362,0.34936209651385525,0.6994112009551535],"dir":"ltr"},{"str":"by","boundary":[0.3543038624947272,0.6841386356241362,0.37517788199792995,0.6994112009551535],"dir":"ltr"},{"str":"a","boundary":[0.3801196479788018,0.6841386356241362,0.39000317994054556,0.6994112009551535],"dir":"ltr"},{"str":"constant","boundary":[0.39494494592141743,0.6841386356241362,0.46743076932884614,0.6994112009551535],"dir":"ltr"},{"str":"factor","boundary":[0.47237253530971796,0.6841386356241362,0.5228773836342285,0.6994112009551535],"dir":"ltr"},{"str":"variable","boundary":[0.27468212901091943,0.7055192459740146,0.3438866198070492,0.7207918113050319],"dir":"ltr"},{"str":"size","boundary":[0.348828385787921,0.7055192459740146,0.3806731257686594,0.7207918113050319],"dir":"ltr"},{"str":"decrease","boundary":[0.3856148917495313,0.7055192459740146,0.4602948592524671,0.7207918113050319],"dir":"ltr"},{"str":"In","boundary":[0.27468212901091943,0.7371456742614853,0.29336200441861515,0.7524182395925025],"dir":"ltr"},{"str":"the","boundary":[0.30049791449499413,0.7371456742614853,0.3279543662847183,0.7524182395925025],"dir":"ltr"},{"str":"decrease-by-a-constant","boundary":[0.33508829965470494,0.7371456742614853,0.5358030667337971,0.7524182395925025],"dir":"ltr"},{"str":"variation,","boundary":[0.5442455797355185,0.7371456742614853,0.6260812243787568,0.7524182395925025],"dir":"ltr"},{"str":"the","boundary":[0.6337706122449934,0.7371456742614853,0.6612270640347175,0.7524182395925025],"dir":"ltr"},{"str":"size","boundary":[0.6683629741110966,0.7371456742614853,0.7002077140918349,0.7524182395925025],"dir":"ltr"},{"str":"of","boundary":[0.707343624168214,0.7371456742614853,0.7249165439961943,0.7524182395925025],"dir":"ltr"},{"str":"an","boundary":[0.7320524540725732,0.7371456742614853,0.752926473575776,0.7524182395925025],"dir":"ltr"},{"str":"instance","boundary":[0.7600623836521552,0.7371456742614853,0.8303540629640767,0.7524182395925025],"dir":"ltr"},{"str":"is","boundary":[0.8374899730404557,0.7371456742614853,0.8506746046774218,0.7524182395925025],"dir":"ltr"},{"str":"reduced","boundary":[0.8578105147538009,0.7371456742614853,0.9270150055499307,0.7524182395925025],"dir":"ltr"},{"str":"by","boundary":[0.23910141394864193,0.7554727526587061,0.25997543345184476,0.7707453179897233],"dir":"ltr"},{"str":"the","boundary":[0.265905552628891,0.7554727526587061,0.29336200441861515,0.7707453179897233],"dir":"ltr"},{"str":"same","boundary":[0.2992921235956614,0.7554727526587061,0.3432145396336506,0.7707453179897233],"dir":"ltr"},{"str":"constant","boundary":[0.34914465881069684,0.7554727526587061,0.42163048221812555,0.7707453179897233],"dir":"ltr"},{"str":"on","boundary":[0.4275606013951718,0.7554727526587061,0.44954157647808995,0.7707453179897233],"dir":"ltr"},{"str":"each","boundary":[0.45547169565513623,0.7554727526587061,0.4950058235021112,0.7707453179897233],"dir":"ltr"},{"str":"iteration","boundary":[0.5009359426791574,0.7554727526587061,0.5745287216663014,0.7707453179897233],"dir":"ltr"},{"str":"of","boundary":[0.5804588408433478,0.7554727526587061,0.5980317606713281,0.7707453179897233],"dir":"ltr"},{"str":"the","boundary":[0.6039618798483744,0.7554727526587061,0.6314183316380985,0.7707453179897233],"dir":"ltr"},{"str":"algorithm.","boundary":[0.6373484508151448,0.7554727526587061,0.7257665277449045,0.7707453179897233],"dir":"ltr"},{"str":"Typically,","boundary":[0.7316966469219506,0.7554727526587061,0.811713721684228,0.7707453179897233],"dir":"ltr"},{"str":"this","boundary":[0.8178810456283562,0.7554727526587061,0.8486385970933027,0.7707453179897233],"dir":"ltr"},{"str":"constant","boundary":[0.854568716270349,0.7554727526587061,0.9270545396777776,0.7707453179897233],"dir":"ltr"},{"str":"is","boundary":[0.23910141394864193,0.7737998310559268,0.2522860455856081,0.789072396386944],"dir":"ltr"},{"str":"equal","boundary":[0.25855220484935365,0.7737998310559268,0.3057954876264888,0.789072396386944],"dir":"ltr"},{"str":"to","boundary":[0.3120616468902343,0.7737998310559268,0.3296345667182147,0.789072396386944],"dir":"ltr"},{"str":"one","boundary":[0.33590072598196025,0.7737998310559268,0.3677652330266221,0.789072396386944],"dir":"ltr"},{"str":"(Figure","boundary":[0.37403139229036764,0.7737998310559268,0.4370092579505988,0.789072396386944],"dir":"ltr"},{"str":"4.1),","boundary":[0.4432754172143444,0.7737998310559268,0.48061540096581223,0.789072396386944],"dir":"ltr"},{"str":"although","boundary":[0.48721760031625705,0.7737998310559268,0.5630242904628316,0.789072396386944],"dir":"ltr"},{"str":"other","boundary":[0.5692904497265772,0.7737998310559268,0.615426776923997,0.789072396386944],"dir":"ltr"},{"str":"constant","boundary":[0.6216929361877426,0.7737998310559268,0.6941787595951712,0.789072396386944],"dir":"ltr"},{"str":"size","boundary":[0.7004449188589169,0.7737998310559268,0.7322896588396552,0.789072396386944],"dir":"ltr"},{"str":"reductions","boundary":[0.7385558181034009,0.7737998310559268,0.8286343284027334,0.789072396386944],"dir":"ltr"},{"str":"do","boundary":[0.834900487666479,0.7737998310559268,0.856881462749397,0.789072396386944],"dir":"ltr"},{"str":"happen","boundary":[0.8631476220131427,0.7737998310559268,0.9268766361024664,0.789072396386944],"dir":"ltr"},{"str":"occasionally.","boundary":[0.23910141394864193,0.7921269094531476,0.3465749405006435,0.8073994747841649],"dir":"ltr"},{"str":"Consider,","boundary":[0.27468212901091943,0.8104539878503685,0.35726892208325023,0.8257265531813858],"dir":"ltr"},{"str":"as","boundary":[0.3617758126578054,0.8104539878503685,0.3793487324857858,0.8257265531813858],"dir":"ltr"},{"str":"an","boundary":[0.38373702067680004,0.8104539878503685,0.4046110401800028,0.8257265531813858],"dir":"ltr"},{"str":"example,","boundary":[0.40899932837101705,0.8104539878503685,0.48569553639414853,0.8257265531813858],"dir":"ltr"},{"str":"the","boundary":[0.4902024269687037,0.8104539878503685,0.5176588787584278,0.8257265531813858],"dir":"ltr"},{"str":"exponentiation","boundary":[0.5220471669494421,0.8104539878503685,0.6516795721596731,0.8257265531813858],"dir":"ltr"},{"str":"problem","boundary":[0.6560678603506875,0.8104539878503685,0.7285734508220397,0.8257265531813858],"dir":"ltr"},{"str":"of","boundary":[0.7329617390130538,0.8104539878503685,0.7505346588410343,0.8257265531813858],"dir":"ltr"},{"str":"computing","boundary":[0.7549229470320485,0.8104539878503685,0.8460886458471729,0.8257265531813858],"dir":"ltr"},{"str":"a","boundary":[0.8505401886427422,0.8110648904636092,0.8604237206044858,0.8263374557946265],"dir":"ltr"},{"str":"n","boundary":[0.8613150783223528,0.8080987434124589,0.8693949197685399,0.8195532440602177],"dir":"ltr"},{"str":"where","boundary":[0.8742853167006716,0.8104554716619674,0.9270040761846128,0.8257280369929846],"dir":"ltr"},{"str":"a","boundary":[0.2391023448216781,0.8293934526724288,0.24898587678342188,0.8446660180034461],"dir":"ltr"},{"str":"=","boundary":[0.2550187846928702,0.8320661516053567,0.2704370945531904,0.847338716936374],"dir":"ltr"},{"str":"0","boundary":[0.2749677056044538,0.8287825500591881,0.28485123756619757,0.8440551153902054],"dir":"ltr"},{"str":"and","boundary":[0.2911371638938666,0.8287825500591881,0.3230016709385285,0.8440551153902054],"dir":"ltr"},{"str":"n","boundary":[0.3291867852401877,0.8293934526724288,0.33995983507848837,0.8446660180034461],"dir":"ltr"},{"str":"is","boundary":[0.3461449493801476,0.8287825500591881,0.35932958101711376,0.8440551153902054],"dir":"ltr"},{"str":"a","boundary":[0.36551667202516536,0.8287825500591881,0.3754002039869091,0.8440551153902054],"dir":"ltr"},{"str":"nonnegative","boundary":[0.38158729499496064,0.8287825500591881,0.4870445810267665,0.8440551153902054],"dir":"ltr"},{"str":"integer.","boundary":[0.49323167203481816,0.8287825500591881,0.5582257782152451,0.8440551153902054],"dir":"ltr"},{"str":"The","boundary":[0.5644128692232967,0.8287825500591881,0.5976808378065261,0.8440551153902054],"dir":"ltr"},{"str":"relationship","boundary":[0.6038679288145777,0.8287825500591881,0.7060438822350846,0.8440551153902054],"dir":"ltr"},{"str":"between","boundary":[0.7122309732431361,0.8287825500591881,0.7847167966505647,0.8440551153902054],"dir":"ltr"},{"str":"a","boundary":[0.7909038876586164,0.8287825500591881,0.8007874196203602,0.8440551153902054],"dir":"ltr"},{"str":"solution","boundary":[0.8069745106284117,0.8287825500591881,0.876198768488465,0.8440551153902054],"dir":"ltr"},{"str":"to","boundary":[0.8823858594965165,0.8287825500591881,0.8999587793244969,0.8440551153902054],"dir":"ltr"},{"str":"an","boundary":[0.9061458703325485,0.8287825500591881,0.9270198898357512,0.8440551153902054],"dir":"ltr"},{"str":"instance","boundary":[0.23910234482167805,0.8471096284564088,0.3093940241335996,0.8623821937874261],"dir":"ltr"},{"str":"of","boundary":[0.3139799829638487,0.8471096284564088,0.33155290279182914,0.8623821937874261],"dir":"ltr"},{"str":"size","boundary":[0.33613886162207823,0.8471096284564088,0.36798360160281657,0.8623821937874261],"dir":"ltr"},{"str":"n","boundary":[0.37257549055224276,0.8477205310696495,0.38334854039054345,0.8629930964006668],"dir":"ltr"},{"str":"and","boundary":[0.3879344992207926,0.8471096284564088,0.41979900626545447,0.8623821937874261],"dir":"ltr"},{"str":"an","boundary":[0.42438496509570356,0.8471096284564088,0.4452589845989064,0.8623821937874261],"dir":"ltr"},{"str":"instance","boundary":[0.44984494342915543,0.8471096284564088,0.520136622741077,0.8623821937874261],"dir":"ltr"},{"str":"of","boundary":[0.5247225815713261,0.8471096284564088,0.5422955013993065,0.8623821937874261],"dir":"ltr"},{"str":"size","boundary":[0.5468814602295556,0.8471096284564088,0.578726200210294,0.8623821937874261],"dir":"ltr"},{"str":"n","boundary":[0.5833180891597202,0.8477205310696495,0.5940911389980209,0.8629930964006668],"dir":"ltr"},{"str":"−","boundary":[0.5983845452822024,0.8503932300025775,0.6138028551425226,0.8656657953335947],"dir":"ltr"},{"str":"1","boundary":[0.6180962614267042,0.8471096284564088,0.6279797933884479,0.8623821937874261],"dir":"ltr"},{"str":"is","boundary":[0.6316169331503696,0.8471096284564088,0.6448015647873359,0.8623821937874261],"dir":"ltr"},{"str":"obtained","boundary":[0.6493875236175848,0.8471096284564088,0.7251942137641594,0.8623821937874261],"dir":"ltr"},{"str":"by","boundary":[0.7297801725944085,0.8471096284564088,0.7506541920976113,0.8623821937874261],"dir":"ltr"},{"str":"the","boundary":[0.7552401509278605,0.8471096284564088,0.7826966027175846,0.8623821937874261],"dir":"ltr"},{"str":"obvious","boundary":[0.7872825615478337,0.8471096284564088,0.8543126753123799,0.8623821937874261],"dir":"ltr"},{"str":"formula","boundary":[0.8588986341426289,0.8471096284564088,0.9269961693590433,0.8623821937874261],"dir":"ltr"},{"str":"a","boundary":[0.23910234482167822,0.8664523324481422,0.248985876783422,0.8817248977791595],"dir":"ltr"},{"str":"n","boundary":[0.24987458878694538,0.8634856690553289,0.25795443023313236,0.8749401697030875],"dir":"ltr"},{"str":"=","boundary":[0.2629678430409648,0.8691244658610904,0.27838615290128504,0.8843970311921076],"dir":"ltr"},{"str":"a","boundary":[0.28290688042058665,0.8664517669281624,0.2927904123823304,0.8817243322591797],"dir":"ltr"},{"str":"n","boundary":[0.29368014529857456,0.8634856690553289,0.30175998674476157,0.8749401697030875],"dir":"ltr"},{"str":"−","boundary":[0.30175998674476157,0.8654902066686866,0.31332379652095577,0.8769447073164454],"dir":"ltr"},{"str":"1","boundary":[0.31332379652095577,0.8630274890294184,0.3207364950954393,0.8744819896771772],"dir":"ltr"},{"str":".","boundary":[0.3250372888400995,0.8633214015209458,0.33047323141905854,0.8785939668519631],"dir":"ltr"},{"str":"a.","boundary":[0.3349919822319678,0.8664522774138044,0.3520904925257845,0.8817248427448217],"dir":"ltr"},{"str":"So","boundary":[0.3572872536312694,0.8658413748005637,0.3792682287141875,0.881113940131581],"dir":"ltr"},{"str":"the","boundary":[0.38535648440262166,0.8658413748005637,0.4128129361923458,0.881113940131581],"dir":"ltr"},{"str":"function","boundary":[0.41890119188077996,0.8658413748005637,0.4902998267724168,0.881113940131581],"dir":"ltr"},{"str":"f","boundary":[0.4963821523416739,0.8664522774138044,0.5069772986046632,0.8817248427448217],"dir":"ltr"},{"str":"(n)","boundary":[0.5103376994716561,0.8664522774138044,0.5358569789968786,0.8817248427448217],"dir":"ltr"},{"str":"=","boundary":[0.54037770651618,0.8691249763467322,0.5557960163765002,0.8843975416777495],"dir":"ltr"},{"str":"a","boundary":[0.5618822953585421,0.8664522774138044,0.5717658273202858,0.8817248427448217],"dir":"ltr"},{"str":"n","boundary":[0.5726563418635312,0.8634856690553289,0.5807361833097183,0.8749401697030875],"dir":"ltr"},{"str":"can","boundary":[0.5873170564692214,0.8658408643149218,0.6169676523544526,0.881113429645939],"dir":"ltr"},{"str":"be","boundary":[0.6230559080428869,0.8658408643149218,0.6439299275460897,0.881113429645939],"dir":"ltr"},{"str":"computed","boundary":[0.6500181832345239,0.8658408643149218,0.7356886382789186,0.881113429645939],"dir":"ltr"},{"str":"either","boundary":[0.7417768939673528,0.8658408643149218,0.7923015093557869,0.881113429645939],"dir":"ltr"},{"str":"“top","boundary":[0.7983897650442211,0.8658408643149218,0.8368367043754043,0.881113429645939],"dir":"ltr"},{"str":"down”","boundary":[0.8429249600638383,0.8658408643149218,0.9000517748027173,0.881113429645939],"dir":"ltr"},{"str":"by","boundary":[0.9061400304911514,0.8658408643149218,0.9270140499943541,0.881113429645939],"dir":"ltr"},{"str":"using","boundary":[0.23910243509945792,0.8841679427121426,0.28415157378108596,0.8994405080431599],"dir":"ltr"},{"str":"its","boundary":[0.28909333976195783,0.8841679427121426,0.3088604036854453,0.8994405080431599],"dir":"ltr"},{"str":"recursive","boundary":[0.3138021696663172,0.8841679427121426,0.3917832368444754,0.8994405080431599],"dir":"ltr"},{"str":"definition","boundary":[0.3967250028253473,0.8841679427121426,0.4791338923223667,0.8994405080431599],"dir":"ltr"},{"str":"131","boundary":[0.8940247970124459,0.9329332438140808,0.9269962596368231,0.9482058091450981],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92705,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":195,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/08b9bd7dad7d48fde47dfdf3217361fb.jpg","blurred":"/storage/books/4a8b03583f119702/pages/dcab48e5bb1343543faf830937d2cd0b.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07295,0.05179]},"elements":[{"words":[{"str":"5","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Divide-and-Conquer","boundary":[0.14421784044919886,0.17005356781848974,0.6195773865383952,0.20670781659232623],"dir":"ltr"},{"str":"Whatever","boundary":[0.23910077902799318,0.27434437041309123,0.31925622323773495,0.2896169357441086],"dir":"ltr"},{"str":"man","boundary":[0.32330847134204993,0.27434437041309123,0.3606484550935178,0.2896169357441086],"dir":"ltr"},{"str":"prays","boundary":[0.36470070319783277,0.27434437041309123,0.4104812232446298,0.2896169357441086],"dir":"ltr"},{"str":"for,","boundary":[0.4145334713489448,0.27434437041309123,0.4432747822936956,0.2896169357441086],"dir":"ltr"},{"str":"he","boundary":[0.44750493397332197,0.27434437041309123,0.4672719978968095,0.2896169357441086],"dir":"ltr"},{"str":"prays","boundary":[0.47132424600112444,0.27434437041309123,0.5171047660479214,0.2896169357441086],"dir":"ltr"},{"str":"for","boundary":[0.5211570141522364,0.27434437041309123,0.5464193218464534,0.2896169357441086],"dir":"ltr"},{"str":"a","boundary":[0.5504715699507683,0.27434437041309123,0.560355101912512,0.2896169357441086],"dir":"ltr"},{"str":"miracle.","boundary":[0.5644073500168271,0.27434437041309123,0.6314374637813731,0.2896169357441086],"dir":"ltr"},{"str":"Every","boundary":[0.6354897118856881,0.27434437041309123,0.6859945602101987,0.2896169357441086],"dir":"ltr"},{"str":"prayer","boundary":[0.6900468083145136,0.27434437041309123,0.7446039047433392,0.2896169357441086],"dir":"ltr"},{"str":"reduces","boundary":[0.748656152847654,0.27434437041309123,0.8123456328091306,0.2896169357441086],"dir":"ltr"},{"str":"itself","boundary":[0.8163978809134458,0.27434437041309123,0.8559320087604207,0.2896169357441086],"dir":"ltr"},{"str":"to","boundary":[0.23910077902799318,0.2926729760668451,0.25558651034018176,0.30794554139786245],"dir":"ltr"},{"str":"this—Great","boundary":[0.26052827632105363,0.2926729760668451,0.35827640742269934,0.30794554139786245],"dir":"ltr"},{"str":"God,","boundary":[0.3632181734035712,0.2926729760668451,0.4066068787156263,0.30794554139786245],"dir":"ltr"},{"str":"grant","boundary":[0.4115486446964982,0.2926729760668451,0.4554908277984109,0.30794554139786245],"dir":"ltr"},{"str":"that","boundary":[0.46043259377928275,0.2926729760668451,0.4922971008239446,0.30794554139786245],"dir":"ltr"},{"str":"twice","boundary":[0.4972388668048165,0.2926729760668451,0.5400543272630904,0.30794554139786245],"dir":"ltr"},{"str":"two","boundary":[0.5449960932439623,0.2926729760668451,0.5757536447089089,0.30794554139786245],"dir":"ltr"},{"str":"be","boundary":[0.5806954106897808,0.2926729760668451,0.6004624746132683,0.30794554139786245],"dir":"ltr"},{"str":"not","boundary":[0.6054042405941401,0.2926729760668451,0.6328804594477877,0.30794554139786245],"dir":"ltr"},{"str":"four.","boundary":[0.6378222254286596,0.2926729760668451,0.6775540239148695,0.30794554139786245],"dir":"ltr"},{"str":"—Ivan","boundary":[0.2912118912764499,0.31459936951926604,0.34651536966601,0.32910835257342996],"dir":"ltr"},{"str":"Turgenev","boundary":[0.351210062228791,0.31459936951926604,0.42739553313760087,0.32910835257342996],"dir":"ltr"},{"str":"(1818–1883),","boundary":[0.43209022570038186,0.31459936951926604,0.535899267648595,0.32910835257342996],"dir":"ltr"},{"str":"Russian","boundary":[0.5405939602113761,0.31459936951926604,0.6053056024967491,0.32910835257342996],"dir":"ltr"},{"str":"novelist","boundary":[0.6100002950595301,0.31459936951926604,0.6736603262108404,0.32910835257342996],"dir":"ltr"},{"str":"and","boundary":[0.6783550187736214,0.31459936951926604,0.7086263964184332,0.32910835257342996],"dir":"ltr"},{"str":"short-story","boundary":[0.7133210889812143,0.31459936951926604,0.8020132208772727,0.32910835257342996],"dir":"ltr"},{"str":"writer","boundary":[0.8067079134400535,0.31459936951926604,0.8557392825657382,0.32910835257342996],"dir":"ltr"},{"str":"ivide-and-conquer","boundary":[0.2884995896299513,0.4008957539079762,0.44558844662990654,0.4161683192389935],"dir":"ltr"},{"str":"is","boundary":[0.45440455713978195,0.4008957539079762,0.4675891887767481,0.4161683192389935],"dir":"ltr"},{"str":"probably","boundary":[0.4764052992866235,0.4008957539079762,0.5533189450129135,0.4161683192389935],"dir":"ltr"},{"str":"the","boundary":[0.5621350555227889,0.4008957539079762,0.589591507312513,0.4161683192389935],"dir":"ltr"},{"str":"best-known","boundary":[0.5984076178223884,0.4008957539079762,0.6983696600834648,0.4161683192389935],"dir":"ltr"},{"str":"general","boundary":[0.7071857705933402,0.4008957539079762,0.7708950176187405,0.4161683192389935],"dir":"ltr"},{"str":"algorithm","boundary":[0.7797111281286159,0.4008957539079762,0.8631874390775035,0.4161683192389935],"dir":"ltr"},{"str":"design","boundary":[0.8720035495873789,0.4008957539079762,0.9269362202307507,0.4161683192389935],"dir":"ltr"},{"str":"technique.","boundary":[0.2884995896299513,0.41922435956173004,0.3772932407742572,0.4344969248927474],"dir":"ltr"},{"str":"Though","boundary":[0.3803373686184743,0.41922435956173004,0.4465767998260809,0.4344969248927474],"dir":"ltr"},{"str":"its","boundary":[0.44962092767029793,0.41922435956173004,0.46938799159378547,0.4344969248927474],"dir":"ltr"},{"str":"fame","boundary":[0.4724321194380025,0.41922435956173004,0.5152475798962765,0.4344969248927474],"dir":"ltr"},{"str":"may","boundary":[0.5182917077404936,0.41922435956173004,0.5545247359122462,0.4344969248927474],"dir":"ltr"},{"str":"have","boundary":[0.5575688637564632,0.41922435956173004,0.5982099471831536,0.4344969248927474],"dir":"ltr"},{"str":"something","boundary":[0.6012540750273706,0.41922435956173004,0.6902256297469879,0.4344969248927474],"dir":"ltr"},{"str":"to","boundary":[0.6932697575912049,0.41922435956173004,0.7108426774191853,0.4344969248927474],"dir":"ltr"},{"str":"do","boundary":[0.7138868052634024,0.41922435956173004,0.7358677803463206,0.4344969248927474],"dir":"ltr"},{"str":"with","boundary":[0.7389119081905375,0.41922435956173004,0.7762518919420055,0.4344969248927474],"dir":"ltr"},{"str":"its","boundary":[0.7792960197862225,0.41922435956173004,0.79906308370971,0.4344969248927474],"dir":"ltr"},{"str":"catchy","boundary":[0.8021072115539271,0.41922435956173004,0.8570003480694518,0.4344969248927474],"dir":"ltr"},{"str":"name,","boundary":[0.860044475913669,0.41922435956173004,0.9114783762425834,0.4344969248927474],"dir":"ltr"},{"str":"it","boundary":[0.9148980783013468,0.41922435956173004,0.9269757543585976,0.4344969248927474],"dir":"ltr"},{"str":"isDwell","boundary":[0.23910077902799318,0.39959761068927646,0.2912076773874691,0.4528240032899682],"dir":"ltr"},{"str":"deserved:","boundary":[0.29498318659685524,0.43755143795895085,0.3768188312400935,0.4528240032899682],"dir":"ltr"},{"str":"quite","boundary":[0.3805943404494796,0.43755143795895085,0.4245365235513923,0.4528240032899682],"dir":"ltr"},{"str":"a","boundary":[0.4283120327607785,0.43755143795895085,0.43819556472252225,0.4528240032899682],"dir":"ltr"},{"str":"few","boundary":[0.4419710739319083,0.43755143795895085,0.47270885833293136,0.4528240032899682],"dir":"ltr"},{"str":"very","boundary":[0.47648436754231754,0.43755143795895085,0.5138243512937855,0.4528240032899682],"dir":"ltr"},{"str":"efficient","boundary":[0.5175998605031715,0.43755143795895085,0.5867845842353777,0.4528240032899682],"dir":"ltr"},{"str":"algorithms","boundary":[0.5905600934447639,0.43755143795895085,0.6817257922598883,0.4528240032899682],"dir":"ltr"},{"str":"are","boundary":[0.6855013014692745,0.43755143795895085,0.7129577532589986,0.4528240032899682],"dir":"ltr"},{"str":"specific","boundary":[0.7167332624683846,0.43755143795895085,0.7793355539140696,0.4528240032899682],"dir":"ltr"},{"str":"implementations","boundary":[0.7831110631234557,0.43755143795895085,0.9269955214225213,0.4528240032899682],"dir":"ltr"},{"str":"of","boundary":[0.23910169688515603,0.4558785163561717,0.25667461671313646,0.471151081687189],"dir":"ltr"},{"str":"this","boundary":[0.2641663339401382,0.4558785163561717,0.2949238854050848,0.471151081687189],"dir":"ltr"},{"str":"general","boundary":[0.3024156026320865,0.4558785163561717,0.36612484965748676,0.471151081687189],"dir":"ltr"},{"str":"strategy.","boundary":[0.3736165668844885,0.4558785163561717,0.4448175311368905,0.471151081687189],"dir":"ltr"},{"str":"Divide-and-conquer","boundary":[0.4523092483638922,0.4558785163561717,0.6258640696121125,0.471151081687189],"dir":"ltr"},{"str":"algorithms","boundary":[0.6333557868391143,0.4558785163561717,0.7245214856542387,0.471151081687189],"dir":"ltr"},{"str":"work","boundary":[0.7320132028812406,0.4558785163561717,0.7759553859831533,0.471151081687189],"dir":"ltr"},{"str":"according","boundary":[0.783447103210155,0.4558785163561717,0.8669234141590428,0.471151081687189],"dir":"ltr"},{"str":"to","boundary":[0.8744151313860444,0.4558785163561717,0.8919880512140248,0.471151081687189],"dir":"ltr"},{"str":"the","boundary":[0.8994797684410266,0.4558785163561717,0.9269362202307507,0.471151081687189],"dir":"ltr"},{"str":"following","boundary":[0.23910169688515603,0.4742055947533925,0.31929667522274485,0.48947816008440986],"dir":"ltr"},{"str":"general","boundary":[0.3242384412036167,0.4742055947533925,0.38794768822901693,0.48947816008440986],"dir":"ltr"},{"str":"plan:","boundary":[0.3928894542098889,0.4742055947533925,0.43519097100615217,0.48947816008440986],"dir":"ltr"},{"str":"1.","boundary":[0.23910169688515603,0.5011967994628994,0.25392699482777165,0.5164693647939168],"dir":"ltr"},{"str":"A","boundary":[0.27468241194743354,0.5011967994628994,0.29124721151531613,0.5164693647939168],"dir":"ltr"},{"str":"problem","boundary":[0.29761220609867906,0.5011967994628994,0.3701177965700312,0.5164693647939168],"dir":"ltr"},{"str":"is","boundary":[0.3764827911533942,0.5011967994628994,0.3896674227903604,0.5164693647939168],"dir":"ltr"},{"str":"divided","boundary":[0.39603241737372336,0.5011967994628994,0.4597614314630471,0.5164693647939168],"dir":"ltr"},{"str":"into","boundary":[0.46612642604641,0.5011967994628994,0.500185077186579,0.5164693647939168],"dir":"ltr"},{"str":"several","boundary":[0.506550071769942,0.5011967994628994,0.5669582191201198,0.5164693647939168],"dir":"ltr"},{"str":"subproblems","boundary":[0.5733232137034827,0.5011967994628994,0.6831885549902263,0.5164693647939168],"dir":"ltr"},{"str":"of","boundary":[0.6895535495735893,0.5011967994628994,0.7071264694015698,0.5164693647939168],"dir":"ltr"},{"str":"the","boundary":[0.7134914639849326,0.5011967994628994,0.7409479157746567,0.5164693647939168],"dir":"ltr"},{"str":"same","boundary":[0.7473129103580197,0.5011967994628994,0.791235326396009,0.5164693647939168],"dir":"ltr"},{"str":"type,","boundary":[0.797600320979372,0.5011967994628994,0.8391506893465428,0.5164693647939168],"dir":"ltr"},{"str":"ideally","boundary":[0.8458714910805283,0.5011967994628994,0.9029983058194072,0.5164693647939168],"dir":"ltr"},{"str":"of","boundary":[0.9093633004027702,0.5011967994628994,0.9269362202307506,0.5164693647939168],"dir":"ltr"},{"str":"about","boundary":[0.27468241194743354,0.5195238778601202,0.32411983882007583,0.5347964431911376],"dir":"ltr"},{"str":"equal","boundary":[0.3290616048009477,0.5195238778601202,0.3763048875780829,0.5347964431911376],"dir":"ltr"},{"str":"size.","boundary":[0.3812466535589547,0.5195238778601202,0.41730177815539593,0.5347964431911376],"dir":"ltr"},{"str":"2.","boundary":[0.23910169688515603,0.5409054693235444,0.25392699482777165,0.5561780346545618],"dir":"ltr"},{"str":"The","boundary":[0.27468241194743354,0.5409054693235444,0.30795038053066304,0.5561780346545618],"dir":"ltr"},{"str":"subproblems","boundary":[0.3144735116254139,0.5409054693235444,0.4243388529121575,0.5561780346545618],"dir":"ltr"},{"str":"are","boundary":[0.43086198400690834,0.5409054693235444,0.4583184357966325,0.5561780346545618],"dir":"ltr"},{"str":"solved","boundary":[0.4648415668913834,0.5409054693235444,0.5197742375347552,0.5561780346545618],"dir":"ltr"},{"str":"(typically","boundary":[0.526297368629506,0.5409054693235444,0.6064725799031714,0.5561780346545618],"dir":"ltr"},{"str":"recursively,","boundary":[0.6129957109979222,0.5409054693235444,0.7094787500084647,0.5561780346545618],"dir":"ltr"},{"str":"though","boundary":[0.7163774553177619,0.5409054693235444,0.7768053697318631,0.5561780346545618],"dir":"ltr"},{"str":"sometimes","boundary":[0.783328500826614,0.5409054693235444,0.8744744325778149,0.5561780346545618],"dir":"ltr"},{"str":"a","boundary":[0.8809975636725659,0.5409054693235444,0.8908810956343096,0.5561780346545618],"dir":"ltr"},{"str":"dif-","boundary":[0.8974042267290603,0.5409054693235444,0.9270548226142915,0.5561780346545618],"dir":"ltr"},{"str":"ferent","boundary":[0.27468241194743354,0.5592325477207652,0.3262942158516594,0.5745051130517826],"dir":"ltr"},{"str":"algorithm","boundary":[0.3340824390375135,0.5592325477207652,0.41755874998640125,0.5745051130517826],"dir":"ltr"},{"str":"is","boundary":[0.42534697317225534,0.5592325477207652,0.43853160480922154,0.5745051130517826],"dir":"ltr"},{"str":"employed,","boundary":[0.4463198279950756,0.5592325477207652,0.5358448605045506,0.5745051130517826],"dir":"ltr"},{"str":"especially","boundary":[0.5443446979916501,0.5592325477207652,0.6278210089405379,0.5745051130517826],"dir":"ltr"},{"str":"when","boundary":[0.6356092321263919,0.5592325477207652,0.6817455593238118,0.5745051130517826],"dir":"ltr"},{"str":"subproblems","boundary":[0.6895337825096658,0.5592325477207652,0.7993991237964094,0.5745051130517826],"dir":"ltr"},{"str":"become","boundary":[0.8071873469822635,0.5592325477207652,0.8741779266189627,0.5745051130517826],"dir":"ltr"},{"str":"small","boundary":[0.8819661498048167,0.5592325477207652,0.9269955214225212,0.5745051130517826],"dir":"ltr"},{"str":"enough).","boundary":[0.27468241194743354,0.5775596261179862,0.35104257988386584,0.5928321914490035],"dir":"ltr"},{"str":"3.","boundary":[0.23910169688515603,0.5989412175814104,0.25392699482777165,0.6142137829124278],"dir":"ltr"},{"str":"If","boundary":[0.27468241194743354,0.5989412175814104,0.28895423210019155,0.6142137829124278],"dir":"ltr"},{"str":"necessary,","boundary":[0.29379716276144596,0.5989412175814104,0.37928971423052943,0.6142137829124278],"dir":"ltr"},{"str":"the","boundary":[0.3841524119557074,0.5989412175814104,0.4116088637454315,0.6142137829124278],"dir":"ltr"},{"str":"solutions","boundary":[0.41645179440668595,0.5989412175814104,0.49336544013297584,0.6142137829124278],"dir":"ltr"},{"str":"to","boundary":[0.49820837079423025,0.5989412175814104,0.5157812906222107,0.6142137829124278],"dir":"ltr"},{"str":"the","boundary":[0.5206242212834651,0.5989412175814104,0.5480806730731892,0.6142137829124278],"dir":"ltr"},{"str":"subproblems","boundary":[0.5529236037344436,0.5989412175814104,0.6627889450211872,0.6142137829124278],"dir":"ltr"},{"str":"are","boundary":[0.6676318756824416,0.5989412175814104,0.6950883274721658,0.6142137829124278],"dir":"ltr"},{"str":"combined","boundary":[0.6999312581334203,0.5989412175814104,0.7845145246620233,0.6142137829124278],"dir":"ltr"},{"str":"to","boundary":[0.7893574553232776,0.5989412175814104,0.806930375151258,0.6142137829124278],"dir":"ltr"},{"str":"get","boundary":[0.8117733058125126,0.5989412175814104,0.8381228020225215,0.6142137829124278],"dir":"ltr"},{"str":"a","boundary":[0.8429657326837757,0.5989412175814104,0.8528492646455195,0.6142137829124278],"dir":"ltr"},{"str":"solution","boundary":[0.857692195306774,0.5989412175814104,0.9269164531668271,0.6142137829124278],"dir":"ltr"},{"str":"to","boundary":[0.27468241194743354,0.6172682959786312,0.29225533177541396,0.6325408613096485],"dir":"ltr"},{"str":"the","boundary":[0.29719709775628583,0.6172682959786312,0.32465354954601,0.6325408613096485],"dir":"ltr"},{"str":"original","boundary":[0.3295953155268818,0.6172682959786312,0.3955184737117127,0.6325408613096485],"dir":"ltr"},{"str":"problem.","boundary":[0.40046023969258454,0.6172682959786312,0.47790759614480866,0.6325408613096485],"dir":"ltr"},{"str":"The","boundary":[0.27468241194743354,0.644259500688138,0.30795038053066304,0.6595320660191554],"dir":"ltr"},{"str":"divide-and-conquer","boundary":[0.3116072873565082,0.644259500688138,0.4796866318979225,0.6595320660191554],"dir":"ltr"},{"str":"technique","boundary":[0.4833435387237677,0.644259500688138,0.5679268052523707,0.6595320660191554],"dir":"ltr"},{"str":"is","boundary":[0.5715837120782159,0.644259500688138,0.584768343715182,0.6595320660191554],"dir":"ltr"},{"str":"diagrammed","boundary":[0.5884252505410272,0.644259500688138,0.6960569136044167,0.6595320660191554],"dir":"ltr"},{"str":"in","boundary":[0.6997138204302618,0.644259500688138,0.7161995517424503,0.6595320660191554],"dir":"ltr"},{"str":"Figure","boundary":[0.7198564585682956,0.644259500688138,0.7751449363622901,0.6595320660191554],"dir":"ltr"},{"str":"5.1,","boundary":[0.7788018431881354,0.644259500688138,0.8084524390733666,0.6595320660191554],"dir":"ltr"},{"str":"which","boundary":[0.8123663177302172,0.644259500688138,0.8628909331186513,0.6595320660191554],"dir":"ltr"},{"str":"depicts","boundary":[0.8665478399444964,0.644259500688138,0.9269559872946741,0.6595320660191554],"dir":"ltr"},{"str":"the","boundary":[0.23910169688515603,0.6625865790853588,0.2665581486748802,0.6778591444163762],"dir":"ltr"},{"str":"case","boundary":[0.26956274239125033,0.6625865790853588,0.3057957705630029,0.6778591444163762],"dir":"ltr"},{"str":"of","boundary":[0.30880036427937296,0.6625865790853588,0.3263732841073534,0.6778591444163762],"dir":"ltr"},{"str":"dividing","boundary":[0.32937787782372346,0.6625865790853588,0.3986021356837767,0.6778591444163762],"dir":"ltr"},{"str":"a","boundary":[0.4016067294001468,0.6625865790853588,0.4114902613618906,0.6778591444163762],"dir":"ltr"},{"str":"problem","boundary":[0.41449485507826067,0.6625865790853588,0.48700044554961286,0.6778591444163762],"dir":"ltr"},{"str":"into","boundary":[0.49000503926598293,0.6625865790853588,0.5240636904061519,0.6778591444163762],"dir":"ltr"},{"str":"two","boundary":[0.527068284122522,0.6625865790853588,0.5589130241032604,0.6778591444163762],"dir":"ltr"},{"str":"smaller","boundary":[0.5619176178196306,0.6625865790853588,0.6245199092653154,0.6778591444163762],"dir":"ltr"},{"str":"subproblems,","boundary":[0.6275245029816855,0.6625865790853588,0.7412444217335092,0.6778591444163762],"dir":"ltr"},{"str":"by","boundary":[0.744644356728349,0.6625865790853588,0.7655183762315518,0.6778591444163762],"dir":"ltr"},{"str":"far","boundary":[0.768522969947922,0.6625865790853588,0.7926783220624238,0.6778591444163762],"dir":"ltr"},{"str":"the","boundary":[0.7956829157787939,0.6625865790853588,0.823139367568518,0.6778591444163762],"dir":"ltr"},{"str":"most","boundary":[0.8261439612848881,0.6625865790853588,0.8678722332273703,0.6778591444163762],"dir":"ltr"},{"str":"widely","boundary":[0.8708768269437404,0.6625865790853588,0.926896686102904,0.6778591444163762],"dir":"ltr"},{"str":"occurring","boundary":[0.23910169688515603,0.6809136574825797,0.32038386373853667,0.696186222813597],"dir":"ltr"},{"str":"case","boundary":[0.3234872927745242,0.6809136574825797,0.35972032094627676,0.696186222813597],"dir":"ltr"},{"str":"(at","boundary":[0.3628237499822643,0.6809136574825797,0.38697910209676606,0.696186222813597],"dir":"ltr"},{"str":"least","boundary":[0.3900825311327536,0.6809136574825797,0.4296166589797286,0.696186222813597],"dir":"ltr"},{"str":"for","boundary":[0.4327200880157162,0.6809136574825797,0.45798239570993327,0.696186222813597],"dir":"ltr"},{"str":"divide-and-conquer","boundary":[0.46108582474592075,0.6809136574825797,0.629165169287335,0.696186222813597],"dir":"ltr"},{"str":"algorithms","boundary":[0.6322685983233226,0.6809136574825797,0.723434297138447,0.696186222813597],"dir":"ltr"},{"str":"designed","boundary":[0.7265377261744346,0.6809136574825797,0.8023444163210092,0.696186222813597],"dir":"ltr"},{"str":"to","boundary":[0.8054478453569967,0.6809136574825797,0.823020765184977,0.696186222813597],"dir":"ltr"},{"str":"be","boundary":[0.8261241942209646,0.6809136574825797,0.8469982137241674,0.696186222813597],"dir":"ltr"},{"str":"executed","boundary":[0.850101642760155,0.6809136574825797,0.9269757543585978,0.696186222813597],"dir":"ltr"},{"str":"on","boundary":[0.23910169688515603,0.6992407358798004,0.26108267196807416,0.7145133012108177],"dir":"ltr"},{"str":"a","boundary":[0.26602443794894604,0.6992407358798004,0.2759079699106898,0.7145133012108177],"dir":"ltr"},{"str":"single-processor","boundary":[0.28084973589156165,0.6992407358798004,0.4192587174838212,0.7145133012108177],"dir":"ltr"},{"str":"computer).","boundary":[0.424200483464693,0.6992407358798004,0.519200992680974,0.7145133012108177],"dir":"ltr"},{"str":"As","boundary":[0.27468241194743354,0.7175678142770211,0.29893659938155276,0.7328403796080385],"dir":"ltr"},{"str":"an","boundary":[0.3019807272257698,0.7175678142770211,0.32285474672897263,0.7328403796080385],"dir":"ltr"},{"str":"example,","boundary":[0.32589887457318967,0.7175678142770211,0.4025950825963212,0.7328403796080385],"dir":"ltr"},{"str":"let","boundary":[0.4060147846550845,0.7175678142770211,0.42797599267407915,0.7328403796080385],"dir":"ltr"},{"str":"us","boundary":[0.4310201205182962,0.7175678142770211,0.4496999959259919,0.7328403796080385],"dir":"ltr"},{"str":"consider","boundary":[0.452744123770209,0.7175678142770211,0.5252497142415612,0.7328403796080385],"dir":"ltr"},{"str":"the","boundary":[0.5282938420857782,0.7175678142770211,0.5557502938755023,0.7328403796080385],"dir":"ltr"},{"str":"problem","boundary":[0.5587944217197195,0.7175678142770211,0.6313000121910717,0.7328403796080385],"dir":"ltr"},{"str":"of","boundary":[0.6343441400352887,0.7175678142770211,0.6519170598632691,0.7328403796080385],"dir":"ltr"},{"str":"computing","boundary":[0.6549611877074861,0.7175678142770211,0.7461268865226105,0.7328403796080385],"dir":"ltr"},{"str":"the","boundary":[0.7491710143668275,0.7175678142770211,0.7766274661565516,0.7328403796080385],"dir":"ltr"},{"str":"sum","boundary":[0.7796715940007688,0.7175678142770211,0.8148174336567297,0.7328403796080385],"dir":"ltr"},{"str":"of","boundary":[0.8178615615009466,0.7175678142770211,0.835434481328927,0.7328403796080385],"dir":"ltr"},{"str":"n","boundary":[0.8384865159987137,0.7181787168902618,0.8492595658370143,0.7334512822212791],"dir":"ltr"},{"str":"numbers","boundary":[0.8523036936812315,0.7175678142770211,0.9270034282480908,0.7328403796080385],"dir":"ltr"},{"str":"a0,...,an","boundary":[0.2391016968851561,0.7365048107706991,0.32653379680926936,0.753973468469951],"dir":"ltr"},{"str":"−","boundary":[0.32653527934898424,0.7445235054355501,0.3380990891251785,0.7559780060833088],"dir":"ltr"},{"str":"1.Ifn>1,","boundary":[0.3380990891251785,0.7358939081574584,0.4249011382022073,0.7535152884440407],"dir":"ltr"},{"str":"we","boundary":[0.4307719561874831,0.7358939081574584,0.45492730830198486,0.7511664734884757],"dir":"ltr"},{"str":"can","boundary":[0.46062022271194925,0.7358939081574584,0.4902708185971805,0.7511664734884757],"dir":"ltr"},{"str":"divide","boundary":[0.49596373300714486,0.7358939081574584,0.5487022595550096,0.7511664734884757],"dir":"ltr"},{"str":"the","boundary":[0.5543951739649741,0.7358939081574584,0.5818516257546982,0.7511664734884757],"dir":"ltr"},{"str":"problem","boundary":[0.5875445401646626,0.7358939081574584,0.6600501306360148,0.7511664734884757],"dir":"ltr"},{"str":"into","boundary":[0.665743045045979,0.7358939081574584,0.699801696186148,0.7511664734884757],"dir":"ltr"},{"str":"two","boundary":[0.7054946105961126,0.7358939081574584,0.737339350576851,0.7511664734884757],"dir":"ltr"},{"str":"instances","boundary":[0.7430322649868153,0.7358939081574584,0.8210133321649735,0.7511664734884757],"dir":"ltr"},{"str":"of","boundary":[0.826706246574938,0.7358939081574584,0.8442791664029183,0.7511664734884757],"dir":"ltr"},{"str":"the","boundary":[0.8499720808128827,0.7358939081574584,0.8774285326026068,0.7511664734884757],"dir":"ltr"},{"str":"same","boundary":[0.8831214470125712,0.7358939081574584,0.9270438630505605,0.7511664734884757],"dir":"ltr"},{"str":"problem:","boundary":[0.23910062085338654,0.7542209865546791,0.3165479773056106,0.7694935518856963],"dir":"ltr"},{"str":"to","boundary":[0.32145020915863554,0.7542209865546791,0.3390231289866159,0.7694935518856963],"dir":"ltr"},{"str":"compute","boundary":[0.3439253608396408,0.7542209865546791,0.41860532834257663,0.7694935518856963],"dir":"ltr"},{"str":"the","boundary":[0.4235075601956015,0.7542209865546791,0.45096401198532565,0.7694935518856963],"dir":"ltr"},{"str":"sum","boundary":[0.45586624383835056,0.7542209865546791,0.4910120834943113,0.7694935518856963],"dir":"ltr"},{"str":"of","boundary":[0.4959143153473362,0.7542209865546791,0.5134872351753166,0.7694935518856963],"dir":"ltr"},{"str":"the","boundary":[0.5183894670283414,0.7542209865546791,0.5458459188180655,0.7694935518856963],"dir":"ltr"},{"str":"first","boundary":[0.5507481506710905,0.7542209865546791,0.5836998462315443,0.7694935518856963],"dir":"ltr"},{"str":"\u000e","boundary":[0.5885605672503297,0.7575045881008479,0.5973371436323581,0.7727771534318651],"dir":"ltr"},{"str":"n/2","boundary":[0.5973371436323581,0.7542209865546791,0.6272842454764417,0.770104454498937],"dir":"ltr"},{"str":"\u000f","boundary":[0.627422614923906,0.7575045881008479,0.6361991913059346,0.7727771534318651],"dir":"ltr"},{"str":"numbers","boundary":[0.6410974697461748,0.7542209865546791,0.7157972043130341,0.7694935518856963],"dir":"ltr"},{"str":"and","boundary":[0.7206994361660589,0.7542209865546791,0.7525639432107207,0.7694935518856963],"dir":"ltr"},{"str":"to","boundary":[0.7574661750637457,0.7542209865546791,0.7750390948917261,0.7694935518856963],"dir":"ltr"},{"str":"compute","boundary":[0.779941326744751,0.7542209865546791,0.854621294247687,0.7694935518856963],"dir":"ltr"},{"str":"the","boundary":[0.8595235261007118,0.7542209865546791,0.8869799778904359,0.7694935518856963],"dir":"ltr"},{"str":"sum","boundary":[0.8918822097434607,0.7542209865546791,0.9270280493994215,0.7694935518856963],"dir":"ltr"},{"str":"of","boundary":[0.23909864414699403,0.7725480649518999,0.2566715639749744,0.7878206302829172],"dir":"ltr"},{"str":"the","boundary":[0.26232494425709185,0.7725480649518999,0.289781396046816,0.7878206302829172],"dir":"ltr"},{"str":"remaining","boundary":[0.29543477632893345,0.7725480649518999,0.3822121869530436,0.7878206302829172],"dir":"ltr"},{"str":"\u0007","boundary":[0.38787149735433807,0.7758316664980687,0.39664807373636657,0.791104231829086],"dir":"ltr"},{"str":"n/2","boundary":[0.39664807373636657,0.7725480649518999,0.4265951755804501,0.7884315328961579],"dir":"ltr"},{"str":"\b","boundary":[0.42673354502791455,0.7758316664980687,0.435510121409943,0.791104231829086],"dir":"ltr"},{"str":"numbers.","boundary":[0.44116547839845277,0.7725480649518999,0.5197197904303921,0.7878206302829172],"dir":"ltr"},{"str":"(Of","boundary":[0.5253731707125096,0.7725480649518999,0.5561109551135327,0.7878206302829172],"dir":"ltr"},{"str":"course,","boundary":[0.56176433539565,0.7725480649518999,0.6219945791705164,0.7878206302829172],"dir":"ltr"},{"str":"if","boundary":[0.6278258630279453,0.7725480649518999,0.6399035390851961,0.7878206302829172],"dir":"ltr"},{"str":"n","boundary":[0.645564826192883,0.7731589675651406,0.6563378760311837,0.7884315328961579],"dir":"ltr"},{"str":"=","boundary":[0.6608091858906765,0.7758316664980687,0.6762274957509967,0.791104231829086],"dir":"ltr"},{"str":"1","boundary":[0.6807007823168819,0.7725480649518999,0.6905843142786257,0.7878206302829172],"dir":"ltr"},{"str":",","boundary":[0.6896354952102983,0.7731589675651406,0.6961783933689727,0.7884315328961579],"dir":"ltr"},{"str":"we","boundary":[0.7018337503574825,0.7725480649518999,0.7259891024719842,0.7878206302829172],"dir":"ltr"},{"str":"simply","boundary":[0.7316424827541017,0.7725480649518999,0.7876623419132652,0.7878206302829172],"dir":"ltr"},{"str":"return","boundary":[0.7933157221953826,0.7725480649518999,0.8471414372590391,0.7878206302829172],"dir":"ltr"},{"str":"a0","boundary":[0.8528007476603336,0.7731589675651406,0.8700988086727914,0.7901690773209027],"dir":"ltr"},{"str":"as","boundary":[0.8763210310308162,0.7725492300242356,0.8938939508587965,0.7878217953552529],"dir":"ltr"},{"str":"the","boundary":[0.8995473311409139,0.7725492300242356,0.927003782930638,0.7878217953552529],"dir":"ltr"},{"str":"answer.)","boundary":[0.23910402827409588,0.7908763084214565,0.31178752232075946,0.8061488737524738],"dir":"ltr"},{"str":"Once","boundary":[0.3165316176623964,0.7908763084214565,0.36264817779589276,0.8061488737524738],"dir":"ltr"},{"str":"each","boundary":[0.36739227313752987,0.7908763084214565,0.40692640098450483,0.8061488737524738],"dir":"ltr"},{"str":"of","boundary":[0.41167049632614183,0.7908763084214565,0.4292434161541222,0.8061488737524738],"dir":"ltr"},{"str":"these","boundary":[0.43398751149575926,0.7908763084214565,0.4790168831134638,0.8061488737524738],"dir":"ltr"},{"str":"two","boundary":[0.4837609784551008,0.7908763084214565,0.5156057184358391,0.8061488737524738],"dir":"ltr"},{"str":"sums","boundary":[0.5203498137774761,0.7908763084214565,0.5631850412996736,0.8061488737524738],"dir":"ltr"},{"str":"is","boundary":[0.5679291366413105,0.7908763084214565,0.5811137682782767,0.8061488737524738],"dir":"ltr"},{"str":"computed","boundary":[0.5858578636199138,0.7908763084214565,0.6715283186643085,0.8061488737524738],"dir":"ltr"},{"str":"by","boundary":[0.6762724140059455,0.7908763084214565,0.6971464335091483,0.8061488737524738],"dir":"ltr"},{"str":"applying","boundary":[0.7018905288507854,0.7908763084214565,0.7755030749018528,0.8061488737524738],"dir":"ltr"},{"str":"the","boundary":[0.7802471702434899,0.7908763084214565,0.807703622033214,0.8061488737524738],"dir":"ltr"},{"str":"same","boundary":[0.8124477173748509,0.7908763084214565,0.8563701334128402,0.8061488737524738],"dir":"ltr"},{"str":"method","boundary":[0.8611142287544771,0.7908763084214565,0.9270176198753843,0.8061488737524738],"dir":"ltr"},{"str":"recursively,","boundary":[0.23910402827409588,0.8092033868186772,0.3355870672846384,0.8244759521496945],"dir":"ltr"},{"str":"we","boundary":[0.34052883326551026,0.8092033868186772,0.364684185380012,0.8244759521496945],"dir":"ltr"},{"str":"can","boundary":[0.3696259513608839,0.8092033868186772,0.39927654724611517,0.8244759521496945],"dir":"ltr"},{"str":"add","boundary":[0.404218313226987,0.8092033868186772,0.43608282027164885,0.8244759521496945],"dir":"ltr"},{"str":"their","boundary":[0.4410245862525208,0.8092033868186772,0.4816656696792111,0.8244759521496945],"dir":"ltr"},{"str":"values","boundary":[0.48660743566008297,0.8092033868186772,0.5404331507237394,0.8244759521496945],"dir":"ltr"},{"str":"to","boundary":[0.5453749167046114,0.8092033868186772,0.5629478365325917,0.8244759521496945],"dir":"ltr"},{"str":"get","boundary":[0.5678896025134635,0.8092033868186772,0.5942390987234725,0.8244759521496945],"dir":"ltr"},{"str":"the","boundary":[0.5991808647043442,0.8092033868186772,0.6266373164940683,0.8244759521496945],"dir":"ltr"},{"str":"sum","boundary":[0.6315790824749402,0.8092033868186772,0.6667249221309011,0.8244759521496945],"dir":"ltr"},{"str":"in","boundary":[0.6716666881117729,0.8092033868186772,0.6881524194239614,0.8244759521496945],"dir":"ltr"},{"str":"question:","boundary":[0.6930941854048334,0.8092033868186772,0.7716484974367728,0.8244759521496945],"dir":"ltr"},{"str":"a0","boundary":[0.32130734030631103,0.8381311528121571,0.33860276532664757,0.8551417889046765],"dir":"ltr"},{"str":"+","boundary":[0.34356328130792874,0.8408055431541783,0.35898159116824896,0.8560781084851955],"dir":"ltr"},{"str":"...+","boundary":[0.36337185606565553,0.8350004410718588,0.4082766951806421,0.8560781084851955],"dir":"ltr"},{"str":"an","boundary":[0.412668936784441,0.8381328442212503,0.4306349895575096,0.855599968930587],"dir":"ltr"},{"str":"−","boundary":[0.4306349895575096,0.846150005896186,0.4421987993337039,0.8576045065439447],"dir":"ltr"},{"str":"1","boundary":[0.4421987993337039,0.8436872882569179,0.44961149790818733,0.8551417889046765],"dir":"ltr"},{"str":"=","boundary":[0.453785307523092,0.8408055431541783,0.4692036173834122,0.8560781084851955],"dir":"ltr"},{"str":"(a0","boundary":[0.4735958589872111,0.8381328442212503,0.4982654672240478,0.8551417889046765],"dir":"ltr"},{"str":"+","boundary":[0.5032277689196536,0.8408055431541783,0.5186460787799738,0.8560781084851955],"dir":"ltr"},{"str":"...+","boundary":[0.5230363436773805,0.8350004410718588,0.567941182792367,0.8560781084851955],"dir":"ltr"},{"str":"a","boundary":[0.5723314476897737,0.8381328442212503,0.5822149796515174,0.8534054095522676],"dir":"ltr"},{"str":"\u000e","boundary":[0.5822198341357503,0.846150005896186,0.5888023104698916,0.8576045065439447],"dir":"ltr"},{"str":"n/2","boundary":[0.5888008279301767,0.8436872882569179,0.6112613046108617,0.855599968930587],"dir":"ltr"},{"str":"\u000f−","boundary":[0.6113665649306194,0.846150005896186,0.6295128510409551,0.8576045065439447],"dir":"ltr"},{"str":"1","boundary":[0.6295113685012401,0.8436872882569179,0.6369240670757236,0.8551417889046765],"dir":"ltr"},{"str":")","boundary":[0.6367059464360424,0.8381328442212503,0.6440790612795033,0.8534054095522676],"dir":"ltr"},{"str":"+","boundary":[0.6484713028833022,0.8408055431541783,0.6638896127436225,0.8560781084851955],"dir":"ltr"},{"str":"(a","boundary":[0.6682818543474214,0.8381328442212503,0.6855385011526259,0.8534054095522676],"dir":"ltr"},{"str":"\u000e","boundary":[0.6855412649622101,0.846150005896186,0.6921237412963515,0.8576045065439447],"dir":"ltr"},{"str":"n/2","boundary":[0.6921222587566366,0.8436872882569179,0.7145827354373215,0.855599968930587],"dir":"ltr"},{"str":"\u000f","boundary":[0.7146879957570792,0.846150005896186,0.7212704720912205,0.8576045065439447],"dir":"ltr"},{"str":"+","boundary":[0.7261563452137296,0.8408055431541783,0.7415746550740498,0.8560781084851955],"dir":"ltr"},{"str":"...+","boundary":[0.7459688733842412,0.8350004410718588,0.7908717357928354,0.8560781084851955],"dir":"ltr"},{"str":"an","boundary":[0.795262000690242,0.8381328442212503,0.8132282518760134,0.855599968930587],"dir":"ltr"},{"str":"−","boundary":[0.8132282518760134,0.846150005896186,0.8247920616522078,0.8576045065439447],"dir":"ltr"},{"str":"1","boundary":[0.8247920616522078,0.8436872882569179,0.8322047602266912,0.8551417889046765],"dir":"ltr"},{"str":").","boundary":[0.8319857126028627,0.8381328442212503,0.8447947700252826,0.8534054095522676],"dir":"ltr"},{"str":"Is","boundary":[0.2746849725824101,0.865838804988249,0.29006374831488335,0.8811113703192661],"dir":"ltr"},{"str":"this","boundary":[0.29783220443681396,0.865838804988249,0.32858975590176054,0.8811113703192661],"dir":"ltr"},{"str":"an","boundary":[0.3363582120236911,0.865838804988249,0.35723223152689393,0.8811113703192661],"dir":"ltr"},{"str":"efficient","boundary":[0.3650006876488245,0.865838804988249,0.4341854113810308,0.8811113703192661],"dir":"ltr"},{"str":"way","boundary":[0.4419538675029613,0.865838804988249,0.4759927515792068,0.8811113703192661],"dir":"ltr"},{"str":"to","boundary":[0.48376120770113745,0.865838804988249,0.5013341275291179,0.8811113703192661],"dir":"ltr"},{"str":"compute","boundary":[0.5091025836510484,0.865838804988249,0.5837825511539841,0.8811113703192661],"dir":"ltr"},{"str":"the","boundary":[0.5915510072759148,0.865838804988249,0.6190074590656389,0.8811113703192661],"dir":"ltr"},{"str":"sum","boundary":[0.6267759151875696,0.865838804988249,0.6619217548435304,0.8811113703192661],"dir":"ltr"},{"str":"of","boundary":[0.6696902109654609,0.865838804988249,0.6872631307934413,0.8811113703192661],"dir":"ltr"},{"str":"n","boundary":[0.6950513539792953,0.8664497076014895,0.7058244038175959,0.8817222729325068],"dir":"ltr"},{"str":"numbers?","boundary":[0.7135948366459188,0.865838804988249,0.7981781031745219,0.8811113703192661],"dir":"ltr"},{"str":"A","boundary":[0.8059465592964525,0.865838804988249,0.822511358864335,0.8811113703192661],"dir":"ltr"},{"str":"moment","boundary":[0.8302798149862656,0.865838804988249,0.901658682813979,0.8811113703192661],"dir":"ltr"},{"str":"of","boundary":[0.9094271389359095,0.865838804988249,0.9270000587638899,0.8811113703192661],"dir":"ltr"},{"str":"reflection","boundary":[0.2391042575201324,0.8841674106420029,0.320386424373513,0.8994399759730201],"dir":"ltr"},{"str":"(why","boundary":[0.3275025673859685,0.8841674106420029,0.37033779490816593,0.8994399759730201],"dir":"ltr"},{"str":"could","boundary":[0.3774539379206215,0.8841674106420029,0.4246972206977566,0.8994399759730201],"dir":"ltr"},{"str":"it","boundary":[0.43181336371021206,0.8841674106420029,0.44389103976746297,0.8994399759730201],"dir":"ltr"},{"str":"be","boundary":[0.45100718277991847,0.8841674106420029,0.47188120228312125,0.8994399759730201],"dir":"ltr"},{"str":"more","boundary":[0.47899734529557675,0.8841674106420029,0.5240267169132813,0.8994399759730201],"dir":"ltr"},{"str":"efficient","boundary":[0.5311428599257368,0.8841674106420029,0.6003275836579431,0.8994399759730201],"dir":"ltr"},{"str":"than","boundary":[0.6074437266703987,0.8841674106420029,0.6458906660015818,0.8994399759730201],"dir":"ltr"},{"str":"the","boundary":[0.6530068090140373,0.8841674106420029,0.6804632608037614,0.8994399759730201],"dir":"ltr"},{"str":"brute-force","boundary":[0.687579403816217,0.8841674106420029,0.7842205793381473,0.8994399759730201],"dir":"ltr"},{"str":"summation?),","boundary":[0.7913367223506027,0.8841674106420029,0.9094053951655936,0.8994399759730201],"dir":"ltr"},{"str":"a","boundary":[0.9170750159679066,0.8841674106420029,0.9269585479296504,0.8994399759730201],"dir":"ltr"},{"str":"169","boundary":[0.8940266194331203,0.932934239000474,0.9269980820574976,0.9482068043314913],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92705,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":227,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/5a6075d0f96340d0703147c20be09248.jpg","blurred":"/storage/books/4a8b03583f119702/pages/dc629c3f57a6e6f4eb86d247b76e40ee.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07293,0.05179]},"elements":[{"words":[{"str":"6","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Transform-and-Conquer","boundary":[0.14421784044919886,0.17005356781848974,0.7155032350605864,0.20670781659232623],"dir":"ltr"},{"str":"That’s","boundary":[0.23910077902799318,0.27434437041309123,0.2903765428455198,0.2896169357441086],"dir":"ltr"},{"str":"the","boundary":[0.2953183088263916,0.27434437041309123,0.32058061652060865,0.2896169357441086],"dir":"ltr"},{"str":"secret","boundary":[0.3255223825014805,0.27434437041309123,0.3727261311507687,0.2896169357441086],"dir":"ltr"},{"str":"to","boundary":[0.37766789713164056,0.27434437041309123,0.3941536284438291,0.2896169357441086],"dir":"ltr"},{"str":"life...replace","boundary":[0.39909539442470104,0.27434437041309123,0.5269902747160575,0.2896169357441086],"dir":"ltr"},{"str":"one","boundary":[0.5319320406969293,0.27434437041309123,0.562689592161876,0.2896169357441086],"dir":"ltr"},{"str":"worry","boundary":[0.5676313581427479,0.27434437041309123,0.618155973531182,0.2896169357441086],"dir":"ltr"},{"str":"with","boundary":[0.6230977395120537,0.27434437041309123,0.6593505347477299,0.2896169357441086],"dir":"ltr"},{"str":"another.","boundary":[0.6642923007286017,0.27434437041309123,0.7325875065842511,0.2896169357441086],"dir":"ltr"},{"str":"—Charles","boundary":[0.4037138778588346,0.29627247508083515,0.48510106812720577,0.310781458134999],"dir":"ltr"},{"str":"M.","boundary":[0.48981453946023795,0.29627247508083515,0.5122363911400799,0.310781458134999],"dir":"ltr"},{"str":"Schulz","boundary":[0.516949862473112,0.29627247508083515,0.5701688973647974,0.310781458134999],"dir":"ltr"},{"str":"(1922–2000),","boundary":[0.5748823686978294,0.29627247508083515,0.6786914106460425,0.310781458134999],"dir":"ltr"},{"str":"American","boundary":[0.6834048819790748,0.29627247508083515,0.7648671873284505,0.310781458134999],"dir":"ltr"},{"str":"cartoonist,","boundary":[0.7695806586614825,0.29627247508083515,0.8556625414926347,0.310781458134999],"dir":"ltr"},{"str":"the","boundary":[0.6772961480163842,0.314600222474855,0.7033798598951954,0.32910920552901884],"dir":"ltr"},{"str":"creator","boundary":[0.7081308887687298,0.314600222474855,0.7665516430199762,0.32910920552901884],"dir":"ltr"},{"str":"of","boundary":[0.7713026718935106,0.314600222474855,0.7879969986467599,0.32910920552901884],"dir":"ltr"},{"str":"Peanuts","boundary":[0.7927367602581435,0.314600222474855,0.8553639590456419,0.32910920552901884],"dir":"ltr"},{"str":"his","boundary":[0.278654351319837,0.4066352681511787,0.30282947049826225,0.421907833482196],"dir":"ltr"},{"str":"chapter","boundary":[0.30818634482152735,0.4066352681511787,0.37298278036271937,0.421907833482196],"dir":"ltr"},{"str":"deals","boundary":[0.3783396546859845,0.4066352681511787,0.4222818377878972,0.421907833482196],"dir":"ltr"},{"str":"with","boundary":[0.42763871211116233,0.4066352681511787,0.46497869586263024,0.421907833482196],"dir":"ltr"},{"str":"a","boundary":[0.47033557018589534,0.4066352681511787,0.48021910214763913,0.421907833482196],"dir":"ltr"},{"str":"group","boundary":[0.4855759764709043,0.4066352681511787,0.5361203589232618,0.421907833482196],"dir":"ltr"},{"str":"of","boundary":[0.541477233246527,0.4066352681511787,0.5590501530745073,0.421907833482196],"dir":"ltr"},{"str":"design","boundary":[0.5644070273977725,0.4066352681511787,0.6193396980411443,0.421907833482196],"dir":"ltr"},{"str":"methods","boundary":[0.6246965723644095,0.4066352681511787,0.6982893513515533,0.421907833482196],"dir":"ltr"},{"str":"that","boundary":[0.7036462256748184,0.4066352681511787,0.7376851097510638,0.421907833482196],"dir":"ltr"},{"str":"are","boundary":[0.7430419840743291,0.4066352681511787,0.7704984358640532,0.421907833482196],"dir":"ltr"},{"str":"based","boundary":[0.7758553101873183,0.4066352681511787,0.8252927370599606,0.421907833482196],"dir":"ltr"},{"str":"on","boundary":[0.8306496113832258,0.4066352681511787,0.8526305864661439,0.421907833482196],"dir":"ltr"},{"str":"the","boundary":[0.8579874607894089,0.4066352681511787,0.885443912579133,0.421907833482196],"dir":"ltr"},{"str":"idea","boundary":[0.8908007869023982,0.4066352681511787,0.9270535821380742,0.421907833482196],"dir":"ltr"},{"str":"of","boundary":[0.278654351319837,0.42496387380493256,0.29622727114781744,0.4402364391359499],"dir":"ltr"},{"str":"transformation.","boundary":[0.30439106854821774,0.42496387380493256,0.4378385170956819,0.4402364391359499],"dir":"ltr"},{"str":"We","boundary":[0.44600231449608224,0.42496387380493256,0.47419014765097545,0.4402364391359499],"dir":"ltr"},{"str":"call","boundary":[0.48235394505137574,0.42496387380493256,0.512004540936607,0.4402364391359499],"dir":"ltr"},{"str":"this","boundary":[0.5201683383370074,0.42496387380493256,0.5509258898019539,0.4402364391359499],"dir":"ltr"},{"str":"general","boundary":[0.5590896872023543,0.42496387380493256,0.6227989342277546,0.4402364391359499],"dir":"ltr"},{"str":"technique","boundary":[0.6309627316281547,0.42496387380493256,0.7155459981567578,0.4402364391359499],"dir":"ltr"},{"str":"transform-and-conquer","boundary":[0.7237750268681057,0.42496387380493256,0.9270002110654808,0.4402364391359499],"dir":"ltr"},{"str":"Tbecause","boundary":[0.23910045640893848,0.4053371249324789,0.30719799162535294,0.4585635175331707],"dir":"ltr"},{"str":"these","boundary":[0.31134907504928533,0.44329095220215337,0.35637844666698987,0.4585635175331707],"dir":"ltr"},{"str":"methods","boundary":[0.3605295300909222,0.44329095220215337,0.4341223090780662,0.4585635175331707],"dir":"ltr"},{"str":"work","boundary":[0.4382733925019986,0.44329095220215337,0.4822155756039113,0.4585635175331707],"dir":"ltr"},{"str":"as","boundary":[0.4863666590278437,0.44329095220215337,0.5039395788558241,0.4585635175331707],"dir":"ltr"},{"str":"two-stage","boundary":[0.5080906622797565,0.44329095220215337,0.5904402505850055,0.4585635175331707],"dir":"ltr"},{"str":"procedures.","boundary":[0.5945913340089378,0.44329095220215337,0.6940196655440799,0.4585635175331707],"dir":"ltr"},{"str":"First,","boundary":[0.6981707489680123,0.44329095220215337,0.7419152614306902,0.4585635175331707],"dir":"ltr"},{"str":"in","boundary":[0.7462244813660105,0.44329095220215337,0.762710212678199,0.4585635175331707],"dir":"ltr"},{"str":"the","boundary":[0.7668612961021315,0.44329095220215337,0.7943177478918556,0.4585635175331707],"dir":"ltr"},{"str":"transformation","boundary":[0.7984688313157879,0.44329095220215337,0.9269745138823803,0.4585635175331707],"dir":"ltr"},{"str":"stage,","boundary":[0.23910045640893848,0.4616180305993742,0.28723325706263053,0.4768905959303915],"dir":"ltr"},{"str":"the","boundary":[0.2932029103675238,0.4616180305993742,0.32065936215724794,0.4768905959303915],"dir":"ltr"},{"str":"problem’s","boundary":[0.3264115777589828,0.4616180305993742,0.4117459927166784,0.4768905959303915],"dir":"ltr"},{"str":"instance","boundary":[0.4174982083184133,0.4616180305993742,0.4877898876303349,0.4768905959303915],"dir":"ltr"},{"str":"is","boundary":[0.4935421032320697,0.4616180305993742,0.5067267348690359,0.4768905959303915],"dir":"ltr"},{"str":"modified","boundary":[0.5124789504707707,0.4616180305993742,0.5882856406173453,0.4768905959303915],"dir":"ltr"},{"str":"to","boundary":[0.5940378562190802,0.4616180305993742,0.6116107760470606,0.4768905959303915],"dir":"ltr"},{"str":"be,","boundary":[0.6173629916487954,0.4616180305993742,0.642447395767701,0.4768905959303915],"dir":"ltr"},{"str":"for","boundary":[0.6484170490725943,0.4616180305993742,0.6736793567668113,0.4768905959303915],"dir":"ltr"},{"str":"one","boundary":[0.6794315723685461,0.4616180305993742,0.7112960794132079,0.4768905959303915],"dir":"ltr"},{"str":"reason","boundary":[0.7170482950149428,0.4616180305993742,0.7741751097538218,0.4768905959303915],"dir":"ltr"},{"str":"or","boundary":[0.7799273253555565,0.4616180305993742,0.7986072007632522,0.4768905959303915],"dir":"ltr"},{"str":"another,","boundary":[0.8043594163649873,0.4616180305993742,0.875955721895859,0.4768905959303915],"dir":"ltr"},{"str":"more","boundary":[0.8819253752007523,0.4616180305993742,0.9269547468184568,0.4768905959303915],"dir":"ltr"},{"str":"amenable","boundary":[0.23910045640893848,0.479945108996595,0.32257676735782626,0.4952176743276123],"dir":"ltr"},{"str":"to","boundary":[0.3275185333386981,0.479945108996595,0.34509145316667855,0.4952176743276123],"dir":"ltr"},{"str":"solution.","boundary":[0.3500332191475504,0.479945108996595,0.42419924298847556,0.4952176743276123],"dir":"ltr"},{"str":"Then,","boundary":[0.42914100896934737,0.479945108996595,0.4783412310749078,0.4952176743276123],"dir":"ltr"},{"str":"in","boundary":[0.4832829970557797,0.479945108996595,0.49976872836796826,0.4952176743276123],"dir":"ltr"},{"str":"the","boundary":[0.5047104943488402,0.479945108996595,0.5321669461385643,0.4952176743276123],"dir":"ltr"},{"str":"second","boundary":[0.5371087121194361,0.479945108996595,0.5964296709538222,0.4952176743276123],"dir":"ltr"},{"str":"or","boundary":[0.601371436934694,0.479945108996595,0.6200513123423896,0.4952176743276123],"dir":"ltr"},{"str":"conquering","boundary":[0.6249930783232616,0.479945108996595,0.721673787973039,0.4952176743276123],"dir":"ltr"},{"str":"stage,","boundary":[0.7266155539539109,0.479945108996595,0.774748354607603,0.4952176743276123],"dir":"ltr"},{"str":"it","boundary":[0.7796901205884749,0.479945108996595,0.7917677966457256,0.4952176743276123],"dir":"ltr"},{"str":"is","boundary":[0.7967095626265976,0.479945108996595,0.8098941942635638,0.4952176743276123],"dir":"ltr"},{"str":"solved.","boundary":[0.8148359602444356,0.479945108996595,0.8747103968686792,0.4952176743276123],"dir":"ltr"},{"str":"There","boundary":[0.274681171471216,0.49827218739381585,0.3255220598824259,0.5135447527248331],"dir":"ltr"},{"str":"are","boundary":[0.3298905810095166,0.49827218739381585,0.3573470327992408,0.5135447527248331],"dir":"ltr"},{"str":"three","boundary":[0.36171555392633153,0.49827218739381585,0.4067449255440361,0.5135447527248331],"dir":"ltr"},{"str":"major","boundary":[0.4111134466711268,0.49827218739381585,0.46163806205956087,0.5135447527248331],"dir":"ltr"},{"str":"variations","boundary":[0.4660065831866516,0.49827218739381585,0.5505898497152546,0.5135447527248331],"dir":"ltr"},{"str":"of","boundary":[0.5549583708423453,0.49827218739381585,0.5725312906703257,0.5135447527248331],"dir":"ltr"},{"str":"this","boundary":[0.5768998117974166,0.49827218739381585,0.6076573632623631,0.5135447527248331],"dir":"ltr"},{"str":"idea","boundary":[0.6120258843894538,0.49827218739381585,0.6482786796251299,0.5135447527248331],"dir":"ltr"},{"str":"that","boundary":[0.6526472007522206,0.49827218739381585,0.6866860848284662,0.5135447527248331],"dir":"ltr"},{"str":"differ","boundary":[0.6910546059555569,0.49827218739381585,0.7382781216687685,0.5135447527248331],"dir":"ltr"},{"str":"by","boundary":[0.7426466427958592,0.49827218739381585,0.763520662299062,0.5135447527248331],"dir":"ltr"},{"str":"what","boundary":[0.7678891834261529,0.49827218739381585,0.809617455368635,0.5135447527248331],"dir":"ltr"},{"str":"we","boundary":[0.8139859764957257,0.49827218739381585,0.8381413286102275,0.5135447527248331],"dir":"ltr"},{"str":"transform","boundary":[0.8425098497373181,0.49827218739381585,0.9270733492019977,0.5135447527248331],"dir":"ltr"},{"str":"a","boundary":[0.23910045640893848,0.5165992657910367,0.24898398837068225,0.5318718311220539],"dir":"ltr"},{"str":"given","boundary":[0.2539257543515541,0.5165992657910367,0.3000620815489739,0.5318718311220539],"dir":"ltr"},{"str":"instance","boundary":[0.30500384752984583,0.5165992657910367,0.3752955268417674,0.5318718311220539],"dir":"ltr"},{"str":"to","boundary":[0.38023729282263924,0.5165992657910367,0.39781021265061967,0.5318718311220539],"dir":"ltr"},{"str":"(Figure","boundary":[0.4027519786314916,0.5165992657910367,0.46572984429172276,0.5318718311220539],"dir":"ltr"},{"str":"6.1):","boundary":[0.47067161027259463,0.5165992657910367,0.5080115940240625,0.5318718311220539],"dir":"ltr"},{"str":"Transformation","boundary":[0.27468212901091943,0.5447990502551072,0.40759586683244947,0.5600716155861245],"dir":"ltr"},{"str":"to","boundary":[0.41868518969352597,0.5447990502551072,0.4362581095215064,0.5600716155861245],"dir":"ltr"},{"str":"a","boundary":[0.4473474323825828,0.5447990502551072,0.4572309643443266,0.5600716155861245],"dir":"ltr"},{"str":"simpler","boundary":[0.4683202872054031,0.5447990502551072,0.5320295342308032,0.5600716155861245],"dir":"ltr"},{"str":"or","boundary":[0.5431188570918798,0.5447990502551072,0.5617987324995755,0.5600716155861245],"dir":"ltr"},{"str":"more","boundary":[0.572888055360652,0.5447990502551072,0.6179174269783565,0.5600716155861245],"dir":"ltr"},{"str":"convenient","boundary":[0.629006749839433,0.5447990502551072,0.7234735483297798,0.5600716155861245],"dir":"ltr"},{"str":"instance","boundary":[0.7345628711908563,0.5447990502551072,0.8048545505027778,0.5600716155861245],"dir":"ltr"},{"str":"of","boundary":[0.8159438733638543,0.5447990502551072,0.8335167931918347,0.5600716155861245],"dir":"ltr"},{"str":"the","boundary":[0.8446061160529112,0.5447990502551072,0.8720625678426354,0.5600716155861245],"dir":"ltr"},{"str":"same","boundary":[0.8831518907037118,0.5447990502551072,0.9270743067417011,0.5600716155861245],"dir":"ltr"},{"str":"problem—we","boundary":[0.27468212901091943,0.563126128652328,0.39111013552026086,0.5783986939833453],"dir":"ltr"},{"str":"call","boundary":[0.39605190150113273,0.563126128652328,0.425702497386364,0.5783986939833453],"dir":"ltr"},{"str":"it","boundary":[0.4306442633672359,0.563126128652328,0.44272193942448673,0.5783986939833453],"dir":"ltr"},{"str":"instance","boundary":[0.44766568211175095,0.563126128652328,0.5190445499394644,0.5783986939833453],"dir":"ltr"},{"str":"simplification","boundary":[0.5245397937101938,0.563126128652328,0.645336321346626,0.5783986939833453],"dir":"ltr"},{"str":".","boundary":[0.6451999286055539,0.563126128652328,0.6501416945864258,0.5783986939833453],"dir":"ltr"},{"str":"Transformation","boundary":[0.27468212901091943,0.5845080880333319,0.40759586683244947,0.5997806533643492],"dir":"ltr"},{"str":"to","boundary":[0.4123004280462395,0.5845080880333319,0.4298733478742199,0.5997806533643492],"dir":"ltr"},{"str":"a","boundary":[0.4345779090880099,0.5845080880333319,0.4444614410497537,0.5997806533643492],"dir":"ltr"},{"str":"different","boundary":[0.44916600226354364,0.5845080880333319,0.5238459697664793,0.5997806533643492],"dir":"ltr"},{"str":"representation","boundary":[0.5285505309802695,0.5845080880333319,0.6537748809355628,0.5997806533643492],"dir":"ltr"},{"str":"of","boundary":[0.6584794421493531,0.5845080880333319,0.6760523619773334,0.5997806533643492],"dir":"ltr"},{"str":"the","boundary":[0.6807569231911232,0.5845080880333319,0.7082133749808474,0.5997806533643492],"dir":"ltr"},{"str":"same","boundary":[0.7129179361946375,0.5845080880333319,0.7568403522326267,0.5997806533643492],"dir":"ltr"},{"str":"instance—we","boundary":[0.7615449134464167,0.5845080880333319,0.8757590087963275,0.5997806533643492],"dir":"ltr"},{"str":"call","boundary":[0.8804635700101174,0.5845080880333319,0.9101141658953487,0.5997806533643492],"dir":"ltr"},{"str":"it","boundary":[0.9148187271091388,0.5845080880333319,0.9268964031663895,0.5997806533643492],"dir":"ltr"},{"str":"representation","boundary":[0.27468212901091943,0.6028351664305527,0.3989774269618089,0.61810773176157],"dir":"ltr"},{"str":"change","boundary":[0.40447267073253845,0.6028351664305527,0.4648017498270223,0.61810773176157],"dir":"ltr"},{"str":".","boundary":[0.4655351078985836,0.6028351664305527,0.47047687387945547,0.61810773176157],"dir":"ltr"},{"str":"Transformation","boundary":[0.27468212901091943,0.6242171258115566,0.40759586683244947,0.6394896911425739],"dir":"ltr"},{"str":"to","boundary":[0.41267600226078577,0.6242171258115566,0.4302489220887662,0.6394896911425739],"dir":"ltr"},{"str":"an","boundary":[0.43532905751710244,0.6242171258115566,0.4562030770203052,0.6394896911425739],"dir":"ltr"},{"str":"instance","boundary":[0.4612832124486415,0.6242171258115566,0.531574891760563,0.6394896911425739],"dir":"ltr"},{"str":"of","boundary":[0.5366550271888993,0.6242171258115566,0.5542279470168797,0.6394896911425739],"dir":"ltr"},{"str":"a","boundary":[0.5593080824452159,0.6242171258115566,0.5691916144069596,0.6394896911425739],"dir":"ltr"},{"str":"different","boundary":[0.574271749835296,0.6242171258115566,0.6489517173382318,0.6394896911425739],"dir":"ltr"},{"str":"problem","boundary":[0.6540318527665682,0.6242171258115566,0.7265374432379204,0.6394896911425739],"dir":"ltr"},{"str":"for","boundary":[0.7316175786662565,0.6242171258115566,0.7568798863604735,0.6394896911425739],"dir":"ltr"},{"str":"which","boundary":[0.76196002178881,0.6242171258115566,0.8124846371772441,0.6394896911425739],"dir":"ltr"},{"str":"an","boundary":[0.8175647726055802,0.6242171258115566,0.838438792108783,0.6394896911425739],"dir":"ltr"},{"str":"algorithm","boundary":[0.8435189275371194,0.6242171258115566,0.9269952384860071,0.6394896911425739],"dir":"ltr"},{"str":"is","boundary":[0.27468212901091943,0.6425442042087774,0.28786676064788563,0.6578167695397947],"dir":"ltr"},{"str":"already","boundary":[0.29280852662875745,0.6425442042087774,0.3565177736541577,0.6578167695397947],"dir":"ltr"},{"str":"available—we","boundary":[0.3614595396350296,0.6425442042087774,0.48227583433538523,0.6578167695397947],"dir":"ltr"},{"str":"call","boundary":[0.48721760031625705,0.6425442042087774,0.5168681962014883,0.6578167695397947],"dir":"ltr"},{"str":"it","boundary":[0.5218099621823602,0.6425442042087774,0.533887638239611,0.6578167695397947],"dir":"ltr"},{"str":"problem","boundary":[0.5388333576332677,0.6425442042087774,0.6113191810406965,0.6578167695397947],"dir":"ltr"},{"str":"reduction","boundary":[0.6168144248114259,0.6425442042087774,0.6991837801805983,0.6578167695397947],"dir":"ltr"},{"str":".","boundary":[0.6990473874395263,0.6425442042087774,0.7039891534203983,0.6578167695397947],"dir":"ltr"},{"str":"In","boundary":[0.27468212901091954,0.6707449960925008,0.29336200441861526,0.6860175614235182],"dir":"ltr"},{"str":"the","boundary":[0.3021385808006437,0.6707449960925008,0.3295950325903679,0.6860175614235182],"dir":"ltr"},{"str":"first","boundary":[0.3383716089723963,0.6707449960925008,0.37132330453285,0.6860175614235182],"dir":"ltr"},{"str":"three","boundary":[0.3800998809148784,0.6707449960925008,0.42512925253258294,0.6860175614235182],"dir":"ltr"},{"str":"sections","boundary":[0.43390582891461144,0.6707449960925008,0.5020033641310259,0.6860175614235182],"dir":"ltr"},{"str":"of","boundary":[0.5107799405130544,0.6707449960925008,0.5283528603410348,0.6860175614235182],"dir":"ltr"},{"str":"this","boundary":[0.5371294367230633,0.6707449960925008,0.5678869881880099,0.6860175614235182],"dir":"ltr"},{"str":"chapter,","boundary":[0.5766635645700382,0.6707449960925008,0.6460459589414794,0.6860175614235182],"dir":"ltr"},{"str":"we","boundary":[0.6557713543918352,0.6707449960925008,0.6799267065063369,0.6860175614235182],"dir":"ltr"},{"str":"encounter","boundary":[0.6887032828883655,0.6707449960925008,0.7754806935124756,0.6860175614235182],"dir":"ltr"},{"str":"examples","boundary":[0.7842572698945042,0.6707449960925008,0.8644324811681694,0.6860175614235182],"dir":"ltr"},{"str":"of","boundary":[0.8732090575501978,0.6707449960925008,0.8907819773781782,0.6860175614235182],"dir":"ltr"},{"str":"the","boundary":[0.8995585537602067,0.6707449960925008,0.9270150055499308,0.6860175614235182],"dir":"ltr"},{"str":"instance-simplification","boundary":[0.23910141394864204,0.6890720744897216,0.4313163435406346,0.704344639820739],"dir":"ltr"},{"str":"variety.","boundary":[0.4367918202474406,0.6890720744897216,0.49921620811781414,0.704344639820739],"dir":"ltr"},{"str":"Section","boundary":[0.5046916848246202,0.6890720744897216,0.5684009318500205,0.704344639820739],"dir":"ltr"},{"str":"6.1","boundary":[0.5738764085568265,0.6890720744897216,0.5985852384611859,0.704344639820739],"dir":"ltr"},{"str":"deals","boundary":[0.6040607151679919,0.6890720744897216,0.6480028982699046,0.704344639820739],"dir":"ltr"},{"str":"with","boundary":[0.6534783749767108,0.6890720744897216,0.6908183587281788,0.704344639820739],"dir":"ltr"},{"str":"the","boundary":[0.6962938354349847,0.6890720744897216,0.7237502872247088,0.704344639820739],"dir":"ltr"},{"str":"simple","boundary":[0.7292257639315148,0.6890720744897216,0.7852456230906784,0.704344639820739],"dir":"ltr"},{"str":"but","boundary":[0.7907210997974845,0.6890720744897216,0.8192845071669239,0.704344639820739],"dir":"ltr"},{"str":"fruitful","boundary":[0.82475998387373,0.6890720744897216,0.8851681312239078,0.704344639820739],"dir":"ltr"},{"str":"idea","boundary":[0.8906436079307138,0.6890720744897216,0.9268964031663899,0.704344639820739],"dir":"ltr"},{"str":"of","boundary":[0.23910141394864204,0.7073991528869424,0.25667433377662247,0.7226717182179597],"dir":"ltr"},{"str":"presorting.","boundary":[0.26501603475233415,0.7073991528869424,0.3574863597864087,0.7226717182179597],"dir":"ltr"},{"str":"Many","boundary":[0.36582806076212043,0.7073991528869424,0.41524572057083914,0.7226717182179597],"dir":"ltr"},{"str":"algorithmic","boundary":[0.42358742154655094,0.7073991528869424,0.5213355526481966,0.7226717182179597],"dir":"ltr"},{"str":"problems","boundary":[0.5296772536239084,0.7073991528869424,0.6098722319614972,0.7226717182179597],"dir":"ltr"},{"str":"are","boundary":[0.6182139329372088,0.7073991528869424,0.6456703847269329,0.7226717182179597],"dir":"ltr"},{"str":"easier","boundary":[0.6540120857026448,0.7073991528869424,0.7045367010910788,0.7226717182179597],"dir":"ltr"},{"str":"to","boundary":[0.7128784020667907,0.7073991528869424,0.730451321894771,0.7226717182179597],"dir":"ltr"},{"str":"solve","boundary":[0.7387930228704827,0.7073991528869424,0.7827352059723954,0.7226717182179597],"dir":"ltr"},{"str":"if","boundary":[0.7910769069481071,0.7073991528869424,0.8031545830053579,0.7226717182179597],"dir":"ltr"},{"str":"their","boundary":[0.8114962839810697,0.7073991528869424,0.8521373674077599,0.7226717182179597],"dir":"ltr"},{"str":"input","boundary":[0.8604790683834718,0.7073991528869424,0.9055282070650998,0.7226717182179597],"dir":"ltr"},{"str":"is","boundary":[0.9138699080408117,0.7073991528869424,0.9270545396777778,0.7226717182179597],"dir":"ltr"},{"str":"sorted.","boundary":[0.23910141394864204,0.7257262312841631,0.29786889499317043,0.7409987966151804],"dir":"ltr"},{"str":"Of","boundary":[0.30441179315184475,0.7257262312841631,0.32746018968663115,0.7409987966151804],"dir":"ltr"},{"str":"course,","boundary":[0.3340030878453055,0.7257262312841631,0.39423333162017193,0.7409987966151804],"dir":"ltr"},{"str":"the","boundary":[0.4011913381212396,0.7257262312841631,0.42864778991096375,0.7409987966151804],"dir":"ltr"},{"str":"benefits","boundary":[0.43519068806963807,0.7257262312841631,0.5022010347702607,0.7409987966151804],"dir":"ltr"},{"str":"of","boundary":[0.508743932928935,0.7257262312841631,0.5263168527569154,0.7409987966151804],"dir":"ltr"},{"str":"sorting","boundary":[0.5328597509155898,0.7257262312841631,0.5921807097499758,0.7409987966151804],"dir":"ltr"},{"str":"should","boundary":[0.5987236079086501,0.7257262312841631,0.6558701897114525,0.7409987966151804],"dir":"ltr"},{"str":"more","boundary":[0.662413087870127,0.7257262312841631,0.7074424594878315,0.7409987966151804],"dir":"ltr"},{"str":"than","boundary":[0.7139853576465057,0.7257262312841631,0.7524322969776889,0.7409987966151804],"dir":"ltr"},{"str":"compensate","boundary":[0.7589751951363635,0.7257262312841631,0.8611116144290234,0.7409987966151804],"dir":"ltr"},{"str":"for","boundary":[0.8676545125876978,0.7257262312841631,0.8929168202819148,0.7409987966151804],"dir":"ltr"},{"str":"the","boundary":[0.8994597184405893,0.7257262312841631,0.9269161702303134,0.7409987966151804],"dir":"ltr"},{"str":"simpler","boundary":[0.5256507852820608,0.7907379392187038,0.5841865008453403,0.8045348484571713],"dir":"ltr"},{"str":"instance","boundary":[0.5891507866679736,0.7907379392187038,0.6556329309761156,0.8045348484571713],"dir":"ltr"},{"str":"or","boundary":[0.5827043579558491,0.8060676850735649,0.5985793583023272,0.8198645943120323],"dir":"ltr"},{"str":"problem's","boundary":[0.3231007808613265,0.822037607517091,0.40249363973696434,0.8358345167555584],"dir":"ltr"},{"str":"another","boundary":[0.5003400704439301,0.8213974309284261,0.5608757860508604,0.8351943401668935],"dir":"ltr"},{"str":"representation","boundary":[0.5658400718734936,0.8213974309284261,0.6809472172428956,0.8351943401668935],"dir":"ltr"},{"str":"solution","boundary":[0.7809472194254353,0.822037607517091,0.8434650779327696,0.8358345167555584],"dir":"ltr"},{"str":"instance","boundary":[0.3295579238593991,0.8373673533719522,0.3960400681675411,0.8511642626104197],"dir":"ltr"},{"str":"or","boundary":[0.5827043579558491,0.8367271767832873,0.5985793583023272,0.8505240860217548],"dir":"ltr"},{"str":"another","boundary":[0.4799900699997833,0.8520569226381484,0.5405257856067136,0.8658538318766158],"dir":"ltr"},{"str":"problem's","boundary":[0.55045435725198,0.8520569226381484,0.6298472161276178,0.8658538318766158],"dir":"ltr"},{"str":"instance","boundary":[0.634811501950251,0.8520569226381484,0.7012936462583931,0.8658538318766158],"dir":"ltr"},{"str":"FIGURE","boundary":[0.23910077902799318,0.8825251879594339,0.3043562471188863,0.8962705887367444],"dir":"ltr"},{"str":"6.1","boundary":[0.3093019996077817,0.8825251879594339,0.33403076205225873,0.8962705887367444],"dir":"ltr"},{"str":"Transform-and-conquer","boundary":[0.3429260003416389,0.8825251879594339,0.5251894328910393,0.8962705887367444],"dir":"ltr"},{"str":"strategy.","boundary":[0.5301351853799346,0.8825251879594339,0.598343872582902,0.8962705887367444],"dir":"ltr"},{"str":"201","boundary":[0.8940253964965859,0.9329341022884333,0.9269968591209631,0.9482066676194506],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92707,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":279,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/cec3239c8469f209b167e2020a1cb91a.jpg","blurred":"/storage/books/4a8b03583f119702/pages/ceeae6cf8d745e670f6d58eeff61c1a3.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07291,0.05179]},"elements":[{"words":[{"str":"7","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Space","boundary":[0.14421784044919886,0.17005356781848974,0.28995681505858123,0.20670781659232623],"dir":"ltr"},{"str":"and","boundary":[0.3057546921890904,0.17005356781848974,0.39375788160979497,0.20670781659232623],"dir":"ltr"},{"str":"Time","boundary":[0.40955575874030414,0.17005356781848974,0.5277314702481074,0.20670781659232623],"dir":"ltr"},{"str":"Trade-Offs","boundary":[0.5435293473786166,0.17005356781848974,0.7968646743363321,0.20670781659232623],"dir":"ltr"},{"str":"Things","boundary":[0.23910077902799318,0.27434437041309123,0.2973345493465874,0.2896169357441086],"dir":"ltr"},{"str":"which","boundary":[0.3041344193362671,0.27434437041309123,0.35442182995761934,0.2896169357441086],"dir":"ltr"},{"str":"matter","boundary":[0.361221699947299,0.27434437041309123,0.415027647947032,0.2896169357441086],"dir":"ltr"},{"str":"most","boundary":[0.4218275179367117,0.27434437041309123,0.46246860136340207,0.2896169357441086],"dir":"ltr"},{"str":"must","boundary":[0.4692684713530817,0.27434437041309123,0.5099095547797721,0.2896169357441086],"dir":"ltr"},{"str":"never","boundary":[0.5167094247694517,0.27434437041309123,0.5628259849029481,0.2896169357441086],"dir":"ltr"},{"str":"be","boundary":[0.5696258548926277,0.27434437041309123,0.5893929188161152,0.2896169357441086],"dir":"ltr"},{"str":"at","boundary":[0.5961927888057951,0.27434437041309123,0.6115715645382683,0.2896169357441086],"dir":"ltr"},{"str":"the","boundary":[0.618371434527948,0.27434437041309123,0.643633742222165,0.2896169357441086],"dir":"ltr"},{"str":"mercy","boundary":[0.6504336122118446,0.27434437041309123,0.702025649052147,0.2896169357441086],"dir":"ltr"},{"str":"of","boundary":[0.7088255190418268,0.27434437041309123,0.7263984388698072,0.2896169357441086],"dir":"ltr"},{"str":"things","boundary":[0.7331983088594868,0.27434437041309123,0.7837426913118444,0.2896169357441086],"dir":"ltr"},{"str":"which","boundary":[0.7905425613015242,0.27434437041309123,0.8408299719228763,0.2896169357441086],"dir":"ltr"},{"str":"matter","boundary":[0.23910077902799318,0.2926729760668451,0.29290672702772613,0.30794554139786245],"dir":"ltr"},{"str":"less.","boundary":[0.29784849300859806,0.2926729760668451,0.3313536663589094,0.30794554139786245],"dir":"ltr"},{"str":"—Johann","boundary":[0.49049959403868154,0.31459936951926604,0.56783056993281,0.32910835257342996],"dir":"ltr"},{"str":"Wolfgang","boundary":[0.5725628200360932,0.31459936951926604,0.6504759378080065,0.32910835257342996],"dir":"ltr"},{"str":"von","boundary":[0.6552081879112898,0.31459936951926604,0.6854795655561016,0.32910835257342996],"dir":"ltr"},{"str":"Goethe","boundary":[0.6902118156593848,0.31459936951926604,0.7517498457723178,0.32910835257342996],"dir":"ltr"},{"str":"(1749–1832)","boundary":[0.7564820958756012,0.31459936951926604,0.8555964452610335,0.32910835257342996],"dir":"ltr"},{"str":"pace","boundary":[0.2819162561529341,0.4109950914705344,0.3214503839999091,0.4262676568015517],"dir":"ltr"},{"str":"and","boundary":[0.32587820631877035,0.4109950914705344,0.3577427133634322,0.4262676568015517],"dir":"ltr"},{"str":"time","boundary":[0.3621705356822934,0.4109950914705344,0.4005977079495531,0.4262676568015517],"dir":"ltr"},{"str":"trade-offs","boundary":[0.4050255302684143,0.4109950914705344,0.4884820741533786,0.4262676568015517],"dir":"ltr"},{"str":"in","boundary":[0.4929098964722397,0.4109950914705344,0.5093956277844283,0.4262676568015517],"dir":"ltr"},{"str":"algorithm","boundary":[0.5138234501032896,0.4109950914705344,0.5972997610521772,0.4262676568015517],"dir":"ltr"},{"str":"design","boundary":[0.6017275833710385,0.4109950914705344,0.6566602540144103,0.4262676568015517],"dir":"ltr"},{"str":"are","boundary":[0.6610880763332714,0.4109950914705344,0.6885445281229955,0.4262676568015517],"dir":"ltr"},{"str":"a","boundary":[0.6929723504418568,0.4109950914705344,0.7028558824036005,0.4262676568015517],"dir":"ltr"},{"str":"well-known","boundary":[0.7072837047224618,0.4109950914705344,0.8072457469835381,0.4262676568015517],"dir":"ltr"},{"str":"issue","boundary":[0.8116735693023992,0.4109950914705344,0.8534216083088049,0.4262676568015517],"dir":"ltr"},{"str":"for","boundary":[0.857849430627666,0.4109950914705344,0.883111738321883,0.4262676568015517],"dir":"ltr"},{"str":"both","boundary":[0.8875395606407442,0.4109950914705344,0.9270934555516428,0.4262676568015517],"dir":"ltr"},{"str":"theoreticians","boundary":[0.2819162561529341,0.42932216986775523,0.392849018891546,0.4445947351987726],"dir":"ltr"},{"str":"and","boundary":[0.39889774045213316,0.42932216986775523,0.43076224749679504,0.4445947351987726],"dir":"ltr"},{"str":"practitioners","boundary":[0.4368109690573822,0.42932216986775523,0.5455495877004869,0.4445947351987726],"dir":"ltr"},{"str":"of","boundary":[0.5515983092610741,0.42932216986775523,0.5691712290890545,0.4445947351987726],"dir":"ltr"},{"str":"computing.","boundary":[0.5752199506496416,0.42932216986775523,0.6709716082950151,0.4445947351987726],"dir":"ltr"},{"str":"Consider,","boundary":[0.6770203298556023,0.42932216986775523,0.7596071229279332,0.4445947351987726],"dir":"ltr"},{"str":"as","boundary":[0.7659325833834492,0.42932216986775523,0.7835055032114295,0.4445947351987726],"dir":"ltr"},{"str":"an","boundary":[0.7895542247720166,0.42932216986775523,0.8104282442752194,0.4445947351987726],"dir":"ltr"},{"str":"example,","boundary":[0.8164769658358068,0.42932216986775523,0.8931731738589382,0.4445947351987726],"dir":"ltr"},{"str":"the","boundary":[0.8994986343144543,0.42932216986775523,0.9269550861041784,0.4445947351987726],"dir":"ltr"},{"str":"Sproblem","boundary":[0.23910077902799318,0.4103837277339273,0.31160638616601233,0.4629218135959934],"dir":"ltr"},{"str":"of","boundary":[0.3177341759822934,0.44764924826497604,0.33530709581027385,0.4629218135959934],"dir":"ltr"},{"str":"computing","boundary":[0.34143488562655494,0.44764924826497604,0.43260058444167937,0.4629218135959934],"dir":"ltr"},{"str":"values","boundary":[0.43872837425796046,0.44764924826497604,0.49255408932161693,0.4629218135959934],"dir":"ltr"},{"str":"of","boundary":[0.4986818791378981,0.44764924826497604,0.5162547989658784,0.4629218135959934],"dir":"ltr"},{"str":"a","boundary":[0.5223825887821596,0.44764924826497604,0.5322661207439032,0.4629218135959934],"dir":"ltr"},{"str":"function","boundary":[0.5383939105601844,0.44764924826497604,0.6097925454518213,0.4629218135959934],"dir":"ltr"},{"str":"at","boundary":[0.6159203352681024,0.44764924826497604,0.6323862995163675,0.4629218135959934],"dir":"ltr"},{"str":"many","boundary":[0.6385140893326485,0.44764924826497604,0.6857376050458602,0.4629218135959934],"dir":"ltr"},{"str":"points","boundary":[0.6918653948621414,0.44764924826497604,0.7446039214100061,0.4629218135959934],"dir":"ltr"},{"str":"in","boundary":[0.7507317112262871,0.44764924826497604,0.7672174425384757,0.4629218135959934],"dir":"ltr"},{"str":"its","boundary":[0.7733452323547568,0.44764924826497604,0.7931122962782443,0.4629218135959934],"dir":"ltr"},{"str":"domain.","boundary":[0.7992400860945253,0.44764924826497604,0.8689980546805128,0.4629218135959934],"dir":"ltr"},{"str":"If","boundary":[0.8751258444967939,0.44764924826497604,0.8893976646495518,0.4629218135959934],"dir":"ltr"},{"str":"it","boundary":[0.8955254544658331,0.44764924826497604,0.907603130523084,0.4629218135959934],"dir":"ltr"},{"str":"is","boundary":[0.9137309203393651,0.44764924826497604,0.9269155519763312,0.4629218135959934],"dir":"ltr"},{"str":"time","boundary":[0.23910079569466017,0.46597632666219685,0.27752796796191986,0.4812488919932142],"dir":"ltr"},{"str":"that","boundary":[0.28120464185168853,0.46597632666219685,0.31524352592793403,0.4812488919932142],"dir":"ltr"},{"str":"is","boundary":[0.3189201998177027,0.46597632666219685,0.3321048314546689,0.4812488919932142],"dir":"ltr"},{"str":"at","boundary":[0.33578150534443757,0.46597632666219685,0.3522474695927027,0.4812488919932142],"dir":"ltr"},{"str":"a","boundary":[0.3559241434824713,0.46597632666219685,0.36580767544421505,0.4812488919932142],"dir":"ltr"},{"str":"premium,","boundary":[0.3694843493339838,0.46597632666219685,0.45240718249301387,0.4812488919932142],"dir":"ltr"},{"str":"we","boundary":[0.4563408282137878,0.46597632666219685,0.48049618032828956,0.4812488919932142],"dir":"ltr"},{"str":"can","boundary":[0.4841728542180583,0.46597632666219685,0.5138234501032896,0.4812488919932142],"dir":"ltr"},{"str":"precompute","boundary":[0.5175001239930582,0.46597632666219685,0.6207434988654333,0.4812488919932142],"dir":"ltr"},{"str":"the","boundary":[0.6244201727552021,0.46597632666219685,0.6518766245449262,0.4812488919932142],"dir":"ltr"},{"str":"function’s","boundary":[0.6555532984346949,0.46597632666219685,0.7397807578126752,0.4812488919932142],"dir":"ltr"},{"str":"values","boundary":[0.7434574317024438,0.46597632666219685,0.7972831467661003,0.4812488919932142],"dir":"ltr"},{"str":"and","boundary":[0.800959820655869,0.46597632666219685,0.8328243277005308,0.4812488919932142],"dir":"ltr"},{"str":"store","boundary":[0.8365010015902995,0.46597632666219685,0.879336229112497,0.4812488919932142],"dir":"ltr"},{"str":"them","boundary":[0.8830129030022656,0.46597632666219685,0.926935319040255,0.4812488919932142],"dir":"ltr"},{"str":"in","boundary":[0.23910079569466017,0.48430340505941766,0.25558652700684875,0.499575970390435],"dir":"ltr"},{"str":"a","boundary":[0.26108177077757827,0.48430340505941766,0.27096530273932207,0.499575970390435],"dir":"ltr"},{"str":"table.","boundary":[0.2764605465100516,0.48430340505941766,0.3235061586479518,0.499575970390435],"dir":"ltr"},{"str":"This","boundary":[0.32900140241868137,0.48430340505941766,0.3655704706771332,0.499575970390435],"dir":"ltr"},{"str":"is","boundary":[0.3710657144478628,0.48430340505941766,0.38425034608482894,0.499575970390435],"dir":"ltr"},{"str":"exactly","boundary":[0.3897455898555584,0.48430340505941766,0.4501339701418127,0.499575970390435],"dir":"ltr"},{"str":"what","boundary":[0.45562921391254235,0.48430340505941766,0.49735748585502443,0.499575970390435],"dir":"ltr"},{"str":"human","boundary":[0.502852729625754,0.48430340505941766,0.56217368846014,0.499575970390435],"dir":"ltr"},{"str":"computers","boundary":[0.5676689322308694,0.48430340505941766,0.6577276754662786,0.499575970390435],"dir":"ltr"},{"str":"had","boundary":[0.663222919237008,0.48430340505941766,0.6950874262816699,0.499575970390435],"dir":"ltr"},{"str":"to","boundary":[0.7005826700523994,0.48430340505941766,0.7181555898803799,0.499575970390435],"dir":"ltr"},{"str":"do","boundary":[0.7236508336511093,0.48430340505941766,0.7456318087340273,0.499575970390435],"dir":"ltr"},{"str":"before","boundary":[0.7511270525047569,0.48430340505941766,0.8071469116639205,0.499575970390435],"dir":"ltr"},{"str":"the","boundary":[0.8126421554346499,0.48430340505941766,0.840098607224374,0.499575970390435],"dir":"ltr"},{"str":"advent","boundary":[0.8455938509951036,0.48430340505941766,0.9038078542497743,0.499575970390435],"dir":"ltr"},{"str":"of","boundary":[0.9093030980205038,0.48430340505941766,0.9268760178484842,0.499575970390435],"dir":"ltr"},{"str":"electronic","boundary":[0.23910079569466017,0.5026304834566385,0.32366429515933975,0.5179030487876558],"dir":"ltr"},{"str":"computers,","boundary":[0.33103741000280057,0.5026304834566385,0.42495073070328976,0.5179030487876558],"dir":"ltr"},{"str":"in","boundary":[0.43293662452837867,0.5026304834566385,0.4494223558405673,0.5179030487876558],"dir":"ltr"},{"str":"the","boundary":[0.45679547068402804,0.5026304834566385,0.4842519224737522,0.5179030487876558],"dir":"ltr"},{"str":"process","boundary":[0.491625037317213,0.5026304834566385,0.5553342843426132,0.5179030487876558],"dir":"ltr"},{"str":"burdening","boundary":[0.5627073991860742,0.5026304834566385,0.6506115324538231,0.5179030487876558],"dir":"ltr"},{"str":"libraries","boundary":[0.6579846472972838,0.5026304834566385,0.728296093673129,0.5179030487876558],"dir":"ltr"},{"str":"with","boundary":[0.7356692085165898,0.5026304834566385,0.7730091922680578,0.5179030487876558],"dir":"ltr"},{"str":"thick","boundary":[0.7803823071115185,0.5026304834566385,0.8232175346337158,0.5179030487876558],"dir":"ltr"},{"str":"volumes","boundary":[0.8305906494771768,0.5026304834566385,0.9019892843688135,0.5179030487876558],"dir":"ltr"},{"str":"of","boundary":[0.9093623992122745,0.5026304834566385,0.9269353190402548,0.5179030487876558],"dir":"ltr"},{"str":"mathematical","boundary":[0.23910079569466017,0.5209575618538593,0.3554892680761546,0.5362301271848766],"dir":"ltr"},{"str":"tables.","boundary":[0.36074730707980224,0.5209575618538593,0.4151264999333164,0.5362301271848766],"dir":"ltr"},{"str":"Though","boundary":[0.42038453893696415,0.5209575618538593,0.48662397014457076,0.5362301271848766],"dir":"ltr"},{"str":"such","boundary":[0.4918820091482184,0.5209575618538593,0.5303289484794016,0.5362301271848766],"dir":"ltr"},{"str":"tables","boundary":[0.5355869874830493,0.5209575618538593,0.5861116028714835,0.5362301271848766],"dir":"ltr"},{"str":"have","boundary":[0.5913696418751311,0.5209575618538593,0.6320107253018213,0.5362301271848766],"dir":"ltr"},{"str":"lost","boundary":[0.6372687643054691,0.5209575618538593,0.6680263157704157,0.5362301271848766],"dir":"ltr"},{"str":"much","boundary":[0.6732843547740635,0.5209575618538593,0.720507870487275,0.5362301271848766],"dir":"ltr"},{"str":"of","boundary":[0.7257659094909228,0.5209575618538593,0.7433388293189033,0.5362301271848766],"dir":"ltr"},{"str":"their","boundary":[0.7485968683225509,0.5209575618538593,0.7892379517492412,0.5362301271848766],"dir":"ltr"},{"str":"appeal","boundary":[0.7944959907528889,0.5209575618538593,0.8516228054917678,0.5362301271848766],"dir":"ltr"},{"str":"with","boundary":[0.8568808444954155,0.5209575618538593,0.8942208282468834,0.5362301271848766],"dir":"ltr"},{"str":"the","boundary":[0.8994788672505311,0.5209575618538593,0.9269353190402552,0.5362301271848766],"dir":"ltr"},{"str":"widespread","boundary":[0.23910079569466017,0.5392861675076132,0.3368686938602294,0.5545587328386306],"dir":"ltr"},{"str":"use","boundary":[0.3400116570240639,0.5392861675076132,0.36857506439350335,0.5545587328386306],"dir":"ltr"},{"str":"of","boundary":[0.37171802755733785,0.5392861675076132,0.3892909473853182,0.5545587328386306],"dir":"ltr"},{"str":"electronic","boundary":[0.3924339105491528,0.5392861675076132,0.47699741001383233,0.5545587328386306],"dir":"ltr"},{"str":"computers,","boundary":[0.48014037317766683,0.5392861675076132,0.574053693878156,0.5545587328386306],"dir":"ltr"},{"str":"the","boundary":[0.5775524641926132,0.5392861675076132,0.6050089159823373,0.5545587328386306],"dir":"ltr"},{"str":"underlying","boundary":[0.6081518791461719,0.5392861675076132,0.7004443006049351,0.5545587328386306],"dir":"ltr"},{"str":"idea","boundary":[0.7035872637687695,0.5392861675076132,0.7398400590044456,0.5545587328386306],"dir":"ltr"},{"str":"has","boundary":[0.74298302216828,0.5392861675076132,0.7715464295377196,0.5545587328386306],"dir":"ltr"},{"str":"proven","boundary":[0.774689392701554,0.5392861675076132,0.8351173071156552,0.5545587328386306],"dir":"ltr"},{"str":"to","boundary":[0.8382602702794898,0.5392861675076132,0.8558331901074703,0.5545587328386306],"dir":"ltr"},{"str":"be","boundary":[0.8589761532713047,0.5392861675076132,0.8798501727745074,0.5545587328386306],"dir":"ltr"},{"str":"quite","boundary":[0.8829931359383419,0.5392861675076132,0.9269353190402547,0.5545587328386306],"dir":"ltr"},{"str":"useful","boundary":[0.23910079569466017,0.557613245904834,0.2907323666628095,0.5728858112358514],"dir":"ltr"},{"str":"in","boundary":[0.2977299072917241,0.557613245904834,0.31421563860391266,0.5728858112358514],"dir":"ltr"},{"str":"the","boundary":[0.3212131792328273,0.557613245904834,0.34866963102255144,0.5728858112358514],"dir":"ltr"},{"str":"development","boundary":[0.355667171651466,0.557613245904834,0.46770688996979315,0.5728858112358514],"dir":"ltr"},{"str":"of","boundary":[0.47470443059870776,0.557613245904834,0.49227735042668813,0.5728858112358514],"dir":"ltr"},{"str":"several","boundary":[0.49927489105560274,0.557613245904834,0.5596830384057805,0.5728858112358514],"dir":"ltr"},{"str":"important","boundary":[0.5666805790346952,0.557613245904834,0.6523510340790899,0.5728858112358514],"dir":"ltr"},{"str":"algorithms","boundary":[0.6593485747080045,0.557613245904834,0.7505142735231288,0.5728858112358514],"dir":"ltr"},{"str":"for","boundary":[0.7575118141520435,0.557613245904834,0.7827741218462605,0.5728858112358514],"dir":"ltr"},{"str":"other","boundary":[0.789771662475175,0.557613245904834,0.8359079896725949,0.5728858112358514],"dir":"ltr"},{"str":"problems.","boundary":[0.8429055303015095,0.557613245904834,0.9269550861041783,0.5728858112358514],"dir":"ltr"},{"str":"In","boundary":[0.23910079569466017,0.5759403243020548,0.25778067110235586,0.5912128896330722],"dir":"ltr"},{"str":"somewhat","boundary":[0.2637700914711726,0.5759403243020548,0.35052773503135926,0.5912128896330722],"dir":"ltr"},{"str":"more","boundary":[0.3565171554001759,0.5759403243020548,0.40154652701788046,0.5912128896330722],"dir":"ltr"},{"str":"general","boundary":[0.40753594738669724,0.5759403243020548,0.47124519441209745,0.5912128896330722],"dir":"ltr"},{"str":"terms,","boundary":[0.47723461478091417,0.5759403243020548,0.5293998964749977,0.5912128896330722],"dir":"ltr"},{"str":"the","boundary":[0.5356462886748199,0.5759403243020548,0.563102740464544,0.5912128896330722],"dir":"ltr"},{"str":"idea","boundary":[0.5690921608333607,0.5759403243020548,0.6053449560690367,0.5912128896330722],"dir":"ltr"},{"str":"is","boundary":[0.6113343764378535,0.5759403243020548,0.6245190080748196,0.5912128896330722],"dir":"ltr"},{"str":"to","boundary":[0.6305084284436364,0.5759403243020548,0.6480813482716169,0.5912128896330722],"dir":"ltr"},{"str":"preprocess","boundary":[0.6540707686404335,0.5759403243020548,0.7463434230352732,0.5912128896330722],"dir":"ltr"},{"str":"the","boundary":[0.7523328434040899,0.5759403243020548,0.779789295193814,0.5912128896330722],"dir":"ltr"},{"str":"problem’s","boundary":[0.7857787155626308,0.5759403243020548,0.8711131305203264,0.5912128896330722],"dir":"ltr"},{"str":"input,","boundary":[0.8771025508891431,0.5759403243020548,0.927093455551643,0.5912128896330722],"dir":"ltr"},{"str":"in","boundary":[0.23910079569466017,0.5942674026992756,0.25558652700684875,0.609539968030293],"dir":"ltr"},{"str":"whole","boundary":[0.26167478269528294,0.5942674026992756,0.31330635366343224,0.609539968030293],"dir":"ltr"},{"str":"or","boundary":[0.3193946093518664,0.5942674026992756,0.33807448475956214,0.609539968030293],"dir":"ltr"},{"str":"in","boundary":[0.3441627404479963,0.5942674026992756,0.3606484717601849,0.609539968030293],"dir":"ltr"},{"str":"part,","boundary":[0.36673672744861896,0.5942674026992756,0.40682433308545163,0.609539968030293],"dir":"ltr"},{"str":"and","boundary":[0.4131893276688146,0.5942674026992756,0.4450538347134765,0.609539968030293],"dir":"ltr"},{"str":"store","boundary":[0.4511420904019106,0.5942674026992756,0.493977317924108,0.609539968030293],"dir":"ltr"},{"str":"the","boundary":[0.5000655736125422,0.5942674026992756,0.5275220254022663,0.609539968030293],"dir":"ltr"},{"str":"additional","boundary":[0.5336102810907004,0.5942674026992756,0.620407458778734,0.609539968030293],"dir":"ltr"},{"str":"information","boundary":[0.6264957144671683,0.5942674026992756,0.7286519008237518,0.609539968030293],"dir":"ltr"},{"str":"obtained","boundary":[0.7347401565121858,0.5942674026992756,0.8105468466587604,0.609539968030293],"dir":"ltr"},{"str":"to","boundary":[0.8166351023471946,0.5942674026992756,0.834208022175175,0.609539968030293],"dir":"ltr"},{"str":"accelerate","boundary":[0.8402962778636092,0.5942674026992756,0.9270341543598724,0.609539968030293],"dir":"ltr"},{"str":"solving","boundary":[0.23910079569466017,0.6129992040777683,0.2995287101087615,0.6282717694087857],"dir":"ltr"},{"str":"the","boundary":[0.30652625073767603,0.6129992040777683,0.33398270252740014,0.6282717694087857],"dir":"ltr"},{"str":"problem","boundary":[0.34098024315631476,0.6129992040777683,0.41348583362766694,0.6282717694087857],"dir":"ltr"},{"str":"afterward.","boundary":[0.4204833742565815,0.6129992040777683,0.5088816841224176,0.6282717694087857],"dir":"ltr"},{"str":"We","boundary":[0.5158792247513322,0.6129992040777683,0.5440670579062254,0.6282717694087857],"dir":"ltr"},{"str":"call","boundary":[0.55106459853514,0.6129992040777683,0.5807151944203712,0.6282717694087857],"dir":"ltr"},{"str":"this","boundary":[0.5877127350492857,0.6129992040777683,0.6184702865142323,0.6282717694087857],"dir":"ltr"},{"str":"approach","boundary":[0.625467827143147,0.6129992040777683,0.7056628054807358,0.6282717694087857],"dir":"ltr"},{"str":"input","boundary":[0.7126247653945882,0.6129992040777683,0.7587610925920081,0.6282717694087857],"dir":"ltr"},{"str":"enhancement","boundary":[0.7665295487139386,0.6129992040777683,0.8796366884841342,0.6282717694087857],"dir":"ltr"},{"str":"1","boundary":[0.8809541660525709,0.6101837973353486,0.8883668646270545,0.6216382979831072],"dir":"ltr"},{"str":"and","boundary":[0.8951404758860023,0.6129971726208517,0.9270049829306641,0.6282697379518691],"dir":"ltr"},{"str":"discuss","boundary":[0.239105228274122,0.6313257782746057,0.298426187108508,0.646598343605623],"dir":"ltr"},{"str":"the","boundary":[0.3033679530893799,0.6313257782746057,0.3308244048791041,0.646598343605623],"dir":"ltr"},{"str":"following","boundary":[0.3357661708599759,0.6313257782746057,0.4159611491975647,0.646598343605623],"dir":"ltr"},{"str":"algorithms","boundary":[0.4209029151784366,0.6313257782746057,0.512068613993561,0.646598343605623],"dir":"ltr"},{"str":"based","boundary":[0.5170103799744329,0.6313257782746057,0.5664478068470751,0.646598343605623],"dir":"ltr"},{"str":"on","boundary":[0.571389572827947,0.6313257782746057,0.5933705479108651,0.646598343605623],"dir":"ltr"},{"str":"it:","boundary":[0.598312313891737,0.6313257782746057,0.6153317559298598,0.646598343605623],"dir":"ltr"},{"str":"counting","boundary":[0.27468212901091943,0.662794817032227,0.34938186357777873,0.6780673823632444],"dir":"ltr"},{"str":"methods","boundary":[0.35432362955865065,0.662794817032227,0.4279164085457946,0.6780673823632444],"dir":"ltr"},{"str":"for","boundary":[0.4328581745266664,0.662794817032227,0.4581204822208835,0.6780673823632444],"dir":"ltr"},{"str":"sorting","boundary":[0.4630622482017553,0.662794817032227,0.5223832070361414,0.6780673823632444],"dir":"ltr"},{"str":"(Section","boundary":[0.5273249730170132,0.662794817032227,0.59872360790865,0.6780673823632444],"dir":"ltr"},{"str":"7.1)","boundary":[0.6036653738895219,0.662794817032227,0.6360635916601179,0.6780673823632444],"dir":"ltr"},{"str":"Boyer-Moore","boundary":[0.27468212901091943,0.6841769603720208,0.39111013552026086,0.6994495257030381],"dir":"ltr"},{"str":"algorithm","boundary":[0.3985425515554922,0.6841769603720208,0.4820188625043799,0.6994495257030381],"dir":"ltr"},{"str":"for","boundary":[0.4894512785396112,0.6841769603720208,0.5147135862338282,0.6994495257030381],"dir":"ltr"},{"str":"string","boundary":[0.5221460022690595,0.6841769603720208,0.5704764735619865,0.6994495257030381],"dir":"ltr"},{"str":"matching","boundary":[0.5779088895972178,0.6841769603720208,0.6569771452911678,0.6994495257030381],"dir":"ltr"},{"str":"and","boundary":[0.6644095613263991,0.6841769603720208,0.6962740683710609,0.6994495257030381],"dir":"ltr"},{"str":"its","boundary":[0.7037064844062924,0.6841769603720208,0.72347354832978,0.6994495257030381],"dir":"ltr"},{"str":"simplified","boundary":[0.7309059643650112,0.6841769603720208,0.8144020423778224,0.6994495257030381],"dir":"ltr"},{"str":"version","boundary":[0.8218344584130537,0.6841769603720208,0.884456516922662,0.6994495257030381],"dir":"ltr"},{"str":"sug-","boundary":[0.8918889329578935,0.6841769603720208,0.9270347726138544,0.6994495257030381],"dir":"ltr"},{"str":"gested","boundary":[0.27468212901091943,0.7025055660257746,0.3295950325903677,0.717778131356792],"dir":"ltr"},{"str":"by","boundary":[0.33453679857123964,0.7025055660257746,0.35541081807444247,0.717778131356792],"dir":"ltr"},{"str":"Horspool","boundary":[0.3603525840553143,0.7025055660257746,0.4416545179726184,0.717778131356792],"dir":"ltr"},{"str":"(Section","boundary":[0.44659628395349027,0.7025055660257746,0.5179949188451272,0.717778131356792],"dir":"ltr"},{"str":"7.2)","boundary":[0.5229366848259991,0.7025055660257746,0.555334902596595,0.717778131356792],"dir":"ltr"},{"str":"The","boundary":[0.27468212901091943,0.7339762141468689,0.30795009759414893,0.7492487794778863],"dir":"ltr"},{"str":"other","boundary":[0.3113104984611418,0.7339762141468689,0.35744682565856156,0.7492487794778863],"dir":"ltr"},{"str":"type","boundary":[0.36080722652555447,0.7339762141468689,0.39814721027702243,0.7492487794778863],"dir":"ltr"},{"str":"of","boundary":[0.40150761114401534,0.7339762141468689,0.4190805309719957,0.7492487794778863],"dir":"ltr"},{"str":"technique","boundary":[0.42244093183898856,0.7339762141468689,0.5070241983675916,0.7492487794778863],"dir":"ltr"},{"str":"that","boundary":[0.5103845992345845,0.7339762141468689,0.5444234833108299,0.7492487794778863],"dir":"ltr"},{"str":"exploits","boundary":[0.5477838841778229,0.7339762141468689,0.6147942308784455,0.7492487794778863],"dir":"ltr"},{"str":"space-for-time","boundary":[0.6181546317454385,0.7339762141468689,0.7411453034773777,0.7492487794778863],"dir":"ltr"},{"str":"trade-offs","boundary":[0.7445057043443706,0.7339762141468689,0.8279622482293348,0.7492487794778863],"dir":"ltr"},{"str":"simply","boundary":[0.8313226490963277,0.7339762141468689,0.8873425082554913,0.7492487794778863],"dir":"ltr"},{"str":"uses","boundary":[0.8907029091224843,0.7339762141468689,0.9269557043581603,0.7492487794778863],"dir":"ltr"},{"str":"extra","boundary":[0.23910141394864193,0.7523032925440897,0.28302382998663117,0.767575857875107],"dir":"ltr"},{"str":"space","boundary":[0.2875900217529568,0.7523032925440897,0.33481353746616843,0.767575857875107],"dir":"ltr"},{"str":"to","boundary":[0.33937972923249404,0.7523032925440897,0.35695264906047447,0.767575857875107],"dir":"ltr"},{"str":"facilitate","boundary":[0.3615188408268001,0.7523032925440897,0.4361790412658124,0.767575857875107],"dir":"ltr"},{"str":"faster","boundary":[0.440745233032138,0.7523032925440897,0.48905593726114144,0.767575857875107],"dir":"ltr"},{"str":"and/or","boundary":[0.493622129027467,0.7523032925440897,0.549661755250554,0.767575857875107],"dir":"ltr"},{"str":"more","boundary":[0.5542279470168797,0.7523032925440897,0.5992573186345842,0.767575857875107],"dir":"ltr"},{"str":"flexible","boundary":[0.60382351040091,0.7523032925440897,0.6664455689105184,0.767575857875107],"dir":"ltr"},{"str":"access","boundary":[0.671011760676844,0.7523032925440897,0.7237107530968617,0.767575857875107],"dir":"ltr"},{"str":"to","boundary":[0.7282769448631873,0.7523032925440897,0.7458498646911677,0.767575857875107],"dir":"ltr"},{"str":"the","boundary":[0.7504160564574934,0.7523032925440897,0.7778725082472175,0.767575857875107],"dir":"ltr"},{"str":"data.","boundary":[0.7824387000135432,0.7523032925440897,0.8247204497458829,0.767575857875107],"dir":"ltr"},{"str":"We","boundary":[0.8292866415122085,0.7523032925440897,0.8574744746671017,0.767575857875107],"dir":"ltr"},{"str":"call","boundary":[0.8620406664334274,0.7523032925440897,0.8916912623186586,0.767575857875107],"dir":"ltr"},{"str":"this","boundary":[0.8962574540849844,0.7523032925440897,0.9270150055499309,0.767575857875107],"dir":"ltr"},{"str":"approach","boundary":[0.23910141394864193,0.7706303709413105,0.31929639228623075,0.7859029362723277],"dir":"ltr"},{"str":"prestructuring","boundary":[0.3248944247893624,0.7706303709413105,0.44679790800550995,0.7859029362723277],"dir":"ltr"},{"str":".","boundary":[0.4472940613099894,0.7706303709413105,0.45223582729086126,0.7859029362723277],"dir":"ltr"},{"str":"This","boundary":[0.45782990638120824,0.7706303709413105,0.4943989746396601,0.7859029362723277],"dir":"ltr"},{"str":"name","boundary":[0.4999930537300071,0.7706303709413105,0.5472165694432187,0.7859029362723277],"dir":"ltr"},{"str":"highlights","boundary":[0.5528106485335657,0.7706303709413105,0.636306726546377,0.7859029362723277],"dir":"ltr"},{"str":"two","boundary":[0.6419008056367239,0.7706303709413105,0.6737455456174622,0.7859029362723277],"dir":"ltr"},{"str":"facets","boundary":[0.6793396247078093,0.7706303709413105,0.7287375174526045,0.7859029362723277],"dir":"ltr"},{"str":"of","boundary":[0.7343315965429514,0.7706303709413105,0.7519045163709319,0.7859029362723277],"dir":"ltr"},{"str":"this","boundary":[0.7574985954612788,0.7706303709413105,0.7882561469262255,0.7859029362723277],"dir":"ltr"},{"str":"variation","boundary":[0.7938502260165724,0.7706303709413105,0.8707441046789387,0.7859029362723277],"dir":"ltr"},{"str":"of","boundary":[0.8763381837692857,0.7706303709413105,0.8939111035972661,0.7859029362723277],"dir":"ltr"},{"str":"the","boundary":[0.899505182687613,0.7706303709413105,0.9269616344773371,0.7859029362723277],"dir":"ltr"},{"str":"space-for-time","boundary":[0.23910141394864198,0.7889574493385314,0.36209208568058127,0.8042300146695486],"dir":"ltr"},{"str":"trade-off:","boundary":[0.3685361485196382,0.7889574493385314,0.4492450705192377,0.8042300146695486],"dir":"ltr"},{"str":"some","boundary":[0.4556891333582946,0.7889574493385314,0.5007185049759991,0.8042300146695486],"dir":"ltr"},{"str":"processing","boundary":[0.507162567815056,0.7889574493385314,0.5972410781143885,0.8042300146695486],"dir":"ltr"},{"str":"is","boundary":[0.6036851409534456,0.7889574493385314,0.6168697725904118,0.8042300146695486],"dir":"ltr"},{"str":"done","boundary":[0.6233138354294687,0.7889574493385314,0.6661688300155896,0.8042300146695486],"dir":"ltr"},{"str":"before","boundary":[0.6726128928546465,0.7889574493385314,0.7286327520138101,0.8042300146695486],"dir":"ltr"},{"str":"a","boundary":[0.7350768148528671,0.7889574493385314,0.7449603468146108,0.8042300146695486],"dir":"ltr"},{"str":"problem","boundary":[0.7514044096536678,0.7889574493385314,0.82391000012502,0.8042300146695486],"dir":"ltr"},{"str":"in","boundary":[0.8303540629640768,0.7889574493385314,0.8468397942762653,0.8042300146695486],"dir":"ltr"},{"str":"question","boundary":[0.8532838571153224,0.7889574493385314,0.9268964031663898,0.8042300146695486],"dir":"ltr"},{"str":"1.","boundary":[0.20450752430472768,0.8405337110828974,0.2163677924207256,0.8527517940075096],"dir":"ltr"},{"str":"The","boundary":[0.23909206613097758,0.8405337110828974,0.26570650778327687,0.8527517940075096],"dir":"ltr"},{"str":"standard","boundary":[0.27154175969634786,0.8405337110828974,0.3313016973101561,0.8527517940075096],"dir":"ltr"},{"str":"terms","boundary":[0.3371211355324057,0.8405337110828974,0.3757697958997376,0.8527517940075096],"dir":"ltr"},{"str":"used","boundary":[0.3816050478128086,0.8405337110828974,0.413248243146291,0.8527517940075096],"dir":"ltr"},{"str":"synonymously","boundary":[0.419083495059362,0.8405337110828974,0.5166381537361502,0.8527517940075096],"dir":"ltr"},{"str":"for","boundary":[0.5224575919583998,0.8405337110828974,0.5426674888280604,0.8527517940075096],"dir":"ltr"},{"str":"this","boundary":[0.5484869270503098,0.8405337110828974,0.5730930299683001,0.8527517940075096],"dir":"ltr"},{"str":"technique","boundary":[0.5789282818813712,0.8405337110828974,0.6465950649058446,0.8527517940075096],"dir":"ltr"},{"str":"are","boundary":[0.6524303168189155,0.8405337110828974,0.6743955333697437,0.8527517940075096],"dir":"ltr"},{"str":"preprocessing","boundary":[0.6802244598064862,0.8405337110828974,0.7743949886475097,0.8527517940075096],"dir":"ltr"},{"str":"and","boundary":[0.7806192573547853,0.8405337110828974,0.8061109269587702,0.8527517940075096],"dir":"ltr"},{"str":"preconditioning","boundary":[0.8119382720264304,0.8405337110828974,0.9226499214665655,0.8527517940075096],"dir":"ltr"},{"str":".","boundary":[0.9230452637370988,0.8405337110828974,0.9269986864424316,0.8527517940075096],"dir":"ltr"},{"str":"Confusingly,","boundary":[0.23910155434547029,0.8558063147386628,0.32421083834587133,0.8680243976632749],"dir":"ltr"},{"str":"these","boundary":[0.327974496761348,0.8558063147386628,0.36399808445233905,0.8680243976632749],"dir":"ltr"},{"str":"terms","boundary":[0.3677143017953517,0.8558063147386628,0.4063629621626836,0.8680243976632749],"dir":"ltr"},{"str":"can","boundary":[0.4100791795056962,0.8558063147386628,0.43379971573769205,0.8680243976632749],"dir":"ltr"},{"str":"also","boundary":[0.43751593308070474,0.8558063147386628,0.4647629223658573,0.8680243976632749],"dir":"ltr"},{"str":"be","boundary":[0.46847913970887,0.8558063147386628,0.48517839721619505,0.8680243976632749],"dir":"ltr"},{"str":"applied","boundary":[0.4888946145592077,0.8558063147386628,0.5398779537671774,0.8680243976632749],"dir":"ltr"},{"str":"to","boundary":[0.5435941711101901,0.8558063147386628,0.557652542250353,0.8680243976632749],"dir":"ltr"},{"str":"methods","boundary":[0.5613687595933656,0.8558063147386628,0.6202431305211793,0.8680243976632749],"dir":"ltr"},{"str":"that","boundary":[0.6239593478641919,0.8558063147386628,0.6511905234585231,0.8680243976632749],"dir":"ltr"},{"str":"use","boundary":[0.6549067408015358,0.8558063147386628,0.6777575240383584,0.8680243976632749],"dir":"ltr"},{"str":"the","boundary":[0.6814737413813711,0.8558063147386628,0.7034389579321992,0.8680243976632749],"dir":"ltr"},{"str":"idea","boundary":[0.7071551752752119,0.8558063147386628,0.736157484241532,0.8680243976632749],"dir":"ltr"},{"str":"of","boundary":[0.7398737015845449,0.8558063147386628,0.7539320727247077,0.8680243976632749],"dir":"ltr"},{"str":"preprocessing","boundary":[0.7576482900677204,0.8558063147386628,0.8525620623773463,0.8680243976632749],"dir":"ltr"},{"str":"but","boundary":[0.8562782797203591,0.8558063147386628,0.8791290629571817,0.8680243976632749],"dir":"ltr"},{"str":"do","boundary":[0.8828452803001944,0.8558063147386628,0.9004301044935139,0.8680243976632749],"dir":"ltr"},{"str":"not","boundary":[0.9041463218365268,0.8558063147386628,0.9269971050733494,0.8680243976632749],"dir":"ltr"},{"str":"use","boundary":[0.23910155434547029,0.8710776965861354,0.2619523375822929,0.8832957795107476],"dir":"ltr"},{"str":"extra","boundary":[0.26612715195912423,0.8710776965861354,0.3012651729641207,0.8832957795107476],"dir":"ltr"},{"str":"space","boundary":[0.30543998734095196,0.8710776965861354,0.3432188947131107,0.8832957795107476],"dir":"ltr"},{"str":"(see","boundary":[0.34739370908994194,0.8710776965861354,0.3755104513702677,0.8832957795107476],"dir":"ltr"},{"str":"Chapter","boundary":[0.37968526574709893,0.8710776965861354,0.4359187503077504,0.8832957795107476],"dir":"ltr"},{"str":"6).","boundary":[0.44009356468458166,0.8710776965861354,0.45810535853007717,0.8832957795107476],"dir":"ltr"},{"str":"Thus,","boundary":[0.4622801729069083,0.8710776965861354,0.49901537668485924,0.8832957795107476],"dir":"ltr"},{"str":"in","boundary":[0.5032534458249759,0.8710776965861354,0.5164420639699655,0.8832957795107476],"dir":"ltr"},{"str":"order","boundary":[0.5206168783467968,0.8710776965861354,0.5584115994097768,0.8832957795107476],"dir":"ltr"},{"str":"to","boundary":[0.5625864137866081,0.8710776965861354,0.5766447849267708,0.8832957795107476],"dir":"ltr"},{"str":"avoid","boundary":[0.5808195993036023,0.8710776965861354,0.6186143203665823,0.8832957795107476],"dir":"ltr"},{"str":"confusion,","boundary":[0.6227891347434135,0.8710776965861354,0.6935395874780463,0.8832957795107476],"dir":"ltr"},{"str":"we","boundary":[0.6977776566181629,0.8710776965861354,0.7171019868018289,0.8832957795107476],"dir":"ltr"},{"str":"use","boundary":[0.7212768011786601,0.8710776965861354,0.7441275844154828,0.8832957795107476],"dir":"ltr"},{"str":"“input","boundary":[0.7483023987923141,0.8710776965861354,0.7922486455847917,0.8832957795107476],"dir":"ltr"},{"str":"enhancement”","boundary":[0.7964234599616231,0.8710776965861354,0.8965873776239308,0.8832957795107476],"dir":"ltr"},{"str":"as","boundary":[0.9007621920007621,0.8710776965861354,0.914820563140925,0.8832957795107476],"dir":"ltr"},{"str":"a","boundary":[0.9189953775177564,0.8710776965861354,0.9269022229284217,0.8832957795107476],"dir":"ltr"},{"str":"special","boundary":[0.23910155434547029,0.8863503002419006,0.28567287381428874,0.8985683831665128],"dir":"ltr"},{"str":"name","boundary":[0.2896262965196214,0.8863503002419006,0.3274052038917801,0.8985683831665128],"dir":"ltr"},{"str":"for","boundary":[0.3313586265971127,0.8863503002419006,0.3515685234667732,0.8985683831665128],"dir":"ltr"},{"str":"the","boundary":[0.3555219461721058,0.8863503002419006,0.377487162722934,0.8985683831665128],"dir":"ltr"},{"str":"space-for-time","boundary":[0.38144058542826653,0.8863503002419006,0.47983336971858526,0.8985683831665128],"dir":"ltr"},{"str":"trade-off","boundary":[0.483786792423918,0.8863503002419006,0.5444006693420781,0.8985683831665128],"dir":"ltr"},{"str":"technique","boundary":[0.5483540920474106,0.8863503002419006,0.616020875071884,0.8985683831665128],"dir":"ltr"},{"str":"being","boundary":[0.6199742977772167,0.8863503002419006,0.6577690188401968,0.8985683831665128],"dir":"ltr"},{"str":"discussed","boundary":[0.6617224415455294,0.8863503002419006,0.7258785852076675,0.8985683831665128],"dir":"ltr"},{"str":"here.","boundary":[0.7298320079130001,0.8863503002419006,0.7639579527054314,0.8985683831665128],"dir":"ltr"},{"str":"253","boundary":[0.8940253964965859,0.9329341022884333,0.9269968591209631,0.9482066676194506],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92709,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":309,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/b063a72fe676442f94b9e53dd52b94f9.jpg","blurred":"/storage/books/4a8b03583f119702/pages/358e97d7202d3e4722211e038bd6c2ba.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07291,0.05179]},"elements":[{"words":[{"str":"8","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Dynamic","boundary":[0.14421784044919886,0.17005356781848974,0.35561525934874566,0.20670781659232623],"dir":"ltr"},{"str":"Programming","boundary":[0.3714131364792549,0.17005356781848974,0.6983770079010854,0.20670781659232623],"dir":"ltr"},{"str":"An","boundary":[0.23910077902799318,0.27456512096090674,0.2654700423019255,0.2898376862919241],"dir":"ltr"},{"str":"idea,","boundary":[0.2746221928985002,0.27456512096090674,0.3147097985353329,0.2898376862919241],"dir":"ltr"},{"str":"like","boundary":[0.32490960351985243,0.27456512096090674,0.355667154984799,0.2898376862919241],"dir":"ltr"},{"str":"a","boundary":[0.3648193055813737,0.27456512096090674,0.37470283754311745,0.2898376862919241],"dir":"ltr"},{"str":"ghost...must","boundary":[0.3838549881396922,0.27456512096090674,0.5106765168600033,0.2898376862919241],"dir":"ltr"},{"str":"be","boundary":[0.519828667456578,0.27456512096090674,0.5395957313800656,0.2898376862919241],"dir":"ltr"},{"str":"spoken","boundary":[0.5487478819766403,0.27456512096090674,0.6091757963907416,0.2898376862919241],"dir":"ltr"},{"str":"to","boundary":[0.6183279469873163,0.27456512096090674,0.6348136782995049,0.2898376862919241],"dir":"ltr"},{"str":"a","boundary":[0.6439658288960796,0.27456512096090674,0.6538493608578233,0.2898376862919241],"dir":"ltr"},{"str":"little","boundary":[0.663001511454398,0.27456512096090674,0.699254306690074,0.2898376862919241],"dir":"ltr"},{"str":"before","boundary":[0.7084064572866487,0.27456512096090674,0.7622124052863817,0.2898376862919241],"dir":"ltr"},{"str":"it","boundary":[0.7713645558829564,0.27456512096090674,0.7823550434244155,0.2898376862919241],"dir":"ltr"},{"str":"will","boundary":[0.7915071940209902,0.27456512096090674,0.8222647454859369,0.2898376862919241],"dir":"ltr"},{"str":"explain","boundary":[0.23910077902799318,0.29289219935812755,0.3006158819578863,0.3081647646891449],"dir":"ltr"},{"str":"itself.","boundary":[0.30555764793875817,0.29289219935812755,0.34894635325081325,0.3081647646891449],"dir":"ltr"},{"str":"—Charles","boundary":[0.5987218186228968,0.31482012006708154,0.680109008891268,0.32932910312124547],"dir":"ltr"},{"str":"Dickens","boundary":[0.6848412589945513,0.31482012006708154,0.751618566007548,0.32932910312124547],"dir":"ltr"},{"str":"(1812–1870)","boundary":[0.7563508161108312,0.31482012006708154,0.8554651654962633,0.32932910312124547],"dir":"ltr"},{"str":"ynamic","boundary":[0.2884995896299513,0.42196670029494676,0.3499949254959209,0.4372392656259641],"dir":"ltr"},{"str":"programming","boundary":[0.3557471410976558,0.42196670029494676,0.4721751476069973,0.4372392656259641],"dir":"ltr"},{"str":"is","boundary":[0.47792736320873214,0.42196670029494676,0.4911119948456983,0.4372392656259641],"dir":"ltr"},{"str":"an","boundary":[0.4968642104474332,0.42196670029494676,0.5177382299506359,0.4372392656259641],"dir":"ltr"},{"str":"algorithm","boundary":[0.5234904455523708,0.42196670029494676,0.6069667565012585,0.4372392656259641],"dir":"ltr"},{"str":"design","boundary":[0.6127189721029934,0.42196670029494676,0.6676516427463652,0.4372392656259641],"dir":"ltr"},{"str":"technique","boundary":[0.6734038583481001,0.42196670029494676,0.7579871248767032,0.4372392656259641],"dir":"ltr"},{"str":"with","boundary":[0.763739340478438,0.42196670029494676,0.8010793242299059,0.4372392656259641],"dir":"ltr"},{"str":"a","boundary":[0.8068315398316407,0.42196670029494676,0.8167150717933843,0.4372392656259641],"dir":"ltr"},{"str":"rather","boundary":[0.8224672873951192,0.42196670029494676,0.8751860468790604,0.4372392656259641],"dir":"ltr"},{"str":"inter-","boundary":[0.8809382624807952,0.42196670029494676,0.9270745896782151,0.4372392656259641],"dir":"ltr"},{"str":"esting","boundary":[0.2884995896299513,0.44029377869216757,0.33902420501838537,0.4555663440231849],"dir":"ltr"},{"str":"history.","boundary":[0.3438276015517928,0.44029377869216757,0.4062717564860899,0.4555663440231849],"dir":"ltr"},{"str":"It","boundary":[0.4110751530194974,0.44029377869216757,0.42534697317225534,0.4555663440231849],"dir":"ltr"},{"str":"was","boundary":[0.4301503697056628,0.44029377869216757,0.4619951096864012,0.4555663440231849],"dir":"ltr"},{"str":"invented","boundary":[0.4667985062198087,0.44029377869216757,0.541498240786668,0.4555663440231849],"dir":"ltr"},{"str":"by","boundary":[0.5463016373200754,0.44029377869216757,0.5671756568232782,0.4555663440231849],"dir":"ltr"},{"str":"a","boundary":[0.5719790533566856,0.44029377869216757,0.5818625853184294,0.4555663440231849],"dir":"ltr"},{"str":"prominent","boundary":[0.5866659818518369,0.44029377869216757,0.6767444921511694,0.4555663440231849],"dir":"ltr"},{"str":"U.S.","boundary":[0.6815478886845769,0.44029377869216757,0.7158832787196747,0.4555663440231849],"dir":"ltr"},{"str":"mathematician,","boundary":[0.7206866752530822,0.44029377869216757,0.8530074011569075,0.4555663440231849],"dir":"ltr"},{"str":"Richard","boundary":[0.8578305647542385,0.44029377869216757,0.9270350555503682,0.4555663440231849],"dir":"ltr"},{"str":"DBellman,","boundary":[0.23910077902799318,0.42066855707624695,0.31652928627345667,0.4738934224204057],"dir":"ltr"},{"str":"in","boundary":[0.3208582732727004,0.4586208570893884,0.33734400458488895,0.4738934224204057],"dir":"ltr"},{"str":"the","boundary":[0.34151485507274487,0.4586208570893884,0.36897130686246904,0.4738934224204057],"dir":"ltr"},{"str":"1950s","boundary":[0.37314215735032485,0.4586208570893884,0.4203656730635365,0.4738934224204057],"dir":"ltr"},{"str":"as","boundary":[0.4245365235513924,0.4586208570893884,0.44210944337937275,0.4738934224204057],"dir":"ltr"},{"str":"a","boundary":[0.4462802938672287,0.4586208570893884,0.4561638258289724,0.4738934224204057],"dir":"ltr"},{"str":"general","boundary":[0.46033467631682823,0.4586208570893884,0.5240439233422285,0.4738934224204057],"dir":"ltr"},{"str":"method","boundary":[0.5282147738300844,0.4586208570893884,0.5941181649509918,0.4738934224204057],"dir":"ltr"},{"str":"for","boundary":[0.5982890154388476,0.4586208570893884,0.6235513231330645,0.4738934224204057],"dir":"ltr"},{"str":"optimizing","boundary":[0.6277221736209204,0.4586208570893884,0.7188878724360448,0.4738934224204057],"dir":"ltr"},{"str":"multistage","boundary":[0.7230587229239006,0.4586208570893884,0.8120105105795944,0.4738934224204057],"dir":"ltr"},{"str":"decision","boundary":[0.8161813610674501,0.4586208570893884,0.8864928074432953,0.4738934224204057],"dir":"ltr"},{"str":"pro-","boundary":[0.890663657931151,0.4586208570893884,0.926916453166827,0.4738934224204057],"dir":"ltr"},{"str":"cesses.","boundary":[0.23910169688515603,0.47694793548660924,0.294568078254462,0.4922205008176265],"dir":"ltr"},{"str":"Thus,","boundary":[0.30085400458213096,0.47694793548660924,0.34677289407639245,0.4922205008176265],"dir":"ltr"},{"str":"the","boundary":[0.3533948604907608,0.47694793548660924,0.38085131228048497,0.4922205008176265],"dir":"ltr"},{"str":"word","boundary":[0.387137238608154,0.47694793548660924,0.4310794217100667,0.4922205008176265],"dir":"ltr"},{"str":"“programming”","boundary":[0.43736534803773575,0.47694793548660924,0.5735604184705646,0.4922205008176265],"dir":"ltr"},{"str":"in","boundary":[0.5798463447982337,0.47694793548660924,0.5963320761104223,0.4922205008176265],"dir":"ltr"},{"str":"the","boundary":[0.6026180024380914,0.47694793548660924,0.6300744542278155,0.4922205008176265],"dir":"ltr"},{"str":"name","boundary":[0.6363603805554846,0.47694793548660924,0.6835838962686962,0.4922205008176265],"dir":"ltr"},{"str":"of","boundary":[0.6898698225963652,0.47694793548660924,0.7074427424243456,0.4922205008176265],"dir":"ltr"},{"str":"this","boundary":[0.7137286687520147,0.47694793548660924,0.7444862202169612,0.4922205008176265],"dir":"ltr"},{"str":"technique","boundary":[0.7507721465446303,0.47694793548660924,0.8353554130732334,0.4922205008176265],"dir":"ltr"},{"str":"stands","boundary":[0.8416413394009024,0.47694793548660924,0.8954670544645588,0.4922205008176265],"dir":"ltr"},{"str":"for","boundary":[0.9017529807922278,0.47694793548660924,0.9270152884864448,0.4922205008176265],"dir":"ltr"},{"str":"“planning”","boundary":[0.23910169688515603,0.49527501388383005,0.3335882624394263,0.5105475792148474],"dir":"ltr"},{"str":"and","boundary":[0.3378777153108231,0.49527501388383005,0.369742222355485,0.5105475792148474],"dir":"ltr"},{"str":"does","boundary":[0.37403167522688174,0.49527501388383005,0.41358557013778025,0.5105475792148474],"dir":"ltr"},{"str":"not","boundary":[0.41787502300917706,0.49527501388383005,0.4464384303786165,0.5105475792148474],"dir":"ltr"},{"str":"refer","boundary":[0.4507278832500133,0.49527501388383005,0.4924561551924954,0.5105475792148474],"dir":"ltr"},{"str":"to","boundary":[0.49674560806389223,0.49527501388383005,0.5143185278918726,0.5105475792148474],"dir":"ltr"},{"str":"computer","boundary":[0.5186079807632694,0.49527501388383005,0.6009773361324419,0.5105475792148474],"dir":"ltr"},{"str":"programming.","boundary":[0.6052667890038386,0.49527501388383005,0.726280754343429,0.5105475792148474],"dir":"ltr"},{"str":"After","boundary":[0.7305702072148259,0.49527501388383005,0.7778727911837315,0.5105475792148474],"dir":"ltr"},{"str":"proving","boundary":[0.7821622440551281,0.49527501388383005,0.848085402239959,0.5105475792148474],"dir":"ltr"},{"str":"its","boundary":[0.8523748551113559,0.49527501388383005,0.8721419190348434,0.5105475792148474],"dir":"ltr"},{"str":"worth","boundary":[0.8764313719062401,0.49527501388383005,0.9269559872946742,0.5105475792148474],"dir":"ltr"},{"str":"as","boundary":[0.23910169688515603,0.5136020922810508,0.25667461671313646,0.5288746576120682],"dir":"ltr"},{"str":"an","boundary":[0.26373145853382146,0.5136020922810508,0.2846054780370243,0.5288746576120682],"dir":"ltr"},{"str":"important","boundary":[0.29166231985770935,0.5136020922810508,0.3773327749021042,0.5288746576120682],"dir":"ltr"},{"str":"tool","boundary":[0.3843896167227892,0.5136020922810508,0.4184482678629582,0.5288746576120682],"dir":"ltr"},{"str":"of","boundary":[0.4255051096836432,0.5136020922810508,0.4430780295116236,0.5288746576120682],"dir":"ltr"},{"str":"applied","boundary":[0.4501348713323086,0.5136020922810508,0.5138638854216323,0.5288746576120682],"dir":"ltr"},{"str":"mathematics,","boundary":[0.5209207272423173,0.5136020922810508,0.6334743892226552,0.5288746576120682],"dir":"ltr"},{"str":"dynamic","boundary":[0.6410649417692745,0.5136020922810508,0.7135507651767031,0.5288746576120682],"dir":"ltr"},{"str":"programming","boundary":[0.7206076069973882,0.5136020922810508,0.8370356135067296,0.5288746576120682],"dir":"ltr"},{"str":"has","boundary":[0.8440924553274147,0.5136020922810508,0.8726558626968542,0.5288746576120682],"dir":"ltr"},{"str":"even-","boundary":[0.8797127045175392,0.5136020922810508,0.9269362202307508,0.5288746576120682],"dir":"ltr"},{"str":"tually","boundary":[0.23910169688515603,0.5319291706782717,0.287432168178083,0.547201736009289],"dir":"ltr"},{"str":"come","boundary":[0.2943901746791506,0.5319291706782717,0.3405067348126469,0.547201736009289],"dir":"ltr"},{"str":"to","boundary":[0.3474647413137146,0.5319291706782717,0.36503766114169495,0.547201736009289],"dir":"ltr"},{"str":"be","boundary":[0.37199566764276254,0.5319291706782717,0.3928696871459654,0.547201736009289],"dir":"ltr"},{"str":"considered,","boundary":[0.39982769364703297,0.5319291706782717,0.4981490696024598,0.547201736009289],"dir":"ltr"},{"str":"at","boundary":[0.5056210197655381,0.5319291706782717,0.5220869840138032,0.547201736009289],"dir":"ltr"},{"str":"least","boundary":[0.5290449905148709,0.5319291706782717,0.5685791183618459,0.547201736009289],"dir":"ltr"},{"str":"in","boundary":[0.5755371248629134,0.5319291706782717,0.592022856175102,0.547201736009289],"dir":"ltr"},{"str":"computer","boundary":[0.5989808626761697,0.5319291706782717,0.6813502180453421,0.547201736009289],"dir":"ltr"},{"str":"science","boundary":[0.6883082245464096,0.5319291706782717,0.7498035604123792,0.547201736009289],"dir":"ltr"},{"str":"circles,","boundary":[0.7567615669134471,0.5319291706782717,0.81442209237826,0.547201736009289],"dir":"ltr"},{"str":"as","boundary":[0.8218940425413385,0.5319291706782717,0.8394669623693188,0.547201736009289],"dir":"ltr"},{"str":"a","boundary":[0.8464249688703863,0.5319291706782717,0.8563085008321301,0.547201736009289],"dir":"ltr"},{"str":"general","boundary":[0.8632665073331977,0.5319291706782717,0.9269757543585979,0.547201736009289],"dir":"ltr"},{"str":"algorithm","boundary":[0.23910169688515603,0.5502562490754925,0.3225780078340438,0.5655288144065098],"dir":"ltr"},{"str":"design","boundary":[0.32910113892879467,0.5502562490754925,0.38403380957216643,0.5655288144065098],"dir":"ltr"},{"str":"technique","boundary":[0.3905569406669173,0.5502562490754925,0.47514020719552036,0.5655288144065098],"dir":"ltr"},{"str":"that","boundary":[0.4816633382902712,0.5502562490754925,0.5157022223665166,0.5655288144065098],"dir":"ltr"},{"str":"does","boundary":[0.5222253534612675,0.5502562490754925,0.5617792483721661,0.5655288144065098],"dir":"ltr"},{"str":"not","boundary":[0.5683023794669169,0.5502562490754925,0.5968657868363564,0.5655288144065098],"dir":"ltr"},{"str":"have","boundary":[0.6033889179311072,0.5502562490754925,0.6440300013577974,0.5655288144065098],"dir":"ltr"},{"str":"to","boundary":[0.6505531324525483,0.5502562490754925,0.6681260522805288,0.5655288144065098],"dir":"ltr"},{"str":"be","boundary":[0.6746491833752796,0.5502562490754925,0.6955232028784823,0.5655288144065098],"dir":"ltr"},{"str":"limited","boundary":[0.7020463339732332,0.5502562490754925,0.7624544813234111,0.5655288144065098],"dir":"ltr"},{"str":"to","boundary":[0.768977612418162,0.5502562490754925,0.7865505322461424,0.5655288144065098],"dir":"ltr"},{"str":"special","boundary":[0.7930736633408932,0.5502562490754925,0.8512876665955639,0.5655288144065098],"dir":"ltr"},{"str":"types","boundary":[0.8578107976903145,0.5502562490754925,0.9028401693080191,0.5655288144065098],"dir":"ltr"},{"str":"of","boundary":[0.90936330040277,0.5502562490754925,0.9269362202307504,0.5655288144065098],"dir":"ltr"},{"str":"optimization","boundary":[0.23910169688515603,0.5685833274727133,0.3478403155282608,0.5838558928037306],"dir":"ltr"},{"str":"problems.","boundary":[0.3519716318882697,0.5685833274727133,0.4360211876909386,0.5838558928037306],"dir":"ltr"},{"str":"It","boundary":[0.44015250405094747,0.5685833274727133,0.4544243242037055,0.5838558928037306],"dir":"ltr"},{"str":"is","boundary":[0.4585556405637143,0.5685833274727133,0.4717402722006805,0.5838558928037306],"dir":"ltr"},{"str":"from","boundary":[0.47587158856068934,0.5685833274727133,0.5175998605031715,0.5838558928037306],"dir":"ltr"},{"str":"this","boundary":[0.5217311768631803,0.5685833274727133,0.5524887283281269,0.5838558928037306],"dir":"ltr"},{"str":"point","boundary":[0.5566200446881359,0.5685833274727133,0.6016691833697638,0.5838558928037306],"dir":"ltr"},{"str":"of","boundary":[0.6058004997297728,0.5685833274727133,0.6233734195577532,0.5838558928037306],"dir":"ltr"},{"str":"view","boundary":[0.627504735917762,0.5685833274727133,0.667038863764737,0.5838558928037306],"dir":"ltr"},{"str":"that","boundary":[0.6711701801247459,0.5685833274727133,0.7052090642009914,0.5838558928037306],"dir":"ltr"},{"str":"we","boundary":[0.7093403805610002,0.5685833274727133,0.7334957326755019,0.5838558928037306],"dir":"ltr"},{"str":"will","boundary":[0.7376270490355109,0.5685833274727133,0.7683846005004574,0.5838558928037306],"dir":"ltr"},{"str":"consider","boundary":[0.7725159168604663,0.5685833274727133,0.8450215073318185,0.5838558928037306],"dir":"ltr"},{"str":"this","boundary":[0.8491528236918274,0.5685833274727133,0.8799103751567741,0.5838558928037306],"dir":"ltr"},{"str":"tech-","boundary":[0.8840416915167828,0.5685833274727133,0.9268571519750568,0.5838558928037306],"dir":"ltr"},{"str":"nique","boundary":[0.23910169688515603,0.5869104058699341,0.2874519352420065,0.6021829712009514],"dir":"ltr"},{"str":"here.","boundary":[0.29239370122287833,0.5869104058699341,0.3350510251697644,0.6021829712009514],"dir":"ltr"},{"str":"Dynamic","boundary":[0.27468241194743354,0.6052374842671548,0.3526437120616683,0.6205100495981721],"dir":"ltr"},{"str":"programming","boundary":[0.35762501217038717,0.6052374842671548,0.4740530186797286,0.6205100495981721],"dir":"ltr"},{"str":"is","boundary":[0.4790343187884475,0.6052374842671548,0.49221895042541364,0.6205100495981721],"dir":"ltr"},{"str":"a","boundary":[0.4972002505341325,0.6052374842671548,0.5070837824958763,0.6205100495981721],"dir":"ltr"},{"str":"technique","boundary":[0.512065082604595,0.6052374842671548,0.5966483491331981,0.6205100495981721],"dir":"ltr"},{"str":"for","boundary":[0.601629649241917,0.6052374842671548,0.626891956936134,0.6205100495981721],"dir":"ltr"},{"str":"solving","boundary":[0.6318732570448529,0.6052374842671548,0.6923011714589541,0.6205100495981721],"dir":"ltr"},{"str":"problems","boundary":[0.697282471567673,0.6052374842671548,0.7774774499052618,0.6205100495981721],"dir":"ltr"},{"str":"with","boundary":[0.7824587500139806,0.6052374842671548,0.8197987337654484,0.6205100495981721],"dir":"ltr"},{"str":"overlapping","boundary":[0.8247800338741673,0.6052374842671548,0.9269559872946742,0.6205100495981721],"dir":"ltr"},{"str":"subproblems.","boundary":[0.23910169688515603,0.6235645626643757,0.3528216156369797,0.638837127995393],"dir":"ltr"},{"str":"Typically,","boundary":[0.35606341412043163,0.6235645626643757,0.43608048888270906,0.638837127995393],"dir":"ltr"},{"str":"these","boundary":[0.4396583274528602,0.6235645626643757,0.48468769907056475,0.638837127995393],"dir":"ltr"},{"str":"subproblems","boundary":[0.4879294975540167,0.6235645626643757,0.5977948388407603,0.638837127995393],"dir":"ltr"},{"str":"arise","boundary":[0.6010366373242123,0.6235645626643757,0.6416777207509027,0.638837127995393],"dir":"ltr"},{"str":"from","boundary":[0.6449195192343546,0.6235645626643757,0.6866477911768368,0.638837127995393],"dir":"ltr"},{"str":"a","boundary":[0.6898895896602888,0.6235645626643757,0.6997731216220324,0.638837127995393],"dir":"ltr"},{"str":"recurrence","boundary":[0.7030149201054844,0.6235645626643757,0.7952678074364006,0.638837127995393],"dir":"ltr"},{"str":"relating","boundary":[0.7985096059198525,0.6235645626643757,0.86441299704076,0.638837127995393],"dir":"ltr"},{"str":"a","boundary":[0.8676547955242119,0.6235645626643757,0.8775383274859556,0.638837127995393],"dir":"ltr"},{"str":"given","boundary":[0.8807801259694079,0.6235645626643757,0.9269164531668278,0.638837127995393],"dir":"ltr"},{"str":"problem’s","boundary":[0.23910169688515603,0.6418916410615965,0.3244361118428516,0.6571642063926139],"dir":"ltr"},{"str":"solution","boundary":[0.3310185441293729,0.6418916410615965,0.40024280198942613,0.6571642063926139],"dir":"ltr"},{"str":"to","boundary":[0.4068252342759476,0.6418916410615965,0.42439815410392795,0.6571642063926139],"dir":"ltr"},{"str":"solutions","boundary":[0.4309805863904493,0.6418916410615965,0.5078942321167391,0.6571642063926139],"dir":"ltr"},{"str":"of","boundary":[0.5144766644032605,0.6418916410615965,0.5320495842312408,0.6571642063926139],"dir":"ltr"},{"str":"its","boundary":[0.5386320165177623,0.6418916410615965,0.5583990804412499,0.6571642063926139],"dir":"ltr"},{"str":"smaller","boundary":[0.564981512727771,0.6418916410615965,0.6275838041734558,0.6571642063926139],"dir":"ltr"},{"str":"subproblems.","boundary":[0.6341662364599772,0.6418916410615965,0.7478861552118009,0.6571642063926139],"dir":"ltr"},{"str":"Rather","boundary":[0.7544685874983222,0.6418916410615965,0.8148767348485,0.6571642063926139],"dir":"ltr"},{"str":"than","boundary":[0.8214591671350213,0.6418916410615965,0.8599061064662045,0.6571642063926139],"dir":"ltr"},{"str":"solving","boundary":[0.8664885387527259,0.6418916410615965,0.9269164531668271,0.6571642063926139],"dir":"ltr"},{"str":"overlapping","boundary":[0.23910169688515603,0.6602187194588172,0.341277650305663,0.6754912847898346],"dir":"ltr"},{"str":"subproblems","boundary":[0.34463805117265583,0.6602187194588172,0.45450339245939936,0.6754912847898346],"dir":"ltr"},{"str":"again","boundary":[0.45786379332639227,0.6602187194588172,0.504000120523812,0.6754912847898346],"dir":"ltr"},{"str":"and","boundary":[0.507360521390805,0.6602187194588172,0.5392250284354668,0.6754912847898346],"dir":"ltr"},{"str":"again,","boundary":[0.5425854293024597,0.6602187194588172,0.5936635224807514,0.6754912847898346],"dir":"ltr"},{"str":"dynamic","boundary":[0.5973401963705202,0.6602187194588172,0.6698260197779489,0.6754912847898346],"dir":"ltr"},{"str":"programming","boundary":[0.6731864206449417,0.6602187194588172,0.7896144271542833,0.6754912847898346],"dir":"ltr"},{"str":"suggests","boundary":[0.7929748280212761,0.6602187194588172,0.8632665073331977,0.6754912847898346],"dir":"ltr"},{"str":"solving","boundary":[0.8666269082001907,0.6602187194588172,0.927054822614292,0.6754912847898346],"dir":"ltr"},{"str":"each","boundary":[0.23910169688515603,0.678545797856038,0.27863582473213105,0.6938183631870553],"dir":"ltr"},{"str":"of","boundary":[0.28179855495988904,0.678545797856038,0.29937147478786946,0.6938183631870553],"dir":"ltr"},{"str":"the","boundary":[0.3025342050156275,0.678545797856038,0.32999065680535167,0.6938183631870553],"dir":"ltr"},{"str":"smaller","boundary":[0.3331533870331096,0.678545797856038,0.39575567847879456,0.6938183631870553],"dir":"ltr"},{"str":"subproblems","boundary":[0.39891840870655254,0.678545797856038,0.5087837499932961,0.6938183631870553],"dir":"ltr"},{"str":"only","boundary":[0.511946480221054,0.678545797856038,0.5493062310364455,0.6938183631870553],"dir":"ltr"},{"str":"once","boundary":[0.5524689612642034,0.678545797856038,0.5931100446908937,0.6938183631870553],"dir":"ltr"},{"str":"and","boundary":[0.5962727749186518,0.678545797856038,0.6281372819633136,0.6938183631870553],"dir":"ltr"},{"str":"recording","boundary":[0.6313000121910718,0.678545797856038,0.7136891346241677,0.6938183631870553],"dir":"ltr"},{"str":"the","boundary":[0.7168518648519256,0.678545797856038,0.7443083166416498,0.6938183631870553],"dir":"ltr"},{"str":"results","boundary":[0.7474710468694078,0.678545797856038,0.8034909060285713,0.6938183631870553],"dir":"ltr"},{"str":"in","boundary":[0.8066536362563294,0.678545797856038,0.8231393675685179,0.6938183631870553],"dir":"ltr"},{"str":"a","boundary":[0.826302097796276,0.678545797856038,0.8361856297580196,0.6938183631870553],"dir":"ltr"},{"str":"table","boundary":[0.8393483599857777,0.678545797856038,0.8821835875079751,0.6938183631870553],"dir":"ltr"},{"str":"from","boundary":[0.8853463177357329,0.678545797856038,0.9270745896782151,0.6938183631870553],"dir":"ltr"},{"str":"which","boundary":[0.23910169688515603,0.6968728762532588,0.2896263122735901,0.7121454415842761],"dir":"ltr"},{"str":"a","boundary":[0.294568078254462,0.6968728762532588,0.30445161021620576,0.7121454415842761],"dir":"ltr"},{"str":"solution","boundary":[0.30939337619707763,0.6968728762532588,0.37861763405713084,0.7121454415842761],"dir":"ltr"},{"str":"to","boundary":[0.38355940003800276,0.6968728762532588,0.40113231986598313,0.7121454415842761],"dir":"ltr"},{"str":"the","boundary":[0.40607408584685495,0.6968728762532588,0.4335305376365791,0.7121454415842761],"dir":"ltr"},{"str":"original","boundary":[0.438472303617451,0.6968728762532588,0.5043954618022819,0.7121454415842761],"dir":"ltr"},{"str":"problem","boundary":[0.5093372277831536,0.6968728762532588,0.5818428182545059,0.7121454415842761],"dir":"ltr"},{"str":"can","boundary":[0.5867845842353777,0.6968728762532588,0.616435180120609,0.7121454415842761],"dir":"ltr"},{"str":"then","boundary":[0.6213769461014809,0.6968728762532588,0.6598238854326641,0.7121454415842761],"dir":"ltr"},{"str":"be","boundary":[0.6647656514135359,0.6968728762532588,0.6856396709167387,0.7121454415842761],"dir":"ltr"},{"str":"obtained.","boundary":[0.6905814368976106,0.6968728762532588,0.7713298930250572,0.7121454415842761],"dir":"ltr"},{"str":"This","boundary":[0.27468241194743354,0.7152014819070126,0.31125148020588544,0.73047404723803],"dir":"ltr"},{"str":"technique","boundary":[0.3190792375195865,0.7152014819070126,0.40366250404818954,0.73047404723803],"dir":"ltr"},{"str":"can","boundary":[0.41149026136189065,0.7152014819070126,0.4411408572471219,0.73047404723803],"dir":"ltr"},{"str":"be","boundary":[0.4489686145608229,0.7152014819070126,0.4698426340640257,0.73047404723803],"dir":"ltr"},{"str":"illustrated","boundary":[0.4776703913777268,0.7152014819070126,0.564447802001837,0.73047404723803],"dir":"ltr"},{"str":"by","boundary":[0.572275559315538,0.7152014819070126,0.5931495788187408,0.73047404723803],"dir":"ltr"},{"str":"revisiting","boundary":[0.6009773361324419,0.7152014819070126,0.6800653588903155,0.73047404723803],"dir":"ltr"},{"str":"the","boundary":[0.6878931162040165,0.7152014819070126,0.7153495679937406,0.73047404723803],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.7231773253074418,0.7152014819070126,0.8059222548911605,0.73047404723803],"dir":"ltr"},{"str":"numbers","boundary":[0.8137500122048614,0.7152014819070126,0.8884497467717207,0.73047404723803],"dir":"ltr"},{"str":"dis-","boundary":[0.896277504085422,0.7152014819070126,0.9270350555503685,0.73047404723803],"dir":"ltr"},{"str":"cussed","boundary":[0.23910169688515603,0.7335285603042333,0.2951215560443196,0.7488011256352507],"dir":"ltr"},{"str":"in","boundary":[0.29949007717141035,0.7335285603042333,0.31597580848359896,0.7488011256352507],"dir":"ltr"},{"str":"Section","boundary":[0.3203443296106897,0.7335285603042333,0.38405357663608997,0.7488011256352507],"dir":"ltr"},{"str":"2.5.","boundary":[0.38842209776318065,0.7335285603042333,0.4180726936484119,0.7488011256352507],"dir":"ltr"},{"str":"(If","boundary":[0.4224412147755026,0.7335285603042333,0.44440242279449726,0.7488011256352507],"dir":"ltr"},{"str":"you","boundary":[0.448770943921588,0.7335285603042333,0.4806354509662499,0.7488011256352507],"dir":"ltr"},{"str":"have","boundary":[0.4850039720933406,0.7335285603042333,0.5256450555200309,0.7488011256352507],"dir":"ltr"},{"str":"not","boundary":[0.5300135766471217,0.7335285603042333,0.5585769840165611,0.7488011256352507],"dir":"ltr"},{"str":"read","boundary":[0.5629455051436519,0.7335285603042333,0.6013924444748352,0.7488011256352507],"dir":"ltr"},{"str":"that","boundary":[0.6057609656019259,0.7335285603042333,0.6397998496781714,0.7488011256352507],"dir":"ltr"},{"str":"section,","boundary":[0.6441683708052621,0.7335285603042333,0.7095182841363118,0.7488011256352507],"dir":"ltr"},{"str":"you","boundary":[0.7140054076469434,0.7335285603042333,0.7458699146916052,0.7488011256352507],"dir":"ltr"},{"str":"will","boundary":[0.750238435818696,0.7335285603042333,0.7809959872836426,0.7488011256352507],"dir":"ltr"},{"str":"be","boundary":[0.7853645084107334,0.7335285603042333,0.8062385279139361,0.7488011256352507],"dir":"ltr"},{"str":"able","boundary":[0.8106070490410269,0.7335285603042333,0.8468598442767029,0.7488011256352507],"dir":"ltr"},{"str":"to","boundary":[0.8512283654037938,0.7335285603042333,0.8688012852317742,0.7488011256352507],"dir":"ltr"},{"str":"follow","boundary":[0.873169806358865,0.7335285603042333,0.9269955214225214,0.7488011256352507],"dir":"ltr"},{"str":"the","boundary":[0.23910169688515603,0.7518556387014542,0.2665581486748802,0.7671282040324715],"dir":"ltr"},{"str":"discussion","boundary":[0.27027435669249583,0.7518556387014542,0.35707153438052947,0.7671282040324715],"dir":"ltr"},{"str":"anyway.","boundary":[0.36078774239814515,0.7518556387014542,0.4287073740392482,0.7671282040324715],"dir":"ltr"},{"str":"But","boundary":[0.4324235820568638,0.7518556387014542,0.46426832203760215,0.7671282040324715],"dir":"ltr"},{"str":"it","boundary":[0.46798453005521784,0.7518556387014542,0.48006220611246875,0.7671282040324715],"dir":"ltr"},{"str":"is","boundary":[0.4837784141300844,0.7518556387014542,0.4969630457670506,0.7671282040324715],"dir":"ltr"},{"str":"a","boundary":[0.5006792537846663,0.7518556387014542,0.51056278574641,0.7671282040324715],"dir":"ltr"},{"str":"beautiful","boundary":[0.5142789937640256,0.7518556387014542,0.591172872426392,0.7671282040324715],"dir":"ltr"},{"str":"topic,","boundary":[0.5948890804440077,0.7518556387014542,0.6423102667964542,0.7671282040324715],"dir":"ltr"},{"str":"so","boundary":[0.6462636795811517,0.7518556387014542,0.6649435549888474,0.7671282040324715],"dir":"ltr"},{"str":"if","boundary":[0.6686597630064631,0.7518556387014542,0.6807374390637139,0.7671282040324715],"dir":"ltr"},{"str":"you","boundary":[0.6844536470813295,0.7518556387014542,0.7163181541259913,0.7671282040324715],"dir":"ltr"},{"str":"feel","boundary":[0.720034362143607,0.7518556387014542,0.7518791021243454,0.7671282040324715],"dir":"ltr"},{"str":"a","boundary":[0.755595310141961,0.7518556387014542,0.7654788421037048,0.7671282040324715],"dir":"ltr"},{"str":"temptation","boundary":[0.7691950501213205,0.7518556387014542,0.8636420815477437,0.7671282040324715],"dir":"ltr"},{"str":"to","boundary":[0.8673582895653593,0.7518556387014542,0.8849312093933397,0.7671282040324715],"dir":"ltr"},{"str":"read","boundary":[0.8886474174109555,0.7518556387014542,0.9270943567421387,0.7671282040324715],"dir":"ltr"},{"str":"it,","boundary":[0.23910169688515603,0.770182717098675,0.25612113892327876,0.7854552824296923],"dir":"ltr"},{"str":"do","boundary":[0.2610629049041507,0.770182717098675,0.2830438799870688,0.7854552824296923],"dir":"ltr"},{"str":"succumb","boundary":[0.28798564596794063,0.770182717098675,0.36266561347087645,0.7854552824296923],"dir":"ltr"},{"str":"to","boundary":[0.3676073794517483,0.770182717098675,0.3851802992797287,0.7854552824296923],"dir":"ltr"},{"str":"it.)","boundary":[0.3901220652606006,0.770182717098675,0.41483089516496,0.7854552824296923],"dir":"ltr"},{"str":"The","boundary":[0.41977266114583184,0.770182717098675,0.45304062972906134,0.7854552824296923],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.4579823957099332,0.770182717098675,0.5407273252936519,0.7854552824296923],"dir":"ltr"},{"str":"numbers","boundary":[0.5456690912745237,0.770182717098675,0.6203688258413831,0.7854552824296923],"dir":"ltr"},{"str":"are","boundary":[0.6253105918222549,0.770182717098675,0.652767043611979,0.7854552824296923],"dir":"ltr"},{"str":"the","boundary":[0.6577088095928508,0.770182717098675,0.6851652613825749,0.7854552824296923],"dir":"ltr"},{"str":"elements","boundary":[0.6901070273634469,0.770182717098675,0.7669811389618898,0.7854552824296923],"dir":"ltr"},{"str":"of","boundary":[0.7719229049427617,0.770182717098675,0.7894958247707422,0.7854552824296923],"dir":"ltr"},{"str":"the","boundary":[0.794437590751614,0.770182717098675,0.8218940425413381,0.7854552824296923],"dir":"ltr"},{"str":"sequence","boundary":[0.82683580852221,0.770182717098675,0.9059238312800836,0.7854552824296923],"dir":"ltr"},{"str":"0","boundary":[0.4036941313504671,0.8072263243090575,0.41357766331221085,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.4136764986318283,0.8078372269222982,0.42021939679050263,0.8231097922533155],"dir":"ltr"},{"str":"1","boundary":[0.43449517035604535,0.8072263243090575,0.44437870231778914,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.4434298832494617,0.8078372269222982,0.449972781408136,0.8231097922533155],"dir":"ltr"},{"str":"1","boundary":[0.4642465782672864,0.8072263243090575,0.4741301102290301,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.4731812911607027,0.8078372269222982,0.47972418931937705,0.8231097922533155],"dir":"ltr"},{"str":"2","boundary":[0.4939999628849197,0.8072263243090575,0.5038834948466635,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.5040218642941279,0.8078372269222982,0.5105647624528022,0.8231097922533155],"dir":"ltr"},{"str":"3","boundary":[0.5248405360183449,0.8072263243090575,0.5347240679800885,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.5342101243180779,0.8078372269222982,0.5407530224767524,0.8231097922533155],"dir":"ltr"},{"str":"5","boundary":[0.5550268193359027,0.8072263243090575,0.5649103512976463,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.5644774525977221,0.8078372269222982,0.5710203507563965,0.8231097922533155],"dir":"ltr"},{"str":"8","boundary":[0.5852941476155468,0.8072263243090575,0.5951776795772905,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.595100588027989,0.8078372269222982,0.6016434861866634,0.8231097922533155],"dir":"ltr"},{"str":"13","boundary":[0.6159172830458137,0.8072263243090575,0.6356843469693012,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.6351704033072905,0.8078372269222982,0.641713301465965,0.8231097922533155],"dir":"ltr"},{"str":"21","boundary":[0.6559870983251153,0.8072263243090575,0.6757541622486027,0.8224988896400748],"dir":"ltr"},{"str":",","boundary":[0.6748073198866678,0.8078372269222982,0.6813502180453421,0.8231097922533155],"dir":"ltr"},{"str":"34","boundary":[0.6956240149044924,0.8072263243090575,0.71539107882798,0.8224988896400748],"dir":"ltr"},{"str":",...,","boundary":[0.7154306129558269,0.8078372269222982,0.7667854450290474,0.8231097922533155],"dir":"ltr"},{"str":"which","boundary":[0.23908983664680208,0.8442714587759732,0.2896144520352361,0.8595440241069904],"dir":"ltr"},{"str":"can","boundary":[0.29455621801610804,0.8442714587759732,0.3242068139013393,0.8595440241069904],"dir":"ltr"},{"str":"be","boundary":[0.3291485798822112,0.8442714587759732,0.35002259938541397,0.8595440241069904],"dir":"ltr"},{"str":"defined","boundary":[0.35496436536628584,0.8442714587759732,0.4186933794556095,0.8595440241069904],"dir":"ltr"},{"str":"by","boundary":[0.42363514543648145,0.8442714587759732,0.4445091649396843,0.8595440241069904],"dir":"ltr"},{"str":"the","boundary":[0.4494509309205561,0.8442714587759732,0.47690738271028027,0.8595440241069904],"dir":"ltr"},{"str":"simple","boundary":[0.48184914869115214,0.8442714587759732,0.5378690078503158,0.8595440241069904],"dir":"ltr"},{"str":"recurrence","boundary":[0.5428107738311876,0.8442714587759732,0.6350636611621038,0.8595440241069904],"dir":"ltr"},{"str":"F","boundary":[0.4170428296179984,0.8819259685995964,0.42953561401764245,0.8971985339306136],"dir":"ltr"},{"str":"(n)","boundary":[0.43230300296693075,0.8819259685995964,0.4578222824921531,0.8971985339306136],"dir":"ltr"},{"str":"=","boundary":[0.4622125473895597,0.8845986675325243,0.4776308572498799,0.8998712328635415],"dir":"ltr"},{"str":"F(n","boundary":[0.4820230988536789,0.8819259685995964,0.518196825833661,0.8971985339306136],"dir":"ltr"},{"str":"−","boundary":[0.5198216784881716,0.8845986675325243,0.5352399883484918,0.8998712328635415],"dir":"ltr"},{"str":"1","boundary":[0.5396342066586832,0.8813150659863557,0.5495177386204269,0.8965876313173728],"dir":"ltr"},{"str":")","boundary":[0.5485689195520996,0.8819259685995964,0.5559420343955604,0.8971985339306136],"dir":"ltr"},{"str":"+","boundary":[0.5603322992929669,0.8845986675325243,0.5757506091532872,0.8998712328635415],"dir":"ltr"},{"str":"F(n","boundary":[0.5801448274634785,0.8819259685995964,0.6163185544434606,0.8971985339306136],"dir":"ltr"},{"str":"−","boundary":[0.6179434070979712,0.8845986675325243,0.6333617169582916,0.8998712328635415],"dir":"ltr"},{"str":"2","boundary":[0.6377559352684828,0.8813150659863557,0.6476394672302265,0.8965876313173728],"dir":"ltr"},{"str":")","boundary":[0.647777836677691,0.8819259685995964,0.6551509515211519,0.8971985339306136],"dir":"ltr"},{"str":"for","boundary":[0.6749180154446394,0.8813150659863557,0.7001803231388564,0.8965876313173728],"dir":"ltr"},{"str":"n>1","boundary":[0.7051201124133358,0.8813150659863557,0.7499794872812984,0.8971985339306136],"dir":"ltr"},{"str":"(8.1)","boundary":[0.8868960555473345,0.8813150659863557,0.9269836611841672,0.8965876313173728],"dir":"ltr"},{"str":"283","boundary":[0.894006268440613,0.9329378640617272,0.9269777310649903,0.9482104293927445],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92709,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":341,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/9e1539751a4010094da14e476a0a18ad.jpg","blurred":"/storage/books/4a8b03583f119702/pages/a20a94baa74e57c7a019f43ec3795c80.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07294,0.05179]},"elements":[{"words":[{"str":"9","boundary":[0.14421784044919886,0.07999453587206534,0.20750436345743647,0.15330318671872986],"dir":"ltr"},{"str":"Greedy","boundary":[0.14421784044919886,0.17005356781848974,0.31486337810217685,0.20670781659232623],"dir":"ltr"},{"str":"Technique","boundary":[0.330661255232686,0.17005356781848974,0.5788255052918264,0.20670781659232623],"dir":"ltr"},{"str":"Greed,","boundary":[0.23910077902799318,0.27434437041309123,0.2967415374288827,0.2896169357441086],"dir":"ltr"},{"str":"for","boundary":[0.30168330340975463,0.27434437041309123,0.3269456111039717,0.2896169357441086],"dir":"ltr"},{"str":"lack","boundary":[0.3318873770848435,0.27434437041309123,0.36679601197372247,0.2896169357441086],"dir":"ltr"},{"str":"of","boundary":[0.37173777795459434,0.27434437041309123,0.38931069778257477,0.2896169357441086],"dir":"ltr"},{"str":"a","boundary":[0.39425246376344664,0.27434437041309123,0.4041359957251904,0.2896169357441086],"dir":"ltr"},{"str":"better","boundary":[0.40907776170606225,0.27434437041309123,0.45630127741927384,0.2896169357441086],"dir":"ltr"},{"str":"word,","boundary":[0.4612430434001457,0.27434437041309123,0.5097711853323076,0.2896169357441086],"dir":"ltr"},{"str":"is","boundary":[0.5147129513131795,0.27434437041309123,0.5278975829501457,0.2896169357441086],"dir":"ltr"},{"str":"good!","boundary":[0.5328393489310175,0.27434437041309123,0.5822767758036597,0.2896169357441086],"dir":"ltr"},{"str":"Greed","boundary":[0.5872185417845316,0.27434437041309123,0.6399175342045493,0.2896169357441086],"dir":"ltr"},{"str":"is","boundary":[0.6448593001854211,0.27434437041309123,0.6580439318223873,0.2896169357441086],"dir":"ltr"},{"str":"right!","boundary":[0.6629856978032592,0.27434437041309123,0.7091220250006791,0.2896169357441086],"dir":"ltr"},{"str":"Greed","boundary":[0.7140637909815509,0.27434437041309123,0.7667627834015687,0.2896169357441086],"dir":"ltr"},{"str":"works!","boundary":[0.7717045493824405,0.27434437041309123,0.8299185526371111,0.2896169357441086],"dir":"ltr"},{"str":"—Michael","boundary":[0.37578927407476587,0.29627247508083515,0.46029374020482366,0.310781458134999],"dir":"ltr"},{"str":"Douglas,","boundary":[0.4650072115378558,0.29627247508083515,0.5364979898838848,0.310781458134999],"dir":"ltr"},{"str":"US","boundary":[0.5412114612169167,0.29627247508083515,0.5672951730957279,0.310781458134999],"dir":"ltr"},{"str":"actor","boundary":[0.57200864442876,0.29627247508083515,0.6137350719267574,0.310781458134999],"dir":"ltr"},{"str":"in","boundary":[0.6184485432597895,0.29627247508083515,0.6341100376492269,0.310781458134999],"dir":"ltr"},{"str":"the","boundary":[0.6388235089822589,0.29627247508083515,0.6649072208610701,0.310781458134999],"dir":"ltr"},{"str":"role","boundary":[0.6696206921941023,0.29627247508083515,0.7019765133367888,0.310781458134999],"dir":"ltr"},{"str":"of","boundary":[0.7066899846698209,0.29627247508083515,0.7233843114230701,0.310781458134999],"dir":"ltr"},{"str":"Gordon","boundary":[0.7280977827561023,0.29627247508083515,0.7928094250414753,0.310781458134999],"dir":"ltr"},{"str":"Gecko,","boundary":[0.7975228963745075,0.29627247508083515,0.8557183053827406,0.310781458134999],"dir":"ltr"},{"str":"in","boundary":[0.634093136756001,0.314600222474855,0.6497546311454383,0.32910920552901884],"dir":"ltr"},{"str":"the","boundary":[0.6544868812487216,0.314600222474855,0.6805705931275328,0.32910920552901884],"dir":"ltr"},{"str":"film","boundary":[0.6853028432308159,0.314600222474855,0.7166070532394395,0.32910920552901884],"dir":"ltr"},{"str":"Wall","boundary":[0.7213693493751246,0.314600222474855,0.7578940575135608,0.32910920552901884],"dir":"ltr"},{"str":"Street","boundary":[0.7626263076168439,0.314600222474855,0.807488789746779,0.32910920552901884],"dir":"ltr"},{"str":",","boundary":[0.8084389955214859,0.314600222474855,0.8131336880842669,0.32910920552901884],"dir":"ltr"},{"str":"1987","boundary":[0.8178847169578013,0.314600222474855,0.8554422574600492,0.32910920552901884],"dir":"ltr"},{"str":"et","boundary":[0.27533490680294437,0.42598926583291774,0.2918008710512095,0.4412618311639351],"dir":"ltr"},{"str":"us","boundary":[0.29879841168012405,0.42598926583291774,0.3174782870878198,0.4412618311639351],"dir":"ltr"},{"str":"revisit","boundary":[0.3244758277167343,0.42598926583291774,0.37719458720067545,0.4412618311639351],"dir":"ltr"},{"str":"the","boundary":[0.38419212782959006,0.42598926583291774,0.4116485796193142,0.4412618311639351],"dir":"ltr"},{"str":"change-making","boundary":[0.4186401901290517,0.42598926583291774,0.5525620482106796,0.4412618311639351],"dir":"ltr"},{"str":"problem","boundary":[0.5603502713965337,0.42598926583291774,0.6328360948039624,0.4412618311639351],"dir":"ltr"},{"str":"faced,","boundary":[0.6394936419333929,0.42598926583291774,0.6905519680477611,0.4412618311639351],"dir":"ltr"},{"str":"at","boundary":[0.6980634523386864,0.42598926583291774,0.7145294165869515,0.4412618311639351],"dir":"ltr"},{"str":"least","boundary":[0.721526957215866,0.42598926583291774,0.7610610850628411,0.4412618311639351],"dir":"ltr"},{"str":"subconsciously,","boundary":[0.7680586256917556,0.42598926583291774,0.8986200829063906,0.4412618311639351],"dir":"ltr"},{"str":"by","boundary":[0.9061315671973159,0.42598926583291774,0.9270055867005187,0.4412618311639351],"dir":"ltr"},{"str":"millions","boundary":[0.2753349068029443,0.4443163442301386,0.3434522090832823,0.4595889095611559],"dir":"ltr"},{"str":"of","boundary":[0.35011370962549754,0.4443163442301386,0.36768662945347796,0.4595889095611559],"dir":"ltr"},{"str":"cashiers","boundary":[0.3743481299956932,0.4443163442301386,0.44244566521210765,0.4595889095611559],"dir":"ltr"},{"str":"all","boundary":[0.44910716575432297,0.4443163442301386,0.4699811852575258,0.4595889095611559],"dir":"ltr"},{"str":"over","boundary":[0.4766426857997411,0.4443163442301386,0.5150896251309243,0.4595889095611559],"dir":"ltr"},{"str":"the","boundary":[0.5217511256731395,0.4443163442301386,0.5492075774628636,0.4595889095611559],"dir":"ltr"},{"str":"world:","boundary":[0.555869078005079,0.4443163442301386,0.6102482708585931,0.4595889095611559],"dir":"ltr"},{"str":"give","boundary":[0.6169097714008084,0.4443163442301386,0.6520556110567692,0.4595889095611559],"dir":"ltr"},{"str":"change","boundary":[0.6587171115989845,0.4443163442301386,0.7191252589491622,0.4595889095611559],"dir":"ltr"},{"str":"for","boundary":[0.7257867594913775,0.4443163442301386,0.7510490671855945,0.4595889095611559],"dir":"ltr"},{"str":"a","boundary":[0.7577105677278099,0.4443163442301386,0.7675940996895536,0.4595889095611559],"dir":"ltr"},{"str":"specific","boundary":[0.7742556002317689,0.4443163442301386,0.8368578916774538,0.4595889095611559],"dir":"ltr"},{"str":"amount","boundary":[0.8435193922196692,0.4443163442301386,0.9094227833405766,0.4595889095611559],"dir":"ltr"},{"str":"n","boundary":[0.9162305601558257,0.44492724684337925,0.9270036099941265,0.4601998121743966],"dir":"ltr"},{"str":"Lwith","boundary":[0.23910077902799318,0.424691122614218,0.2764418623826596,0.47791751521490977],"dir":"ltr"},{"str":"the","boundary":[0.279822030313576,0.46264494988389243,0.30727848210330017,0.47791751521490977],"dir":"ltr"},{"str":"least","boundary":[0.31065865003421655,0.46264494988389243,0.3501927778811915,0.47791751521490977],"dir":"ltr"},{"str":"number","boundary":[0.3535729458121079,0.46264494988389243,0.4205832925127305,0.47791751521490977],"dir":"ltr"},{"str":"of","boundary":[0.4239634604436469,0.46264494988389243,0.4415363802716273,0.47791751521490977],"dir":"ltr"},{"str":"coins","boundary":[0.4449165482025436,0.46264494988389243,0.48885873130445634,0.47791751521490977],"dir":"ltr"},{"str":"of","boundary":[0.4922388992353726,0.46264494988389243,0.509811819063353,0.47791751521490977],"dir":"ltr"},{"str":"the","boundary":[0.5131919869942694,0.46264494988389243,0.5406484387839935,0.47791751521490977],"dir":"ltr"},{"str":"denominations","boundary":[0.5440286067149099,0.46264494988389243,0.6714668678296338,0.47791751521490977],"dir":"ltr"},{"str":"...","boundary":[0.7564268553585226,0.46012308716354405,0.7859114079067966,0.4753956524945614],"dir":"ltr"},{"str":"used","boundary":[0.8301801570079002,0.462644587699695,0.8697340519187986,0.47791715303071236],"dir":"ltr"},{"str":"in","boundary":[0.873114219849715,0.462644587699695,0.8895999511619036,0.47791715303071236],"dir":"ltr"},{"str":"that","boundary":[0.8929801190928199,0.462644587699695,0.9270190031690654,0.47791715303071236],"dir":"ltr"},{"str":"d1","boundary":[0.6747877345687799,0.46325585249713314,0.6920849158986787,0.480264434996362],"dir":"ltr"},{"str":">d2","boundary":[0.6958230112183593,0.4632554903129357,0.7324956310663728,0.480264434996362],"dir":"ltr"},{"str":">","boundary":[0.7370492025943277,0.4632554903129357,0.7524675124546479,0.47852805564395307],"dir":"ltr"},{"str":">dm","boundary":[0.7854765325004799,0.4632554903129357,0.826312561685393,0.4807226150222723],"dir":"ltr"},{"str":"locale.","boundary":[0.2391034348613844,0.48097166609691583,0.29383843486552136,0.49624423142793317],"dir":"ltr"},{"str":"(Here,","boundary":[0.2973174381160551,0.48097166609691583,0.3531396266359838,0.49624423142793317],"dir":"ltr"},{"str":"unlike","boundary":[0.35691513584536994,0.48097166609691583,0.41076061797294994,0.49624423142793317],"dir":"ltr"},{"str":"Section","boundary":[0.41423962122348373,0.48097166609691583,0.477948868248884,0.49624423142793317],"dir":"ltr"},{"str":"8.1,","boundary":[0.4814278714994178,0.48097166609691583,0.511078467384649,0.49624423142793317],"dir":"ltr"},{"str":"we","boundary":[0.5148539765940351,0.48097166609691583,0.5390093287085369,0.49624423142793317],"dir":"ltr"},{"str":"assume","boundary":[0.5424883319590706,0.48097166609691583,0.6050906234047556,0.49624423142793317],"dir":"ltr"},{"str":"that","boundary":[0.6085696266552894,0.48097166609691583,0.6426085107315348,0.49624423142793317],"dir":"ltr"},{"str":"the","boundary":[0.6460875139820687,0.48097166609691583,0.6735439657717928,0.49624423142793317],"dir":"ltr"},{"str":"denominations","boundary":[0.6770229690223265,0.48097166609691583,0.8044612301370505,0.49624423142793317],"dir":"ltr"},{"str":"are","boundary":[0.8079402333875844,0.48097166609691583,0.8353966851773085,0.49624423142793317],"dir":"ltr"},{"str":"ordered","boundary":[0.8388756884278422,0.48097166609691583,0.9069929907081802,0.49624423142793317],"dir":"ltr"},{"str":"in","boundary":[0.910471993958714,0.48097166609691583,0.9269577252709026,0.49624423142793317],"dir":"ltr"},{"str":"decreasing","boundary":[0.2391034348613844,0.49929874449413664,0.33026913367650884,0.514571309825154],"dir":"ltr"},{"str":"order.)","boundary":[0.3338667393105835,0.49929874449413664,0.39338536878420444,0.514571309825154],"dir":"ltr"},{"str":"For","boundary":[0.3969829744182792,0.49929874449413664,0.42665333736743394,0.514571309825154],"dir":"ltr"},{"str":"example,","boundary":[0.4302509430015087,0.49929874449413664,0.5069471510246402,0.514571309825154],"dir":"ltr"},{"str":"the","boundary":[0.5108017284897203,0.49929874449413664,0.5382581802794444,0.514571309825154],"dir":"ltr"},{"str":"widely","boundary":[0.5418557859135191,0.49929874449413664,0.5978756450726828,0.514571309825154],"dir":"ltr"},{"str":"used","boundary":[0.6014732507067574,0.49929874449413664,0.641027145617656,0.514571309825154],"dir":"ltr"},{"str":"coin","boundary":[0.6446247512517306,0.49929874449413664,0.6808775464874067,0.514571309825154],"dir":"ltr"},{"str":"denominations","boundary":[0.6844751521214814,0.49929874449413664,0.8119134132362055,0.514571309825154],"dir":"ltr"},{"str":"in","boundary":[0.8155110188702801,0.49929874449413664,0.8319967501824685,0.514571309825154],"dir":"ltr"},{"str":"the","boundary":[0.8355943558165433,0.49929874449413664,0.8630508076062674,0.514571309825154],"dir":"ltr"},{"str":"United","boundary":[0.8666484132403421,0.49929874449413664,0.92705656059052,0.514571309825154],"dir":"ltr"},{"str":"States","boundary":[0.2391034348613844,0.5176258228913575,0.2907152387656103,0.5328983882223748],"dir":"ltr"},{"str":"are","boundary":[0.29632908491988075,0.5176258228913575,0.3237855367096049,0.5328983882223748],"dir":"ltr"},{"str":"d1","boundary":[0.3294112431022294,0.5182367255045982,0.3467059401066772,0.5352466513015701],"dir":"ltr"},{"str":"=","boundary":[0.3509579243264626,0.5209088725611566,0.36637623418678283,0.536181437892174],"dir":"ltr"},{"str":"25","boundary":[0.37084359063349104,0.5176252710149879,0.3906106545569786,0.5328978363460052],"dir":"ltr"},{"str":"(quarter),","boundary":[0.3957896253049323,0.5176252710149879,0.47981941404367767,0.5328978363460052],"dir":"ltr"},{"str":"d2","boundary":[0.4856151171860442,0.5182361736282285,0.502912292722292,0.5352466513015701],"dir":"ltr"},{"str":"=","boundary":[0.5079777690233243,0.5209088725611566,0.5233960788836445,0.536181437892174],"dir":"ltr"},{"str":"10","boundary":[0.527865412036745,0.5176252710149879,0.5476324759602326,0.5328978363460052],"dir":"ltr"},{"str":"(dime),d3","boundary":[0.5533451574341204,0.5176252710149879,0.6410253909747604,0.5352466513015701],"dir":"ltr"},{"str":"=","boundary":[0.6456007879000172,0.5209088725611566,0.6610190977603374,0.536181437892174],"dir":"ltr"},{"str":"5","boundary":[0.6654884309134379,0.5176252710149879,0.6753719628751816,0.5328978363460052],"dir":"ltr"},{"str":"(nickel)","boundary":[0.6805509336231353,0.5176252710149879,0.747561280323758,0.5328978363460052],"dir":"ltr"},{"str":",","boundary":[0.7475652337365428,0.5182361736282285,0.7541081318952172,0.5335087389592459],"dir":"ltr"},{"str":"and","boundary":[0.7597279081686648,0.5176252710149879,0.7915924152133266,0.5328978363460052],"dir":"ltr"},{"str":"d4","boundary":[0.7972141681931664,0.5182361736282285,0.8145115058722748,0.5352466513015701],"dir":"ltr"},{"str":"=","boundary":[0.8195035694732922,0.5209088725611566,0.8349218793336124,0.536181437892174],"dir":"ltr"},{"str":"1","boundary":[0.8393912124867129,0.5176252710149879,0.8492747444484566,0.5328978363460052],"dir":"ltr"},{"str":"(penny).","boundary":[0.8539397715343997,0.5176252710149879,0.9269988397956095,0.5328978363460052],"dir":"ltr"},{"str":"How","boundary":[0.23910303855185203,0.5359523494122087,0.28083131049433413,0.551224914743226],"dir":"ltr"},{"str":"would","boundary":[0.2861288836258288,0.5359523494122087,0.3388674101736935,0.551224914743226],"dir":"ltr"},{"str":"you","boundary":[0.3441649833051881,0.5359523494122087,0.37602949034984995,0.551224914743226],"dir":"ltr"},{"str":"give","boundary":[0.3813270634813446,0.5359523494122087,0.4164729031373054,0.551224914743226],"dir":"ltr"},{"str":"change","boundary":[0.4217704762688,0.5359523494122087,0.48217862361897784,0.551224914743226],"dir":"ltr"},{"str":"with","boundary":[0.48747619675047255,0.5359523494122087,0.5248161805019405,0.551224914743226],"dir":"ltr"},{"str":"coins","boundary":[0.530113753633435,0.5359523494122087,0.5740559367353478,0.551224914743226],"dir":"ltr"},{"str":"of","boundary":[0.5793535098668424,0.5359523494122087,0.5969264296948228,0.551224914743226],"dir":"ltr"},{"str":"these","boundary":[0.6022240028263175,0.5359523494122087,0.6472533744440221,0.551224914743226],"dir":"ltr"},{"str":"denominations","boundary":[0.6525509475755167,0.5359523494122087,0.7799892086902407,0.551224914743226],"dir":"ltr"},{"str":"of,","boundary":[0.7852867818217354,0.5359523494122087,0.8068131144344133,0.551224914743226],"dir":"ltr"},{"str":"say,","boundary":[0.8122095228855253,0.5359523494122087,0.8427891707751605,0.551224914743226],"dir":"ltr"},{"str":"48","boundary":[0.8481855792262726,0.5359523494122087,0.8679526431497601,0.551224914743226],"dir":"ltr"},{"str":"cents?","boundary":[0.8731711480255608,0.5359523494122087,0.9269770960252939,0.551224914743226],"dir":"ltr"},{"str":"If","boundary":[0.23910303855185203,0.5542794278094295,0.25337485870460996,0.5695519931404468],"dir":"ltr"},{"str":"you","boundary":[0.2579805845987826,0.5542794278094295,0.28984509164344446,0.5695519931404468],"dir":"ltr"},{"str":"came","boundary":[0.29445081753761704,0.5542794278094295,0.3394604220913981,0.5695519931404468],"dir":"ltr"},{"str":"up","boundary":[0.34406614798557067,0.5542794278094295,0.3660471230684888,0.5695519931404468],"dir":"ltr"},{"str":"with","boundary":[0.3706528489626614,0.5542794278094295,0.4079928327141293,0.5695519931404468],"dir":"ltr"},{"str":"the","boundary":[0.41259855860830186,0.5542794278094295,0.440055010398026,0.5695519931404468],"dir":"ltr"},{"str":"answer","boundary":[0.4446607362921986,0.5542794278094295,0.5050688836423765,0.5695519931404468],"dir":"ltr"},{"str":"1","boundary":[0.509674609536549,0.5542794278094295,0.5195581414982927,0.5695519931404468],"dir":"ltr"},{"str":"quarter,","boundary":[0.5241638673924653,0.5542794278094295,0.5924590732481146,0.5695519931404468],"dir":"ltr"},{"str":"2","boundary":[0.5971241003340577,0.5542794278094295,0.6070076322958013,0.5695519931404468],"dir":"ltr"},{"str":"dimes,","boundary":[0.6116133581899741,0.5542794278094295,0.6659925510434882,0.5695519931404468],"dir":"ltr"},{"str":"and","boundary":[0.6706575781294313,0.5542794278094295,0.7025220851740931,0.5695519931404468],"dir":"ltr"},{"str":"3","boundary":[0.7071278110682657,0.5542794278094295,0.7170113430300095,0.5695519931404468],"dir":"ltr"},{"str":"pennies,","boundary":[0.7216170689241821,0.5542794278094295,0.791394804574093,0.5695519931404468],"dir":"ltr"},{"str":"you","boundary":[0.7960598316600361,0.5542794278094295,0.827924338704698,0.5695519931404468],"dir":"ltr"},{"str":"followed—","boundary":[0.8325300645988705,0.5542794278094295,0.9269968630892172,0.5695519931404468],"dir":"ltr"},{"str":"consciously","boundary":[0.23910303855185203,0.5726065062066503,0.33687093671742124,0.5878790715376676],"dir":"ltr"},{"str":"or","boundary":[0.3406464459268073,0.5726065062066503,0.359326321334503,0.5878790715376676],"dir":"ltr"},{"str":"not—a","boundary":[0.3631018305438891,0.5726065062066503,0.42131583379855986,0.5878790715376676],"dir":"ltr"},{"str":"logical","boundary":[0.42509134300794593,0.5726065062066503,0.4811112021671095,0.5878790715376676],"dir":"ltr"},{"str":"strategy","boundary":[0.48488671137649564,0.5726065062066503,0.5529644795289865,0.5878790715376676],"dir":"ltr"},{"str":"of","boundary":[0.5567399887383727,0.5726065062066503,0.5743129085663531,0.5878790715376676],"dir":"ltr"},{"str":"making","boundary":[0.5780884177757393,0.5726065062066503,0.6417976648011394,0.5878790715376676],"dir":"ltr"},{"str":"a","boundary":[0.6455731740105254,0.5726065062066503,0.6554567059722691,0.5878790715376676],"dir":"ltr"},{"str":"sequence","boundary":[0.6592322151816554,0.5726065062066503,0.7383202379395288,0.5878790715376676],"dir":"ltr"},{"str":"of","boundary":[0.7420957471489149,0.5726065062066503,0.7596686669768954,0.5878790715376676],"dir":"ltr"},{"str":"best","boundary":[0.7634441761862815,0.5726065062066503,0.7985900158422423,0.5878790715376676],"dir":"ltr"},{"str":"choices","boundary":[0.8023655250516283,0.5726065062066503,0.8649678164973132,0.5878790715376676],"dir":"ltr"},{"str":"among","boundary":[0.8687433257066993,0.5726065062066503,0.9269573289613701,0.5878790715376676],"dir":"ltr"},{"str":"the","boundary":[0.23910303855185203,0.5909335846038711,0.26655949034157617,0.6062061499348884],"dir":"ltr"},{"str":"currently","boundary":[0.27106638091613133,0.5909335846038711,0.34904744809428956,0.6062061499348884],"dir":"ltr"},{"str":"available","boundary":[0.35355433866884467,0.5909335846038711,0.430448217331211,0.6062061499348884],"dir":"ltr"},{"str":"alternatives.","boundary":[0.4349551079057662,0.5909335846038711,0.5387519605679991,0.6062061499348884],"dir":"ltr"},{"str":"Indeed,","boundary":[0.5432588511425542,0.5909335846038711,0.6086285315375275,0.6062061499348884],"dir":"ltr"},{"str":"in","boundary":[0.6132342574317,0.5909335846038711,0.6297199887438886,0.6062061499348884],"dir":"ltr"},{"str":"the","boundary":[0.6342268793184438,0.5909335846038711,0.6616833311081679,0.6062061499348884],"dir":"ltr"},{"str":"first","boundary":[0.6661902216827231,0.5909335846038711,0.6991419172431768,0.6062061499348884],"dir":"ltr"},{"str":"step,","boundary":[0.703648807817732,0.5909335846038711,0.7429457308976253,0.6062061499348884],"dir":"ltr"},{"str":"you","boundary":[0.7475514567917977,0.5909335846038711,0.7794159638364595,0.6062061499348884],"dir":"ltr"},{"str":"could","boundary":[0.7839228544110147,0.5909335846038711,0.8311661371881498,0.6062061499348884],"dir":"ltr"},{"str":"have","boundary":[0.835673027762705,0.5909335846038711,0.8763141111893953,0.6062061499348884],"dir":"ltr"},{"str":"given","boundary":[0.8808210017639505,0.5909335846038711,0.9269573289613704,0.6062061499348884],"dir":"ltr"},{"str":"one","boundary":[0.23910303855185203,0.6092606630010918,0.2709675455965139,0.6245332283321092],"dir":"ltr"},{"str":"coin","boundary":[0.27541513497929854,0.6092606630010918,0.3116679302149747,0.6245332283321092],"dir":"ltr"},{"str":"of","boundary":[0.31611551959775935,0.6092606630010918,0.3336884394257397,0.6245332283321092],"dir":"ltr"},{"str":"any","boundary":[0.3381360288085244,0.6092606630010918,0.36889358027347097,0.6245332283321092],"dir":"ltr"},{"str":"of","boundary":[0.37334116965625563,0.6092606630010918,0.39091408948423606,0.6245332283321092],"dir":"ltr"},{"str":"the","boundary":[0.3953616788670207,0.6092606630010918,0.4228181306567449,0.6245332283321092],"dir":"ltr"},{"str":"four","boundary":[0.42726572003952956,0.6092606630010918,0.46351851527520566,0.6245332283321092],"dir":"ltr"},{"str":"denominations.","boundary":[0.4679661046579903,0.6092606630010918,0.5992589432377944,0.6245332283321092],"dir":"ltr"},{"str":"“Greedy”","boundary":[0.603706532620579,0.6092606630010918,0.6882700320852586,0.6245332283321092],"dir":"ltr"},{"str":"thinking","boundary":[0.6927176214680434,0.6092606630010918,0.7641360234236038,0.6245332283321092],"dir":"ltr"},{"str":"leads","boundary":[0.7685836128063884,0.6092606630010918,0.8125257959083011,0.6245332283321092],"dir":"ltr"},{"str":"to","boundary":[0.8169733852910858,0.6092606630010918,0.8345463051190662,0.6245332283321092],"dir":"ltr"},{"str":"giving","boundary":[0.8389938945018509,0.6092606630010918,0.8906254654700002,0.6245332283321092],"dir":"ltr"},{"str":"one","boundary":[0.895073054852785,0.6092606630010918,0.9269375618974468,0.6245332283321092],"dir":"ltr"},{"str":"quarter","boundary":[0.23910303855185203,0.6275877413983125,0.3028122855772523,0.6428603067293299],"dir":"ltr"},{"str":"because","boundary":[0.30696336900118465,0.6275877413983125,0.3750609042175991,0.6428603067293299],"dir":"ltr"},{"str":"it","boundary":[0.3792119876415315,0.6275877413983125,0.3912896636987824,0.6428603067293299],"dir":"ltr"},{"str":"reduces","boundary":[0.3954407471227147,0.6275877413983125,0.4613441382436221,0.6428603067293299],"dir":"ltr"},{"str":"the","boundary":[0.46549522166755447,0.6275877413983125,0.49295167345727864,0.6428603067293299],"dir":"ltr"},{"str":"remaining","boundary":[0.497102756881211,0.6275877413983125,0.5838801675053212,0.6428603067293299],"dir":"ltr"},{"str":"amount","boundary":[0.5880312509292535,0.6275877413983125,0.6539346420501609,0.6428603067293299],"dir":"ltr"},{"str":"the","boundary":[0.6580857254740933,0.6275877413983125,0.6855421772638174,0.6428603067293299],"dir":"ltr"},{"str":"most,","boundary":[0.6896932606877498,0.6275877413983125,0.7363632986111037,0.6428603067293299],"dir":"ltr"},{"str":"namely,","boundary":[0.7406725185464241,0.6275877413983125,0.8063980060920201,0.6428603067293299],"dir":"ltr"},{"str":"to","boundary":[0.8107072260273405,0.6275877413983125,0.8282801458553208,0.6428603067293299],"dir":"ltr"},{"str":"23","boundary":[0.8324312292792531,0.6275877413983125,0.8521982932027407,0.6428603067293299],"dir":"ltr"},{"str":"cents.","boundary":[0.856349376626673,0.6275877413983125,0.9041263701297424,0.6428603067293299],"dir":"ltr"},{"str":"In","boundary":[0.9082774535536747,0.6275877413983125,0.9269573289613704,0.6428603067293299],"dir":"ltr"},{"str":"the","boundary":[0.23910303855185203,0.6459148197955333,0.2665594903415761,0.6611873851265507],"dir":"ltr"},{"str":"second","boundary":[0.2719558987926882,0.6459148197955333,0.3312768576270742,0.6611873851265507],"dir":"ltr"},{"str":"step,","boundary":[0.3366732660781864,0.6459148197955333,0.3759701891580795,0.6611873851265507],"dir":"ltr"},{"str":"you","boundary":[0.3814851999927325,0.6459148197955333,0.41334970703739443,0.6611873851265507],"dir":"ltr"},{"str":"had","boundary":[0.4187461154885065,0.6459148197955333,0.45061062253316836,0.6611873851265507],"dir":"ltr"},{"str":"the","boundary":[0.45600703098428047,0.6459148197955333,0.4834634827740046,0.6611873851265507],"dir":"ltr"},{"str":"same","boundary":[0.48885989122511664,0.6459148197955333,0.5327823072631059,0.6611873851265507],"dir":"ltr"},{"str":"coins","boundary":[0.5381787157142179,0.6459148197955333,0.5821208988161307,0.6611873851265507],"dir":"ltr"},{"str":"at","boundary":[0.5875173072672427,0.6459148197955333,0.6039832715155078,0.6611873851265507],"dir":"ltr"},{"str":"your","boundary":[0.6093796799666199,0.6459148197955333,0.6489335748775185,0.6611873851265507],"dir":"ltr"},{"str":"disposal,","boundary":[0.6543299833286305,0.6459148197955333,0.7284960071695555,0.6611873851265507],"dir":"ltr"},{"str":"but","boundary":[0.7340110180042086,0.6459148197955333,0.7625744253736481,0.6611873851265507],"dir":"ltr"},{"str":"you","boundary":[0.7679708338247602,0.6459148197955333,0.799835340869422,0.6611873851265507],"dir":"ltr"},{"str":"could","boundary":[0.8052317493205341,0.6459148197955333,0.8524750320976692,0.6611873851265507],"dir":"ltr"},{"str":"not","boundary":[0.8578714405487814,0.6459148197955333,0.8864348479182208,0.6611873851265507],"dir":"ltr"},{"str":"give","boundary":[0.8918312563693329,0.6459148197955333,0.9269770960252938,0.6611873851265507],"dir":"ltr"},{"str":"a","boundary":[0.23910303855185203,0.6642418981927543,0.2489865705135958,0.6795144635237715],"dir":"ltr"},{"str":"quarter,","boundary":[0.2540074047501616,0.6642418981927543,0.32230261060581095,0.6795144635237715],"dir":"ltr"},{"str":"because","boundary":[0.3273432119063003,0.6642418981927543,0.3954407471227147,0.6795144635237715],"dir":"ltr"},{"str":"it","boundary":[0.40046158135928056,0.6642418981927543,0.4125392574165314,0.6795144635237715],"dir":"ltr"},{"str":"would","boundary":[0.4175600916530973,0.6642418981927543,0.47029861820096197,0.6795144635237715],"dir":"ltr"},{"str":"have","boundary":[0.4753194524375277,0.6642418981927543,0.515960535864218,0.6795144635237715],"dir":"ltr"},{"str":"violated","boundary":[0.5209813701007838,0.6642418981927543,0.5901858608969135,0.6795144635237715],"dir":"ltr"},{"str":"the","boundary":[0.5952066951334795,0.6642418981927543,0.6226631469232036,0.6795144635237715],"dir":"ltr"},{"str":"problem’s","boundary":[0.6276839811597694,0.6642418981927543,0.713018396117465,0.6795144635237715],"dir":"ltr"},{"str":"constraints.","boundary":[0.7180392303540308,0.6642418981927543,0.8152536507297423,0.6795144635237715],"dir":"ltr"},{"str":"So","boundary":[0.8202744849663083,0.6642418981927543,0.8422554600492264,0.6795144635237715],"dir":"ltr"},{"str":"your","boundary":[0.8472762942857922,0.6642418981927543,0.8868301891966908,0.6795144635237715],"dir":"ltr"},{"str":"best","boundary":[0.8918510234332565,0.6642418981927543,0.9269968630892174,0.6795144635237715],"dir":"ltr"},{"str":"selection","boundary":[0.23910303855185203,0.682568976589975,0.3148899616345031,0.6978415419209922],"dir":"ltr"},{"str":"in","boundary":[0.32093868319509034,0.682568976589975,0.3374244145072789,0.6978415419209922],"dir":"ltr"},{"str":"this","boundary":[0.34347313606786606,0.682568976589975,0.37423068753281263,0.6978415419209922],"dir":"ltr"},{"str":"step","boundary":[0.3802794090933998,0.682568976589975,0.4154252487493606,0.6978415419209922],"dir":"ltr"},{"str":"was","boundary":[0.42147397030994777,0.682568976589975,0.4533187102906861,0.6978415419209922],"dir":"ltr"},{"str":"one","boundary":[0.45936743185127327,0.682568976589975,0.49123193889593514,0.6978415419209922],"dir":"ltr"},{"str":"dime,","boundary":[0.4972806604565223,0.682568976589975,0.5443262725944226,0.6978415419209922],"dir":"ltr"},{"str":"reducing","boundary":[0.5506517330499385,0.682568976589975,0.6253514676167978,0.6978415419209922],"dir":"ltr"},{"str":"the","boundary":[0.6314001891773849,0.682568976589975,0.658856640967109,0.6978415419209922],"dir":"ltr"},{"str":"remaining","boundary":[0.6649053625276964,0.682568976589975,0.7516827731518065,0.6978415419209922],"dir":"ltr"},{"str":"amount","boundary":[0.7577314947123938,0.682568976589975,0.8236348858333011,0.6978415419209922],"dir":"ltr"},{"str":"to","boundary":[0.8296836073938884,0.682568976589975,0.8472565272218687,0.6978415419209922],"dir":"ltr"},{"str":"13","boundary":[0.8533052487824558,0.682568976589975,0.8730723127059434,0.6978415419209922],"dir":"ltr"},{"str":"cents.","boundary":[0.8791210342665304,0.682568976589975,0.9268980277695997,0.6978415419209922],"dir":"ltr"},{"str":"Giving","boundary":[0.23910303855185203,0.7008960549871956,0.29731704180652274,0.716168620318213],"dir":"ltr"},{"str":"one","boundary":[0.3022588077873946,0.7008960549871956,0.3341233148320565,0.716168620318213],"dir":"ltr"},{"str":"more","boundary":[0.33906508081292835,0.7008960549871956,0.3840944524306329,0.716168620318213],"dir":"ltr"},{"str":"dime","boundary":[0.38903621841150476,0.7008960549871956,0.4318714459337022,0.716168620318213],"dir":"ltr"},{"str":"left","boundary":[0.4368132119145741,0.7008960549871956,0.46535685222009004,0.716168620318213],"dir":"ltr"},{"str":"you","boundary":[0.47029861820096186,0.7008960549871956,0.5021631252456238,0.716168620318213],"dir":"ltr"},{"str":"with","boundary":[0.5071048912264957,0.7008960549871956,0.5444448749779637,0.716168620318213],"dir":"ltr"},{"str":"3","boundary":[0.5493866409588354,0.7008960549871956,0.559270172920579,0.716168620318213],"dir":"ltr"},{"str":"cents","boundary":[0.564211938901451,0.7008960549871956,0.6081343549394403,0.716168620318213],"dir":"ltr"},{"str":"to","boundary":[0.6130761209203123,0.7008960549871956,0.6306490407482926,0.716168620318213],"dir":"ltr"},{"str":"be","boundary":[0.6355908067291645,0.7008960549871956,0.6564648262323672,0.716168620318213],"dir":"ltr"},{"str":"given","boundary":[0.6614065922132393,0.7008960549871956,0.707542919410659,0.716168620318213],"dir":"ltr"},{"str":"with","boundary":[0.7124846853915309,0.7008960549871956,0.7498246691429988,0.716168620318213],"dir":"ltr"},{"str":"three","boundary":[0.7547664351238706,0.7008960549871956,0.7997958067415751,0.716168620318213],"dir":"ltr"},{"str":"pennies.","boundary":[0.8047375727224471,0.7008960549871956,0.8745153083723579,0.716168620318213],"dir":"ltr"},{"str":"Is","boundary":[0.27468375361412956,0.7192231333844165,0.2900625293466028,0.7344956987154339],"dir":"ltr"},{"str":"this","boundary":[0.29425314689838217,0.7192231333844165,0.32501069836332874,0.7344956987154339],"dir":"ltr"},{"str":"solution","boundary":[0.3292013159151081,0.7192231333844165,0.39842557377516136,0.7344956987154339],"dir":"ltr"},{"str":"to","boundary":[0.4026161913269407,0.7192231333844165,0.42018911115492114,0.7344956987154339],"dir":"ltr"},{"str":"the","boundary":[0.42437972870670043,0.7192231333844165,0.4518361804964246,0.7344956987154339],"dir":"ltr"},{"str":"instance","boundary":[0.45602679804820395,0.7192231333844165,0.5263184773601256,0.7344956987154339],"dir":"ltr"},{"str":"of","boundary":[0.5305090949119048,0.7192231333844165,0.5480820147398853,0.7344956987154339],"dir":"ltr"},{"str":"the","boundary":[0.5522726322916646,0.7192231333844165,0.5797290840813887,0.7344956987154339],"dir":"ltr"},{"str":"change-making","boundary":[0.5839197016331681,0.7192231333844165,0.7146195282952674,0.7344956987154339],"dir":"ltr"},{"str":"problem","boundary":[0.7188101458470468,0.7192231333844165,0.791315736318399,0.7344956987154339],"dir":"ltr"},{"str":"optimal?","boundary":[0.7955063538701783,0.7192231333844165,0.8712932769528294,0.7344956987154339],"dir":"ltr"},{"str":"Yes,","boundary":[0.8754838945046087,0.7192231333844165,0.9104715976491816,0.7344956987154339],"dir":"ltr"},{"str":"it","boundary":[0.9148203517123489,0.7192231333844165,0.9268980277695997,0.7344956987154339],"dir":"ltr"},{"str":"is.","boundary":[0.23910303855185203,0.7375502117816373,0.2561422476538982,0.7528227771126547],"dir":"ltr"},{"str":"In","boundary":[0.2611828489543876,0.7375502117816373,0.27986272436208326,0.7528227771126547],"dir":"ltr"},{"str":"fact,","boundary":[0.2849033256625726,0.7375502117816373,0.32167006456025937,0.7528227771126547],"dir":"ltr"},{"str":"one","boundary":[0.32673043292467213,0.7375502117816373,0.358594939969334,0.7528227771126547],"dir":"ltr"},{"str":"can","boundary":[0.3636355412698233,0.7375502117816373,0.39328613715505456,0.7528227771126547],"dir":"ltr"},{"str":"prove","boundary":[0.39832673845554384,0.7375502117816373,0.4477641653281861,0.7528227771126547],"dir":"ltr"},{"str":"that","boundary":[0.45280476662867547,0.7375502117816373,0.48684365070492097,0.7528227771126547],"dir":"ltr"},{"str":"the","boundary":[0.49188425200541025,0.7375502117816373,0.5193407037951343,0.7528227771126547],"dir":"ltr"},{"str":"greedy","boundary":[0.5243813050956238,0.7375502117816373,0.5825953083502945,0.7528227771126547],"dir":"ltr"},{"str":"algorithm","boundary":[0.5876359096507837,0.7375502117816373,0.6711122205996715,0.7528227771126547],"dir":"ltr"},{"str":"yields","boundary":[0.6761528219001607,0.7375502117816373,0.725590248772803,0.7528227771126547],"dir":"ltr"},{"str":"an","boundary":[0.7306308500732923,0.7375502117816373,0.7515048695764951,0.7528227771126547],"dir":"ltr"},{"str":"optimal","boundary":[0.7565454708769844,0.7375502117816373,0.8224488619978918,0.7528227771126547],"dir":"ltr"},{"str":"solution","boundary":[0.8274894632983811,0.7375502117816373,0.8967137211584343,0.7528227771126547],"dir":"ltr"},{"str":"for","boundary":[0.9017543224589237,0.7375502117816373,0.9270166301531407,0.7528227771126547],"dir":"ltr"},{"str":"every","boundary":[0.23910303855185203,0.7558772901788581,0.28632655426506365,0.7711498555098754],"dir":"ltr"},{"str":"positive","boundary":[0.2918020309718697,0.7558772901788581,0.35881237767249236,0.7711498555098754],"dir":"ltr"},{"str":"integer","boundary":[0.3642878543792984,0.7558772901788581,0.4246960017294762,0.7711498555098754],"dir":"ltr"},{"str":"amount","boundary":[0.4301714784362823,0.7558772901788581,0.4960748695571896,0.7711498555098754],"dir":"ltr"},{"str":"with","boundary":[0.5015503462639956,0.7558772901788581,0.5388903300154635,0.7711498555098754],"dir":"ltr"},{"str":"these","boundary":[0.5443658067222695,0.7558772901788581,0.589395178339974,0.7711498555098754],"dir":"ltr"},{"str":"coin","boundary":[0.5948706550467802,0.7558772901788581,0.6311234502824562,0.7711498555098754],"dir":"ltr"},{"str":"denominations.","boundary":[0.6365989269892622,0.7558772901788581,0.7678917655690662,0.7711498555098754],"dir":"ltr"},{"str":"At","boundary":[0.7733672422758724,0.7558772901788581,0.7965144741302763,0.7711498555098754],"dir":"ltr"},{"str":"the","boundary":[0.8019899508370822,0.7558772901788581,0.8294464026268064,0.7711498555098754],"dir":"ltr"},{"str":"same","boundary":[0.8349218793336125,0.7558772901788581,0.8788442953716018,0.7711498555098754],"dir":"ltr"},{"str":"time,","boundary":[0.8843197720784077,0.7558772901788581,0.9269573289613703,0.7711498555098754],"dir":"ltr"},{"str":"it","boundary":[0.23910303855185203,0.7742058958326118,0.2511807146091029,0.7894784611636292],"dir":"ltr"},{"str":"is","boundary":[0.2568340948912203,0.7742058958326118,0.2700187265281865,0.7894784611636292],"dir":"ltr"},{"str":"easy","boundary":[0.2756721068103039,0.7742058958326118,0.3130120905617718,0.7894784611636292],"dir":"ltr"},{"str":"to","boundary":[0.31866547084388924,0.7742058958326118,0.33623839067186967,0.7894784611636292],"dir":"ltr"},{"str":"give","boundary":[0.34189177095398704,0.7742058958326118,0.3770376106099479,0.7894784611636292],"dir":"ltr"},{"str":"an","boundary":[0.38269099089206526,0.7742058958326118,0.4035650103952681,0.7894784611636292],"dir":"ltr"},{"str":"example","boundary":[0.4092183906773855,0.7742058958326118,0.48170421408481423,0.7894784611636292],"dir":"ltr"},{"str":"of","boundary":[0.48735759436693155,0.7742058958326118,0.504930514194912,0.7894784611636292],"dir":"ltr"},{"str":"coin","boundary":[0.5105838944770293,0.7742058958326118,0.5468366897127054,0.7894784611636292],"dir":"ltr"},{"str":"denominations","boundary":[0.552490069994823,0.7742058958326118,0.679928331109547,0.7894784611636292],"dir":"ltr"},{"str":"that","boundary":[0.6855817113916644,0.7742058958326118,0.7196205954679098,0.7894784611636292],"dir":"ltr"},{"str":"do","boundary":[0.7252739757500272,0.7742058958326118,0.7472549508329454,0.7894784611636292],"dir":"ltr"},{"str":"not","boundary":[0.7529083311150628,0.7742058958326118,0.7814717384845024,0.7894784611636292],"dir":"ltr"},{"str":"yield","boundary":[0.7871251187666197,0.7742058958326118,0.8288731577730253,0.7894784611636292],"dir":"ltr"},{"str":"an","boundary":[0.8345265380551429,0.7742058958326118,0.8554005575583457,0.7894784611636292],"dir":"ltr"},{"str":"optimal","boundary":[0.8610539378404631,0.7742058958326118,0.9269573289613704,0.7894784611636292],"dir":"ltr"},{"str":"solution","boundary":[0.23910303855185203,0.7925329742298328,0.30832729641190526,0.80780553956085],"dir":"ltr"},{"str":"for","boundary":[0.31326906239277713,0.7925329742298328,0.3385313700869942,0.80780553956085],"dir":"ltr"},{"str":"some","boundary":[0.34347313606786606,0.7925329742298328,0.3885025076855706,0.80780553956085],"dir":"ltr"},{"str":"amounts—e.g.,","boundary":[0.39344427366644247,0.7925329742298328,0.5203092899273853,0.80780553956085],"dir":"ltr"},{"str":"d1","boundary":[0.5252550093210419,0.7931438768430735,0.5425491983492879,0.810153133857865],"dir":"ltr"},{"str":"=","boundary":[0.5467257857420309,0.7958153551174514,0.5621440956023512,0.8110879204484686],"dir":"ltr"},{"str":"25,d2","boundary":[0.5665343604997578,0.7925317535712828,0.6146503903991155,0.810153133857865],"dir":"ltr"},{"str":"=","boundary":[0.6196404698731055,0.7958153551174514,0.6350587797334257,0.8110879204484686],"dir":"ltr"},{"str":"10,d3","boundary":[0.639452998043617,0.7925317535712828,0.6880988047005691,0.810153133857865],"dir":"ltr"},{"str":"=","boundary":[0.6926007889258108,0.7958153551174514,0.708019098786131,0.8110879204484686],"dir":"ltr"},{"str":"1","boundary":[0.7124093636835377,0.7925317535712828,0.7222928956452814,0.8078043189023],"dir":"ltr"},{"str":"and","boundary":[0.7262858425578259,0.7925317535712828,0.7581503496024877,0.8078043189023],"dir":"ltr"},{"str":"n","boundary":[0.7630921155833595,0.7931426561845234,0.7738651654216603,0.8084152215155407],"dir":"ltr"},{"str":"=","boundary":[0.7782593837318516,0.7958153551174514,0.7936776935921719,0.8110879204484686],"dir":"ltr"},{"str":"30.","boundary":[0.7980679584895785,0.7925317535712828,0.822925041373364,0.8078043189023],"dir":"ltr"},{"str":"The","boundary":[0.27468157004265337,0.8108588319685035,0.30794953862588287,0.8261313972995207],"dir":"ltr"},{"str":"approach","boundary":[0.31304944111814265,0.8108588319685035,0.39324441945573146,0.8261313972995207],"dir":"ltr"},{"str":"applied","boundary":[0.39834432194799124,0.8108588319685035,0.46207333603731493,0.8261313972995207],"dir":"ltr"},{"str":"in","boundary":[0.4671732385295747,0.8108588319685035,0.48365896984176326,0.8261313972995207],"dir":"ltr"},{"str":"the","boundary":[0.488758872334023,0.8108588319685035,0.5162153241237472,0.8261313972995207],"dir":"ltr"},{"str":"opening","boundary":[0.5213152266160069,0.8108588319685035,0.5905394844760602,0.8261313972995207],"dir":"ltr"},{"str":"paragraph","boundary":[0.5956393869683199,0.8108588319685035,0.6835237531721454,0.8261313972995207],"dir":"ltr"},{"str":"to","boundary":[0.6886236556644052,0.8108588319685035,0.7061965754923857,0.8261313972995207],"dir":"ltr"},{"str":"the","boundary":[0.7112964779846453,0.8108588319685035,0.7387529297743695,0.8261313972995207],"dir":"ltr"},{"str":"change-making","boundary":[0.7438528322666293,0.8108588319685035,0.8745526589287288,0.8261313972995207],"dir":"ltr"},{"str":"prob-","boundary":[0.8796525614209885,0.8108588319685035,0.9268958441981235,0.8261313972995207],"dir":"ltr"},{"str":"lem","boundary":[0.23910085498037587,0.8291874376222574,0.2709455949611142,0.8444600029532747],"dir":"ltr"},{"str":"is","boundary":[0.27723152128878326,0.8291874376222574,0.2904161529257494,0.8444600029532747],"dir":"ltr"},{"str":"called","boundary":[0.29670207925341846,0.8291874376222574,0.3472266946418525,0.8444600029532747],"dir":"ltr"},{"str":"greedy","boundary":[0.3535066908503445,0.8291874376222574,0.4093881805620436,0.8444600029532747],"dir":"ltr"},{"str":".","boundary":[0.409350623140589,0.8291874376222574,0.4142923891214609,0.8444600029532747],"dir":"ltr"},{"str":"Computer","boundary":[0.42057831544912994,0.8291874376222574,0.5084429145890318,0.8444600029532747],"dir":"ltr"},{"str":"scientists","boundary":[0.5147288409167009,0.8291874376222574,0.5916029525151438,0.8444600029532747],"dir":"ltr"},{"str":"consider","boundary":[0.5978888788428127,0.8291874376222574,0.670394469314165,0.8444600029532747],"dir":"ltr"},{"str":"it","boundary":[0.676680395641834,0.8291874376222574,0.6887580716990848,0.8444600029532747],"dir":"ltr"},{"str":"a","boundary":[0.6950439980267539,0.8291874376222574,0.7049275299884976,0.8444600029532747],"dir":"ltr"},{"str":"general","boundary":[0.7112134563161668,0.8291874376222574,0.7749227033415671,0.8444600029532747],"dir":"ltr"},{"str":"design","boundary":[0.7812086296692361,0.8291874376222574,0.8361413003126079,0.8444600029532747],"dir":"ltr"},{"str":"technique","boundary":[0.8424272266402768,0.8291874376222574,0.9270104931688798,0.8444600029532747],"dir":"ltr"},{"str":"despite","boundary":[0.23910085498037587,0.8475145160194781,0.30061595791026896,0.8627870813504954],"dir":"ltr"},{"str":"the","boundary":[0.30739606083602516,0.8475145160194781,0.3348525126257494,0.8627870813504954],"dir":"ltr"},{"str":"fact","boundary":[0.3416326155515056,0.8475145160194781,0.37345758846832044,0.8627870813504954],"dir":"ltr"},{"str":"that","boundary":[0.3802376913940767,0.8475145160194781,0.41427657547032215,0.8627870813504954],"dir":"ltr"},{"str":"it","boundary":[0.42105667839607835,0.8475145160194781,0.43313435445332926,0.8627870813504954],"dir":"ltr"},{"str":"is","boundary":[0.4399144573790854,0.8475145160194781,0.45309908901605156,0.8627870813504954],"dir":"ltr"},{"str":"applicable","boundary":[0.4598791919418078,0.8475145160194781,0.5477635581456332,0.8627870813504954],"dir":"ltr"},{"str":"to","boundary":[0.5545436610713895,0.8475145160194781,0.57211658089937,0.8627870813504954],"dir":"ltr"},{"str":"optimization","boundary":[0.5788966838251262,0.8475145160194781,0.687635302468231,0.8627870813504954],"dir":"ltr"},{"str":"problems","boundary":[0.694415405393987,0.8475145160194781,0.7746103837315759,0.8627870813504954],"dir":"ltr"},{"str":"only.","boundary":[0.7813904866573321,0.8475145160194781,0.8218734335726345,0.8627870813504954],"dir":"ltr"},{"str":"The","boundary":[0.8286535364983908,0.8475145160194781,0.8619215050816202,0.8627870813504954],"dir":"ltr"},{"str":"greedy","boundary":[0.8687016080073765,0.8475145160194781,0.9269156112620471,0.8627870813504954],"dir":"ltr"},{"str":"approach","boundary":[0.23910085498037587,0.865841594416699,0.3192958333179647,0.8811141597477161],"dir":"ltr"},{"str":"suggests","boundary":[0.32524571955893444,0.865841594416699,0.395537398870856,0.8811141597477161],"dir":"ltr"},{"str":"constructing","boundary":[0.40148728511182574,0.865841594416699,0.5069248040797081,0.8811141597477161],"dir":"ltr"},{"str":"a","boundary":[0.5128746903206779,0.865841594416699,0.5227582222824216,0.8811141597477161],"dir":"ltr"},{"str":"solution","boundary":[0.5287081085233913,0.865841594416699,0.5979323663834445,0.8811141597477161],"dir":"ltr"},{"str":"through","boundary":[0.6038822526244143,0.865841594416699,0.6719995549047523,0.8811141597477161],"dir":"ltr"},{"str":"a","boundary":[0.677949441145722,0.865841594416699,0.6878329731074656,0.8811141597477161],"dir":"ltr"},{"str":"sequence","boundary":[0.6937828593484355,0.865841594416699,0.772870882106309,0.8811141597477161],"dir":"ltr"},{"str":"of","boundary":[0.7788207683472788,0.865841594416699,0.7963936881752591,0.8811141597477161],"dir":"ltr"},{"str":"steps,","boundary":[0.8023435744162288,0.865841594416699,0.8490333794035062,0.8811141597477161],"dir":"ltr"},{"str":"each","boundary":[0.8552204704115578,0.865841594416699,0.8947545982585329,0.8811141597477161],"dir":"ltr"},{"str":"ex-","boundary":[0.9007044844995027,0.865841594416699,0.9270539807095115,0.8811141597477161],"dir":"ltr"},{"str":"panding","boundary":[0.23910085498037587,0.8841686728139196,0.30832511284042907,0.8994412381449368],"dir":"ltr"},{"str":"a","boundary":[0.3126145657118259,0.8841686728139196,0.32249809767356963,0.8994412381449368],"dir":"ltr"},{"str":"partially","boundary":[0.32678755054496644,0.8841686728139196,0.3981861854366033,0.8994412381449368],"dir":"ltr"},{"str":"constructed","boundary":[0.4024756383080001,0.8841686728139196,0.502417913505153,0.8994412381449368],"dir":"ltr"},{"str":"solution","boundary":[0.5067073663765497,0.8841686728139196,0.5759316242366029,0.8994412381449368],"dir":"ltr"},{"str":"obtained","boundary":[0.5802210771079997,0.8841686728139196,0.6560277672545743,0.8994412381449368],"dir":"ltr"},{"str":"so","boundary":[0.660317220125971,0.8841686728139196,0.6789970955336667,0.8994412381449368],"dir":"ltr"},{"str":"far,","boundary":[0.6832865484050635,0.8841686728139196,0.7120278593498145,0.8994412381449368],"dir":"ltr"},{"str":"until","boundary":[0.7164359146047522,0.8841686728139196,0.7559898095156506,0.8994412381449368],"dir":"ltr"},{"str":"a","boundary":[0.7602792623870475,0.8841686728139196,0.7701627943487911,0.8994412381449368],"dir":"ltr"},{"str":"complete","boundary":[0.774452247220188,0.8841686728139196,0.853520502914138,0.8994412381449368],"dir":"ltr"},{"str":"solution","boundary":[0.8578099557855347,0.8841686728139196,0.9270342136455879,0.8994412381449368],"dir":"ltr"},{"str":"315","boundary":[0.894023216893364,0.932933973915858,0.9269946795177411,0.9482065392468751],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92706,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":371,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/8f2e9dcbd3c48b457029079b2600f0af.jpg","blurred":"/storage/books/4a8b03583f119702/pages/d426b350fdfaaefbf7e79d6ed4a1abf3.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07289,0.05179]},"elements":[{"words":[{"str":"10","boundary":[0.14421784044919886,0.07999453587206534,0.24707030063050256,0.15330318671872986],"dir":"ltr"},{"str":"Iterative","boundary":[0.14421784044919886,0.17005356781848974,0.34214199476897206,0.20670781659232623],"dir":"ltr"},{"str":"Improvement","boundary":[0.3579398718994813,0.17005356781848974,0.6769810842198252,0.20670781659232623],"dir":"ltr"},{"str":"The","boundary":[0.23910077902799318,0.27434437041309123,0.27205247458844684,0.2896169357441086],"dir":"ltr"},{"str":"most","boundary":[0.2767175016743899,0.27434437041309123,0.3173585851010802,0.2896169357441086],"dir":"ltr"},{"str":"successful","boundary":[0.32202361218702324,0.27434437041309123,0.4054801560719875,0.2896169357441086],"dir":"ltr"},{"str":"men","boundary":[0.4101451831579306,0.27434437041309123,0.44637821132968314,0.2896169357441086],"dir":"ltr"},{"str":"in","boundary":[0.45104323841562627,0.27434437041309123,0.4675289697278149,0.2896169357441086],"dir":"ltr"},{"str":"the","boundary":[0.47219399681375795,0.27434437041309123,0.497456304507975,0.2896169357441086],"dir":"ltr"},{"str":"end","boundary":[0.502121331593918,0.27434437041309123,0.5328788830588647,0.2896169357441086],"dir":"ltr"},{"str":"are","boundary":[0.5375439101448076,0.27434437041309123,0.5638934063548166,0.2896169357441086],"dir":"ltr"},{"str":"those","boundary":[0.5685584334407595,0.27434437041309123,0.6125006165426723,0.2896169357441086],"dir":"ltr"},{"str":"whose","boundary":[0.6171656436286154,0.27434437041309123,0.6698844031125565,0.2896169357441086],"dir":"ltr"},{"str":"success","boundary":[0.6745494301984996,0.27434437041309123,0.7349378104847539,0.2896169357441086],"dir":"ltr"},{"str":"is","boundary":[0.739602837570697,0.27434437041309123,0.7527874692076632,0.2896169357441086],"dir":"ltr"},{"str":"the","boundary":[0.7574524962936063,0.27434437041309123,0.7827148039878233,0.2896169357441086],"dir":"ltr"},{"str":"result","boundary":[0.7873798310737662,0.27434437041309123,0.8335161582711861,0.2896169357441086],"dir":"ltr"},{"str":"of","boundary":[0.838181185357129,0.27434437041309123,0.8557541051851095,0.2896169357441086],"dir":"ltr"},{"str":"steady","boundary":[0.23910077902799318,0.2926729760668451,0.2918195385119343,0.30794554139786245],"dir":"ltr"},{"str":"accretion.","boundary":[0.29676130449280624,0.2926729760668451,0.378577182072121,0.30794554139786245],"dir":"ltr"},{"str":"—Alexander","boundary":[0.5355551505775925,0.31459936951926604,0.6410355030781558,0.32910835257342996],"dir":"ltr"},{"str":"Graham","boundary":[0.645767753181439,0.31459936951926604,0.7135778925582476,0.32910835257342996],"dir":"ltr"},{"str":"Bell","boundary":[0.7183101426615308,0.31459936951926604,0.7516987961680293,0.32910835257342996],"dir":"ltr"},{"str":"(1835–1910)","boundary":[0.7564310462713125,0.31459936951926604,0.8555453956567448,0.32910835257342996],"dir":"ltr"},{"str":"he","boundary":[0.278654351319837,0.40766237139448674,0.29952837082303985,0.4229349367255041],"dir":"ltr"},{"str":"greedy","boundary":[0.3035806189273547,0.40766237139448674,0.36179462218202546,0.4229349367255041],"dir":"ltr"},{"str":"strategy,","boundary":[0.3658468702863404,0.40766237139448674,0.4370478345387424,0.4229349367255041],"dir":"ltr"},{"str":"considered","boundary":[0.4412779862183688,0.40766237139448674,0.5346575961929237,0.4229349367255041],"dir":"ltr"},{"str":"in","boundary":[0.5387098442972388,0.40766237139448674,0.5551955756094273,0.4229349367255041],"dir":"ltr"},{"str":"the","boundary":[0.5592478237137422,0.40766237139448674,0.5867042755034663,0.4229349367255041],"dir":"ltr"},{"str":"preceding","boundary":[0.5907565236077813,0.40766237139448674,0.6753397901363843,0.4229349367255041],"dir":"ltr"},{"str":"chapter,","boundary":[0.6793920382406992,0.40766237139448674,0.7487744326121403,0.4229349367255041],"dir":"ltr"},{"str":"constructs","boundary":[0.7530045842917666,0.40766237139448674,0.8397622278519533,0.4229349367255041],"dir":"ltr"},{"str":"a","boundary":[0.8438144759562682,0.40766237139448674,0.8536980079180119,0.4229349367255041],"dir":"ltr"},{"str":"solution","boundary":[0.8577502560223269,0.40766237139448674,0.9269745138823802,0.4229349367255041],"dir":"ltr"},{"str":"to","boundary":[0.278654351319837,0.4259894497917076,0.29622727114781744,0.4412620151227249],"dir":"ltr"},{"str":"an","boundary":[0.3022364585805576,0.4259894497917076,0.3231104780837604,0.4412620151227249],"dir":"ltr"},{"str":"optimization","boundary":[0.3291196655165006,0.4259894497917076,0.43785828415960537,0.4412620151227249],"dir":"ltr"},{"str":"problem","boundary":[0.4438674715923456,0.4259894497917076,0.5163730620636977,0.4412620151227249],"dir":"ltr"},{"str":"piece","boundary":[0.522382249496438,0.4259894497917076,0.5674116211141425,0.4412620151227249],"dir":"ltr"},{"str":"by","boundary":[0.5734208085468826,0.4259894497917076,0.5942948280500854,0.4412620151227249],"dir":"ltr"},{"str":"piece,","boundary":[0.6003040154828256,0.4259894497917076,0.6495437717162329,0.4412620151227249],"dir":"ltr"},{"str":"always","boundary":[0.6558099309799785,0.4259894497917076,0.712916978654934,0.4412620151227249],"dir":"ltr"},{"str":"adding","boundary":[0.7189261660876742,0.4259894497917076,0.7771599364062683,0.4412620151227249],"dir":"ltr"},{"str":"a","boundary":[0.7831691238390085,0.4259894497917076,0.7930526558007521,0.4412620151227249],"dir":"ltr"},{"str":"locally","boundary":[0.7990618432334925,0.4259894497917076,0.855081702392656,0.4412620151227249],"dir":"ltr"},{"str":"optimal","boundary":[0.8610908898253963,0.4259894497917076,0.9269942809463037,0.4412620151227249],"dir":"ltr"},{"str":"Tpiece","boundary":[0.23910045640893854,0.40636422817578705,0.28412982802664305,0.45958909351994576],"dir":"ltr"},{"str":"to","boundary":[0.2910087662720167,0.4443165281889284,0.30858168609999714,0.45958909351994576],"dir":"ltr"},{"str":"a","boundary":[0.3154606243453708,0.4443165281889284,0.32534415630711455,0.45958909351994576],"dir":"ltr"},{"str":"partially","boundary":[0.33222309455248816,0.4443165281889284,0.40362172944412505,0.45958909351994576],"dir":"ltr"},{"str":"constructed","boundary":[0.4105006676894987,0.4443165281889284,0.5104429428866516,0.45958909351994576],"dir":"ltr"},{"str":"solution.","boundary":[0.5173218811320252,0.4443165281889284,0.5914879049729503,0.45958909351994576],"dir":"ltr"},{"str":"In","boundary":[0.598366843218324,0.4443165281889284,0.6170467186260197,0.45958909351994576],"dir":"ltr"},{"str":"this","boundary":[0.6239256568713933,0.4443165281889284,0.65468320833634,0.45958909351994576],"dir":"ltr"},{"str":"chapter,","boundary":[0.6615621465817135,0.4443165281889284,0.7309445409531548,0.45958909351994576],"dir":"ltr"},{"str":"we","boundary":[0.7383176557966155,0.4443165281889284,0.7624730079111173,0.45958909351994576],"dir":"ltr"},{"str":"discuss","boundary":[0.7693519461564908,0.4443165281889284,0.8286729049908769,0.45958909351994576],"dir":"ltr"},{"str":"a","boundary":[0.8355518432362504,0.4443165281889284,0.8454353751979942,0.45958909351994576],"dir":"ltr"},{"str":"different","boundary":[0.8523143134433679,0.4443165281889284,0.9269942809463037,0.45958909351994576],"dir":"ltr"},{"str":"approach","boundary":[0.23910045640893854,0.4626436065861492,0.31929543474652733,0.47791617191716657],"dir":"ltr"},{"str":"to","boundary":[0.3249883491564918,0.4626436065861492,0.34256126898447214,0.47791617191716657],"dir":"ltr"},{"str":"designing","boundary":[0.3482541833944366,0.4626436065861492,0.4295561173117407,0.47791617191716657],"dir":"ltr"},{"str":"algorithms","boundary":[0.4352490317217051,0.4626436065861492,0.5264147305368295,0.47791617191716657],"dir":"ltr"},{"str":"for","boundary":[0.5321076449467939,0.4626436065861492,0.5573699526410109,0.47791617191716657],"dir":"ltr"},{"str":"optimization","boundary":[0.5630628670509754,0.4626436065861492,0.6718014856940802,0.47791617191716657],"dir":"ltr"},{"str":"problems.","boundary":[0.6774944001040445,0.4626436065861492,0.7615439559067134,0.47791617191716657],"dir":"ltr"},{"str":"It","boundary":[0.7672368703166778,0.4626436065861492,0.7815086904694357,0.47791617191716657],"dir":"ltr"},{"str":"starts","boundary":[0.7872016048794002,0.4626436065861492,0.8333181650128966,0.47791617191716657],"dir":"ltr"},{"str":"with","boundary":[0.8390110794228609,0.4626436065861492,0.8763510631743288,0.47791617191716657],"dir":"ltr"},{"str":"some","boundary":[0.882043977584293,0.4626436065861492,0.9270733492019976,0.47791617191716657],"dir":"ltr"},{"str":"feasible","boundary":[0.23910045640893854,0.48097068498337003,0.3050038475298459,0.4962432503143874],"dir":"ltr"},{"str":"solution","boundary":[0.31059792662019287,0.48097068498337003,0.37982218448024613,0.4962432503143874],"dir":"ltr"},{"str":"(a","boundary":[0.3854162635705931,0.48097068498337003,0.40298918339857354,0.4962432503143874],"dir":"ltr"},{"str":"solution","boundary":[0.4085832624889204,0.48097068498337003,0.4778075203489737,0.4962432503143874],"dir":"ltr"},{"str":"that","boundary":[0.4834015994393206,0.48097068498337003,0.5174404835155662,0.4962432503143874],"dir":"ltr"},{"str":"satisfies","boundary":[0.523034562605913,0.48097068498337003,0.5889379537268203,0.4962432503143874],"dir":"ltr"},{"str":"all","boundary":[0.5945320328171674,0.48097068498337003,0.6154060523203702,0.4962432503143874],"dir":"ltr"},{"str":"the","boundary":[0.6210001314107173,0.48097068498337003,0.6484565832004414,0.4962432503143874],"dir":"ltr"},{"str":"constraints","boundary":[0.6540506622907882,0.48097068498337003,0.7474105052014198,0.4962432503143874],"dir":"ltr"},{"str":"of","boundary":[0.7530045842917669,0.48097068498337003,0.7705775041197472,0.4962432503143874],"dir":"ltr"},{"str":"the","boundary":[0.7761715832100943,0.48097068498337003,0.8036280349998184,0.4962432503143874],"dir":"ltr"},{"str":"problem)","boundary":[0.8092221140901653,0.48097068498337003,0.8894170924277541,0.4962432503143874],"dir":"ltr"},{"str":"and","boundary":[0.8950111715181011,0.48097068498337003,0.9268756785627629,0.4962432503143874],"dir":"ltr"},{"str":"proceeds","boundary":[0.23910045640893854,0.49929776338059084,0.3159943350713049,0.5145703287116081],"dir":"ltr"},{"str":"to","boundary":[0.3226953697413672,0.49929776338059084,0.3402682895693476,0.5145703287116081],"dir":"ltr"},{"str":"improve","boundary":[0.34696932423940985,0.49929776338059084,0.41836795913104674,0.5145703287116081],"dir":"ltr"},{"str":"it","boundary":[0.4250689938011091,0.49929776338059084,0.4371466698583599,0.5145703287116081],"dir":"ltr"},{"str":"by","boundary":[0.4438477045284222,0.49929776338059084,0.46472172403162504,0.5145703287116081],"dir":"ltr"},{"str":"repeated","boundary":[0.4714227587016873,0.49929776338059084,0.5472096817843385,0.5145703287116081],"dir":"ltr"},{"str":"applications","boundary":[0.5539107164544006,0.49929776338059084,0.6571738583906993,0.5145703287116081],"dir":"ltr"},{"str":"of","boundary":[0.6638748930607616,0.49929776338059084,0.681447812888742,0.5145703287116081],"dir":"ltr"},{"str":"some","boundary":[0.6881488475588042,0.49929776338059084,0.7331782191765088,0.5145703287116081],"dir":"ltr"},{"str":"simple","boundary":[0.739879253846571,0.49929776338059084,0.7958991130057346,0.5145703287116081],"dir":"ltr"},{"str":"step.","boundary":[0.8026001476757968,0.49929776338059084,0.8418970707556899,0.5145703287116081],"dir":"ltr"},{"str":"This","boundary":[0.8485981054257522,0.49929776338059084,0.8851671736842041,0.5145703287116081],"dir":"ltr"},{"str":"step","boundary":[0.8918682083542663,0.49929776338059084,0.9270140480102271,0.5145703287116081],"dir":"ltr"},{"str":"typically","boundary":[0.23910045640893854,0.5176248417778117,0.3115862798163672,0.532897407108829],"dir":"ltr"},{"str":"involves","boundary":[0.3186035875092053,0.5176248417778117,0.38891503388505033,0.532897407108829],"dir":"ltr"},{"str":"a","boundary":[0.3959323415778884,0.5176248417778117,0.4058158735396322,0.532897407108829],"dir":"ltr"},{"str":"small,","boundary":[0.41283318123247026,0.5176248417778117,0.46280431883104667,0.532897407108829],"dir":"ltr"},{"str":"localized","boundary":[0.47033557018589545,0.5176248417778117,0.5461224932685466,0.532897407108829],"dir":"ltr"},{"str":"change","boundary":[0.5531398009613846,0.5176248417778117,0.6135479483115625,0.532897407108829],"dir":"ltr"},{"str":"yielding","boundary":[0.6205652560044005,0.5176248417778117,0.6886825582847385,0.532897407108829],"dir":"ltr"},{"str":"a","boundary":[0.6956998659775765,0.5176248417778117,0.7055833979393202,0.532897407108829],"dir":"ltr"},{"str":"feasible","boundary":[0.7126007056321584,0.5176248417778117,0.7785040967530658,0.532897407108829],"dir":"ltr"},{"str":"solution","boundary":[0.7855214044459037,0.5176248417778117,0.8547456623059569,0.532897407108829],"dir":"ltr"},{"str":"with","boundary":[0.861762969998795,0.5176248417778117,0.899102953750263,0.532897407108829],"dir":"ltr"},{"str":"an","boundary":[0.9061202614431009,0.5176248417778117,0.9269942809463037,0.532897407108829],"dir":"ltr"},{"str":"improved","boundary":[0.23910045640893854,0.5359519201750325,0.3214895788420345,0.5512244855060499],"dir":"ltr"},{"str":"value","boundary":[0.3288824607494188,0.5359519201750325,0.3750187879468386,0.5512244855060499],"dir":"ltr"},{"str":"of","boundary":[0.3824116698542229,0.5359519201750325,0.39998458968220335,0.5512244855060499],"dir":"ltr"},{"str":"the","boundary":[0.4073774715895877,0.5359519201750325,0.43483392337931187,0.5512244855060499],"dir":"ltr"},{"str":"objective","boundary":[0.44222680528669617,0.5359519201750325,0.5202078724648544,0.5512244855060499],"dir":"ltr"},{"str":"function.","boundary":[0.5276007543722387,0.5359519201750325,0.6039411552447475,0.5512244855060499],"dir":"ltr"},{"str":"When","boundary":[0.6113340371521317,0.5359519201750325,0.6626098009696583,0.5512244855060499],"dir":"ltr"},{"str":"no","boundary":[0.6700026828770426,0.5359519201750325,0.6919836579599608,0.5512244855060499],"dir":"ltr"},{"str":"such","boundary":[0.699376539867345,0.5359519201750325,0.7378234791985282,0.5512244855060499],"dir":"ltr"},{"str":"change","boundary":[0.7452163611059124,0.5359519201750325,0.8056245084560902,0.5512244855060499],"dir":"ltr"},{"str":"improves","boundary":[0.8130173903634745,0.5359519201750325,0.8921054131213481,0.5512244855060499],"dir":"ltr"},{"str":"the","boundary":[0.8994982950287325,0.5359519201750325,0.9269547468184566,0.5512244855060499],"dir":"ltr"},{"str":"value","boundary":[0.23910045640893854,0.5542789985722533,0.28523678360635835,0.5695515639032707],"dir":"ltr"},{"str":"of","boundary":[0.29023785077900077,0.5542789985722533,0.30781077060698114,0.5695515639032707],"dir":"ltr"},{"str":"the","boundary":[0.31281183777962346,0.5542789985722533,0.3402682895693476,0.5695515639032707],"dir":"ltr"},{"str":"objective","boundary":[0.34526935674198994,0.5542789985722533,0.42325042392014817,0.5695515639032707],"dir":"ltr"},{"str":"function,","boundary":[0.4282514910927905,0.5542789985722533,0.5045918919652992,0.5695515639032707],"dir":"ltr"},{"str":"the","boundary":[0.509612726201865,0.5542789985722533,0.5370691779915892,0.5695515639032707],"dir":"ltr"},{"str":"algorithm","boundary":[0.5420702451642315,0.5542789985722533,0.6255465561131193,0.5695515639032707],"dir":"ltr"},{"str":"returns","boundary":[0.6305476232857615,0.5542789985722533,0.6920627262156547,0.5695515639032707],"dir":"ltr"},{"str":"the","boundary":[0.697063793388297,0.5542789985722533,0.7245202451780212,0.5695515639032707],"dir":"ltr"},{"str":"last","boundary":[0.7295213123506635,0.5542789985722533,0.7591719082358948,0.5695515639032707],"dir":"ltr"},{"str":"feasible","boundary":[0.7641729754085371,0.5542789985722533,0.8300763665294445,0.5695515639032707],"dir":"ltr"},{"str":"solution","boundary":[0.8350774337020869,0.5542789985722533,0.90430169156214,0.5695515639032707],"dir":"ltr"},{"str":"as","boundary":[0.9093027587347824,0.5542789985722533,0.9268756785627628,0.5695515639032707],"dir":"ltr"},{"str":"optimal","boundary":[0.23910045640893854,0.5726060769694741,0.3050038475298459,0.5878786423004915],"dir":"ltr"},{"str":"and","boundary":[0.30994561351071775,0.5726060769694741,0.3418101205553796,0.5878786423004915],"dir":"ltr"},{"str":"stops.","boundary":[0.34675188653625144,0.5726060769694741,0.3945486471032443,0.5878786423004915],"dir":"ltr"},{"str":"There","boundary":[0.27468117147121607,0.5909331553666949,0.3255220598824259,0.6062057206977122],"dir":"ltr"},{"str":"can","boundary":[0.3307207976943031,0.5909331553666949,0.36037139357953435,0.6062057206977122],"dir":"ltr"},{"str":"be","boundary":[0.3655701313914116,0.5909331553666949,0.3864441508946144,0.6062057206977122],"dir":"ltr"},{"str":"several","boundary":[0.39164288870649167,0.5909331553666949,0.45205103605666946,0.6062057206977122],"dir":"ltr"},{"str":"obstacles","boundary":[0.45724977386854665,0.5909331553666949,0.5352308410467049,0.6062057206977122],"dir":"ltr"},{"str":"to","boundary":[0.5404295788585821,0.5909331553666949,0.5580024986865625,0.6062057206977122],"dir":"ltr"},{"str":"the","boundary":[0.5632012364984397,0.5909331553666949,0.5906576882881638,0.6062057206977122],"dir":"ltr"},{"str":"successful","boundary":[0.595856426100041,0.5909331553666949,0.6804199255647205,0.6062057206977122],"dir":"ltr"},{"str":"implementation","boundary":[0.6856186633765978,0.5909331553666949,0.8218137338094268,0.6062057206977122],"dir":"ltr"},{"str":"of","boundary":[0.827012471621304,0.5909331553666949,0.8445853914492844,0.6062057206977122],"dir":"ltr"},{"str":"this","boundary":[0.8497841292611615,0.5909331553666949,0.8805416807261082,0.6062057206977122],"dir":"ltr"},{"str":"idea.","boundary":[0.8857404185379854,0.5909331553666949,0.9269349797545333,0.6062057206977122],"dir":"ltr"},{"str":"First,","boundary":[0.23910045640893854,0.6092602337639157,0.2828449688716164,0.624532799094933],"dir":"ltr"},{"str":"we","boundary":[0.28750999595755944,0.6092602337639157,0.3116653480720612,0.624532799094933],"dir":"ltr"},{"str":"need","boundary":[0.3162513069023103,0.6092602337639157,0.35799934590871596,0.624532799094933],"dir":"ltr"},{"str":"an","boundary":[0.362585304738965,0.6092602337639157,0.38345932424216783,0.624532799094933],"dir":"ltr"},{"str":"initial","boundary":[0.3880452830724169,0.6092602337639157,0.43748270994505917,0.624532799094933],"dir":"ltr"},{"str":"feasible","boundary":[0.44206866877530826,0.6092602337639157,0.5079720598962156,0.624532799094933],"dir":"ltr"},{"str":"solution.","boundary":[0.5125580187264647,0.6092602337639157,0.5867240425673897,0.624532799094933],"dir":"ltr"},{"str":"For","boundary":[0.5913100013976389,0.6092602337639157,0.6209803643467936,0.624532799094933],"dir":"ltr"},{"str":"some","boundary":[0.6255663231770427,0.6092602337639157,0.6705956947947472,0.624532799094933],"dir":"ltr"},{"str":"problems,","boundary":[0.6751816536249964,0.6092602337639157,0.7592312094276652,0.624532799094933],"dir":"ltr"},{"str":"we","boundary":[0.7638962365136082,0.6092602337639157,0.78805158862811,0.624532799094933],"dir":"ltr"},{"str":"can","boundary":[0.792637547458359,0.6092602337639157,0.8222881433435902,0.624532799094933],"dir":"ltr"},{"str":"always","boundary":[0.8268741021738394,0.6092602337639157,0.8839811498487948,0.624532799094933],"dir":"ltr"},{"str":"start","boundary":[0.888567108679044,0.6092602337639157,0.9269942809463037,0.624532799094933],"dir":"ltr"},{"str":"with","boundary":[0.23910045640893854,0.6275873121611365,0.2764404401604065,0.6428598774921538],"dir":"ltr"},{"str":"a","boundary":[0.27995897753878723,0.6275873121611365,0.289842509500531,0.6428598774921538],"dir":"ltr"},{"str":"trivial","boundary":[0.2933610468789118,0.6275873121611365,0.3438856622673458,0.6428598774921538],"dir":"ltr"},{"str":"solution","boundary":[0.3474041996457266,0.6275873121611365,0.41662845750577987,0.6428598774921538],"dir":"ltr"},{"str":"or","boundary":[0.42014699488416063,0.6275873121611365,0.43882687029185635,0.6428598774921538],"dir":"ltr"},{"str":"use","boundary":[0.44234540767023717,0.6275873121611365,0.47090881503967663,0.6428598774921538],"dir":"ltr"},{"str":"an","boundary":[0.47442735241805734,0.6275873121611365,0.49530137192126017,0.6428598774921538],"dir":"ltr"},{"str":"approximate","boundary":[0.49881990929964093,0.6275873121611365,0.6075585279427457,0.6428598774921538],"dir":"ltr"},{"str":"solution","boundary":[0.6110770653211265,0.6275873121611365,0.6803013231811798,0.6428598774921538],"dir":"ltr"},{"str":"obtained","boundary":[0.6838198605595606,0.6275873121611365,0.7596265507061352,0.6428598774921538],"dir":"ltr"},{"str":"by","boundary":[0.763145088084516,0.6275873121611365,0.7840191075877188,0.6428598774921538],"dir":"ltr"},{"str":"some","boundary":[0.7875376449660996,0.6275873121611365,0.832567016583804,0.6428598774921538],"dir":"ltr"},{"str":"other","boundary":[0.8360855539621849,0.6275873121611365,0.8822218811596048,0.6428598774921538],"dir":"ltr"},{"str":"(e.g.,","boundary":[0.8857404185379855,0.6275873121611365,0.9269349797545334,0.6428598774921538],"dir":"ltr"},{"str":"greedy)","boundary":[0.23910045640893854,0.6459143905583572,0.3050038475298459,0.6611869558893746],"dir":"ltr"},{"str":"algorithm.","boundary":[0.30968864167971244,0.6459143905583572,0.39810671860947205,0.6611869558893746],"dir":"ltr"},{"str":"But","boundary":[0.4027915127593386,0.6459143905583572,0.434636252740077,0.6611869558893746],"dir":"ltr"},{"str":"for","boundary":[0.4393210468899435,0.6459143905583572,0.46458335458416056,0.6611869558893746],"dir":"ltr"},{"str":"others,","boundary":[0.46926814873402706,0.6459143905583572,0.5269484412627635,0.6611869558893746],"dir":"ltr"},{"str":"finding","boundary":[0.5316925366044006,0.6459143905583572,0.5910332625027102,0.6611869558893746],"dir":"ltr"},{"str":"an","boundary":[0.5957180566525766,0.6459143905583572,0.6165920761557794,0.6611869558893746],"dir":"ltr"},{"str":"initial","boundary":[0.6212768703056459,0.6459143905583572,0.6707142971782882,0.6611869558893746],"dir":"ltr"},{"str":"solution","boundary":[0.6753990913281547,0.6459143905583572,0.7446233491882079,0.6611869558893746],"dir":"ltr"},{"str":"may","boundary":[0.7493081433380745,0.6459143905583572,0.785541171509827,0.6611869558893746],"dir":"ltr"},{"str":"require","boundary":[0.7902259656596936,0.6459143905583572,0.8528480241693019,0.6611869558893746],"dir":"ltr"},{"str":"as","boundary":[0.8575328183191685,0.6459143905583572,0.8751057381471489,0.6611869558893746],"dir":"ltr"},{"str":"much","boundary":[0.8797905322970154,0.6459143905583572,0.927014048010227,0.6611869558893746],"dir":"ltr"},{"str":"effort","boundary":[0.23910045640893854,0.6642414689555779,0.287411160637942,0.6795140342865953],"dir":"ltr"},{"str":"as","boundary":[0.29174014763718575,0.6642414689555779,0.3093130674651662,0.6795140342865953],"dir":"ltr"},{"str":"solving","boundary":[0.3136420544644099,0.6642414689555779,0.37406996887851124,0.6795140342865953],"dir":"ltr"},{"str":"the","boundary":[0.378398955877755,0.6642414689555779,0.4058554076674792,0.6795140342865953],"dir":"ltr"},{"str":"problem","boundary":[0.4101843946667229,0.6642414689555779,0.4826899851380751,0.6795140342865953],"dir":"ltr"},{"str":"after","boundary":[0.4870189721373189,0.6642414689555779,0.5276402885000857,0.6795140342865953],"dir":"ltr"},{"str":"a","boundary":[0.5319692754993295,0.6642414689555779,0.5418528074610732,0.6795140342865953],"dir":"ltr"},{"str":"feasible","boundary":[0.5461817944603169,0.6642414689555779,0.6120851855812243,0.6795140342865953],"dir":"ltr"},{"str":"solution","boundary":[0.616414172580468,0.6642414689555779,0.6856384304405213,0.6795140342865953],"dir":"ltr"},{"str":"has","boundary":[0.6899674174397651,0.6642414689555779,0.7185308248092046,0.6795140342865953],"dir":"ltr"},{"str":"been","boundary":[0.7228598118084483,0.6642414689555779,0.7646078508148539,0.6795140342865953],"dir":"ltr"},{"str":"identified.","boundary":[0.7689368378140977,0.6642414689555779,0.8551805377122736,0.6795140342865953],"dir":"ltr"},{"str":"Second,","boundary":[0.8595095247115174,0.6642414689555779,0.9270733492019978,0.6795140342865953],"dir":"ltr"},{"str":"it","boundary":[0.23910045640893854,0.6825685473527987,0.2511781324661894,0.6978411126838161],"dir":"ltr"},{"str":"is","boundary":[0.2555861877211271,0.6825685473527987,0.2687708193580933,0.6978411126838161],"dir":"ltr"},{"str":"not","boundary":[0.27317887461303103,0.6825685473527987,0.3017422819824705,0.6978411126838161],"dir":"ltr"},{"str":"always","boundary":[0.30615033723740814,0.6825685473527987,0.36325738491236353,0.6978411126838161],"dir":"ltr"},{"str":"clear","boundary":[0.3676654401673013,0.6825685473527987,0.4093937121097834,0.6978411126838161],"dir":"ltr"},{"str":"what","boundary":[0.4138017673647212,0.6825685473527987,0.45553003930720326,0.6978411126838161],"dir":"ltr"},{"str":"changes","boundary":[0.459938094562141,0.6825685473527987,0.5280356297785556,0.6978411126838161],"dir":"ltr"},{"str":"should","boundary":[0.5324436850334932,0.6825685473527987,0.5895902668362956,0.6978411126838161],"dir":"ltr"},{"str":"be","boundary":[0.5939983220912333,0.6825685473527987,0.614872341594436,0.6978411126838161],"dir":"ltr"},{"str":"allowed","boundary":[0.6192803968493739,0.6825685473527987,0.6862907435499965,0.6978411126838161],"dir":"ltr"},{"str":"in","boundary":[0.6906987988049342,0.6825685473527987,0.7071845301171227,0.6978411126838161],"dir":"ltr"},{"str":"a","boundary":[0.7115925853720604,0.6825685473527987,0.7214761173338041,0.6978411126838161],"dir":"ltr"},{"str":"feasible","boundary":[0.7258841725887419,0.6825685473527987,0.7917875637096493,0.6978411126838161],"dir":"ltr"},{"str":"solution","boundary":[0.7961956189645869,0.6825685473527987,0.8654198768246402,0.6978411126838161],"dir":"ltr"},{"str":"so","boundary":[0.8698279320795779,0.6825685473527987,0.8885078074872735,0.6978411126838161],"dir":"ltr"},{"str":"that","boundary":[0.8929158627422111,0.6825685473527987,0.9269547468184566,0.6978411126838161],"dir":"ltr"},{"str":"we","boundary":[0.23910045640893854,0.7008956257500196,0.2632558085234403,0.7161681910810369],"dir":"ltr"},{"str":"can","boundary":[0.2673278236916787,0.7008956257500196,0.2969784195769099,0.7161681910810369],"dir":"ltr"},{"str":"check","boundary":[0.3010504347451484,0.7008956257500196,0.3504680945538672,0.7161681910810369],"dir":"ltr"},{"str":"efficiently","boundary":[0.3545401097221056,0.7008956257500196,0.43910360918678515,0.7161681910810369],"dir":"ltr"},{"str":"whether","boundary":[0.4431756243550236,0.7008956257500196,0.5134673036669453,0.7161681910810369],"dir":"ltr"},{"str":"the","boundary":[0.5175393188351837,0.7008956257500196,0.5449957706249078,0.7161681910810369],"dir":"ltr"},{"str":"current","boundary":[0.5490677857931461,0.7008956257500196,0.611670077238831,0.7161681910810369],"dir":"ltr"},{"str":"solution","boundary":[0.6157420924070695,0.7008956257500196,0.6849663502671227,0.7161681910810369],"dir":"ltr"},{"str":"is","boundary":[0.6890383654353611,0.7008956257500196,0.7022229970723274,0.7161681910810369],"dir":"ltr"},{"str":"locally","boundary":[0.7062950122405658,0.7008956257500196,0.7623148713997294,0.7161681910810369],"dir":"ltr"},{"str":"optimal","boundary":[0.7663868865679678,0.7008956257500196,0.8322902776888752,0.7161681910810369],"dir":"ltr"},{"str":"and,","boundary":[0.8363622928571136,0.7008956257500196,0.8731685658826474,0.7161681910810369],"dir":"ltr"},{"str":"if","boundary":[0.8774184846261971,0.7008956257500196,0.889496160683448,0.7161681910810369],"dir":"ltr"},{"str":"not,","boundary":[0.8935681758516864,0.7008956257500196,0.9270733492019978,0.7161681910810369],"dir":"ltr"},{"str":"replace","boundary":[0.23910045640893854,0.7192227041472403,0.3017027478546235,0.7344952694782576],"dir":"ltr"},{"str":"it","boundary":[0.3068421844747302,0.7192227041472403,0.31891986053198107,0.7344952694782576],"dir":"ltr"},{"str":"with","boundary":[0.3240592971520878,0.7192227041472403,0.36139928090355566,0.7344952694782576],"dir":"ltr"},{"str":"a","boundary":[0.36653871752366246,0.7192227041472403,0.3764222494854062,0.7344952694782576],"dir":"ltr"},{"str":"better","boundary":[0.38156168610551294,0.7192227041472403,0.4331734900097388,0.7344952694782576],"dir":"ltr"},{"str":"one.","boundary":[0.4383129266298456,0.7192227041472403,0.4743878182902103,0.7344952694782576],"dir":"ltr"},{"str":"Third—and","boundary":[0.47952725491031706,0.7192227041472403,0.5787183816783773,0.7344952694782576],"dir":"ltr"},{"str":"this","boundary":[0.583857818298484,0.7192227041472403,0.6146153697634306,0.7344952694782576],"dir":"ltr"},{"str":"is","boundary":[0.6197548063835374,0.7192227041472403,0.6329394380205036,0.7344952694782576],"dir":"ltr"},{"str":"the","boundary":[0.6380788746406104,0.7192227041472403,0.6655353264303345,0.7344952694782576],"dir":"ltr"},{"str":"most","boundary":[0.6706747630504414,0.7192227041472403,0.7124030349929236,0.7344952694782576],"dir":"ltr"},{"str":"fundamental","boundary":[0.7175424716130303,0.7192227041472403,0.826281090256135,0.7344952694782576],"dir":"ltr"},{"str":"difficulty—","boundary":[0.8314205268762419,0.7192227041472403,0.9269745138823805,0.7344952694782576],"dir":"ltr"},{"str":"is","boundary":[0.23910045640893854,0.737549782544461,0.2522850880459047,0.7528223478754784],"dir":"ltr"},{"str":"an","boundary":[0.2566338421090719,0.737549782544461,0.27750786161227475,0.7528223478754784],"dir":"ltr"},{"str":"issue","boundary":[0.28185661567544207,0.737549782544461,0.3236046546818477,0.7528223478754784],"dir":"ltr"},{"str":"of","boundary":[0.3279534087450149,0.737549782544461,0.3455263285729953,0.7528223478754784],"dir":"ltr"},{"str":"local","boundary":[0.3498750826361625,0.737549782544461,0.39051616606285283,0.7528223478754784],"dir":"ltr"},{"str":"versus","boundary":[0.3948649201260201,0.737549782544461,0.44869063518967656,0.7528223478754784],"dir":"ltr"},{"str":"global","boundary":[0.4530393892528438,0.737549782544461,0.5057779158007085,0.7528223478754784],"dir":"ltr"},{"str":"extremum","boundary":[0.5101266698638757,0.737549782544461,0.5979715019398542,0.7528223478754784],"dir":"ltr"},{"str":"(maximum","boundary":[0.6023202560030215,0.737549782544461,0.6956603318497295,0.7528223478754784],"dir":"ltr"},{"str":"or","boundary":[0.7000090859128968,0.737549782544461,0.7186889613205923,0.7528223478754784],"dir":"ltr"},{"str":"minimum).","boundary":[0.7230377153837597,0.737549782544461,0.8180382246000406,0.7528223478754784],"dir":"ltr"},{"str":"Think","boundary":[0.8223869786632079,0.737549782544461,0.8732476341383412,0.7528223478754784],"dir":"ltr"},{"str":"about","boundary":[0.8775963882015085,0.737549782544461,0.9270338150741507,0.7528223478754784],"dir":"ltr"},{"str":"the","boundary":[0.23910045640893854,0.7558768609416818,0.26655690819866273,0.7711494262726992],"dir":"ltr"},{"str":"problem","boundary":[0.27045101979158975,0.7558768609416818,0.34295661026294194,0.7711494262726992],"dir":"ltr"},{"str":"of","boundary":[0.34685072185586896,0.7558768609416818,0.3644236416838494,0.7711494262726992],"dir":"ltr"},{"str":"finding","boundary":[0.36831775327677635,0.7558768609416818,0.42765847917508587,0.7711494262726992],"dir":"ltr"},{"str":"the","boundary":[0.4315525907680129,0.7558768609416818,0.4590090425577371,0.7711494262726992],"dir":"ltr"},{"str":"highest","boundary":[0.4629031541506641,0.7558768609416818,0.5244182570805572,0.7711494262726992],"dir":"ltr"},{"str":"point","boundary":[0.5283123686734842,0.7558768609416818,0.5733615073551123,0.7711494262726992],"dir":"ltr"},{"str":"in","boundary":[0.5772556189480393,0.7558768609416818,0.5937413502602279,0.7711494262726992],"dir":"ltr"},{"str":"a","boundary":[0.597635461853155,0.7558768609416818,0.6075189938148986,0.7711494262726992],"dir":"ltr"},{"str":"hilly","boundary":[0.6114131054078257,0.7558768609416818,0.648772856223217,0.7711494262726992],"dir":"ltr"},{"str":"area","boundary":[0.652666967816144,0.7558768609416818,0.6900069515676119,0.7711494262726992],"dir":"ltr"},{"str":"with","boundary":[0.6939010631605389,0.7558768609416818,0.7312410469120069,0.7711494262726992],"dir":"ltr"},{"str":"no","boundary":[0.7351351585049338,0.7558768609416818,0.757116133587852,0.7711494262726992],"dir":"ltr"},{"str":"map","boundary":[0.7610102451807791,0.7558768609416818,0.7983502289322469,0.7711494262726992],"dir":"ltr"},{"str":"on","boundary":[0.802244340525174,0.7558768609416818,0.8242253156080921,0.7711494262726992],"dir":"ltr"},{"str":"a","boundary":[0.828119427201019,0.7558768609416818,0.8380029591627628,0.7711494262726992],"dir":"ltr"},{"str":"foggy","boundary":[0.8418970707556899,0.7558768609416818,0.8891205864689015,0.7711494262726992],"dir":"ltr"},{"str":"day.","boundary":[0.8930146980618286,0.7558768609416818,0.9268954456266861,0.7711494262726992],"dir":"ltr"},{"str":"A","boundary":[0.23910045640893854,0.7742039393389026,0.2556652559768211,0.78947650466992],"dir":"ltr"},{"str":"logical","boundary":[0.2594802993140542,0.7742039393389026,0.3155001584732178,0.78947650466992],"dir":"ltr"},{"str":"thing","boundary":[0.3193152018104508,0.7742039393389026,0.36325738491236353,0.78947650466992],"dir":"ltr"},{"str":"to","boundary":[0.3670724282495967,0.7742039393389026,0.38464534807757705,0.78947650466992],"dir":"ltr"},{"str":"do","boundary":[0.38846039141481015,0.7742039393389026,0.4104413664977283,0.78947650466992],"dir":"ltr"},{"str":"would","boundary":[0.41425640983496137,0.7742039393389026,0.466994936382826,0.78947650466992],"dir":"ltr"},{"str":"be","boundary":[0.47080997972005906,0.7742039393389026,0.4916839992232619,0.78947650466992],"dir":"ltr"},{"str":"to","boundary":[0.495499042560495,0.7742039393389026,0.5130719623884754,0.78947650466992],"dir":"ltr"},{"str":"start","boundary":[0.5168870057257084,0.7742039393389026,0.5553141779929681,0.78947650466992],"dir":"ltr"},{"str":"walking","boundary":[0.5591292213302013,0.7742039393389026,0.6261395680308238,0.78947650466992],"dir":"ltr"},{"str":"“up","boundary":[0.6299546113680571,0.7742039393389026,0.6618191184127189,0.78947650466992],"dir":"ltr"},{"str":"the","boundary":[0.6656341617499519,0.7742039393389026,0.693090613539676,0.78947650466992],"dir":"ltr"},{"str":"hill”","boundary":[0.6969056568769092,0.7742039393389026,0.7342654076923005,0.78947650466992],"dir":"ltr"},{"str":"from","boundary":[0.7380804510295337,0.7742039393389026,0.7798087229720158,0.78947650466992],"dir":"ltr"},{"str":"the","boundary":[0.783623766309249,0.7742039393389026,0.8110802180989731,0.78947650466992],"dir":"ltr"},{"str":"point","boundary":[0.8148952614362062,0.7742039393389026,0.8599444001178341,0.78947650466992],"dir":"ltr"},{"str":"you","boundary":[0.8637594434550674,0.7742039393389026,0.8956239504997292,0.78947650466992],"dir":"ltr"},{"str":"are","boundary":[0.8994389938369622,0.7742039393389026,0.9268954456266864,0.78947650466992],"dir":"ltr"},{"str":"at","boundary":[0.23910045640893854,0.7925310177361234,0.25556642065720364,0.8078035830671407],"dir":"ltr"},{"str":"until","boundary":[0.2611407326836271,0.7925310177361234,0.3006946275945256,0.8078035830671407],"dir":"ltr"},{"str":"it","boundary":[0.3062689396209491,0.7925310177361234,0.3183466156782,0.8078035830671407],"dir":"ltr"},{"str":"becomes","boundary":[0.32392092770462344,0.7925310177361234,0.3986008952075592,0.8078035830671407],"dir":"ltr"},{"str":"impossible","boundary":[0.4041752072339827,0.7925310177361234,0.49536067311303056,0.8078035830671407],"dir":"ltr"},{"str":"to","boundary":[0.500934985139454,0.7925310177361234,0.5185079049674344,0.8078035830671407],"dir":"ltr"},{"str":"do","boundary":[0.5240822169938579,0.7925310177361234,0.546063192076776,0.8078035830671407],"dir":"ltr"},{"str":"so","boundary":[0.5516375041031996,0.7925310177361234,0.5703173795108951,0.8078035830671407],"dir":"ltr"},{"str":"because","boundary":[0.5758916915373187,0.7925310177361234,0.6439892267537332,0.8078035830671407],"dir":"ltr"},{"str":"no","boundary":[0.6495635387801566,0.7925310177361234,0.6715445138630748,0.8078035830671407],"dir":"ltr"},{"str":"direction","boundary":[0.6771188258894982,0.7925310177361234,0.7540127045518648,0.8078035830671407],"dir":"ltr"},{"str":"would","boundary":[0.7595870165782881,0.7925310177361234,0.8123255431261528,0.8078035830671407],"dir":"ltr"},{"str":"lead","boundary":[0.8178998551525762,0.7925310177361234,0.8541526503882523,0.8078035830671407],"dir":"ltr"},{"str":"up.","boundary":[0.8597269624146758,0.7925310177361234,0.8858590209215264,0.8078035830671407],"dir":"ltr"},{"str":"You","boundary":[0.8914333329479497,0.7925310177361234,0.9269745138823803,0.8078035830671407],"dir":"ltr"},{"str":"will","boundary":[0.23910045640893854,0.8108596233898774,0.26985800787388514,0.8261321887208947],"dir":"ltr"},{"str":"have","boundary":[0.27523464926107366,0.8108596233898774,0.31587573268776403,0.8261321887208947],"dir":"ltr"},{"str":"reached","boundary":[0.32125237407495266,0.8108596233898774,0.3893499092913671,0.8261321887208947],"dir":"ltr"},{"str":"a","boundary":[0.3947265506785557,0.8108596233898774,0.40461008264029946,0.8261321887208947],"dir":"ltr"},{"str":"local","boundary":[0.4099867240274881,0.8108596233898774,0.45062780745417835,0.8261321887208947],"dir":"ltr"},{"str":"highest","boundary":[0.456004448841367,0.8108596233898774,0.5175195517712602,0.8261321887208947],"dir":"ltr"},{"str":"point,","boundary":[0.5228961931584486,0.8108596233898774,0.5728870978209486,0.8261321887208947],"dir":"ltr"},{"str":"but","boundary":[0.5783823415916781,0.8108596233898774,0.6069457489611176,0.8261321887208947],"dir":"ltr"},{"str":"because","boundary":[0.6123223903483063,0.8108596233898774,0.6804199255647208,0.8261321887208947],"dir":"ltr"},{"str":"of","boundary":[0.6857965669519092,0.8108596233898774,0.7033694867798895,0.8261321887208947],"dir":"ltr"},{"str":"a","boundary":[0.7087461281670782,0.8108596233898774,0.7186296601288218,0.8261321887208947],"dir":"ltr"},{"str":"limited","boundary":[0.7240063015160104,0.8108596233898774,0.7844144488661883,0.8261321887208947],"dir":"ltr"},{"str":"feasibility,","boundary":[0.7897910902533769,0.8108596233898774,0.8763905973021756,0.8261321887208947],"dir":"ltr"},{"str":"there","boundary":[0.8818858410729051,0.8108596233898774,0.9269152126906096,0.8261321887208947],"dir":"ltr"},{"str":"will","boundary":[0.23910045640893854,0.8291867017870982,0.26985800787388514,0.8444592671181154],"dir":"ltr"},{"str":"be","boundary":[0.2761637012654776,0.8291867017870982,0.29703772076868046,0.8444592671181154],"dir":"ltr"},{"str":"no","boundary":[0.3033434141602729,0.8291867017870982,0.325324389243191,0.8444592671181154],"dir":"ltr"},{"str":"simple","boundary":[0.3316300826347836,0.8291867017870982,0.3876499417939472,0.8444592671181154],"dir":"ltr"},{"str":"way","boundary":[0.39395563518553967,0.8291867017870982,0.42799451926178517,0.8444592671181154],"dir":"ltr"},{"str":"to","boundary":[0.4343002126533777,0.8291867017870982,0.45187313248135813,0.8444592671181154],"dir":"ltr"},{"str":"tell","boundary":[0.4581788258729506,0.8291867017870982,0.4856352776626748,0.8444592671181154],"dir":"ltr"},{"str":"whether","boundary":[0.4919409710542673,0.8291867017870982,0.562232650366189,0.8444592671181154],"dir":"ltr"},{"str":"the","boundary":[0.5685383437577812,0.8291867017870982,0.5959947955475053,0.8444592671181154],"dir":"ltr"},{"str":"point","boundary":[0.6023004889390979,0.8291867017870982,0.6473496276207259,0.8444592671181154],"dir":"ltr"},{"str":"is","boundary":[0.6536553210123185,0.8291867017870982,0.6668399526492846,0.8444592671181154],"dir":"ltr"},{"str":"the","boundary":[0.6731456460408771,0.8291867017870982,0.7006020978306012,0.8444592671181154],"dir":"ltr"},{"str":"highest","boundary":[0.7069077912221938,0.8291867017870982,0.768422894152087,0.8444592671181154],"dir":"ltr"},{"str":"(global","boundary":[0.7747285875436795,0.8291867017870982,0.8351565019577807,0.8444592671181154],"dir":"ltr"},{"str":"maximum","boundary":[0.8414621953493732,0.8291867017870982,0.9271128833298445,0.8444592671181154],"dir":"ltr"},{"str":"you","boundary":[0.23910045640893854,0.8475137801843189,0.27096496345360044,0.8627863455153362],"dir":"ltr"},{"str":"are","boundary":[0.27590672943447225,0.8475137801843189,0.3033631812241964,0.8627863455153362],"dir":"ltr"},{"str":"after)","boundary":[0.3083049472050683,0.8475137801843189,0.35661565143407176,0.8627863455153362],"dir":"ltr"},{"str":"in","boundary":[0.3615574174149437,0.8475137801843189,0.37804314872713224,0.8627863455153362],"dir":"ltr"},{"str":"the","boundary":[0.3829849147080041,0.8475137801843189,0.4104413664977283,0.8627863455153362],"dir":"ltr"},{"str":"entire","boundary":[0.4153831324786001,0.8475137801843189,0.4659077478670341,0.8627863455153362],"dir":"ltr"},{"str":"area.","boundary":[0.4708495138479061,0.8475137801843189,0.5131312635802459,0.8627863455153362],"dir":"ltr"},{"str":"Fortunately,","boundary":[0.27468117147121607,0.8658408585815396,0.3777664098322034,0.8811134239125569],"dir":"ltr"},{"str":"there","boundary":[0.385534865954134,0.8658408585815396,0.43056423757183854,0.8811134239125569],"dir":"ltr"},{"str":"are","boundary":[0.437759448839988,0.8658408585815396,0.4652159006297122,0.8811134239125569],"dir":"ltr"},{"str":"important","boundary":[0.4724111118978616,0.8658408585815396,0.5580815669422564,0.8811134239125569],"dir":"ltr"},{"str":"problems","boundary":[0.565276778210406,0.8658408585815396,0.6454717565479948,0.8811134239125569],"dir":"ltr"},{"str":"that","boundary":[0.6526669678161442,0.8658408585815396,0.6867058518923898,0.8811134239125569],"dir":"ltr"},{"str":"can","boundary":[0.6939010631605391,0.8658408585815396,0.7235516590457703,0.8811134239125569],"dir":"ltr"},{"str":"be","boundary":[0.7307468703139198,0.8658408585815396,0.7516208898171226,0.8811134239125569],"dir":"ltr"},{"str":"solved","boundary":[0.7588161010852723,0.8658408585815396,0.8137487717286441,0.8811134239125569],"dir":"ltr"},{"str":"by","boundary":[0.8209439829967934,0.8658408585815396,0.8418180024999962,0.8811134239125569],"dir":"ltr"},{"str":"iterative-","boundary":[0.8490132137681458,0.8658408585815396,0.9269745138823805,0.8811134239125569],"dir":"ltr"},{"str":"improvement","boundary":[0.23910045640893854,0.8841679369787605,0.35442150733856465,0.8994405023097778],"dir":"ltr"},{"str":"algorithms.","boundary":[0.3623876340997301,0.8841679369787605,0.4574079103799346,0.8994405023097778],"dir":"ltr"},{"str":"The","boundary":[0.4653740371411001,0.8841679369787605,0.4986420057243296,0.8994405023097778],"dir":"ltr"},{"str":"most","boundary":[0.506608132485495,0.8841679369787605,0.5483364044279772,0.8994405023097778],"dir":"ltr"},{"str":"important","boundary":[0.5563025311891426,0.8841679369787605,0.6419729862335375,0.8994405023097778],"dir":"ltr"},{"str":"of","boundary":[0.649939112994703,0.8841679369787605,0.6675120328226833,0.8994405023097778],"dir":"ltr"},{"str":"them","boundary":[0.6754781595838487,0.8841679369787605,0.719400575621838,0.8994405023097778],"dir":"ltr"},{"str":"is","boundary":[0.7273667023830034,0.8841679369787605,0.7405513340199695,0.8994405023097778],"dir":"ltr"},{"str":"linear","boundary":[0.748517460781135,0.8841679369787605,0.7979548876537772,0.8994405023097778],"dir":"ltr"},{"str":"programming.","boundary":[0.8059210144149427,0.8841679369787605,0.9269349797545332,0.8994405023097778],"dir":"ltr"},{"str":"345","boundary":[0.8940228183219265,0.9329332380806987,0.9269942809463038,0.9482058034117159],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92711,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":413,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/7cd0d7733911c89db6b6347317a65edd.jpg","blurred":"/storage/books/4a8b03583f119702/pages/17294d3d703aaf7bdd2bff61c86d37fb.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07291,0.05179]},"elements":[{"words":[{"str":"11","boundary":[0.14421784044919886,0.07999453587206534,0.23126290222994425,0.15330318671872986],"dir":"ltr"},{"str":"Limitations","boundary":[0.14421784044919886,0.17005356781848974,0.41316128024756754,0.20670781659232623],"dir":"ltr"},{"str":"of","boundary":[0.4289591573780768,0.17005356781848974,0.4788197245377321,0.20670781659232623],"dir":"ltr"},{"str":"Algorithm","boundary":[0.49461760166824126,0.17005356781848974,0.7374210105389506,0.20670781659232623],"dir":"ltr"},{"str":"Power","boundary":[0.7532188876694599,0.17005356781848974,0.9068330803078649,0.20670781659232623],"dir":"ltr"},{"str":"Intellect","boundary":[0.23910077902799318,0.27456512096090674,0.30609135866469234,0.2898376862919241],"dir":"ltr"},{"str":"distinguishes","boundary":[0.31302959810183645,0.27456512096090674,0.42070079529307286,0.2898376862919241],"dir":"ltr"},{"str":"between","boundary":[0.42763903473021697,0.27456512096090674,0.4957168028827079,0.2898376862919241],"dir":"ltr"},{"str":"the","boundary":[0.502655042319852,0.27456512096090674,0.527917350014069,0.2898376862919241],"dir":"ltr"},{"str":"possible","boundary":[0.5348555894512131,0.27456512096090674,0.6029728917315512,0.2898376862919241],"dir":"ltr"},{"str":"and","boundary":[0.6099111311686953,0.27456512096090674,0.6417756382133571,0.2898376862919241],"dir":"ltr"},{"str":"the","boundary":[0.6487138776505013,0.27456512096090674,0.6739761853447183,0.2898376862919241],"dir":"ltr"},{"str":"impossible;","boundary":[0.6809144247818624,0.27456512096090674,0.7759347010620667,0.2898376862919241],"dir":"ltr"},{"str":"reason","boundary":[0.7838612936953854,0.27456512096090674,0.839881152854549,0.2898376862919241],"dir":"ltr"},{"str":"distinguishes","boundary":[0.23910077902799318,0.29289219935812755,0.3467719762192296,0.3081647646891449],"dir":"ltr"},{"str":"between","boundary":[0.35159513981656054,0.29289219935812755,0.41967290796905155,0.3081647646891449],"dir":"ltr"},{"str":"the","boundary":[0.42449607156638247,0.29289219935812755,0.44975837926059953,0.3081647646891449],"dir":"ltr"},{"str":"sensible","boundary":[0.45458154285793045,0.29289219935812755,0.5204849339788379,0.3081647646891449],"dir":"ltr"},{"str":"and","boundary":[0.5253080975761687,0.29289219935812755,0.5571726046208305,0.3081647646891449],"dir":"ltr"},{"str":"the","boundary":[0.5619957682181616,0.29289219935812755,0.5872580759123786,0.3081647646891449],"dir":"ltr"},{"str":"senseless.","boundary":[0.5920812395097095,0.29289219935812755,0.66950882889801,0.3081647646891449],"dir":"ltr"},{"str":"Even","boundary":[0.674331992495341,0.29289219935812755,0.7182544085333303,0.3081647646891449],"dir":"ltr"},{"str":"the","boundary":[0.7230775721306613,0.29289219935812755,0.7483398798248783,0.3081647646891449],"dir":"ltr"},{"str":"possible","boundary":[0.7531630434222092,0.29289219935812755,0.8212803457025473,0.3081647646891449],"dir":"ltr"},{"str":"can","boundary":[0.8261035092998783,0.29289219935812755,0.8557541051851095,0.3081647646891449],"dir":"ltr"},{"str":"be","boundary":[0.23910077902799318,0.31121927775534836,0.2588678429514807,0.3264918430863657],"dir":"ltr"},{"str":"senseless.","boundary":[0.26380960893235256,0.31121927775534836,0.3412371983206531,0.3264918430863657],"dir":"ltr"},{"str":"—Max","boundary":[0.4099859018052478,0.3331470145055125,0.4652706014245567,0.34765599755967636],"dir":"ltr"},{"str":"Born","boundary":[0.46998407275758886,0.3331470145055125,0.5117292790258373,0.34765599755967636],"dir":"ltr"},{"str":"(1882–1970),","boundary":[0.5164427503588694,0.3331470145055125,0.6202517923070826,0.34765599755967636],"dir":"ltr"},{"str":"My","boundary":[0.6249802866563158,0.3331470145055125,0.6520968308989388,0.34765599755967636],"dir":"ltr"},{"str":"Life","boundary":[0.6568103022319709,0.3331470145055125,0.6901801769682181,0.34765599755967636],"dir":"ltr"},{"str":"and","boundary":[0.6948936483012502,0.3331470145055125,0.725165025946062,0.34765599755967636],"dir":"ltr"},{"str":"My","boundary":[0.7298784972790942,0.3331470145055125,0.7569950415217171,0.34765599755967636],"dir":"ltr"},{"str":"Views","boundary":[0.7617085128547493,0.3331470145055125,0.8086554384825592,0.34765599755967636],"dir":"ltr"},{"str":",","boundary":[0.8087023854081868,0.3331470145055125,0.8133970779709678,0.34765599755967636],"dir":"ltr"},{"str":"1968","boundary":[0.818110549304,0.3331470145055125,0.8556680898062479,0.34765599755967636],"dir":"ltr"},{"str":"n","boundary":[0.2588487953320173,0.42598926583291774,0.2698392828734764,0.4412618311639351],"dir":"ltr"},{"str":"the","boundary":[0.2766589199270796,0.42598926583291774,0.30411537171680375,0.4412618311639351],"dir":"ltr"},{"str":"preceding","boundary":[0.3109350087704069,0.42598926583291774,0.39551827529900996,0.4412618311639351],"dir":"ltr"},{"str":"chapters","boundary":[0.4023379123526131,0.42598926583291774,0.47482373576004183,0.4412618311639351],"dir":"ltr"},{"str":"of","boundary":[0.481643372813645,0.42598926583291774,0.4992162926416254,0.4412618311639351],"dir":"ltr"},{"str":"this","boundary":[0.5060359296952286,0.42598926583291774,0.5367934811601752,0.4412618311639351],"dir":"ltr"},{"str":"book,","boundary":[0.5436131182137783,0.42598926583291774,0.5925168343604865,0.4412618311639351],"dir":"ltr"},{"str":"we","boundary":[0.5998108809482534,0.42598926583291774,0.6239662330627552,0.4412618311639351],"dir":"ltr"},{"str":"encountered","boundary":[0.6307858701163582,0.42598926583291774,0.7384373002436712,0.4412618311639351],"dir":"ltr"},{"str":"dozens","boundary":[0.7452569372972745,0.42598926583291774,0.8045778961316605,0.4412618311639351],"dir":"ltr"},{"str":"of","boundary":[0.8113975331852635,0.42598926583291774,0.828970453013244,0.4412618311639351],"dir":"ltr"},{"str":"algorithms","boundary":[0.8357900900668471,0.42598926583291774,0.9269557888819716,0.4412618311639351],"dir":"ltr"},{"str":"for","boundary":[0.2588487953320173,0.4443163442301386,0.2841111030262344,0.4595889095611559],"dir":"ltr"},{"str":"solving","boundary":[0.2899423868836632,0.4443163442301386,0.35037030129776453,0.4595889095611559],"dir":"ltr"},{"str":"a","boundary":[0.35620158515519335,0.4443163442301386,0.3660851171169371,0.4595889095611559],"dir":"ltr"},{"str":"variety","boundary":[0.3719164009743659,0.4443163442301386,0.4312175927448284,0.4595889095611559],"dir":"ltr"},{"str":"of","boundary":[0.4370488766022572,0.4443163442301386,0.4546217964302376,0.4595889095611559],"dir":"ltr"},{"str":"different","boundary":[0.4604530802876664,0.4443163442301386,0.5351330477906022,0.4595889095611559],"dir":"ltr"},{"str":"problems.","boundary":[0.5409643316480309,0.4443163442301386,0.6250138874506997,0.4595889095611559],"dir":"ltr"},{"str":"A","boundary":[0.6308451713081287,0.4443163442301386,0.6474099708760113,0.4595889095611559],"dir":"ltr"},{"str":"fair","boundary":[0.6532412547334402,0.4443163442301386,0.6828918506186714,0.4595889095611559],"dir":"ltr"},{"str":"assessment","boundary":[0.6887231344761002,0.4443163442301386,0.7831701659025235,0.4595889095611559],"dir":"ltr"},{"str":"of","boundary":[0.7890014497599523,0.4443163442301386,0.8065743695879327,0.4595889095611559],"dir":"ltr"},{"str":"algorithms","boundary":[0.8124056534453615,0.4443163442301386,0.9035713522604859,0.4595889095611559],"dir":"ltr"},{"str":"as","boundary":[0.9094026361179148,0.4443163442301386,0.9269755559458953,0.4595889095611559],"dir":"ltr"},{"str":"Iproblem-solving","boundary":[0.23910077902799318,0.424691122614218,0.3786174356444281,0.47791751521490977],"dir":"ltr"},{"str":"tools","boundary":[0.3851998679309495,0.46264494988389243,0.4269479069373551,0.47791751521490977],"dir":"ltr"},{"str":"is","boundary":[0.43353033922387635,0.46264494988389243,0.44671497086084255,0.47791751521490977],"dir":"ltr"},{"str":"inescapable:","boundary":[0.4532974031473639,0.46264494988389243,0.5582012113893121,0.47791751521490977],"dir":"ltr"},{"str":"they","boundary":[0.5647836436758334,0.46264494988389243,0.6021236274273014,0.47791751521490977],"dir":"ltr"},{"str":"are","boundary":[0.6087060597138225,0.46264494988389243,0.6361625115035466,0.47791751521490977],"dir":"ltr"},{"str":"very","boundary":[0.642744943790068,0.46264494988389243,0.6800849275415359,0.47791751521490977],"dir":"ltr"},{"str":"powerful","boundary":[0.6866673598280573,0.46264494988389243,0.7635612384904236,0.47791751521490977],"dir":"ltr"},{"str":"instruments,","boundary":[0.770143670776945,0.46264494988389243,0.8750474790188932,0.47791751521490977],"dir":"ltr"},{"str":"espe-","boundary":[0.8820252525838844,0.46264494988389243,0.9270546242015889,0.47791751521490977],"dir":"ltr"},{"str":"cially","boundary":[0.2391014984724533,0.48097202828111324,0.2841308700901578,0.4962445936121306],"dir":"ltr"},{"str":"when","boundary":[0.2884203229615546,0.48097202828111324,0.3345566501589744,0.4962445936121306],"dir":"ltr"},{"str":"they","boundary":[0.33884610303037127,0.48097202828111324,0.3761860867818391,0.4962445936121306],"dir":"ltr"},{"str":"are","boundary":[0.38047553965323594,0.48097202828111324,0.4079319914429601,0.4962445936121306],"dir":"ltr"},{"str":"executed","boundary":[0.4122214443143569,0.48097202828111324,0.4890955559127998,0.4962445936121306],"dir":"ltr"},{"str":"by","boundary":[0.4933850087841966,0.48097202828111324,0.5142590282873993,0.4962445936121306],"dir":"ltr"},{"str":"modern","boundary":[0.5185484811587961,0.48097202828111324,0.5855588278594187,0.4962445936121306],"dir":"ltr"},{"str":"computers.","boundary":[0.5898482807308156,0.48097202828111324,0.6837616014313048,0.4962445936121306],"dir":"ltr"},{"str":"But","boundary":[0.6880510543027015,0.48097202828111324,0.7198957942834399,0.4962445936121306],"dir":"ltr"},{"str":"the","boundary":[0.7241852471548366,0.48097202828111324,0.7516416989445607,0.4962445936121306],"dir":"ltr"},{"str":"power","boundary":[0.7559311518159576,0.48097202828111324,0.809756866879614,0.4962445936121306],"dir":"ltr"},{"str":"of","boundary":[0.8140463197510107,0.48097202828111324,0.8316192395789912,0.4962445936121306],"dir":"ltr"},{"str":"algorithms","boundary":[0.8359086924503879,0.48097202828111324,0.9270743912655123,0.4962445936121306],"dir":"ltr"},{"str":"is","boundary":[0.2391014984724533,0.4992991066783341,0.25228613010941947,0.5145716720093514],"dir":"ltr"},{"str":"not","boundary":[0.2561407075744995,0.4992991066783341,0.284704114943939,0.5145716720093514],"dir":"ltr"},{"str":"unlimited,","boundary":[0.28855869240901905,0.4992991066783341,0.3758895808229869,0.5145716720093514],"dir":"ltr"},{"str":"and","boundary":[0.3799615959912253,0.4992991066783341,0.4118261030358872,0.5145716720093514],"dir":"ltr"},{"str":"its","boundary":[0.41568068050096724,0.4992991066783341,0.4354477444244548,0.5145716720093514],"dir":"ltr"},{"str":"limits","boundary":[0.43930232188953483,0.4992991066783341,0.4865258376027465,0.5145716720093514],"dir":"ltr"},{"str":"are","boundary":[0.49038041506782654,0.4992991066783341,0.5178368668575506,0.5145716720093514],"dir":"ltr"},{"str":"the","boundary":[0.5216914443226307,0.4992991066783341,0.5491478961123548,0.5145716720093514],"dir":"ltr"},{"str":"subject","boundary":[0.5530024735774349,0.4992991066783341,0.6134106209276128,0.5145716720093514],"dir":"ltr"},{"str":"of","boundary":[0.6172651983926928,0.4992991066783341,0.6348381182206732,0.5145716720093514],"dir":"ltr"},{"str":"this","boundary":[0.6386926956857533,0.4992991066783341,0.6694502471506999,0.5145716720093514],"dir":"ltr"},{"str":"chapter.","boundary":[0.6733048246157799,0.4992991066783341,0.7426872189872211,0.5145716720093514],"dir":"ltr"},{"str":"As","boundary":[0.7465417964523012,0.4992991066783341,0.7707959838864203,0.5145716720093514],"dir":"ltr"},{"str":"we","boundary":[0.7746505613515003,0.4992991066783341,0.7988059134660022,0.5145716720093514],"dir":"ltr"},{"str":"shall","boundary":[0.8026604909310823,0.4992991066783341,0.8422143858419808,0.5145716720093514],"dir":"ltr"},{"str":"see,","boundary":[0.8460689633070608,0.4992991066783341,0.8777357997124878,0.5145716720093514],"dir":"ltr"},{"str":"some","boundary":[0.8818078148807265,0.4992991066783341,0.9268371864984309,0.5145716720093514],"dir":"ltr"},{"str":"problems","boundary":[0.2391014984724533,0.5176261850755549,0.3192964768100421,0.5328987504065722],"dir":"ltr"},{"str":"cannot","boundary":[0.3237638332567503,0.5176261850755549,0.381977836511421,0.5328987504065722],"dir":"ltr"},{"str":"be","boundary":[0.3864451929581292,0.5176261850755549,0.407319212461332,0.5328987504065722],"dir":"ltr"},{"str":"solved","boundary":[0.4117865689080402,0.5176261850755549,0.466719239551412,0.5328987504065722],"dir":"ltr"},{"str":"by","boundary":[0.47118659599812013,0.5176261850755549,0.49206061550132296,0.5328987504065722],"dir":"ltr"},{"str":"any","boundary":[0.49652797194803117,0.5176261850755549,0.5272855234129777,0.5328987504065722],"dir":"ltr"},{"str":"algorithm.","boundary":[0.531752879859686,0.5176261850755549,0.6201709567894456,0.5328987504065722],"dir":"ltr"},{"str":"Other","boundary":[0.6246383132361537,0.5176261850755549,0.6762501171403796,0.5328987504065722],"dir":"ltr"},{"str":"problems","boundary":[0.6807174735870878,0.5176261850755549,0.7609124519246765,0.5328987504065722],"dir":"ltr"},{"str":"can","boundary":[0.7653798083713846,0.5176261850755549,0.7950304042566159,0.5328987504065722],"dir":"ltr"},{"str":"be","boundary":[0.799497760703324,0.5176261850755549,0.8203717802065268,0.5328987504065722],"dir":"ltr"},{"str":"solved","boundary":[0.824839136653235,0.5176261850755549,0.8797718072966069,0.5328987504065722],"dir":"ltr"},{"str":"algo-","boundary":[0.884239163743315,0.5176261850755549,0.9270743912655124,0.5328987504065722],"dir":"ltr"},{"str":"rithmically","boundary":[0.2391014984724533,0.5359532634727757,0.33135438580336946,0.551225828803793],"dir":"ltr"},{"str":"but","boundary":[0.3367112601266346,0.5359532634727757,0.36527466749607407,0.551225828803793],"dir":"ltr"},{"str":"not","boundary":[0.37063154181933916,0.5359532634727757,0.3991949491887786,0.551225828803793],"dir":"ltr"},{"str":"in","boundary":[0.4045518235120437,0.5359532634727757,0.42103755482423233,0.551225828803793],"dir":"ltr"},{"str":"polynomial","boundary":[0.4263944291474975,0.5359532634727757,0.523075138797275,0.551225828803793],"dir":"ltr"},{"str":"time.","boundary":[0.5284320131205399,0.5359532634727757,0.5710695700035024,0.551225828803793],"dir":"ltr"},{"str":"And","boundary":[0.5764264443267676,0.5359532634727757,0.6149722189775683,0.551225828803793],"dir":"ltr"},{"str":"even","boundary":[0.6203290933008334,0.5359532634727757,0.6609701767275237,0.551225828803793],"dir":"ltr"},{"str":"when","boundary":[0.6663270510507888,0.5359532634727757,0.7124633782482087,0.551225828803793],"dir":"ltr"},{"str":"a","boundary":[0.7178202525714739,0.5359532634727757,0.7277037845332175,0.551225828803793],"dir":"ltr"},{"str":"problem","boundary":[0.7330606588564826,0.5359532634727757,0.8055662493278349,0.551225828803793],"dir":"ltr"},{"str":"can","boundary":[0.8109231236511001,0.5359532634727757,0.8405737195363313,0.551225828803793],"dir":"ltr"},{"str":"be","boundary":[0.8459305938595965,0.5359532634727757,0.8668046133627991,0.551225828803793],"dir":"ltr"},{"str":"solved","boundary":[0.8721614876860643,0.5359532634727757,0.9270941583294361,0.551225828803793],"dir":"ltr"},{"str":"in","boundary":[0.2391014984724533,0.5542803418699965,0.2555872297846419,0.5695529072010138],"dir":"ltr"},{"str":"polynomial","boundary":[0.26129991125852975,0.5542803418699965,0.3579806209083072,0.5695529072010138],"dir":"ltr"},{"str":"time","boundary":[0.36369330238219505,0.5542803418699965,0.4021204746494547,0.5695529072010138],"dir":"ltr"},{"str":"by","boundary":[0.40783315612334264,0.5542803418699965,0.4287071756265455,0.5695529072010138],"dir":"ltr"},{"str":"some","boundary":[0.4344198571004333,0.5542803418699965,0.47944922871813783,0.5695529072010138],"dir":"ltr"},{"str":"algorithms,","boundary":[0.4851619101920257,0.5542803418699965,0.5801821864722302,0.5695529072010138],"dir":"ltr"},{"str":"there","boundary":[0.5860925385853529,0.5542803418699965,0.6311219102030575,0.5695529072010138],"dir":"ltr"},{"str":"are","boundary":[0.6368345916769454,0.5542803418699965,0.6642910434666696,0.5695529072010138],"dir":"ltr"},{"str":"usually","boundary":[0.6700037249405575,0.5542803418699965,0.7304316393546587,0.5695529072010138],"dir":"ltr"},{"str":"lower","boundary":[0.7361443208285466,0.5542803418699965,0.7844747921214736,0.5695529072010138],"dir":"ltr"},{"str":"bounds","boundary":[0.7901874735953616,0.5542803418699965,0.8528292991688935,0.5695529072010138],"dir":"ltr"},{"str":"on","boundary":[0.8585419806427814,0.5542803418699965,0.8805229557256995,0.5695529072010138],"dir":"ltr"},{"str":"their","boundary":[0.8862356371995873,0.5542803418699965,0.9268767206262777,0.5695529072010138],"dir":"ltr"},{"str":"efficiency.","boundary":[0.2391014984724533,0.5726074202672173,0.32313128721119866,0.5878799855982347],"dir":"ltr"},{"str":"We","boundary":[0.2746822135347308,0.5909344986644381,0.30287004668962403,0.6062070639954555],"dir":"ltr"},{"str":"start,","boundary":[0.3070606642414034,0.5909344986644381,0.350429602489535,0.6062070639954555],"dir":"ltr"},{"str":"in","boundary":[0.3547585894887787,0.5909344986644381,0.3712443208009673,0.6062070639954555],"dir":"ltr"},{"str":"Section","boundary":[0.37543493835274666,0.5909344986644381,0.43914418537814687,0.6062070639954555],"dir":"ltr"},{"str":"11.1,","boundary":[0.44333480292992616,0.5909344986644381,0.4828689307769012,0.6062070639954555],"dir":"ltr"},{"str":"with","boundary":[0.48719791777614496,0.5909344986644381,0.5245379015276128,0.6062070639954555],"dir":"ltr"},{"str":"methods","boundary":[0.5287285190793922,0.5909344986644381,0.6023212980665362,0.6062070639954555],"dir":"ltr"},{"str":"for","boundary":[0.6065119156183155,0.5909344986644381,0.6317742233125325,0.6062070639954555],"dir":"ltr"},{"str":"obtaining","boundary":[0.6359648408643119,0.5909344986644381,0.717266774781616,0.6062070639954555],"dir":"ltr"},{"str":"lower","boundary":[0.7214573923333953,0.5909344986644381,0.7697878636263222,0.6062070639954555],"dir":"ltr"},{"str":"bounds,","boundary":[0.7739784811781016,0.5909344986644381,0.8404748842167137,0.6062070639954555],"dir":"ltr"},{"str":"which","boundary":[0.8448038712159575,0.5909344986644381,0.8953284866043916,0.6062070639954555],"dir":"ltr"},{"str":"are","boundary":[0.8995191041561708,0.5909344986644381,0.9269755559458949,0.6062070639954555],"dir":"ltr"},{"str":"estimates","boundary":[0.2391014984724533,0.6092615770616588,0.3192569426821952,0.6245341423926762],"dir":"ltr"},{"str":"on","boundary":[0.3244359134301489,0.6092615770616588,0.346416888513067,0.6245341423926762],"dir":"ltr"},{"str":"a","boundary":[0.35159585926102066,0.6092615770616588,0.36147939122276446,0.6245341423926762],"dir":"ltr"},{"str":"minimum","boundary":[0.36665836197071816,0.6092615770616588,0.4490277173398906,0.6245341423926762],"dir":"ltr"},{"str":"amount","boundary":[0.45420668808784437,0.6092615770616588,0.5201100792087517,0.6245341423926762],"dir":"ltr"},{"str":"of","boundary":[0.5252890499567054,0.6092615770616588,0.5428619697846858,0.6245341423926762],"dir":"ltr"},{"str":"work","boundary":[0.5480409405326395,0.6092615770616588,0.5919831236345523,0.6245341423926762],"dir":"ltr"},{"str":"needed","boundary":[0.597162094382506,0.6092615770616588,0.6597841528921145,0.6245341423926762],"dir":"ltr"},{"str":"to","boundary":[0.664963123640068,0.6092615770616588,0.6825360434680484,0.6245341423926762],"dir":"ltr"},{"str":"solve","boundary":[0.6877150142160022,0.6092615770616588,0.731657197317915,0.6245341423926762],"dir":"ltr"},{"str":"a","boundary":[0.7368361680658687,0.6092615770616588,0.7467197000276123,0.6245341423926762],"dir":"ltr"},{"str":"problem.","boundary":[0.7518986707755662,0.6092615770616588,0.8293460272277902,0.6245341423926762],"dir":"ltr"},{"str":"In","boundary":[0.8345249979757439,0.6092615770616588,0.8532048733834395,0.6245341423926762],"dir":"ltr"},{"str":"general,","boundary":[0.8583838441313933,0.6092615770616588,0.9270348571376654,0.6245341423926762],"dir":"ltr"},{"str":"obtaining","boundary":[0.2391014984724533,0.6275886554588797,0.3204034323897574,0.6428612207898969],"dir":"ltr"},{"str":"a","boundary":[0.3254440336902467,0.6275886554588797,0.33532756565199046,0.6428612207898969],"dir":"ltr"},{"str":"nontrivial","boundary":[0.34036816695247973,0.6275886554588797,0.42386424496529096,0.6428612207898969],"dir":"ltr"},{"str":"lower","boundary":[0.4289048462657803,0.6275886554588797,0.4772353175587073,0.6428612207898969],"dir":"ltr"},{"str":"bound","boundary":[0.4822759188591966,0.6275886554588797,0.5372283565664919,0.6428612207898969],"dir":"ltr"},{"str":"even","boundary":[0.5422689578669811,0.6275886554588797,0.5829100412936714,0.6428612207898969],"dir":"ltr"},{"str":"for","boundary":[0.5879506425941609,0.6275886554588797,0.6132129502883779,0.6428612207898969],"dir":"ltr"},{"str":"a","boundary":[0.6182535515888671,0.6275886554588797,0.6281370835506107,0.6428612207898969],"dir":"ltr"},{"str":"simple-sounding","boundary":[0.6331776848511002,0.6275886554588797,0.7738005776027902,0.6428612207898969],"dir":"ltr"},{"str":"problem","boundary":[0.7788411789032795,0.6275886554588797,0.8513467693746317,0.6428612207898969],"dir":"ltr"},{"str":"is","boundary":[0.856387370675121,0.6275886554588797,0.8695720023120872,0.6428612207898969],"dir":"ltr"},{"str":"a","boundary":[0.8746126036125766,0.6275886554588797,0.8844961355743203,0.6428612207898969],"dir":"ltr"},{"str":"very","boundary":[0.8895367368748097,0.6275886554588797,0.9268767206262777,0.6428612207898969],"dir":"ltr"},{"str":"difficult","boundary":[0.2391014984724533,0.6459157338561005,0.30500488959336064,0.6611882991871177],"dir":"ltr"},{"str":"task.","boundary":[0.3101443262134674,0.6459157338561005,0.35023193185030005,0.6611882991871177],"dir":"ltr"},{"str":"As","boundary":[0.3553713684704068,0.6459157338561005,0.379625555904526,0.6611882991871177],"dir":"ltr"},{"str":"opposed","boundary":[0.3847649925246327,0.6459157338561005,0.45729035005990837,0.6611882991871177],"dir":"ltr"},{"str":"to","boundary":[0.46242978668001516,0.6459157338561005,0.4800027065079956,0.6611882991871177],"dir":"ltr"},{"str":"ascertaining","boundary":[0.4851421431281022,0.6459157338561005,0.5883855180004774,0.6611882991871177],"dir":"ltr"},{"str":"the","boundary":[0.5935249546205842,0.6459157338561005,0.6209814064103083,0.6611882991871177],"dir":"ltr"},{"str":"efficiency","boundary":[0.6261208430304152,0.6459157338561005,0.7070274356692494,0.6611882991871177],"dir":"ltr"},{"str":"of","boundary":[0.7121668722893564,0.6459157338561005,0.7297397921173367,0.6611882991871177],"dir":"ltr"},{"str":"a","boundary":[0.7348792287374434,0.6459157338561005,0.7447627606991871,0.6611882991871177],"dir":"ltr"},{"str":"particular","boundary":[0.749902197319294,0.6459157338561005,0.8333785082681817,0.6611882991871177],"dir":"ltr"},{"str":"algorithm,","boundary":[0.8385179448882885,0.6459157338561005,0.9269360218180481,0.6611882991871177],"dir":"ltr"},{"str":"the","boundary":[0.2391014984724533,0.6642428122533213,0.26655795026217743,0.6795153775843386],"dir":"ltr"},{"str":"task","boundary":[0.2724287682474532,0.6642428122533213,0.307574607903414,0.6795153775843386],"dir":"ltr"},{"str":"here","boundary":[0.31344542588868984,0.6642428122533213,0.351892365219873,0.6795153775843386],"dir":"ltr"},{"str":"is","boundary":[0.3577631832051488,0.6642428122533213,0.370947814842115,0.6795153775843386],"dir":"ltr"},{"str":"to","boundary":[0.37681863282739075,0.6642428122533213,0.3943915526553711,0.6795153775843386],"dir":"ltr"},{"str":"establish","boundary":[0.40026237064064696,0.6642428122533213,0.4749621052075062,0.6795153775843386],"dir":"ltr"},{"str":"a","boundary":[0.48083292319278204,0.6642428122533213,0.4907164551545258,0.6795153775843386],"dir":"ltr"},{"str":"limit","boundary":[0.4965872731398016,0.6642428122533213,0.5361214009867766,0.6795153775843386],"dir":"ltr"},{"str":"on","boundary":[0.5419922189720524,0.6642428122533213,0.5639731940549705,0.6795153775843386],"dir":"ltr"},{"str":"the","boundary":[0.5698440120402464,0.6642428122533213,0.5973004638299705,0.6795153775843386],"dir":"ltr"},{"str":"efficiency","boundary":[0.6031712818152463,0.6642428122533213,0.6840778744540805,0.6795153775843386],"dir":"ltr"},{"str":"of","boundary":[0.6899486924393564,0.6642428122533213,0.7075216122673368,0.6795153775843386],"dir":"ltr"},{"str":"any","boundary":[0.713293594932995,0.6642428122533213,0.7440511463979417,0.6795153775843386],"dir":"ltr"},{"str":"algorithm,","boundary":[0.7497163869184131,0.6642428122533213,0.8381344638481727,0.6795153775843386],"dir":"ltr"},{"str":"known","boundary":[0.8442227195366069,0.6642428122533213,0.902456489855201,0.6795153775843386],"dir":"ltr"},{"str":"or","boundary":[0.9083273078404769,0.6642428122533213,0.9270071832481726,0.6795153775843386],"dir":"ltr"},{"str":"unknown.","boundary":[0.2391014984724533,0.682569890650542,0.3242580098548375,0.6978424559815594],"dir":"ltr"},{"str":"This","boundary":[0.32870559923762216,0.682569890650542,0.36527466749607407,0.6978424559815594],"dir":"ltr"},{"str":"also","boundary":[0.36972225687885873,0.682569890650542,0.4037809080190277,0.6978424559815594],"dir":"ltr"},{"str":"necessitates","boundary":[0.4082284974018124,0.682569890650542,0.5092579611147571,0.6978424559815594],"dir":"ltr"},{"str":"a","boundary":[0.5137055504975417,0.682569890650542,0.5235890824592854,0.6978424559815594],"dir":"ltr"},{"str":"careful","boundary":[0.5280366718420701,0.682569890650542,0.5873378636125326,0.6978424559815594],"dir":"ltr"},{"str":"description","boundary":[0.5917854529953173,0.682569890650542,0.6873592070653795,0.6978424559815594],"dir":"ltr"},{"str":"of","boundary":[0.6918067964481642,0.682569890650542,0.7093797162761446,0.6978424559815594],"dir":"ltr"},{"str":"the","boundary":[0.7138273056589293,0.682569890650542,0.7412837574486534,0.6978424559815594],"dir":"ltr"},{"str":"operations","boundary":[0.7457313468314382,0.682569890650542,0.836916812710486,0.6978424559815594],"dir":"ltr"},{"str":"such","boundary":[0.8413644020932707,0.682569890650542,0.8798113414244538,0.6978424559815594],"dir":"ltr"},{"str":"algo-","boundary":[0.8842589308072386,0.682569890650542,0.927094158329436,0.6978424559815594],"dir":"ltr"},{"str":"rithms","boundary":[0.2391014984724533,0.7008969690477627,0.29401440205190155,0.7161695343787801],"dir":"ltr"},{"str":"are","boundary":[0.29745387117458844,0.7008969690477627,0.3249103229643126,0.7161695343787801],"dir":"ltr"},{"str":"allowed","boundary":[0.3283497920869994,0.7008969690477627,0.39536013878762205,0.7161695343787801],"dir":"ltr"},{"str":"to","boundary":[0.3987996079103089,0.7008969690477627,0.4163725277382893,0.7161695343787801],"dir":"ltr"},{"str":"perform.","boundary":[0.41981199686097603,0.7008969690477627,0.49504544215376955,0.7161695343787801],"dir":"ltr"},{"str":"If","boundary":[0.49848491127645633,0.7008969690477627,0.5127567314292143,0.7161695343787801],"dir":"ltr"},{"str":"we","boundary":[0.5161962005519011,0.7008969690477627,0.5403515526664028,0.7161695343787801],"dir":"ltr"},{"str":"fail","boundary":[0.5437910217890897,0.7008969690477627,0.5712474735788138,0.7161695343787801],"dir":"ltr"},{"str":"to","boundary":[0.5746869427015006,0.7008969690477627,0.5922598625294809,0.7161695343787801],"dir":"ltr"},{"str":"define","boundary":[0.5956993316521679,0.7008969690477627,0.6484378582000325,0.7161695343787801],"dir":"ltr"},{"str":"carefully","boundary":[0.6518773273227193,0.7008969690477627,0.726557294825655,0.7161695343787801],"dir":"ltr"},{"str":"the","boundary":[0.7299967639483418,0.7008969690477627,0.7574532157380659,0.7161695343787801],"dir":"ltr"},{"str":"“rules","boundary":[0.7608926848607528,0.7008969690477627,0.8125242558289022,0.7161695343787801],"dir":"ltr"},{"str":"of","boundary":[0.815963724951589,0.7008969690477627,0.8335366447795693,0.7161695343787801],"dir":"ltr"},{"str":"the","boundary":[0.8369761139022562,0.7008969690477627,0.8644325656919803,0.7161695343787801],"dir":"ltr"},{"str":"game,”","boundary":[0.8678720348146671,0.7008969690477627,0.9269953230098182,0.7161695343787801],"dir":"ltr"},{"str":"so","boundary":[0.2391014984724533,0.7192240474449836,0.257781373880149,0.7344966127760009],"dir":"ltr"},{"str":"to","boundary":[0.2639091636964301,0.7192240474449836,0.2814820835244105,0.7344966127760009],"dir":"ltr"},{"str":"speak,","boundary":[0.2876098733406916,0.7192240474449836,0.34198906619420577,0.7344966127760009],"dir":"ltr"},{"str":"our","boundary":[0.3484133619693392,0.7192240474449836,0.37808372491849396,0.7344966127760009],"dir":"ltr"},{"str":"claims","boundary":[0.3842115147347751,0.7192240474449836,0.4380174627345081,0.7344966127760009],"dir":"ltr"},{"str":"may","boundary":[0.4441452525507892,0.7192240474449836,0.4803782807225418,0.7344966127760009],"dir":"ltr"},{"str":"end","boundary":[0.48650607053882294,0.7192240474449836,0.5183705775834848,0.7344966127760009],"dir":"ltr"},{"str":"up","boundary":[0.5244983673997659,0.7192240474449836,0.546479342482684,0.7344966127760009],"dir":"ltr"},{"str":"in","boundary":[0.5526071322989652,0.7192240474449836,0.5690928636111537,0.7344966127760009],"dir":"ltr"},{"str":"the","boundary":[0.5752206534274349,0.7192240474449836,0.602677105217159,0.7344966127760009],"dir":"ltr"},{"str":"large","boundary":[0.6088048950334402,0.7192240474449836,0.6516401225556375,0.7344966127760009],"dir":"ltr"},{"str":"dustbin","boundary":[0.6577679123719186,0.7192240474449836,0.7214969264612423,0.7344966127760009],"dir":"ltr"},{"str":"of","boundary":[0.7276247162775235,0.7192240474449836,0.7451976361055038,0.7344966127760009],"dir":"ltr"},{"str":"impossibility-related","boundary":[0.7513254259217849,0.7192240474449836,0.9270743912655123,0.7344966127760009],"dir":"ltr"},{"str":"statements","boundary":[0.2391014984724533,0.7375511258422044,0.331334618739446,0.7528236911732217],"dir":"ltr"},{"str":"as,","boundary":[0.3357031398665367,0.7375511258422044,0.35713063715959714,0.7528236911732217],"dir":"ltr"},{"str":"for","boundary":[0.3616177606702289,0.7375511258422044,0.38688006836444594,0.7528236911732217],"dir":"ltr"},{"str":"example,","boundary":[0.3912485894915366,0.7375511258422044,0.46794479751466816,0.7528236911732217],"dir":"ltr"},{"str":"the","boundary":[0.47243192102529985,0.7375511258422044,0.499888372815024,0.7528236911732217],"dir":"ltr"},{"str":"one","boundary":[0.5042568939421147,0.7375511258422044,0.5361214009867765,0.7528236911732217],"dir":"ltr"},{"str":"made","boundary":[0.5404899221138673,0.7375511258422044,0.587713437827079,0.7528236911732217],"dir":"ltr"},{"str":"by","boundary":[0.5920819589541697,0.7375511258422044,0.6129559784573725,0.7528236911732217],"dir":"ltr"},{"str":"the","boundary":[0.6173244995844632,0.7375511258422044,0.6447809513741873,0.7528236911732217],"dir":"ltr"},{"str":"celebrated","boundary":[0.6491494725012782,0.7375511258422044,0.7392082157366872,0.7528236911732217],"dir":"ltr"},{"str":"British","boundary":[0.743576736863778,0.7375511258422044,0.8017907401184486,0.7528236911732217],"dir":"ltr"},{"str":"physicist","boundary":[0.8061592612455394,0.7375511258422044,0.8797520402326834,0.7528236911732217],"dir":"ltr"},{"str":"Lord","boundary":[0.884120561359774,0.7375511258422044,0.9269755559458949,0.7528236911732217],"dir":"ltr"},{"str":"Kelvin","boundary":[0.2391014984724533,0.7558782042394251,0.2960306425720973,0.7711507695704424],"dir":"ltr"},{"str":"in","boundary":[0.3009724085529692,0.7558782042394251,0.3174581398651578,0.7711507695704424],"dir":"ltr"},{"str":"1895:","boundary":[0.3223999058460296,0.7558782042394251,0.3668757996738765,0.7711507695704424],"dir":"ltr"},{"str":"“Heavier-than-air","boundary":[0.37181756565474844,0.7558782042394251,0.5244786003358424,0.7711507695704424],"dir":"ltr"},{"str":"flying","boundary":[0.5294203663167143,0.7558782042394251,0.5766636490938495,0.7711507695704424],"dir":"ltr"},{"str":"machines","boundary":[0.5816054150747213,0.7558782042394251,0.6617806263483866,0.7711507695704424],"dir":"ltr"},{"str":"are","boundary":[0.6667223923292586,0.7558782042394251,0.6941788441189827,0.7711507695704424],"dir":"ltr"},{"str":"impossible.”","boundary":[0.6991206100998546,0.7558782042394251,0.8033128040405573,0.7711507695704424],"dir":"ltr"},{"str":"Section","boundary":[0.2746822135347308,0.7742052826366458,0.33839146056013103,0.7894778479676632],"dir":"ltr"},{"str":"11.2","boundary":[0.34430181267325377,0.7742052826366458,0.3788941745393569,0.7894778479676632],"dir":"ltr"},{"str":"discusses","boundary":[0.3848045266524797,0.7742052826366458,0.4616984053148461,0.7894778479676632],"dir":"ltr"},{"str":"decision","boundary":[0.4676087574279689,0.7742052826366458,0.537920203803814,0.7894778479676632],"dir":"ltr"},{"str":"trees.","boundary":[0.5438305559169367,0.7742052826366458,0.5894134053244989,0.7894778479676632],"dir":"ltr"},{"str":"This","boundary":[0.5953237574376216,0.7742052826366458,0.6318928256960735,0.7894778479676632],"dir":"ltr"},{"str":"technique","boundary":[0.6378031778091963,0.7742052826366458,0.7223864443377993,0.7894778479676632],"dir":"ltr"},{"str":"allows","boundary":[0.7282967964509222,0.7742052826366458,0.7821225115145787,0.7894778479676632],"dir":"ltr"},{"str":"us,","boundary":[0.7880328636277013,0.7742052826366458,0.8105673165004771,0.7894778479676632],"dir":"ltr"},{"str":"among","boundary":[0.8167148733806816,0.7742052826366458,0.8749288766353523,0.7894778479676632],"dir":"ltr"},{"str":"other","boundary":[0.8808392287484752,0.7742052826366458,0.926975555945895,0.7894778479676632],"dir":"ltr"},{"str":"applications,","boundary":[0.2391014984724533,0.7925338882903998,0.34621921787383214,0.8078064536214171],"dir":"ltr"},{"str":"to","boundary":[0.355094629575478,0.7925338882903998,0.37266754940345836,0.8078064536214171],"dir":"ltr"},{"str":"establish","boundary":[0.3807522785481648,0.7925338882903998,0.45545201311502403,0.8078064536214171],"dir":"ltr"},{"str":"lower","boundary":[0.46353674225973046,0.7925338882903998,0.5118672135526574,0.8078064536214171],"dir":"ltr"},{"str":"bounds","boundary":[0.5199519426973639,0.7925338882903998,0.5825937682708957,0.8078064536214171],"dir":"ltr"},{"str":"on","boundary":[0.5906784974156022,0.7925338882903998,0.6126594724985203,0.8078064536214171],"dir":"ltr"},{"str":"the","boundary":[0.6207442016432266,0.7925338882903998,0.6482006534329507,0.8078064536214171],"dir":"ltr"},{"str":"efficiency","boundary":[0.6562853825776571,0.7925338882903998,0.7371919752164915,0.8078064536214171],"dir":"ltr"},{"str":"of","boundary":[0.7452767043611979,0.7925338882903998,0.7628496241891782,0.8078064536214171],"dir":"ltr"},{"str":"comparison-based","boundary":[0.7709343533338846,0.7925338882903998,0.9269162547541245,0.8078064536214171],"dir":"ltr"},{"str":"algorithms","boundary":[0.2391014984724533,0.8108609666876205,0.3302671972875777,0.8261335320186378],"dir":"ltr"},{"str":"for","boundary":[0.3362170835285474,0.8108609666876205,0.36147939122276446,0.8261335320186378],"dir":"ltr"},{"str":"sorting","boundary":[0.3674292774637342,0.8108609666876205,0.4267502362981202,0.8261335320186378],"dir":"ltr"},{"str":"and","boundary":[0.43270012253908996,0.8108609666876205,0.46456462958375183,0.8261335320186378],"dir":"ltr"},{"str":"for","boundary":[0.47051451582472154,0.8108609666876205,0.4957768235189386,0.8261335320186378],"dir":"ltr"},{"str":"searching","boundary":[0.5017267097599084,0.8108609666876205,0.583008876613289,0.8261335320186378],"dir":"ltr"},{"str":"in","boundary":[0.5889587628542586,0.8108609666876205,0.6054444941664471,0.8261335320186378],"dir":"ltr"},{"str":"sorted","boundary":[0.6113943804074169,0.8108609666876205,0.6652200954710734,0.8261335320186378],"dir":"ltr"},{"str":"arrays.","boundary":[0.6711699817120431,0.8108609666876205,0.7277433186610643,0.8261335320186378],"dir":"ltr"},{"str":"As","boundary":[0.7336932049020342,0.8108609666876205,0.7579473923361533,0.8261335320186378],"dir":"ltr"},{"str":"a","boundary":[0.763897278577123,0.8108609666876205,0.7737808105388666,0.8261335320186378],"dir":"ltr"},{"str":"result,","boundary":[0.7797306967798364,0.8108609666876205,0.8330029340536352,0.8261335320186378],"dir":"ltr"},{"str":"we","boundary":[0.8392097921256104,0.8108609666876205,0.8633651442401121,0.8261335320186378],"dir":"ltr"},{"str":"will","boundary":[0.8693150304810818,0.8108609666876205,0.9000725819460283,0.8261335320186378],"dir":"ltr"},{"str":"be","boundary":[0.9060224681869982,0.8108609666876205,0.9268964876902009,0.8261335320186378],"dir":"ltr"},{"str":"able","boundary":[0.2391014984724533,0.8291880450848413,0.2753542937081294,0.8444606104158585],"dir":"ltr"},{"str":"to","boundary":[0.28126464582125216,0.8291880450848413,0.2988375656492326,0.8444606104158585],"dir":"ltr"},{"str":"answer","boundary":[0.30474791776235527,0.8291880450848413,0.36515606511253307,0.8444606104158585],"dir":"ltr"},{"str":"such","boundary":[0.3710664172256559,0.8291880450848413,0.4095133565568391,0.8444606104158585],"dir":"ltr"},{"str":"questions","boundary":[0.41542370866996187,0.8291880450848413,0.496725642587266,0.8444606104158585],"dir":"ltr"},{"str":"as","boundary":[0.5026359947003888,0.8291880450848413,0.5202089145283691,0.8444606104158585],"dir":"ltr"},{"str":"whether","boundary":[0.5261192666414919,0.8291880450848413,0.5964109459534135,0.8444606104158585],"dir":"ltr"},{"str":"it","boundary":[0.6023212980665363,0.8291880450848413,0.6143989741237871,0.8444606104158585],"dir":"ltr"},{"str":"is","boundary":[0.6203093262369098,0.8291880450848413,0.633493957873876,0.8444606104158585],"dir":"ltr"},{"str":"possible","boundary":[0.6394043099869988,0.8291880450848413,0.7086285678470521,0.8444606104158585],"dir":"ltr"},{"str":"to","boundary":[0.7145389199601747,0.8291880450848413,0.7321118397881551,0.8444606104158585],"dir":"ltr"},{"str":"invent","boundary":[0.7380221919012779,0.8291880450848413,0.7918479069649345,0.8444606104158585],"dir":"ltr"},{"str":"a","boundary":[0.7977582590780571,0.8291880450848413,0.8076417910398008,0.8444606104158585],"dir":"ltr"},{"str":"faster","boundary":[0.8135521431529237,0.8291880450848413,0.8618628473819271,0.8444606104158585],"dir":"ltr"},{"str":"sorting","boundary":[0.8677731994950498,0.8291880450848413,0.9270941583294359,0.8444606104158585],"dir":"ltr"},{"str":"algorithm","boundary":[0.2391014984724533,0.8475151234820623,0.32257780942134107,0.8627876888130794],"dir":"ltr"},{"str":"than","boundary":[0.32829049089522894,0.8475151234820623,0.3667374302264121,0.8627876888130794],"dir":"ltr"},{"str":"mergesort","boundary":[0.3724501117003,0.8475151234820623,0.4592077552604867,0.8627876888130794],"dir":"ltr"},{"str":"and","boundary":[0.46492043673437455,0.8475151234820623,0.4967849437790364,0.8627876888130794],"dir":"ltr"},{"str":"whether","boundary":[0.5024976252529243,0.8475151234820623,0.5727893045648459,0.8627876888130794],"dir":"ltr"},{"str":"binary","boundary":[0.5785019860387337,0.8475151234820623,0.6334346566821055,0.8627876888130794],"dir":"ltr"},{"str":"search","boundary":[0.6391473381559934,0.8475151234820623,0.6940602417354418,0.8627876888130794],"dir":"ltr"},{"str":"is","boundary":[0.6997729232093297,0.8475151234820623,0.7129575548462959,0.8627876888130794],"dir":"ltr"},{"str":"the","boundary":[0.7186702363201838,0.8475151234820623,0.7461266881099079,0.8627876888130794],"dir":"ltr"},{"str":"fastest","boundary":[0.7518393695837958,0.8475151234820623,0.8067325060993206,0.8627876888130794],"dir":"ltr"},{"str":"algorithm","boundary":[0.8124451875732086,0.8475151234820623,0.8959214985220963,0.8627876888130794],"dir":"ltr"},{"str":"for","boundary":[0.9016341799959843,0.8475151234820623,0.9268964876902013,0.8627876888130794],"dir":"ltr"},{"str":"searching","boundary":[0.2391014984724533,0.865842201879283,0.3203836653258339,0.8811147672103001],"dir":"ltr"},{"str":"in","boundary":[0.324198708663067,0.865842201879283,0.3406844399752556,0.8811147672103001],"dir":"ltr"},{"str":"a","boundary":[0.34449948331248864,0.865842201879283,0.35438301527423244,0.8811147672103001],"dir":"ltr"},{"str":"sorted","boundary":[0.3581980586114655,0.865842201879283,0.41202377367512194,0.8811147672103001],"dir":"ltr"},{"str":"array.","boundary":[0.415838817012355,0.865842201879283,0.4639913847299706,0.8811147672103001],"dir":"ltr"},{"str":"(What","boundary":[0.4678064280672037,0.865842201879283,0.5223635244960292,0.8811147672103001],"dir":"ltr"},{"str":"does","boundary":[0.5261785678332622,0.865842201879283,0.5657324627441608,0.8811147672103001],"dir":"ltr"},{"str":"your","boundary":[0.5695475060813938,0.865842201879283,0.6091014009922923,0.8811147672103001],"dir":"ltr"},{"str":"intuition","boundary":[0.6129164443295255,0.865842201879283,0.6865289903805929,0.8811147672103001],"dir":"ltr"},{"str":"tell","boundary":[0.6903440337178262,0.865842201879283,0.7178004855075503,0.8811147672103001],"dir":"ltr"},{"str":"you","boundary":[0.7216155288447833,0.865842201879283,0.7534800358894451,0.8811147672103001],"dir":"ltr"},{"str":"the","boundary":[0.7572950792266783,0.865842201879283,0.7847515310164024,0.8811147672103001],"dir":"ltr"},{"str":"answers","boundary":[0.7885665743536355,0.865842201879283,0.85666410957005,0.8811147672103001],"dir":"ltr"},{"str":"to","boundary":[0.8604791529072832,0.865842201879283,0.8780520727352635,0.8811147672103001],"dir":"ltr"},{"str":"these","boundary":[0.8818671160724966,0.865842201879283,0.9268964876902012,0.8811147672103001],"dir":"ltr"},{"str":"questions","boundary":[0.2391014984724533,0.8841692802765037,0.3204034323897574,0.8994418456075209],"dir":"ltr"},{"str":"will","boundary":[0.3251672947953179,0.8841692802765037,0.3559248462602645,0.8994418456075209],"dir":"ltr"},{"str":"turn","boundary":[0.3606887086658249,0.8841692802765037,0.39694150390150107,0.8994418456075209],"dir":"ltr"},{"str":"out","boundary":[0.4017053663070615,0.8841692802765037,0.43026877367650096,0.8994418456075209],"dir":"ltr"},{"str":"to","boundary":[0.43503263608206144,0.8841692802765037,0.4526055559100418,0.8994418456075209],"dir":"ltr"},{"str":"be?)","boundary":[0.4573694183156023,0.8841692802765037,0.49581635764678544,0.8994418456075209],"dir":"ltr"},{"str":"Incidentally,","boundary":[0.5005802200523459,0.8841692802765037,0.6058596025088405,0.8994418456075209],"dir":"ltr"},{"str":"decision","boundary":[0.610662999042248,0.8841692802765037,0.680974445418093,0.8994418456075209],"dir":"ltr"},{"str":"trees","boundary":[0.6857383078236534,0.8841692802765037,0.7274665797661356,0.8994418456075209],"dir":"ltr"},{"str":"are","boundary":[0.732230442171696,0.8841692802765037,0.7596868939614201,0.8994418456075209],"dir":"ltr"},{"str":"also","boundary":[0.7644507563669807,0.8841692802765037,0.7985094075071497,0.8994418456075209],"dir":"ltr"},{"str":"a","boundary":[0.8032732699127102,0.8841692802765037,0.8131568018744538,0.8994418456075209],"dir":"ltr"},{"str":"great","boundary":[0.8179206642800144,0.8841692802765037,0.8618430803180037,0.8994418456075209],"dir":"ltr"},{"str":"vehicle","boundary":[0.8666069427235641,0.8841692802765037,0.9270150900737418,0.8994418456075209],"dir":"ltr"},{"str":"387","boundary":[0.8940238603854413,0.9329345813784419,0.9269953230098185,0.948207146709459],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92709,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":449,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/4ab63736df6f358bea4ee6f4d497a46c.jpg","blurred":"/storage/books/4a8b03583f119702/pages/31c8e1e8be1b33d5878ef2c7d3b6a40f.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.07999,0.07291,0.05179]},"elements":[{"words":[{"str":"12","boundary":[0.14421784044919886,0.07999453587206534,0.27079088646567406,0.15330318671872986],"dir":"ltr"},{"str":"Coping","boundary":[0.14421784044919886,0.17005356781848974,0.3149582602471048,0.20670781659232623],"dir":"ltr"},{"str":"with","boundary":[0.33075613737761406,0.17005356781848974,0.43835248972594715,0.20670781659232623],"dir":"ltr"},{"str":"the","boundary":[0.45415036685645643,0.17005356781848974,0.5315741971176907,0.20670781659232623],"dir":"ltr"},{"str":"Limitations","boundary":[0.5473720742482001,0.17005356781848974,0.8163155140465689,0.20670781659232623],"dir":"ltr"},{"str":"of","boundary":[0.14421784044919886,0.20976111551518684,0.1940784076088541,0.24641536428902333],"dir":"ltr"},{"str":"Algorithm","boundary":[0.20987628473936334,0.20976111551518684,0.4526796936100726,0.24641536428902333],"dir":"ltr"},{"str":"Power","boundary":[0.46847757074058183,0.20976111551518684,0.6220917633789869,0.24641536428902333],"dir":"ltr"},{"str":"Keep","boundary":[0.23910077902799318,0.3142741587391314,0.2819360065501906,0.32954672407014873],"dir":"ltr"},{"str":"on","boundary":[0.28836030232532406,0.3142741587391314,0.3103412774082422,0.32954672407014873],"dir":"ltr"},{"str":"the","boundary":[0.3167655731833756,0.3142741587391314,0.34202788087759267,0.32954672407014873],"dir":"ltr"},{"str":"lookout","boundary":[0.3484521766527261,0.3142741587391314,0.4143951019014804,0.32954672407014873],"dir":"ltr"},{"str":"for","boundary":[0.42081939767661386,0.3142741587391314,0.4460817053708309,0.32954672407014873],"dir":"ltr"},{"str":"novel","boundary":[0.45250600114596434,0.3142741587391314,0.4982865211927614,0.32954672407014873],"dir":"ltr"},{"str":"ideas","boundary":[0.5047108169678948,0.3142741587391314,0.5475460444900923,0.32954672407014873],"dir":"ltr"},{"str":"that","boundary":[0.5539703402652256,0.3142741587391314,0.5858348473098874,0.32954672407014873],"dir":"ltr"},{"str":"others","boundary":[0.5922591430850209,0.3142741587391314,0.6438907140531702,0.32954672407014873],"dir":"ltr"},{"str":"have","boundary":[0.6503150098283036,0.3142741587391314,0.6898491376752786,0.32954672407014873],"dir":"ltr"},{"str":"used","boundary":[0.696273433450412,0.3142741587391314,0.7347203727815952,0.32954672407014873],"dir":"ltr"},{"str":"successfully.","boundary":[0.7411446685567287,0.3142741587391314,0.8438345656392463,0.32954672407014873],"dir":"ltr"},{"str":"Your","boundary":[0.23910077902799318,0.3326012371363522,0.281224392248945,0.34787380246736954],"dir":"ltr"},{"str":"idea","boundary":[0.286897539594986,0.3326012371363522,0.3220433792509467,0.34787380246736954],"dir":"ltr"},{"str":"has","boundary":[0.32771652659698763,0.3326012371363522,0.3562799339664271,0.34787380246736954],"dir":"ltr"},{"str":"to","boundary":[0.36195308131246806,0.3326012371363522,0.3784388126246566,0.34787380246736954],"dir":"ltr"},{"str":"be","boundary":[0.38411195997069747,0.3326012371363522,0.403879023894185,0.34787380246736954],"dir":"ltr"},{"str":"original","boundary":[0.40955217124022597,0.3326012371363522,0.4754753294250568,0.34787380246736954],"dir":"ltr"},{"str":"only","boundary":[0.4811484767710977,0.3326012371363522,0.5185082275864891,0.34787380246736954],"dir":"ltr"},{"str":"in","boundary":[0.52418137493253,0.3326012371363522,0.5406671062447186,0.34787380246736954],"dir":"ltr"},{"str":"its","boundary":[0.5463402535907594,0.3326012371363522,0.5650201289984551,0.34787380246736954],"dir":"ltr"},{"str":"adaptation","boundary":[0.5706932763444961,0.3326012371363522,0.6607915537077522,0.34787380246736954],"dir":"ltr"},{"str":"to","boundary":[0.666464701053793,0.3326012371363522,0.6829504323659815,0.34787380246736954],"dir":"ltr"},{"str":"the","boundary":[0.6886235797120225,0.3326012371363522,0.7138858874062395,0.34787380246736954],"dir":"ltr"},{"str":"problem","boundary":[0.7195590347522804,0.3326012371363522,0.7909576696439173,0.34787380246736954],"dir":"ltr"},{"str":"you’re","boundary":[0.7966308169899583,0.3326012371363522,0.8499623554555277,0.34787380246736954],"dir":"ltr"},{"str":"working","boundary":[0.23910077902799318,0.350928315533573,0.3094122254038382,0.36620088086459035],"dir":"ltr"},{"str":"on.","boundary":[0.31435399138471015,0.350928315533573,0.3412767324485001,0.36620088086459035],"dir":"ltr"},{"str":"—Thomas","boundary":[0.6056999933783728,0.3728560522837372,0.6894720874686368,0.3873650353379011],"dir":"ltr"},{"str":"Edison","boundary":[0.6942043375719199,0.3728560522837372,0.7516110382296058,0.3873650353379011],"dir":"ltr"},{"str":"(1847–1931)","boundary":[0.7563432883328891,0.3728560522837372,0.8554576377183213,0.3873650353379011],"dir":"ltr"},{"str":"s","boundary":[0.2884995896299513,0.462644587699695,0.29618897749618794,0.47791715303071236],"dir":"ltr"},{"str":"we","boundary":[0.3030876828054851,0.462644587699695,0.32724303491998685,0.47791715303071236],"dir":"ltr"},{"str":"saw","boundary":[0.334141740229284,0.462644587699695,0.36598648021002234,0.47791715303071236],"dir":"ltr"},{"str":"in","boundary":[0.3728851855193195,0.462644587699695,0.3893709168315081,0.47791715303071236],"dir":"ltr"},{"str":"the","boundary":[0.3962696221408052,0.462644587699695,0.42372607393052936,0.47791715303071236],"dir":"ltr"},{"str":"previous","boundary":[0.43062477923982645,0.462644587699695,0.5042373252908939,0.47791715303071236],"dir":"ltr"},{"str":"chapter,","boundary":[0.5111360306001911,0.462644587699695,0.5805184249716323,0.47791715303071236],"dir":"ltr"},{"str":"there","boundary":[0.5879113068790166,0.462644587699695,0.6329406784967211,0.47791715303071236],"dir":"ltr"},{"str":"are","boundary":[0.6398393838060183,0.462644587699695,0.6672958355957425,0.47791715303071236],"dir":"ltr"},{"str":"problems","boundary":[0.6741945409050395,0.462644587699695,0.7543895192426283,0.47791715303071236],"dir":"ltr"},{"str":"that","boundary":[0.7612882245519255,0.462644587699695,0.795327108628171,0.47791715303071236],"dir":"ltr"},{"str":"are","boundary":[0.8022258139374682,0.462644587699695,0.8296822657271923,0.47791715303071236],"dir":"ltr"},{"str":"difficult","boundary":[0.8365809710364894,0.462644587699695,0.9024843621573969,0.47791715303071236],"dir":"ltr"},{"str":"to","boundary":[0.909383067466694,0.462644587699695,0.9269559872946743,0.47791715303071236],"dir":"ltr"},{"str":"solve","boundary":[0.2884995896299513,0.48097166609691583,0.33244177273186404,0.49624423142793317],"dir":"ltr"},{"str":"algorithmically.","boundary":[0.33688936211464876,0.48097166609691583,0.46851824078115206,0.49624423142793317],"dir":"ltr"},{"str":"At","boundary":[0.47296583016393673,0.48097166609691583,0.4961130620183406,0.49624423142793317],"dir":"ltr"},{"str":"the","boundary":[0.5005606514011252,0.48097166609691583,0.5280171031908493,0.49624423142793317],"dir":"ltr"},{"str":"same","boundary":[0.532464692573634,0.48097166609691583,0.5763871086116233,0.49624423142793317],"dir":"ltr"},{"str":"time,","boundary":[0.580834697994408,0.48097166609691583,0.6234722548773706,0.49624423142793317],"dir":"ltr"},{"str":"some","boundary":[0.6280186795797726,0.48097166609691583,0.6730480511974772,0.49624423142793317],"dir":"ltr"},{"str":"of","boundary":[0.677495640580262,0.48097166609691583,0.6950685604082424,0.49624423142793317],"dir":"ltr"},{"str":"them","boundary":[0.699516149791027,0.48097166609691583,0.7434385658290164,0.49624423142793317],"dir":"ltr"},{"str":"are","boundary":[0.747886155211801,0.48097166609691583,0.7753426070015251,0.49624423142793317],"dir":"ltr"},{"str":"so","boundary":[0.7797901963843099,0.48097166609691583,0.7984700717920055,0.49624423142793317],"dir":"ltr"},{"str":"important","boundary":[0.8029176611747902,0.48097166609691583,0.8885881162191851,0.49624423142793317],"dir":"ltr"},{"str":"that","boundary":[0.8930357056019698,0.48097166609691583,0.9270745896782152,0.49624423142793317],"dir":"ltr"},{"str":"weAcannot","boundary":[0.23910077902799318,0.4613464444809952,0.32767791032630356,0.514571309825154],"dir":"ltr"},{"str":"just","boundary":[0.33388476839827863,0.49929874449413664,0.3646423198632252,0.514571309825154],"dir":"ltr"},{"str":"sigh","boundary":[0.3708491779352002,0.49929874449413664,0.4049078290753692,0.514571309825154],"dir":"ltr"},{"str":"in","boundary":[0.41111468714734434,0.49929874449413664,0.42760041845953295,0.514571309825154],"dir":"ltr"},{"str":"resignation","boundary":[0.43380727653150797,0.49929874449413664,0.52938103060157,0.514571309825154],"dir":"ltr"},{"str":"and","boundary":[0.5355878886735451,0.49929874449413664,0.5674523957182069,0.514571309825154],"dir":"ltr"},{"str":"do","boundary":[0.573659253790182,0.49929874449413664,0.5956402288731001,0.514571309825154],"dir":"ltr"},{"str":"nothing.","boundary":[0.6018470869450752,0.49929874449413664,0.6723562039601552,0.514571309825154],"dir":"ltr"},{"str":"This","boundary":[0.6785630620321302,0.49929874449413664,0.7151321302905822,0.514571309825154],"dir":"ltr"},{"str":"chapter","boundary":[0.7213389883625573,0.49929874449413664,0.7861354239037492,0.514571309825154],"dir":"ltr"},{"str":"outlines","boundary":[0.7923422819757243,0.49929874449413664,0.8604595842560624,0.514571309825154],"dir":"ltr"},{"str":"several","boundary":[0.8666664423280374,0.49929874449413664,0.9270745896782152,0.514571309825154],"dir":"ltr"},{"str":"ways","boundary":[0.23910169688515603,0.5176258228913575,0.28082996882763817,0.5328983882223748],"dir":"ltr"},{"str":"of","boundary":[0.28577173480851004,0.5176258228913575,0.30334465463649046,0.5328983882223748],"dir":"ltr"},{"str":"dealing","boundary":[0.30828642061736233,0.5176258228913575,0.3709084791269707,0.5328983882223748],"dir":"ltr"},{"str":"with","boundary":[0.3758502451078426,0.5176258228913575,0.4131902288593105,0.5328983882223748],"dir":"ltr"},{"str":"such","boundary":[0.41813199484018243,0.5176258228913575,0.45657893417136564,0.5328983882223748],"dir":"ltr"},{"str":"difficult","boundary":[0.4615207001522375,0.5176258228913575,0.5274240912731449,0.5328983882223748],"dir":"ltr"},{"str":"problems.","boundary":[0.5323658572540166,0.5176258228913575,0.6164154130566856,0.5328983882223748],"dir":"ltr"},{"str":"Sections","boundary":[0.27468241194743354,0.5359529012885783,0.3460810468390704,0.5512254666195956],"dir":"ltr"},{"str":"12.1","boundary":[0.35426461130339426,0.5359529012885783,0.3888569731694974,0.5512254666195956],"dir":"ltr"},{"str":"and","boundary":[0.3970405376338212,0.5359529012885783,0.42890504467848306,0.5512254666195956],"dir":"ltr"},{"str":"12.2","boundary":[0.4370886091428069,0.5359529012885783,0.47168097100891004,0.5512254666195956],"dir":"ltr"},{"str":"introduce","boundary":[0.4798645354732338,0.5359529012885783,0.5622536579063298,0.5512254666195956],"dir":"ltr"},{"str":"two","boundary":[0.5704372223706535,0.5359529012885783,0.6022819623513919,0.5512254666195956],"dir":"ltr"},{"str":"algorithm","boundary":[0.6104655268157158,0.5359529012885783,0.6939418377646035,0.5512254666195956],"dir":"ltr"},{"str":"design","boundary":[0.7021254022289273,0.5359529012885783,0.7570580728722991,0.5512254666195956],"dir":"ltr"},{"str":"techniques—back-","boundary":[0.765241637336623,0.5359529012885783,0.9270034282480907,0.5512254666195956],"dir":"ltr"},{"str":"tracking","boundary":[0.23909972017876382,0.5542799796857991,0.3117832142254273,0.5695525450168164],"dir":"ltr"},{"str":"and","boundary":[0.3195081828067263,0.5542799796857991,0.3513726898513882,0.5695525450168164],"dir":"ltr"},{"str":"branch-and-bound","boundary":[0.35860348183459995,0.5542799796857991,0.5225317429520818,0.5695525450168164],"dir":"ltr"},{"str":"—that","boundary":[0.524273221283741,0.5542799796857991,0.578079169283474,0.5695525450168164],"dir":"ltr"},{"str":"often","boundary":[0.5853139146794704,0.5542799796857991,0.630343286297175,0.5695525450168164],"dir":"ltr"},{"str":"make","boundary":[0.6375780316931714,0.5542799796857991,0.6848015474063831,0.5695525450168164],"dir":"ltr"},{"str":"it","boundary":[0.6920362928023794,0.5542799796857991,0.7041139688596303,0.5695525450168164],"dir":"ltr"},{"str":"possible","boundary":[0.7113487142556268,0.5542799796857991,0.78057297211568,0.5695525450168164],"dir":"ltr"},{"str":"to","boundary":[0.7878077175116764,0.5542799796857991,0.8053806373396568,0.5695525450168164],"dir":"ltr"},{"str":"solve","boundary":[0.8126153827356533,0.5542799796857991,0.856557565837566,0.5695525450168164],"dir":"ltr"},{"str":"at","boundary":[0.8637923112335624,0.5542799796857991,0.8802582754818274,0.5695525450168164],"dir":"ltr"},{"str":"least","boundary":[0.8874930208778239,0.5542799796857991,0.927027148724799,0.5695525450168164],"dir":"ltr"},{"str":"some","boundary":[0.2390957667659791,0.5726070580830199,0.2841251383836836,0.5878796234140372],"dir":"ltr"},{"str":"large","boundary":[0.2901343258164238,0.5726070580830199,0.3329695533386212,0.5878796234140372],"dir":"ltr"},{"str":"instances","boundary":[0.3389787407713615,0.5726070580830199,0.4169598079495197,0.5878796234140372],"dir":"ltr"},{"str":"of","boundary":[0.42296899538225985,0.5726070580830199,0.4405419152102403,0.5878796234140372],"dir":"ltr"},{"str":"difficult","boundary":[0.4465511026429805,0.5726070580830199,0.5124544937638879,0.5878796234140372],"dir":"ltr"},{"str":"combinatorial","boundary":[0.5184636811966281,0.5726070580830199,0.6381927873811919,0.5878796234140372],"dir":"ltr"},{"str":"problems.","boundary":[0.644201974813932,0.5726070580830199,0.7282515306166009,0.5878796234140372],"dir":"ltr"},{"str":"Both","boundary":[0.734260718049341,0.5726070580830199,0.7770959455715385,0.5878796234140372],"dir":"ltr"},{"str":"strategies","boundary":[0.7831051330042786,0.5726070580830199,0.8643675327937357,0.5878796234140372],"dir":"ltr"},{"str":"can","boundary":[0.8703767202264759,0.5726070580830199,0.9000273161117072,0.5878796234140372],"dir":"ltr"},{"str":"be","boundary":[0.9060365035444473,0.5726070580830199,0.9269105230476501,0.5878796234140372],"dir":"ltr"},{"str":"considered","boundary":[0.2390957667659791,0.5909341364802406,0.33247537674053407,0.606206701811258],"dir":"ltr"},{"str":"an","boundary":[0.3411333507390216,0.5909341364802406,0.36200737024222446,0.606206701811258],"dir":"ltr"},{"str":"improvement","boundary":[0.3706653442407119,0.5909341364802406,0.48598639517033804,0.606206701811258],"dir":"ltr"},{"str":"over","boundary":[0.49464436916882554,0.5909341364802406,0.5330913085000087,0.606206701811258],"dir":"ltr"},{"str":"exhaustive","boundary":[0.5417492824984963,0.5909341364802406,0.6329149813136207,0.606206701811258],"dir":"ltr"},{"str":"search,","boundary":[0.6415729553121082,0.5909341364802406,0.7014276248724283,0.606206701811258],"dir":"ltr"},{"str":"discussed","boundary":[0.7110146508753198,0.5909341364802406,0.7912096292129086,0.606206701811258],"dir":"ltr"},{"str":"in","boundary":[0.799867603211396,0.5909341364802406,0.8163533345235846,0.606206701811258],"dir":"ltr"},{"str":"Section","boundary":[0.8250113085220722,0.5909341364802406,0.8887205555474723,0.606206701811258],"dir":"ltr"},{"str":"3.4.","boundary":[0.89737852954596,0.5909341364802406,0.9270291254311912,0.606206701811258],"dir":"ltr"},{"str":"Unlike","boundary":[0.2390957667659791,0.6092612148774614,0.2984167256003651,0.6245337802084788],"dir":"ltr"},{"str":"exhaustive","boundary":[0.3030026844306142,0.6092612148774614,0.39416838324573855,0.6245337802084788],"dir":"ltr"},{"str":"search,","boundary":[0.3987543420759877,0.6092612148774614,0.45860901163630785,0.6245337802084788],"dir":"ltr"},{"str":"they","boundary":[0.46325427165832733,0.6092612148774614,0.5005942554097952,0.6245337802084788],"dir":"ltr"},{"str":"construct","boundary":[0.5051802142400444,0.6092612148774614,0.5842484699339944,0.6245337802084788],"dir":"ltr"},{"str":"candidate","boundary":[0.5888344287642435,0.6092612148774614,0.6723107397131312,0.6245337802084788],"dir":"ltr"},{"str":"solutions","boundary":[0.6768966985433803,0.6092612148774614,0.7538103442696702,0.6245337802084788],"dir":"ltr"},{"str":"one","boundary":[0.7583963030999192,0.6092612148774614,0.790260810144581,0.6245337802084788],"dir":"ltr"},{"str":"component","boundary":[0.7948467689748301,0.6092612148774614,0.8915077115606841,0.6245337802084788],"dir":"ltr"},{"str":"at","boundary":[0.8960936703909331,0.6092612148774614,0.9125596346391982,0.6245337802084788],"dir":"ltr"},{"str":"a","boundary":[0.9171455934694474,0.6092612148774614,0.9270291254311911,0.6245337802084788],"dir":"ltr"},{"str":"time","boundary":[0.2390957667659791,0.6275882932746822,0.27752293903323877,0.6428608586056996],"dir":"ltr"},{"str":"and","boundary":[0.28206936373564095,0.6275882932746822,0.3139338707803028,0.6428608586056996],"dir":"ltr"},{"str":"evaluate","boundary":[0.3184802954827049,0.6275882932746822,0.3909661188901336,0.6428608586056996],"dir":"ltr"},{"str":"the","boundary":[0.39551254359253574,0.6275882932746822,0.4229689953822599,0.6428608586056996],"dir":"ltr"},{"str":"partially","boundary":[0.42751542008466203,0.6275882932746822,0.49891405497629887,0.6428608586056996],"dir":"ltr"},{"str":"constructed","boundary":[0.5034604796787009,0.6275882932746822,0.6034027548758538,0.6428608586056996],"dir":"ltr"},{"str":"solutions:","boundary":[0.607949179578256,0.6275882932746822,0.6898045912854177,0.6428608586056996],"dir":"ltr"},{"str":"if","boundary":[0.6943510159878199,0.6275882932746822,0.7064286920450707,0.6428608586056996],"dir":"ltr"},{"str":"no","boundary":[0.7109751167474728,0.6275882932746822,0.7329560918303909,0.6428608586056996],"dir":"ltr"},{"str":"potential","boundary":[0.7375025165327931,0.6275882932746822,0.8143963951951595,0.6428608586056996],"dir":"ltr"},{"str":"values","boundary":[0.8189428198975616,0.6275882932746822,0.8727685349612181,0.6428608586056996],"dir":"ltr"},{"str":"of","boundary":[0.8773149596636202,0.6275882932746822,0.8948878794916006,0.6428608586056996],"dir":"ltr"},{"str":"the","boundary":[0.8994343041940026,0.6275882932746822,0.9268907559837267,0.6428608586056996],"dir":"ltr"},{"str":"remaining","boundary":[0.2390957667659791,0.645915371671903,0.32587317739008925,0.6611879370029203],"dir":"ltr"},{"str":"components","boundary":[0.33083471043488466,0.645915371671903,0.4351850408869752,0.6611879370029203],"dir":"ltr"},{"str":"can","boundary":[0.44014657393177054,0.645915371671903,0.46979716981700176,0.6611879370029203],"dir":"ltr"},{"str":"lead","boundary":[0.47475870286179717,0.645915371671903,0.5110114980974731,0.6611879370029203],"dir":"ltr"},{"str":"to","boundary":[0.5159730311422686,0.645915371671903,0.533545950970249,0.6611879370029203],"dir":"ltr"},{"str":"a","boundary":[0.5385074840150443,0.645915371671903,0.5483910159767881,0.6611879370029203],"dir":"ltr"},{"str":"solution,","boundary":[0.5533525490215835,0.645915371671903,0.6275185728625086,0.6611879370029203],"dir":"ltr"},{"str":"the","boundary":[0.6324998729712273,0.645915371671903,0.6599563247609515,0.6611879370029203],"dir":"ltr"},{"str":"remaining","boundary":[0.664917857805747,0.645915371671903,0.7516952684298571,0.6611879370029203],"dir":"ltr"},{"str":"components","boundary":[0.7566568014746524,0.645915371671903,0.8610071319267429,0.6611879370029203],"dir":"ltr"},{"str":"are","boundary":[0.8659686649715385,0.645915371671903,0.8934251167612626,0.6611879370029203],"dir":"ltr"},{"str":"not","boundary":[0.898386649806058,0.645915371671903,0.9269500571754974,0.6611879370029203],"dir":"ltr"},{"str":"generated","boundary":[0.2390957667659791,0.6642424500691237,0.32476622181037396,0.679515015400141],"dir":"ltr"},{"str":"at","boundary":[0.32953008421593444,0.6642424500691237,0.34599604846419957,0.679515015400141],"dir":"ltr"},{"str":"all.","boundary":[0.35075991086976005,0.6642424500691237,0.3765756963538347,0.679515015400141],"dir":"ltr"},{"str":"This","boundary":[0.3813395587593952,0.6642424500691237,0.4179086270178471,0.679515015400141],"dir":"ltr"},{"str":"approach","boundary":[0.4226724894234075,0.6642424500691237,0.5028674677609963,0.679515015400141],"dir":"ltr"},{"str":"makes","boundary":[0.5076313301665568,0.6642424500691237,0.5625442337460052,0.679515015400141],"dir":"ltr"},{"str":"it","boundary":[0.5673080961515656,0.6642424500691237,0.5793857722088165,0.679515015400141],"dir":"ltr"},{"str":"possible","boundary":[0.584149634614377,0.6642424500691237,0.6533738924744302,0.679515015400141],"dir":"ltr"},{"str":"to","boundary":[0.6581377548799907,0.6642424500691237,0.6757106747079712,0.679515015400141],"dir":"ltr"},{"str":"solve","boundary":[0.6804745371135316,0.6642424500691237,0.7244167202154443,0.679515015400141],"dir":"ltr"},{"str":"some","boundary":[0.7291805826210047,0.6642424500691237,0.7742099542387092,0.679515015400141],"dir":"ltr"},{"str":"large","boundary":[0.7789738166442698,0.6642424500691237,0.8218090441664673,0.679515015400141],"dir":"ltr"},{"str":"instances","boundary":[0.8265729065720275,0.6642424500691237,0.9045539737501858,0.679515015400141],"dir":"ltr"},{"str":"of","boundary":[0.9093178361557462,0.6642424500691237,0.9268907559837266,0.679515015400141],"dir":"ltr"},{"str":"difficult","boundary":[0.2390957667659791,0.6825695284663446,0.3049991578868864,0.697842093797362],"dir":"ltr"},{"str":"combinatorial","boundary":[0.3099804579956053,0.6825695284663446,0.42970956418016915,0.697842093797362],"dir":"ltr"},{"str":"problems,","boundary":[0.434690864288888,0.6825695284663446,0.5187404200915569,0.697842093797362],"dir":"ltr"},{"str":"though,","boundary":[0.5237414872641992,0.6825695284663446,0.5891111676591724,0.697842093797362],"dir":"ltr"},{"str":"in","boundary":[0.5941122348318147,0.6825695284663446,0.6105979661440033,0.697842093797362],"dir":"ltr"},{"str":"the","boundary":[0.6155792662527221,0.6825695284663446,0.6430357180424462,0.697842093797362],"dir":"ltr"},{"str":"worst","boundary":[0.6480170181511651,0.6825695284663446,0.6952405338643767,0.697842093797362],"dir":"ltr"},{"str":"case,","boundary":[0.7002218339730956,0.6825695284663446,0.740665246760551,0.697842093797362],"dir":"ltr"},{"str":"we","boundary":[0.7456663139331934,0.6825695284663446,0.7698216660476951,0.697842093797362],"dir":"ltr"},{"str":"still","boundary":[0.7748029661564139,0.6825695284663446,0.8055605176213604,0.697842093797362],"dir":"ltr"},{"str":"face","boundary":[0.8105418177300794,0.6825695284663446,0.8456678903221168,0.697842093797362],"dir":"ltr"},{"str":"the","boundary":[0.8506491904308354,0.6825695284663446,0.8781056422205595,0.697842093797362],"dir":"ltr"},{"str":"same","boundary":[0.8830869423292784,0.6825695284663446,0.9270093583672677,0.697842093797362],"dir":"ltr"},{"str":"curse","boundary":[0.2390957667659791,0.7008966068635654,0.2841251383836836,0.7161691721945828],"dir":"ltr"},{"str":"of","boundary":[0.2890669043645555,0.7008966068635654,0.30663982419253594,0.7161691721945828],"dir":"ltr"},{"str":"exponential","boundary":[0.31158159017340775,0.7008966068635654,0.4126505880141994,0.7161691721945828],"dir":"ltr"},{"str":"explosion","boundary":[0.4175923539950713,0.7008966068635654,0.5000012434920906,0.7161691721945828],"dir":"ltr"},{"str":"encountered","boundary":[0.5049430094729626,0.7008966068635654,0.6125944396002755,0.7161691721945828],"dir":"ltr"},{"str":"in","boundary":[0.6175362055811475,0.7008966068635654,0.6340219368933361,0.7161691721945828],"dir":"ltr"},{"str":"exhaustive","boundary":[0.6389637028742078,0.7008966068635654,0.7301294016893323,0.7161691721945828],"dir":"ltr"},{"str":"search.","boundary":[0.7350711676702041,0.7008966068635654,0.7949258372305242,0.7161691721945828],"dir":"ltr"},{"str":"Both","boundary":[0.2746764818282566,0.7192236852607861,0.31751170935045403,0.7344962505918035],"dir":"ltr"},{"str":"backtracking","boundary":[0.322216270564244,0.7192236852607861,0.4331490333028559,0.7344962505918035],"dir":"ltr"},{"str":"and","boundary":[0.43785359451664596,0.7192236852607861,0.46971810156130783,0.7344962505918035],"dir":"ltr"},{"str":"branch-and-bound","boundary":[0.47442266277509787,0.7192236852607861,0.6337254309344836,0.7344962505918035],"dir":"ltr"},{"str":"are","boundary":[0.6384299921482738,0.7192236852607861,0.6658864439379979,0.7344962505918035],"dir":"ltr"},{"str":"based","boundary":[0.6705910051517878,0.7192236852607861,0.72002843202443,0.7344962505918035],"dir":"ltr"},{"str":"on","boundary":[0.7247329932382202,0.7192236852607861,0.7467139683211382,0.7344962505918035],"dir":"ltr"},{"str":"the","boundary":[0.7514185295349284,0.7192236852607861,0.7788749813246525,0.7344962505918035],"dir":"ltr"},{"str":"construction","boundary":[0.7835795425384425,0.7192236852607861,0.8901240170860402,0.7344962505918035],"dir":"ltr"},{"str":"of","boundary":[0.8948285782998302,0.7192236852607861,0.9124014981278106,0.7344962505918035],"dir":"ltr"},{"str":"a","boundary":[0.9171060593416004,0.7192236852607861,0.9269895913033441,0.7344962505918035],"dir":"ltr"},{"str":"state-space","boundary":[0.2390957667659791,0.7375507636580069,0.33462998670819416,0.7528233289890242],"dir":"ltr"},{"str":"tree","boundary":[0.33935431498590773,0.7375507636580069,0.3711792879027226,0.7528233289890242],"dir":"ltr"},{"str":"whose","boundary":[0.3761605880114415,0.7375507636580069,0.42998630307509794,0.7528233289890242],"dir":"ltr"},{"str":"nodes","boundary":[0.4342362218186478,0.7375507636580069,0.48478060427100533,0.7528233289890242],"dir":"ltr"},{"str":"reflect","boundary":[0.48903052301455513,0.7375507636580069,0.5428364710142882,0.7528233289890242],"dir":"ltr"},{"str":"specific","boundary":[0.547086389757838,0.7375507636580069,0.6096886812035229,0.7528233289890242],"dir":"ltr"},{"str":"choices","boundary":[0.6139385999470727,0.7375507636580069,0.6765408913927576,0.7528233289890242],"dir":"ltr"},{"str":"made","boundary":[0.6807908101363074,0.7375507636580069,0.728014325849519,0.7528233289890242],"dir":"ltr"},{"str":"for","boundary":[0.7322642445930689,0.7375507636580069,0.7575265522872859,0.7528233289890242],"dir":"ltr"},{"str":"a","boundary":[0.7617764710308357,0.7375507636580069,0.7716600029925794,0.7528233289890242],"dir":"ltr"},{"str":"solution’s","boundary":[0.7759099217361292,0.7375507636580069,0.8579630040825258,0.7528233289890242],"dir":"ltr"},{"str":"compo-","boundary":[0.8622129228260756,0.7375507636580069,0.9270093583672677,0.7528233289890242],"dir":"ltr"},{"str":"nents.","boundary":[0.2390957667659791,0.7558778420552277,0.289086671428479,0.771150407386245],"dir":"ltr"},{"str":"Both","boundary":[0.2944830798795911,0.7558778420552277,0.3373183074017885,0.771150407386245],"dir":"ltr"},{"str":"techniques","boundary":[0.3427147158529006,0.7558778420552277,0.43498737024774026,0.771150407386245],"dir":"ltr"},{"str":"terminate","boundary":[0.44038377869885237,0.7558778420552277,0.5238403225838165,0.771150407386245],"dir":"ltr"},{"str":"a","boundary":[0.5292367310349286,0.7558778420552277,0.5391202629966724,0.771150407386245],"dir":"ltr"},{"str":"node","boundary":[0.5445166714477846,0.7558778420552277,0.5873716660339054,0.771150407386245],"dir":"ltr"},{"str":"as","boundary":[0.5927680744850176,0.7558778420552277,0.6103409943129979,0.771150407386245],"dir":"ltr"},{"str":"soon","boundary":[0.61573740276411,0.7558778420552277,0.6563982532547238,0.771150407386245],"dir":"ltr"},{"str":"as","boundary":[0.6617946617058359,0.7558778420552277,0.6793675815338163,0.771150407386245],"dir":"ltr"},{"str":"it","boundary":[0.6847639899849283,0.7558778420552277,0.6968416660421791,0.771150407386245],"dir":"ltr"},{"str":"can","boundary":[0.7022380744932913,0.7558778420552277,0.7318886703785226,0.771150407386245],"dir":"ltr"},{"str":"be","boundary":[0.7372850788296346,0.7558778420552277,0.7581590983328373,0.771150407386245],"dir":"ltr"},{"str":"guaranteed","boundary":[0.7635555067839495,0.7558778420552277,0.8602164493698035,0.771150407386245],"dir":"ltr"},{"str":"that","boundary":[0.8656128578209155,0.7558778420552277,0.8996517418971609,0.771150407386245],"dir":"ltr"},{"str":"no","boundary":[0.9050481503482731,0.7558778420552277,0.9270291254311912,0.771150407386245],"dir":"ltr"},{"str":"solution","boundary":[0.2390957667659791,0.7742064477089815,0.30832002462603236,0.7894790130399989],"dir":"ltr"},{"str":"to","boundary":[0.3139338707803028,0.7742064477089815,0.3315067906082832,0.7894790130399989],"dir":"ltr"},{"str":"the","boundary":[0.3371206367625536,0.7742064477089815,0.3645770885522778,0.7894790130399989],"dir":"ltr"},{"str":"problem","boundary":[0.37019093470654824,0.7742064477089815,0.44269652517790037,0.7894790130399989],"dir":"ltr"},{"str":"can","boundary":[0.4483103713321709,0.7742064477089815,0.4779609672174021,0.7894790130399989],"dir":"ltr"},{"str":"be","boundary":[0.4835748133716726,0.7742064477089815,0.5044488328748754,0.7894790130399989],"dir":"ltr"},{"str":"obtained","boundary":[0.5100626790291459,0.7742064477089815,0.5858693691757204,0.7894790130399989],"dir":"ltr"},{"str":"by","boundary":[0.5914832153299909,0.7742064477089815,0.6123572348331937,0.7894790130399989],"dir":"ltr"},{"str":"considering","boundary":[0.6179710809874642,0.7742064477089815,0.7168459347327487,0.7894790130399989],"dir":"ltr"},{"str":"choices","boundary":[0.7224597808870191,0.7742064477089815,0.7850620723327041,0.7894790130399989],"dir":"ltr"},{"str":"that","boundary":[0.7906759184869746,0.7742064477089815,0.82471480256322,0.7894790130399989],"dir":"ltr"},{"str":"correspond","boundary":[0.8303286487174905,0.7742064477089815,0.9270093583672679,0.7894790130399989],"dir":"ltr"},{"str":"to","boundary":[0.2390957667659791,0.7925335261062023,0.25666868659395947,0.8078060914372196],"dir":"ltr"},{"str":"the","boundary":[0.26259880577100575,0.7925335261062023,0.2900552575607299,0.8078060914372196],"dir":"ltr"},{"str":"node’s","boundary":[0.29598537673777614,0.7925335261062023,0.3516691958102404,0.8078060914372196],"dir":"ltr"},{"str":"descendants.","boundary":[0.3575993149872867,0.7925335261062023,0.4658042229044573,0.8078060914372196],"dir":"ltr"},{"str":"The","boundary":[0.47173434208150355,0.7925335261062023,0.505002310664733,0.8078060914372196],"dir":"ltr"},{"str":"techniques","boundary":[0.5109324298417793,0.7925335261062023,0.6032050842366189,0.8078060914372196],"dir":"ltr"},{"str":"differ","boundary":[0.6091352034136653,0.7925335261062023,0.6563587191268769,0.8078060914372196],"dir":"ltr"},{"str":"in","boundary":[0.6622888383039232,0.7925335261062023,0.6787745696161117,0.8078060914372196],"dir":"ltr"},{"str":"the","boundary":[0.6847046887931579,0.7925335261062023,0.712161140582882,0.8078060914372196],"dir":"ltr"},{"str":"nature","boundary":[0.7180912597599284,0.7925335261062023,0.7741111189190919,0.8078060914372196],"dir":"ltr"},{"str":"of","boundary":[0.7800412380961382,0.7925335261062023,0.7976141579241186,0.8078060914372196],"dir":"ltr"},{"str":"problems","boundary":[0.8035442771011649,0.7925335261062023,0.8837392554387538,0.8078060914372196],"dir":"ltr"},{"str":"they","boundary":[0.8896693746157999,0.7925335261062023,0.9270093583672678,0.8078060914372196],"dir":"ltr"},{"str":"can","boundary":[0.2390957667659791,0.8108606045034232,0.2687463626512104,0.8261331698344405],"dir":"ltr"},{"str":"be","boundary":[0.27319395203399505,0.8108606045034232,0.2940679715371979,0.8261331698344405],"dir":"ltr"},{"str":"applied","boundary":[0.2985155609199825,0.8108606045034232,0.36224457500930624,0.8261331698344405],"dir":"ltr"},{"str":"to.","boundary":[0.36669216439209096,0.8108606045034232,0.38841616764400366,0.8261331698344405],"dir":"ltr"},{"str":"Branch-and-bound","boundary":[0.3928637570267884,0.8108606045034232,0.5554478577974732,0.8261331698344405],"dir":"ltr"},{"str":"is","boundary":[0.5598954471802579,0.8108606045034232,0.573080078817224,0.8261331698344405],"dir":"ltr"},{"str":"applicable","boundary":[0.5775276682000088,0.8108606045034232,0.6654120344038342,0.8261331698344405],"dir":"ltr"},{"str":"only","boundary":[0.669859623786619,0.8108606045034232,0.7072193746020103,0.8261331698344405],"dir":"ltr"},{"str":"to","boundary":[0.7116669639847951,0.8108606045034232,0.7292398838127756,0.8261331698344405],"dir":"ltr"},{"str":"optimization","boundary":[0.7336874731955603,0.8108606045034232,0.842426091838665,0.8261331698344405],"dir":"ltr"},{"str":"problems","boundary":[0.8468736812214497,0.8108606045034232,0.9270686595590385,0.8261331698344405],"dir":"ltr"},{"str":"because","boundary":[0.2390957667659791,0.8291876829006439,0.30719330198239353,0.8444602482316612],"dir":"ltr"},{"str":"it","boundary":[0.3142501438030786,0.8291876829006439,0.3263278198603295,0.8444602482316612],"dir":"ltr"},{"str":"is","boundary":[0.3333846616810145,0.8291876829006439,0.34656929331798064,0.8444602482316612],"dir":"ltr"},{"str":"based","boundary":[0.3536261351386657,0.8291876829006439,0.4030635620113079,0.8444602482316612],"dir":"ltr"},{"str":"on","boundary":[0.410120403831993,0.8291876829006439,0.4321013789149111,0.8444602482316612],"dir":"ltr"},{"str":"computing","boundary":[0.4391582207355961,0.8291876829006439,0.5303239195507206,0.8444602482316612],"dir":"ltr"},{"str":"a","boundary":[0.5373807613714056,0.8291876829006439,0.5472642933331493,0.8444602482316612],"dir":"ltr"},{"str":"bound","boundary":[0.5543211351538343,0.8291876829006439,0.6092735728611296,0.8444602482316612],"dir":"ltr"},{"str":"on","boundary":[0.6163304146818147,0.8291876829006439,0.6383113897647328,0.8444602482316612],"dir":"ltr"},{"str":"possible","boundary":[0.6453682315854178,0.8291876829006439,0.714592489445471,0.8444602482316612],"dir":"ltr"},{"str":"values","boundary":[0.7216493312661559,0.8291876829006439,0.7754750463298123,0.8444602482316612],"dir":"ltr"},{"str":"of","boundary":[0.7825318881504973,0.8291876829006439,0.8001048079784778,0.8444602482316612],"dir":"ltr"},{"str":"the","boundary":[0.8071616497991629,0.8291876829006439,0.834618101588887,0.8444602482316612],"dir":"ltr"},{"str":"problem’s","boundary":[0.841674943409572,0.8291876829006439,0.9270093583672676,0.8444602482316612],"dir":"ltr"},{"str":"objective","boundary":[0.2390957667659791,0.8475147612978647,0.3170768339441373,0.8627873266288819],"dir":"ltr"},{"str":"function.","boundary":[0.3248255230021444,0.8475147612978647,0.40116592387465316,0.8627873266288819],"dir":"ltr"},{"str":"Backtracking","boundary":[0.4089146129326603,0.8475147612978647,0.5231287082825711,0.8627873266288819],"dir":"ltr"},{"str":"is","boundary":[0.5308773973405783,0.8475147612978647,0.5440620289775444,0.8627873266288819],"dir":"ltr"},{"str":"not","boundary":[0.5518107180355514,0.8475147612978647,0.5803741254049909,0.8627873266288819],"dir":"ltr"},{"str":"constrained","boundary":[0.5881228144629979,0.8475147612978647,0.6880848567240743,0.8627873266288819],"dir":"ltr"},{"str":"by","boundary":[0.6958335457820813,0.8475147612978647,0.7167075652852841,0.8627873266288819],"dir":"ltr"},{"str":"this","boundary":[0.7244562543432911,0.8475147612978647,0.7552138058082377,0.8627873266288819],"dir":"ltr"},{"str":"demand,","boundary":[0.7629624948662449,0.8475147612978647,0.8371087516432466,0.8627873266288819],"dir":"ltr"},{"str":"but","boundary":[0.8455690550024991,0.8475147612978647,0.8741324623719385,0.8627873266288819],"dir":"ltr"},{"str":"more","boundary":[0.8818811514299457,0.8475147612978647,0.9269105230476502,0.8627873266288819],"dir":"ltr"},{"str":"often","boundary":[0.2390957667659791,0.8658418396950854,0.2841251383836836,0.8811144050261027],"dir":"ltr"},{"str":"than","boundary":[0.2894029444512548,0.8658418396950854,0.327849883782438,0.8811144050261027],"dir":"ltr"},{"str":"not,","boundary":[0.3331276898500092,0.8658418396950854,0.3666328632003205,0.8811144050261027],"dir":"ltr"},{"str":"it","boundary":[0.3719897375235856,0.8658418396950854,0.38406741358083646,0.8811144050261027],"dir":"ltr"},{"str":"applies","boundary":[0.3893452196484076,0.8658418396950854,0.4497731340625089,0.8811144050261027],"dir":"ltr"},{"str":"to","boundary":[0.45505094013008013,0.8658418396950854,0.4726238599580605,0.8811144050261027],"dir":"ltr"},{"str":"nonoptimization","boundary":[0.4779016660256316,0.8658418396950854,0.6196117472931135,0.8811144050261027],"dir":"ltr"},{"str":"problems.","boundary":[0.6248895533606847,0.8658418396950854,0.7089391091633536,0.8811144050261027],"dir":"ltr"},{"str":"The","boundary":[0.7142169152309248,0.8658418396950854,0.7474848838141541,0.8811144050261027],"dir":"ltr"},{"str":"other","boundary":[0.7527626898817256,0.8658418396950854,0.7988990170791453,0.8811144050261027],"dir":"ltr"},{"str":"distinction","boundary":[0.8041768231467163,0.8658418396950854,0.8942553334460489,0.8811144050261027],"dir":"ltr"},{"str":"be-","boundary":[0.8995331395136202,0.8658418396950854,0.9269895913033444,0.8811144050261027],"dir":"ltr"},{"str":"tween","boundary":[0.2390957667659791,0.8841689180923064,0.290707570670205,0.8994414834233235],"dir":"ltr"},{"str":"backtracking","boundary":[0.2950365576694487,0.8841689180923064,0.4059693204080606,0.8994414834233235],"dir":"ltr"},{"str":"and","boundary":[0.4102983074073044,0.8841689180923064,0.44216281445196626,0.8994414834233235],"dir":"ltr"},{"str":"branch-and-bound","boundary":[0.44649180145121,0.8841689180923064,0.6057945696105957,0.8994414834233235],"dir":"ltr"},{"str":"lies","boundary":[0.6101235566098396,0.8841689180923064,0.638686963979279,0.8994414834233235],"dir":"ltr"},{"str":"in","boundary":[0.6430159509785228,0.8841689180923064,0.6595016822907114,0.8994414834233235],"dir":"ltr"},{"str":"the","boundary":[0.6638306692899553,0.8841689180923064,0.6912871210796794,0.8994414834233235],"dir":"ltr"},{"str":"order","boundary":[0.6956161080789232,0.8841689180923064,0.7428593908560582,0.8994414834233235],"dir":"ltr"},{"str":"in","boundary":[0.747188377855302,0.8841689180923064,0.7636741091674906,0.8994414834233235],"dir":"ltr"},{"str":"which","boundary":[0.7680030961667343,0.8841689180923064,0.8185277115551685,0.8994414834233235],"dir":"ltr"},{"str":"nodes","boundary":[0.8228566985544123,0.8841689180923064,0.8734010810067699,0.8994414834233235],"dir":"ltr"},{"str":"of","boundary":[0.8777300680060136,0.8841689180923064,0.8953029878339941,0.8994414834233235],"dir":"ltr"},{"str":"the","boundary":[0.8996319748332379,0.8841689180923064,0.927088426622962,0.8994414834233235],"dir":"ltr"},{"str":"423","boundary":[0.8940181286789672,0.9329342191942445,0.9269895913033444,0.9482067845252617],"dir":"ltr"}],"boundary":[0.14422,0.07999,0.92709,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":497,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/9e6dd95f3a737bbe6f41128a88a71891.jpg","blurred":"/storage/books/4a8b03583f119702/pages/1110b0f08dd9bc7c500f343f39a6d020.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.16303,0.07295,0.05179]},"elements":[{"words":[{"str":"Epilogue","boundary":[0.14421784044919886,0.16302940802619442,0.3516302092617704,0.19968365680003092],"dir":"ltr"}],"boundary":[0.14422,0.16303,0.35163,0.19968],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Science","boundary":[0.23910077902799318,0.3261870233715904,0.30168330340975463,0.34145958870260773],"dir":"ltr"},{"str":"is","boundary":[0.30662506939062645,0.3261870233715904,0.31980970102759265,0.34145958870260773],"dir":"ltr"},{"str":"nothing","boundary":[0.3247514670084646,0.3261870233715904,0.38958743667750356,0.34145958870260773],"dir":"ltr"},{"str":"but","boundary":[0.39452920265837543,0.3261870233715904,0.4220054215120231,0.34145958870260773],"dir":"ltr"},{"str":"trained","boundary":[0.42694718749289495,0.3261870233715904,0.48626814632728094,0.34145958870260773],"dir":"ltr"},{"str":"and","boundary":[0.49120991230815286,0.3261870233715904,0.5230744193528147,0.34145958870260773],"dir":"ltr"},{"str":"organized","boundary":[0.5280161853336865,0.3261870233715904,0.6122436447116668,0.34145958870260773],"dir":"ltr"},{"str":"common","boundary":[0.6171854106925386,0.3261870233715904,0.6918653781954746,0.34145958870260773],"dir":"ltr"},{"str":"sense.","boundary":[0.6968071441763464,0.3261870233715904,0.7451771495971202,0.34145958870260773],"dir":"ltr"},{"str":"—Thomas","boundary":[0.32165236813130166,0.3481135950494189,0.4054244622215656,0.36262257810358284],"dir":"ltr"},{"str":"H.","boundary":[0.4101191547843466,0.3481135950494189,0.4304565629663138,0.36262257810358284],"dir":"ltr"},{"str":"Huxley","boundary":[0.43515125552909484,0.3481135950494189,0.4946236209144044,0.36262257810358284],"dir":"ltr"},{"str":"(1825–1895),","boundary":[0.4993183134771853,0.3481135950494189,0.6031273554253985,0.36262257810358284],"dir":"ltr"},{"str":"English","boundary":[0.6078408267584307,0.3481135950494189,0.6694164144118661,0.36262257810358284],"dir":"ltr"},{"str":"biologist","boundary":[0.6741111069746469,0.3481135950494189,0.7440432473898325,0.36262257810358284],"dir":"ltr"},{"str":"and","boundary":[0.7487379399526136,0.3481135950494189,0.7790093175974255,0.36262257810358284],"dir":"ltr"},{"str":"educator","boundary":[0.7837040101602064,0.3481135950494189,0.8557018153030157,0.36262257810358284],"dir":"ltr"}],"boundary":[0.2391,0.32619,0.8557,0.36262],"dir":"ltr","type":"paragraph"},{"words":[{"str":"ell,","boundary":[0.2984023676238612,0.4582694344811854,0.32421815310793584,0.47354199981220274],"dir":"ltr"},{"str":"we","boundary":[0.33089942071407463,0.4582694344811854,0.3550547728285764,0.47354199981220274],"dir":"ltr"},{"str":"have","boundary":[0.3613802332840924,0.4582694344811854,0.4020213167107827,0.47354199981220274],"dir":"ltr"},{"str":"arrived.","boundary":[0.4083467771662987,0.4582694344811854,0.4748036460770637,0.47354199981220274],"dir":"ltr"},{"str":"It","boundary":[0.48112910653257973,0.4582694344811854,0.4954009266853377,0.47354199981220274],"dir":"ltr"},{"str":"was","boundary":[0.5017263871408537,0.4582694344811854,0.533571127121592,0.47354199981220274],"dir":"ltr"},{"str":"a","boundary":[0.5398965875771081,0.4582694344811854,0.5497801195388518,0.47354199981220274],"dir":"ltr"},{"str":"long","boundary":[0.5561055799943678,0.4582694344811854,0.5934653308097593,0.47354199981220274],"dir":"ltr"},{"str":"road.","boundary":[0.5997907912652751,0.4582694344811854,0.6442864521570456,0.47354199981220274],"dir":"ltr"},{"str":"Not","boundary":[0.6506119126125616,0.4582694344811854,0.6835636081730152,0.47354199981220274],"dir":"ltr"},{"str":"as","boundary":[0.6898890686285313,0.4582694344811854,0.7074619884565116,0.47354199981220274],"dir":"ltr"},{"str":"long","boundary":[0.7137874489120276,0.4582694344811854,0.7511471997274191,0.47354199981220274],"dir":"ltr"},{"str":"as","boundary":[0.757472660182935,0.4582694344811854,0.7750455800109155,0.47354199981220274],"dir":"ltr"},{"str":"it","boundary":[0.7813710404664314,0.4582694344811854,0.7934487165236822,0.47354199981220274],"dir":"ltr"},{"str":"took","boundary":[0.7997741769791984,0.4582694344811854,0.839328071890097,0.47354199981220274],"dir":"ltr"},{"str":"humanity","boundary":[0.8456535323456129,0.4582694344811854,0.9269356991989937,0.47354199981220274],"dir":"ltr"},{"str":"to","boundary":[0.2984023676238612,0.4765965128784062,0.3159752874518416,0.49186907820942355],"dir":"ltr"},{"str":"travel","boundary":[0.32407978366047147,0.4765965128784062,0.3734974434691902,0.49186907820942355],"dir":"ltr"},{"str":"from","boundary":[0.3816019396778201,0.4765965128784062,0.4233302116203022,0.49186907820942355],"dir":"ltr"},{"str":"Euclid’s","boundary":[0.43143470782893206,0.4765965128784062,0.5002833914744391,0.49186907820942355],"dir":"ltr"},{"str":"algorithm,","boundary":[0.5083878876830689,0.4765965128784062,0.5968059646128284,0.49186907820942355],"dir":"ltr"},{"str":"which","boundary":[0.6057011433783979,0.4765965128784062,0.656225758766832,0.49186907820942355],"dir":"ltr"},{"str":"opens","boundary":[0.6643302549754618,0.4765965128784062,0.7148746374278194,0.49186907820942355],"dir":"ltr"},{"str":"this","boundary":[0.7229791336364493,0.4765965128784062,0.7537366851013959,0.49186907820942355],"dir":"ltr"},{"str":"book,","boundary":[0.7618411813100257,0.4765965128784062,0.8107448974567338,0.49186907820942355],"dir":"ltr"},{"str":"to","boundary":[0.8196400762223032,0.4765965128784062,0.8372129960502835,0.49186907820942355],"dir":"ltr"},{"str":"the","boundary":[0.8453174922589134,0.4765965128784062,0.8727739440486375,0.49186907820942355],"dir":"ltr"},{"str":"latest","boundary":[0.8808784402572675,0.4765965128784062,0.9269950003907639,0.49186907820942355],"dir":"ltr"},{"str":"Wdevelopments","boundary":[0.23910077902799318,0.4569712912624857,0.35883028203796247,0.5101961566066443],"dir":"ltr"},{"str":"in","boundary":[0.36509644130170804,0.494923591275627,0.3815821726138966,0.5101961566066443],"dir":"ltr"},{"str":"algorithmics,","boundary":[0.3878483318776421,0.494923591275627,0.4971404283106045,0.5101961566066443],"dir":"ltr"},{"str":"but","boundary":[0.5037426276610494,0.494923591275627,0.5323060350304889,0.5101961566066443],"dir":"ltr"},{"str":"it","boundary":[0.5385721942942344,0.494923591275627,0.5506498703514852,0.5101961566066443],"dir":"ltr"},{"str":"was","boundary":[0.5569160296152308,0.494923591275627,0.5887607695959691,0.5101961566066443],"dir":"ltr"},{"str":"long","boundary":[0.5950269288597146,0.494923591275627,0.6323866796751061,0.5101961566066443],"dir":"ltr"},{"str":"enough.","boundary":[0.6386528389388516,0.494923591275627,0.7073236190090472,0.5101961566066443],"dir":"ltr"},{"str":"So","boundary":[0.7135897782727928,0.494923591275627,0.735570753355711,0.5101961566066443],"dir":"ltr"},{"str":"let","boundary":[0.7418369126194564,0.494923591275627,0.763798120638451,0.5101961566066443],"dir":"ltr"},{"str":"us","boundary":[0.7700642799021966,0.494923591275627,0.7887441553098923,0.5101961566066443],"dir":"ltr"},{"str":"now","boundary":[0.7950103145736378,0.494923591275627,0.8312631098093138,0.5101961566066443],"dir":"ltr"},{"str":"take","boundary":[0.8375292690730596,0.494923591275627,0.8748692528245274,0.5101961566066443],"dir":"ltr"},{"str":"a","boundary":[0.881135412088273,0.494923591275627,0.8910189440500167,0.5101961566066443],"dir":"ltr"},{"str":"last","boundary":[0.8972851033137622,0.494923591275627,0.9269356991989934,0.5101961566066443],"dir":"ltr"},{"str":"look","boundary":[0.23910117585339866,0.5132521969293808,0.27756788224850537,0.5285247622603982],"dir":"ltr"},{"str":"at","boundary":[0.28250964822937724,0.5132521969293808,0.2989756124776423,0.5285247622603982],"dir":"ltr"},{"str":"what","boundary":[0.3039173784585142,0.5132521969293808,0.3456456504009963,0.5285247622603982],"dir":"ltr"},{"str":"we","boundary":[0.3505874163818682,0.5132521969293808,0.37474276849636995,0.5285247622603982],"dir":"ltr"},{"str":"have","boundary":[0.3796845344772418,0.5132521969293808,0.42032561790393214,0.5285247622603982],"dir":"ltr"},{"str":"learned","boundary":[0.42526738388480395,0.5132521969293808,0.49008358648991945,0.5285247622603982],"dir":"ltr"},{"str":"during","boundary":[0.4950253524707914,0.5132521969293808,0.5510649786938784,0.5285247622603982],"dir":"ltr"},{"str":"the","boundary":[0.5560067446747503,0.5132521969293808,0.5834631964644744,0.5285247622603982],"dir":"ltr"},{"str":"journey.","boundary":[0.5884049624453463,0.5132521969293808,0.6574513167300882,0.5285247622603982],"dir":"ltr"},{"str":"We","boundary":[0.2746818909156762,0.5315792753266017,0.3028697240705694,0.546851840657619],"dir":"ltr"},{"str":"started","boundary":[0.30688243804703735,0.5315792753266017,0.36618362981749986,0.546851840657619],"dir":"ltr"},{"str":"with","boundary":[0.3701963437939678,0.5315792753266017,0.4075363275454357,0.546851840657619],"dir":"ltr"},{"str":"the","boundary":[0.4115490415219037,0.5315792753266017,0.43900549331162786,0.546851840657619],"dir":"ltr"},{"str":"well-accepted","boundary":[0.44301820728809577,0.5315792753266017,0.5605136352493055,0.546851840657619],"dir":"ltr"},{"str":"proposition","boundary":[0.5645263492257735,0.5315792753266017,0.6634209700349816,0.546851840657619],"dir":"ltr"},{"str":"that","boundary":[0.6674336840114494,0.5315792753266017,0.7014725680876949,0.546851840657619],"dir":"ltr"},{"str":"the","boundary":[0.7054852820641629,0.5315792753266017,0.7329417338538871,0.546851840657619],"dir":"ltr"},{"str":"notion","boundary":[0.736954447830355,0.5315792753266017,0.792994074053442,0.546851840657619],"dir":"ltr"},{"str":"of","boundary":[0.79700678802991,0.5315792753266017,0.8145797078578904,0.546851840657619],"dir":"ltr"},{"str":"an","boundary":[0.8185924218343583,0.5315792753266017,0.8394664413375611,0.546851840657619],"dir":"ltr"},{"str":"algorithm","boundary":[0.8434791553140291,0.5315792753266017,0.9269554662629168,0.546851840657619],"dir":"ltr"},{"str":"constitutes","boundary":[0.23910117585339866,0.5499063537238226,0.3313540631843149,0.5651789190548399],"dir":"ltr"},{"str":"the","boundary":[0.33750162006451945,0.5499063537238226,0.3649580718542436,0.5651789190548399],"dir":"ltr"},{"str":"cornerstone","boundary":[0.3711056287344483,0.5499063537238226,0.4732618150910317,0.5651789190548399],"dir":"ltr"},{"str":"of","boundary":[0.4794093719712363,0.5499063537238226,0.4969822917992167,0.5651789190548399],"dir":"ltr"},{"str":"computer","boundary":[0.5031298486794213,0.5499063537238226,0.5854992040485938,0.5651789190548399],"dir":"ltr"},{"str":"science.","boundary":[0.5916467609287984,0.5499063537238226,0.6573524814104708,0.5651789190548399],"dir":"ltr"},{"str":"And","boundary":[0.6635000382906755,0.5499063537238226,0.7020458129414762,0.5651789190548399],"dir":"ltr"},{"str":"since","boundary":[0.7081933698216807,0.5499063537238226,0.7510285973438781,0.5651789190548399],"dir":"ltr"},{"str":"computer","boundary":[0.7571761542240828,0.5499063537238226,0.8395455095932552,0.5651789190548399],"dir":"ltr"},{"str":"programs","boundary":[0.8456930664734598,0.5499063537238226,0.9269752333268405,0.5651789190548399],"dir":"ltr"},{"str":"are","boundary":[0.23910117585339866,0.5682334321210434,0.26655762764312285,0.5835059974520607],"dir":"ltr"},{"str":"just","boundary":[0.27244821269232206,0.5682334321210434,0.30320576415726863,0.5835059974520607],"dir":"ltr"},{"str":"implementations","boundary":[0.30909634920646795,0.5682334321210434,0.4529808075055335,0.5835059974520607],"dir":"ltr"},{"str":"of","boundary":[0.45887139255473275,0.5682334321210434,0.4764443123827132,0.5835059974520607],"dir":"ltr"},{"str":"algorithms","boundary":[0.48233489743191243,0.5682334321210434,0.5735005962470369,0.5835059974520607],"dir":"ltr"},{"str":"on","boundary":[0.579391181296236,0.5682334321210434,0.6013721563791542,0.5835059974520607],"dir":"ltr"},{"str":"particular","boundary":[0.6072627414283535,0.5682334321210434,0.6907390523772411,0.5835059974520607],"dir":"ltr"},{"str":"machines,","boundary":[0.6966296374264404,0.5682334321210434,0.7806594261651857,0.5835059974520607],"dir":"ltr"},{"str":"algorithms","boundary":[0.7867674489175434,0.5682334321210434,0.8779331477326677,0.5835059974520607],"dir":"ltr"},{"str":"lie","boundary":[0.8838237327818671,0.5682334321210434,0.9046977522850699,0.5835059974520607],"dir":"ltr"},{"str":"at","boundary":[0.9105883373342692,0.5682334321210434,0.9270543015825342,0.5835059974520607],"dir":"ltr"},{"str":"the","boundary":[0.23910117585339866,0.5865605105182642,0.26655762764312285,0.6018330758492815],"dir":"ltr"},{"str":"heart","boundary":[0.27149939362399467,0.5865605105182642,0.3165287652416992,0.6018330758492815],"dir":"ltr"},{"str":"of","boundary":[0.32147053122257113,0.5865605105182642,0.3390434510505515,0.6018330758492815],"dir":"ltr"},{"str":"practical","boundary":[0.3439852170314234,0.5865605105182642,0.4175582289546439,0.6018330758492815],"dir":"ltr"},{"str":"computing,","boundary":[0.42249999493551577,0.5865605105182642,0.5182516525808893,0.6018330758492815],"dir":"ltr"},{"str":"too.","boundary":[0.523193418561761,0.5865605105182642,0.555907909355133,0.6018330758492815],"dir":"ltr"},{"str":"Like","boundary":[0.2746818909156762,0.604887588915485,0.3142357858265747,0.6201601542465023],"dir":"ltr"},{"str":"any","boundary":[0.31917755180744656,0.604887588915485,0.34993510327239313,0.6201601542465023],"dir":"ltr"},{"str":"science,","boundary":[0.354876869253265,0.604887588915485,0.42058258973493745,0.6201601542465023],"dir":"ltr"},{"str":"computer","boundary":[0.4255243557158094,0.604887588915485,0.5078937110849818,0.6201601542465023],"dir":"ltr"},{"str":"science","boundary":[0.5128354770658538,0.604887588915485,0.5743308129318233,0.6201601542465023],"dir":"ltr"},{"str":"is","boundary":[0.5792725789126952,0.604887588915485,0.5924572105496614,0.6201601542465023],"dir":"ltr"},{"str":"concerned","boundary":[0.5973989765305333,0.604887588915485,0.6863705312501506,0.6201601542465023],"dir":"ltr"},{"str":"with","boundary":[0.6913122972310225,0.604887588915485,0.7286522809824904,0.6201601542465023],"dir":"ltr"},{"str":"classifying","boundary":[0.7335940469633622,0.604887588915485,0.8214586461032641,0.6201601542465023],"dir":"ltr"},{"str":"its","boundary":[0.8264004120841361,0.604887588915485,0.8461674760076235,0.6201601542465023],"dir":"ltr"},{"str":"principal","boundary":[0.8511092419884955,0.604887588915485,0.9269159321350701,0.6201601542465023],"dir":"ltr"},{"str":"subject.","boundary":[0.23910117585339866,0.6232146673127057,0.30445108918444835,0.6384872326437231],"dir":"ltr"},{"str":"Although","boundary":[0.3117056016443683,0.6232146673127057,0.3941935593970816,0.6384872326437231],"dir":"ltr"},{"str":"algorithms","boundary":[0.4014480718570016,0.6232146673127057,0.492613770672126,0.6384872326437231],"dir":"ltr"},{"str":"can","boundary":[0.4998682831320458,0.6232146673127057,0.529518879017277,0.6384872326437231],"dir":"ltr"},{"str":"be","boundary":[0.536773391477197,0.6232146673127057,0.5576474109803998,0.6384872326437231],"dir":"ltr"},{"str":"classified","boundary":[0.5649019234403198,0.6232146673127057,0.6417958021026862,0.6384872326437231],"dir":"ltr"},{"str":"in","boundary":[0.6490503145626061,0.6232146673127057,0.6655360458747946,0.6384872326437231],"dir":"ltr"},{"str":"numerous","boundary":[0.6727905583347147,0.6232146673127057,0.758480780443033,0.6384872326437231],"dir":"ltr"},{"str":"ways,","boundary":[0.7657352929029531,0.6232146673127057,0.8113181423105152,0.6384872326437231],"dir":"ltr"},{"str":"two","boundary":[0.8191458996242161,0.6232146673127057,0.8509906396049545,0.6384872326437231],"dir":"ltr"},{"str":"of","boundary":[0.8582451520648745,0.6232146673127057,0.8758180718928549,0.6384872326437231],"dir":"ltr"},{"str":"them","boundary":[0.8830725843527748,0.6232146673127057,0.9269950003907641,0.6384872326437231],"dir":"ltr"},{"str":"are","boundary":[0.23910117585339866,0.6415417457099264,0.26655762764312285,0.6568143110409438],"dir":"ltr"},{"str":"particularly","boundary":[0.2717365983910765,0.6415417457099264,0.37059168507243756,0.6568143110409438],"dir":"ltr"},{"str":"important.","boundary":[0.3757706558203913,0.6415417457099264,0.466382876845658,0.6568143110409438],"dir":"ltr"},{"str":"We","boundary":[0.47156184759361175,0.6415417457099264,0.49974968074850495,0.6568143110409438],"dir":"ltr"},{"str":"can","boundary":[0.5049286514964587,0.6415417457099264,0.5345792473816899,0.6568143110409438],"dir":"ltr"},{"str":"classify","boundary":[0.5397582181296436,0.6415417457099264,0.6012535539956133,0.6568143110409438],"dir":"ltr"},{"str":"algorithms","boundary":[0.606432524743567,0.6415417457099264,0.6975982235586915,0.6568143110409438],"dir":"ltr"},{"str":"by","boundary":[0.7027771943066451,0.6415417457099264,0.7236512138098479,0.6568143110409438],"dir":"ltr"},{"str":"their","boundary":[0.7288301845578017,0.6415417457099264,0.769471267984492,0.6568143110409438],"dir":"ltr"},{"str":"underlying","boundary":[0.7746502387324459,0.6415417457099264,0.866942660191209,0.6568143110409438],"dir":"ltr"},{"str":"design","boundary":[0.8721216309391625,0.6415417457099264,0.9270543015825343,0.6568143110409438],"dir":"ltr"},{"str":"technique","boundary":[0.23910117585339866,0.6598688241071472,0.3236844423820017,0.6751413894381646],"dir":"ltr"},{"str":"and","boundary":[0.3273215821439234,0.6598688241071472,0.35918608918858524,0.6751413894381646],"dir":"ltr"},{"str":"by","boundary":[0.36282322895050695,0.6598688241071472,0.3836972484537098,0.6751413894381646],"dir":"ltr"},{"str":"their","boundary":[0.3873343882156315,0.6598688241071472,0.4279754716423218,0.6751413894381646],"dir":"ltr"},{"str":"efficiency.","boundary":[0.43161261140424345,0.6598688241071472,0.5156424001429888,0.6751413894381646],"dir":"ltr"},{"str":"These","boundary":[0.5192795399049105,0.6598688241071472,0.5701204283161203,0.6751413894381646],"dir":"ltr"},{"str":"two","boundary":[0.5737575680780421,0.6598688241071472,0.6056023080587805,0.6751413894381646],"dir":"ltr"},{"str":"principal","boundary":[0.6092394478207022,0.6598688241071472,0.6850461379672768,0.6751413894381646],"dir":"ltr"},{"str":"dimensions","boundary":[0.6886832777291985,0.6598688241071472,0.7853639873789758,0.6751413894381646],"dir":"ltr"},{"str":"reflect","boundary":[0.7890011271408975,0.6598688241071472,0.8428070751406306,0.6751413894381646],"dir":"ltr"},{"str":"the","boundary":[0.8464442149025523,0.6598688241071472,0.8739006666922764,0.6751413894381646],"dir":"ltr"},{"str":"needs","boundary":[0.8775378064541982,0.6598688241071472,0.9269752333268405,0.6751413894381646],"dir":"ltr"},{"str":"of","boundary":[0.23910117585339866,0.6781959025043681,0.25667409568137906,0.6934684678353854],"dir":"ltr"},{"str":"computing","boundary":[0.2601926330597598,0.6781959025043681,0.35135833187488424,0.6934684678353854],"dir":"ltr"},{"str":"practice","boundary":[0.354876869253265,0.6781959025043681,0.42295463740575595,0.6934684678353854],"dir":"ltr"},{"str":"as","boundary":[0.42647317478413677,0.6781959025043681,0.44404609461211714,0.6934684678353854],"dir":"ltr"},{"str":"well:","boundary":[0.4475646319904979,0.6781959025043681,0.48765223762733056,0.6934684678353854],"dir":"ltr"},{"str":"we","boundary":[0.4911707750057114,0.6781959025043681,0.5153261271202131,0.6934684678353854],"dir":"ltr"},{"str":"need","boundary":[0.5188446644985939,0.6781959025043681,0.5605927035049996,0.6934684678353854],"dir":"ltr"},{"str":"design","boundary":[0.5641112408833803,0.6781959025043681,0.6190439115267521,0.6934684678353854],"dir":"ltr"},{"str":"techniques","boundary":[0.6225624489051329,0.6781959025043681,0.7148351032999726,0.6934684678353854],"dir":"ltr"},{"str":"as","boundary":[0.7183536406783534,0.6781959025043681,0.7359265605063338,0.6934684678353854],"dir":"ltr"},{"str":"a","boundary":[0.7394450978847146,0.6781959025043681,0.7493286298464583,0.6934684678353854],"dir":"ltr"},{"str":"guide","boundary":[0.752847167224839,0.6781959025043681,0.8000904500019741,0.6934684678353854],"dir":"ltr"},{"str":"for","boundary":[0.8036089873803549,0.6781959025043681,0.8288712950745719,0.6934684678353854],"dir":"ltr"},{"str":"developing","boundary":[0.8323898324529527,0.6781959025043681,0.926876398007223,0.6934684678353854],"dir":"ltr"},{"str":"a","boundary":[0.23910117585339866,0.6965245081581218,0.24898470781514243,0.7117970734891392],"dir":"ltr"},{"str":"new","boundary":[0.254400883330178,0.6965245081581218,0.2895467229861388,0.7117970734891392],"dir":"ltr"},{"str":"algorithm,","boundary":[0.29496289850117435,0.6965245081581218,0.38338097543093397,0.7117970734891392],"dir":"ltr"},{"str":"and","boundary":[0.38891575332951045,0.6965245081581218,0.4207802603741723,0.7117970734891392],"dir":"ltr"},{"str":"we","boundary":[0.4261964358892079,0.6965245081581218,0.4503517880037097,0.7117970734891392],"dir":"ltr"},{"str":"need","boundary":[0.4557679635187452,0.6965245081581218,0.4975160025251509,0.7117970734891392],"dir":"ltr"},{"str":"a","boundary":[0.5029321780401864,0.6965245081581218,0.5128157100019302,0.7117970734891392],"dir":"ltr"},{"str":"framework","boundary":[0.5182318855169658,0.6965245081581218,0.6126789169433889,0.7117970734891392],"dir":"ltr"},{"str":"to","boundary":[0.6180950924584246,0.6965245081581218,0.635668012286405,0.7117970734891392],"dir":"ltr"},{"str":"ascertain","boundary":[0.6410841878014405,0.6965245081581218,0.7179582993998834,0.7117970734891392],"dir":"ltr"},{"str":"the","boundary":[0.723374474914919,0.6965245081581218,0.7508309267046431,0.7117970734891392],"dir":"ltr"},{"str":"efficiency","boundary":[0.7562471022196787,0.6965245081581218,0.837153694858513,0.7117970734891392],"dir":"ltr"},{"str":"of","boundary":[0.8425698703735487,0.6965245081581218,0.8601427902015292,0.7117970734891392],"dir":"ltr"},{"str":"a","boundary":[0.8655589657165648,0.6965245081581218,0.8754424976783085,0.7117970734891392],"dir":"ltr"},{"str":"given","boundary":[0.8808586731933441,0.6965245081581218,0.926995000390764,0.7117970734891392],"dir":"ltr"},{"str":"algorithm.","boundary":[0.23910117585339866,0.7148531138118758,0.32751925278315824,0.7301256791428932],"dir":"ltr"},{"str":"We","boundary":[0.2746818909156762,0.7331801922090965,0.3028697240705694,0.7484527575401139],"dir":"ltr"},{"str":"discussed","boundary":[0.3078114900514412,0.7331801922090965,0.38800646838903,0.7484527575401139],"dir":"ltr"},{"str":"10","boundary":[0.39294823436990195,0.7331801922090965,0.4127152982933895,0.7484527575401139],"dir":"ltr"},{"str":"general","boundary":[0.4176570642742613,0.7331801922090965,0.48136631129966156,0.7484527575401139],"dir":"ltr"},{"str":"design","boundary":[0.48630807728053344,0.7331801922090965,0.5412407479239053,0.7484527575401139],"dir":"ltr"},{"str":"techniques","boundary":[0.546182513904777,0.7331801922090965,0.6384551682996167,0.7484527575401139],"dir":"ltr"},{"str":"in","boundary":[0.6433969342804886,0.7331801922090965,0.6598826655926772,0.7484527575401139],"dir":"ltr"},{"str":"this","boundary":[0.6648244315735492,0.7331801922090965,0.6955819830384957,0.7484527575401139],"dir":"ltr"},{"str":"book:","boundary":[0.7005237490193675,0.7331801922090965,0.7494274651660757,0.7484527575401139],"dir":"ltr"},{"str":"brute","boundary":[0.3883408616502965,0.782474240572586,0.4278890910848809,0.7962196413498964],"dir":"ltr"},{"str":"force","boundary":[0.432336710229571,0.782474240572586,0.47087088249916603,0.7962196413498964],"dir":"ltr"},{"str":"dynamic","boundary":[0.6027161044243595,0.782474240572586,0.6679537820386738,0.7962196413498964],"dir":"ltr"},{"str":"programming","boundary":[0.6724014011833641,0.782474240572586,0.7771873082322628,0.7962196413498964],"dir":"ltr"},{"str":"decrease-and-conquer","boundary":[0.3883408616502965,0.8023280974553332,0.555375646248278,0.8160734982326437],"dir":"ltr"},{"str":"greedy","boundary":[0.6027161044243593,0.8023280974553332,0.6531165245719875,0.8160734982326437],"dir":"ltr"},{"str":"technique","boundary":[0.6575641437166776,0.8023280974553332,0.7305050976895953,0.8160734982326437],"dir":"ltr"},{"str":"divide-and-conquer","boundary":[0.3883408616502965,0.8221819543380806,0.537620750622675,0.8359273551153912],"dir":"ltr"},{"str":"iterative","boundary":[0.6027161044243593,0.8221819543380806,0.6630080295497782,0.8359273551153912],"dir":"ltr"},{"str":"improvement","boundary":[0.6674556486944684,0.8221819543380806,0.7679540508878858,0.8359273551153912],"dir":"ltr"},{"str":"transform-and-conquer","boundary":[0.3883408616502965,0.8420358112208279,0.5662812083910581,0.8557812119981384],"dir":"ltr"},{"str":"backtracking","boundary":[0.6027161044243593,0.8420358112208279,0.7011508113346405,0.8557812119981384],"dir":"ltr"},{"str":"space-time","boundary":[0.3883408616502965,0.8618896681035751,0.46838021577813954,0.8756350688808857],"dir":"ltr"},{"str":"trade-offs","boundary":[0.47282783492282965,0.8618896681035751,0.5459644841381137,0.8756350688808857],"dir":"ltr"},{"str":"branch-and-bound","boundary":[0.6027161044243593,0.8618896681035751,0.7458760694536443,0.8756350688808857],"dir":"ltr"},{"str":"471","boundary":[0.8940253964965859,0.9329341022884333,0.9269968591209631,0.9482066676194506],"dir":"ltr"}],"boundary":[0.2391,0.45697,0.92705,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":501,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/6ad3356d7cc854a80135cfcbc3b19850.jpg","blurred":"/storage/books/4a8b03583f119702/pages/18a4c02c568ab8944e754028b832a221.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.11749,0.07272,0.05179]},"elements":[{"words":[{"str":"APPENDIX","boundary":[0.14421784044919886,0.1174858063376417,0.30406291377915085,0.13886748978046087],"dir":"ltr"},{"str":"A","boundary":[0.31327835862313874,0.1174858063376417,0.3363308077373787,0.13886748978046087],"dir":"ltr"},{"str":"Useful","boundary":[0.14421784044919886,0.17365916009947602,0.2990655009716676,0.2103134088733125],"dir":"ltr"},{"str":"Formulas","boundary":[0.31486337810217685,0.17365916009947602,0.5354169239872741,0.2103134088733125],"dir":"ltr"},{"str":"for","boundary":[0.5512148011177833,0.17365916009947602,0.6207159722775311,0.2103134088733125],"dir":"ltr"},{"str":"the","boundary":[0.6365138494080402,0.17365916009947602,0.7139376796692746,0.2103134088733125],"dir":"ltr"},{"str":"Analysis","boundary":[0.14421784044919886,0.21336670779617312,0.3463168091458033,0.2500209565700096],"dir":"ltr"},{"str":"of","boundary":[0.36211468627631255,0.21336670779617312,0.41197525343596775,0.2500209565700096],"dir":"ltr"},{"str":"Algorithms","boundary":[0.42777313056647703,0.21336670779617312,0.6955305435532458,0.2500209565700096],"dir":"ltr"}],"boundary":[0.14422,0.11749,0.71394,0.25002],"dir":"ltr","type":"paragraph"},{"words":[{"str":"This","boundary":[0.23910077902799318,0.3796730415193825,0.27566984728644506,0.3949456068503998],"dir":"ltr"},{"str":"appendix","boundary":[0.2814615970160269,0.3796730415193825,0.3605693868378239,0.3949456068503998],"dir":"ltr"},{"str":"contains","boundary":[0.36636113656740577,0.3796730415193825,0.4377597714590426,0.3949456068503998],"dir":"ltr"},{"str":"a","boundary":[0.44355152118862445,0.3796730415193825,0.4534350531503682,0.3949456068503998],"dir":"ltr"},{"str":"list","boundary":[0.45922680287995,0.3796730415193825,0.48448911057416705,0.3949456068503998],"dir":"ltr"},{"str":"of","boundary":[0.49028086030374884,0.3796730415193825,0.5078537801317292,0.3949456068503998],"dir":"ltr"},{"str":"useful","boundary":[0.5136455298613111,0.3796730415193825,0.5652771008294605,0.3949456068503998],"dir":"ltr"},{"str":"formulas","boundary":[0.5710688505590423,0.3796730415193825,0.6468557736416933,0.3949456068503998],"dir":"ltr"},{"str":"and","boundary":[0.6526475233712751,0.3796730415193825,0.6845120304159369,0.3949456068503998],"dir":"ltr"},{"str":"rules","boundary":[0.6903037801455187,0.3796730415193825,0.7320518191519244,0.3949456068503998],"dir":"ltr"},{"str":"that","boundary":[0.7378435688815063,0.3796730415193825,0.7718824529577517,0.3949456068503998],"dir":"ltr"},{"str":"are","boundary":[0.7776742026873337,0.3796730415193825,0.8051306544770578,0.3949456068503998],"dir":"ltr"},{"str":"helpful","boundary":[0.8109224042066396,0.3796730415193825,0.871350318620741,0.3949456068503998],"dir":"ltr"},{"str":"in","boundary":[0.8771420683503226,0.3796730415193825,0.8936277996625112,0.3949456068503998],"dir":"ltr"},{"str":"the","boundary":[0.8994195493920931,0.3796730415193825,0.9268760011818172,0.3949456068503998],"dir":"ltr"},{"str":"mathematical","boundary":[0.23910077902799318,0.3980001199166033,0.3554892514094876,0.4132726852476206],"dir":"ltr"},{"str":"analysis","boundary":[0.3629414345086424,0.3980001199166033,0.429951781209265,0.4132726852476206],"dir":"ltr"},{"str":"of","boundary":[0.4374039643084198,0.3980001199166033,0.4549768841364002,0.4132726852476206],"dir":"ltr"},{"str":"algorithms.","boundary":[0.462429067235555,0.3980001199166033,0.5574493435157594,0.4132726852476206],"dir":"ltr"},{"str":"More","boundary":[0.5649015266149141,0.3980001199166033,0.6121250423281258,0.4132726852476206],"dir":"ltr"},{"str":"advanced","boundary":[0.6195772254272807,0.3980001199166033,0.7008593922806612,0.4132726852476206],"dir":"ltr"},{"str":"material","boundary":[0.7083115753798161,0.3980001199166033,0.7796904432075296,0.4132726852476206],"dir":"ltr"},{"str":"can","boundary":[0.7871426263066843,0.3980001199166033,0.8167932221919155,0.4132726852476206],"dir":"ltr"},{"str":"be","boundary":[0.8242454052910702,0.3980001199166033,0.8451194247942729,0.4132726852476206],"dir":"ltr"},{"str":"found","boundary":[0.8525716078934278,0.3980001199166033,0.9031159903457854,0.4132726852476206],"dir":"ltr"},{"str":"in","boundary":[0.9105681734449403,0.3980001199166033,0.9270539047571289,0.4132726852476206],"dir":"ltr"},{"str":"[Gra94],","boundary":[0.23910077902799318,0.41632719831382414,0.3110133575816407,0.4315997636448414],"dir":"ltr"},{"str":"[Gre07],","boundary":[0.3159551235625126,0.41632719831382414,0.3878677021161602,0.4315997636448414],"dir":"ltr"},{"str":"[Pur04],","boundary":[0.392809468097032,0.41632719831382414,0.4614407140393806,0.4315997636448414],"dir":"ltr"},{"str":"and","boundary":[0.4663824800202525,0.41632719831382414,0.4982469870649144,0.4315997636448414],"dir":"ltr"},{"str":"[Sed96].","boundary":[0.5031887530457863,0.41632719831382414,0.5729269545678501,0.4315997636448414],"dir":"ltr"}],"boundary":[0.2391,0.37967,0.92705,0.4316],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Properties","boundary":[0.23910077902799318,0.46582340263999156,0.35514212759238767,0.48415060367640556],"dir":"ltr"},{"str":"of","boundary":[0.36173646424424816,0.46582340263999156,0.3841382323522233,0.48415060367640556],"dir":"ltr"},{"str":"Logarithms","boundary":[0.3907325690040838,0.46582340263999156,0.519938870236761,0.48415060367640556],"dir":"ltr"},{"str":"All","boundary":[0.23910077902799318,0.49562686572920917,0.2666560661373348,0.5108994310602265],"dir":"ltr"},{"str":"logarithm","boundary":[0.2719338722049059,0.49562686572920917,0.35541018315379364,0.5108994310602265],"dir":"ltr"},{"str":"bases","boundary":[0.3606879892213648,0.49562686572920917,0.40682431641878464,0.5108994310602265],"dir":"ltr"},{"str":"are","boundary":[0.41210212248635586,0.49562686572920917,0.43955857427608,0.5108994310602265],"dir":"ltr"},{"str":"assumed","boundary":[0.4448363803436511,0.49562686572920917,0.518429159330795,0.5108994310602265],"dir":"ltr"},{"str":"to","boundary":[0.5237069653983663,0.49562686572920917,0.5412798852263466,0.5108994310602265],"dir":"ltr"},{"str":"be","boundary":[0.5465576912939177,0.49562686572920917,0.5674317107971205,0.5108994310602265],"dir":"ltr"},{"str":"greater","boundary":[0.5727095168646918,0.49562686572920917,0.6342048527306614,0.5108994310602265],"dir":"ltr"},{"str":"than","boundary":[0.6394826587982326,0.49562686572920917,0.6779295981294158,0.5108994310602265],"dir":"ltr"},{"str":"1","boundary":[0.6832074041969869,0.49562686572920917,0.6930909361587306,0.5108994310602265],"dir":"ltr"},{"str":"in","boundary":[0.6983687422263019,0.49562686572920917,0.7148544735384904,0.5108994310602265],"dir":"ltr"},{"str":"the","boundary":[0.7201322796060615,0.49562686572920917,0.7475887313957856,0.5108994310602265],"dir":"ltr"},{"str":"formulas","boundary":[0.7528665374633569,0.49562686572920917,0.828653460546008,0.5108994310602265],"dir":"ltr"},{"str":"below;","boundary":[0.8339312666135792,0.49562686572920917,0.8905046035626004,0.5108994310602265],"dir":"ltr"},{"str":"lg","boundary":[0.895960313205483,0.49562686572920917,0.9113390889379562,0.5108994310602265],"dir":"ltr"},{"str":"x","boundary":[0.915934931300167,0.49623776834244987,0.9258184632619108,0.5115103336734672],"dir":"ltr"},{"str":"denotes","boundary":[0.23910077902799312,0.5139539441264299,0.30611112572861576,0.5292265094574473],"dir":"ltr"},{"str":"the","boundary":[0.31308889929360684,0.5139539441264299,0.340545351083331,0.5292265094574473],"dir":"ltr"},{"str":"logarithm","boundary":[0.3475231246483221,0.5139539441264299,0.4309994355972098,0.5292265094574473],"dir":"ltr"},{"str":"base","boundary":[0.4379772091622009,0.5139539441264299,0.47642414849338416,0.5292265094574473],"dir":"ltr"},{"str":"2,","boundary":[0.4834019220583752,0.5139539441264299,0.4982272200009908,0.5292265094574473],"dir":"ltr"},{"str":"ln","boundary":[0.5057189372279925,0.5139539441264299,0.5222046685401811,0.5292265094574473],"dir":"ltr"},{"str":"x","boundary":[0.5270139951927656,0.5145648467396706,0.5368975271545093,0.529837412070688],"dir":"ltr"},{"str":"denotes","boundary":[0.5450652779676943,0.5139539441264299,0.612075624668317,0.5292265094574473],"dir":"ltr"},{"str":"the","boundary":[0.6190533982333081,0.5139539441264299,0.6465098500230322,0.5292265094574473],"dir":"ltr"},{"str":"logarithm","boundary":[0.6534876235880233,0.5139539441264299,0.736963934536911,0.5292265094574473],"dir":"ltr"},{"str":"base","boundary":[0.7439417081019022,0.5139539441264299,0.7823886474330853,0.5292265094574473],"dir":"ltr"},{"str":"e","boundary":[0.7893802579428228,0.5145648467396706,0.7981568343248514,0.529837412070688],"dir":"ltr"},{"str":"=","boundary":[0.8031717384422401,0.5172375456725987,0.8185900483025603,0.5325101110036161],"dir":"ltr"},{"str":"2","boundary":[0.8232096111414794,0.5139539441264299,0.833093143103223,0.5292265094574473],"dir":"ltr"},{"str":".","boundary":[0.8332315125506875,0.5145648467396706,0.8386674551296466,0.529837412070688],"dir":"ltr"},{"str":"71828","boundary":[0.8386674551296466,0.5139539441264299,0.8880851149383653,0.5292265094574473],"dir":"ltr"},{"str":"...;","boundary":[0.8926256095215904,0.5139539441264299,0.927277272579464,0.529837412070688],"dir":"ltr"},{"str":"x","boundary":[0.2390988023216006,0.5328919251368914,0.24898233428334438,0.5481644904679088],"dir":"ltr"},{"str":",","boundary":[0.25016835811875365,0.5322810225236507,0.25511012409962547,0.5475535878546681],"dir":"ltr"},{"str":"y","boundary":[0.2600518900804974,0.5328919251368914,0.26993542204224114,0.5481644904679088],"dir":"ltr"},{"str":"are","boundary":[0.2760632118585223,0.5322810225236507,0.30351966364824645,0.5475535878546681],"dir":"ltr"},{"str":"arbitrary","boundary":[0.30846142962911827,0.5322810225236507,0.3842483527117694,0.5475535878546681],"dir":"ltr"},{"str":"positive","boundary":[0.3891901186926413,0.5322810225236507,0.4562004653932639,0.5475535878546681],"dir":"ltr"},{"str":"numbers.","boundary":[0.46114223137413585,0.5322810225236507,0.5396965434060752,0.5475535878546681],"dir":"ltr"},{"str":"1.","boundary":[0.2390988023216006,0.5640540674382992,0.25392410026421625,0.5793266327693165],"dir":"ltr"},{"str":"loga","boundary":[0.27467951738387814,0.5640540674382992,0.30862260594216,0.5828427382356623],"dir":"ltr"},{"str":"1","boundary":[0.3141761774919403,0.5640549365822616,0.3240597094536841,0.5793275019132789],"dir":"ltr"},{"str":"=","boundary":[0.32750313198915565,0.5673385381284304,0.34292144184947587,0.5826111034594477],"dir":"ltr"},{"str":"0","boundary":[0.34731170674688244,0.5640549365822616,0.3571952387086262,0.5793275019132789],"dir":"ltr"},{"str":"2.","boundary":[0.23909889200414244,0.590018297644991,0.2539241899467581,0.6052908629760083],"dir":"ltr"},{"str":"loga","boundary":[0.27467960706642,0.590018297644991,0.30862260594216,0.6088069884325427],"dir":"ltr"},{"str":"a","boundary":[0.3141761774919403,0.5906285564024673,0.3240597094536841,0.6059011217334845],"dir":"ltr"},{"str":"=","boundary":[0.3293414689340399,0.5933012553353953,0.3447597787943602,0.6085738206664126],"dir":"ltr"},{"str":"1","boundary":[0.3491520203981591,0.5900176537892265,0.35903555235990287,0.6052902191202438],"dir":"ltr"},{"str":"3.","boundary":[0.23910086871053474,0.6159825421084891,0.2539261666531503,0.6312551074395064],"dir":"ltr"},{"str":"loga","boundary":[0.27468158377281227,0.6159825421084891,0.30862260594216,0.6347697056395076],"dir":"ltr"},{"str":"x","boundary":[0.3141761774919403,0.6165928065993476,0.3240597094536841,0.631865371930365],"dir":"ltr"},{"str":"y","boundary":[0.3252456221779798,0.6136251757365987,0.3326583207524633,0.6250796763843574],"dir":"ltr"},{"str":"=","boundary":[0.33843411452931593,0.6192655055322757,0.3538524243896362,0.6345380708632931],"dir":"ltr"},{"str":"y","boundary":[0.3582466426998275,0.6165928065993476,0.3681301746615713,0.631865371930365],"dir":"ltr"},{"str":"loga","boundary":[0.37370646339438707,0.6159819039861069,0.4076484017542309,0.6347697056395076],"dir":"ltr"},{"str":"x","boundary":[0.41320197330401126,0.6165928065993476,0.423085505265755,0.631865371930365],"dir":"ltr"},{"str":"4.","boundary":[0.23910158109150273,0.6419452650488363,0.25392687903411837,0.6572178303798537],"dir":"ltr"},{"str":"loga","boundary":[0.27468229615378026,0.6419452650488363,0.30862260594216,0.660733955836388],"dir":"ltr"},{"str":"xy","boundary":[0.3141761774919403,0.6425555238063126,0.3347339239723674,0.6578280891373299],"dir":"ltr"},{"str":"=","boundary":[0.3399168481331058,0.6452282227392407,0.355335157993426,0.660500788070258],"dir":"ltr"},{"str":"loga","boundary":[0.35972739959722494,0.6419446211930719,0.3936682427189497,0.660733955836388],"dir":"ltr"},{"str":"x","boundary":[0.39922181426873005,0.6425555238063126,0.4091053462304738,0.6578280891373299],"dir":"ltr"},{"str":"+","boundary":[0.41468361166968193,0.6452282227392407,0.4301019215300022,0.660500788070258],"dir":"ltr"},{"str":"loga","boundary":[0.4344961398401935,0.6419446211930719,0.468436101493645,0.660733955836388],"dir":"ltr"},{"str":"y","boundary":[0.4739898714561281,0.6425555238063126,0.48387340341787183,0.6578280891373299],"dir":"ltr"},{"str":"x","boundary":[0.3165472092897208,0.6629856804086521,0.32643074125146454,0.6782582457396695],"dir":"ltr"},{"str":"5.","boundary":[0.23910378097250315,0.6723186991233991,0.25392907891511873,0.6875912644544164],"dir":"ltr"},{"str":"loga","boundary":[0.27468251932838833,0.6723186991233991,0.30862260594216,0.6911070850299164],"dir":"ltr"},{"str":"=","boundary":[0.3343830310678836,0.6756013289379204,0.3498013409282038,0.6908738942689376],"dir":"ltr"},{"str":"loga","boundary":[0.3541916058256104,0.6723177273917516,0.38813252831241624,0.6911070850299164],"dir":"ltr"},{"str":"x","boundary":[0.39368808398922406,0.6729286529998411,0.4035716159509678,0.6882012183308583],"dir":"ltr"},{"str":"−","boundary":[0.40914790468378365,0.6756013519327692,0.42456621454410387,0.6908739172637864],"dir":"ltr"},{"str":"loga","boundary":[0.4289584561479028,0.6723177503866004,0.46290038708711156,0.6911070850299164],"dir":"ltr"},{"str":"y","boundary":[0.46845395863689193,0.6729286529998411,0.4783374905986357,0.6882012183308583],"dir":"ltr"},{"str":"y","boundary":[0.3165472092897208,0.6847648681365307,0.32643074125146454,0.7000374334675481],"dir":"ltr"},{"str":"logb","boundary":[0.28545593876987163,0.7072189929994055,0.31128093933351253,0.7215266944776794],"dir":"ltr"},{"str":"x","boundary":[0.3153071298975762,0.7076771730253159,0.32271982847205966,0.7191316736730746],"dir":"ltr"},{"str":"x","boundary":[0.3483081504194239,0.7106448038880648,0.35819168238116766,0.7259173692190821],"dir":"ltr"},{"str":"logb","boundary":[0.3593765753038538,0.7072189929994055,0.38520157586749465,0.7215266944776794],"dir":"ltr"},{"str":"a","boundary":[0.3892279648442611,0.7076771730253159,0.39664066341874454,0.7191316736730746],"dir":"ltr"},{"str":"6.","boundary":[0.2391006693454511,0.7100333504715475,0.2539259672880667,0.7253059158025649],"dir":"ltr"},{"str":"a","boundary":[0.2746813844077286,0.7106442530847882,0.2845649163694724,0.7259168184158056],"dir":"ltr"},{"str":"=","boundary":[0.3284956222489124,0.7133175028209929,0.3439139321092326,0.7285900681520102],"dir":"ltr"},{"str":"log","boundary":[0.35182057402782996,0.730210293226448,0.37818983730176225,0.7454828585574654],"dir":"ltr"},{"str":"x","boundary":[0.39094403631028646,0.730818951174535,0.40082756827203025,0.7460915165055524],"dir":"ltr"},{"str":"b","boundary":[0.37834879794015225,0.7375428825568517,0.38576149651463576,0.7489973832046104],"dir":"ltr"},{"str":"log","boundary":[0.4285870126874149,0.7410171374598272,0.4549562759613472,0.7562897027908445],"dir":"ltr"},{"str":"b","boundary":[0.46808491100978966,0.7416280630679166,0.4779684429715334,0.7569006283989339],"dir":"ltr"},{"str":"logb","boundary":[0.48275602585380206,0.7410171604546759,0.5166960231818576,0.759806495097992],"dir":"ltr"},{"str":"x","boundary":[0.5218785629775083,0.7416280630679166,0.531762094939252,0.7569006283989339],"dir":"ltr"},{"str":"7.","boundary":[0.23910077902799318,0.7410171604546759,0.25392607697060876,0.7562897257856932],"dir":"ltr"},{"str":"loga","boundary":[0.2746814940902707,0.7410171604546759,0.30862260594216,0.759806495097992],"dir":"ltr"},{"str":"x","boundary":[0.3141761774919403,0.7416280630679166,0.3240597094536841,0.7569006283989339],"dir":"ltr"},{"str":"=","boundary":[0.32963797489289226,0.7443007620008447,0.3450562847532125,0.759573327331862],"dir":"ltr"},{"str":"=","boundary":[0.40877843792968804,0.744300739005996,0.4241967477900083,0.7595733043370133],"dir":"ltr"},{"str":"a","boundary":[0.45511864088552584,0.7483519944502334,0.4625313394600093,0.759806495097992],"dir":"ltr"},{"str":"logb","boundary":[0.3519700275231553,0.7528533755913656,0.38591030604169313,0.7716427102346818],"dir":"ltr"},{"str":"a","boundary":[0.39109284583734377,0.7534642782046063,0.40097637779908757,0.7687368435356237],"dir":"ltr"},{"str":"Combinatorics","boundary":[0.23910077902799318,0.80309498093399,0.4038405921473145,0.8214221819704041],"dir":"ltr"},{"str":"1.","boundary":[0.23910077902799318,0.8328984440232078,0.25392607697060876,0.848171009354225],"dir":"ltr"},{"str":"Number","boundary":[0.2746814940902707,0.8328984440232078,0.34608012898190754,0.848171009354225],"dir":"ltr"},{"str":"of","boundary":[0.3510218949627794,0.8328984440232078,0.36859481479075984,0.848171009354225],"dir":"ltr"},{"str":"permutations","boundary":[0.3735365807716317,0.8328984440232078,0.48777044318546603,0.848171009354225],"dir":"ltr"},{"str":"of","boundary":[0.4927122091663379,0.8328984440232078,0.5102851289943183,0.848171009354225],"dir":"ltr"},{"str":"an","boundary":[0.5152268949751901,0.8328984440232078,0.5361009144783929,0.848171009354225],"dir":"ltr"},{"str":"n-element","boundary":[0.5410466338720494,0.8328984440232078,0.6275868397290778,0.8487819119674657],"dir":"ltr"},{"str":"set:","boundary":[0.6325286057099497,0.8328984440232078,0.6616257238053234,0.848171009354225],"dir":"ltr"},{"str":"P","boundary":[0.6665674897861952,0.8335093466364485,0.6790405071219158,0.8487819119674657],"dir":"ltr"},{"str":"(n)","boundary":[0.6820055667104389,0.8335093466364485,0.7075248462356613,0.8487819119674657],"dir":"ltr"},{"str":"=","boundary":[0.7119190645458526,0.8361820455693764,0.7273373744061729,0.8514546109003936],"dir":"ltr"},{"str":"n","boundary":[0.7317296160099718,0.8335093466364485,0.7425026658482724,0.8487819119674657],"dir":"ltr"},{"str":"!","boundary":[0.7425026658482724,0.8328984440232078,0.7490850981347937,0.848171009354225],"dir":"ltr"},{"str":"n","boundary":[0.8040039318334191,0.8524458003903768,0.8147769816717197,0.867718365721394],"dir":"ltr"},{"str":"!","boundary":[0.8147769816717197,0.8518348977771362,0.8213594139582411,0.8671074631081533],"dir":"ltr"},{"str":"2.","boundary":[0.23910077902799318,0.8580050141708672,0.25392607697060876,0.8732775795018843],"dir":"ltr"},{"str":"Number","boundary":[0.2746814940902707,0.8580050141708672,0.34608012898190754,0.8732775795018843],"dir":"ltr"},{"str":"of","boundary":[0.3510218949627794,0.8580050141708672,0.36859481479075984,0.8732775795018843],"dir":"ltr"},{"str":"k","boundary":[0.37353855747802406,0.8586159167841079,0.3827104751385223,0.873888482115125],"dir":"ltr"},{"str":"-combinations","boundary":[0.3835011576954618,0.8580050141708672,0.5054244079755328,0.8732775795018843],"dir":"ltr"},{"str":"of","boundary":[0.5103661739564046,0.8580050141708672,0.527939093784385,0.8732775795018843],"dir":"ltr"},{"str":"an","boundary":[0.5328808597652569,0.8580050141708672,0.5537548792684597,0.8732775795018843],"dir":"ltr"},{"str":"n-element","boundary":[0.5586986219557238,0.8580050141708672,0.6452368511063599,0.873888482115125],"dir":"ltr"},{"str":"set:","boundary":[0.6501786170872317,0.8580050141708672,0.6792757351826054,0.8732775795018843],"dir":"ltr"},{"str":"C","boundary":[0.6842194778698695,0.8586159167841079,0.6978587519770758,0.873888482115125],"dir":"ltr"},{"str":"(n,","boundary":[0.699044775812485,0.8586159167841079,0.723733838652921,0.873888482115125],"dir":"ltr"},{"str":"k","boundary":[0.7281221268439353,0.8586159167841079,0.7372940445044335,0.873888482115125],"dir":"ltr"},{"str":")","boundary":[0.7380847270613728,0.8586159167841079,0.7454578419048338,0.873888482115125],"dir":"ltr"},{"str":"=","boundary":[0.7498560136278097,0.8612886157170357,0.76527432348813,0.876561181048053],"dir":"ltr"},{"str":"k","boundary":[0.772041266850107,0.8667261721230165,0.7812131845106052,0.8819987374540338],"dir":"ltr"},{"str":"!","boundary":[0.7820038670675447,0.8661152695097758,0.788586299354066,0.8813878348407931],"dir":"ltr"},{"str":"(n","boundary":[0.7870662121383498,0.8667261721230165,0.8052123768201114,0.8819987374540338],"dir":"ltr"},{"str":"−","boundary":[0.8096046184239103,0.8693988710559445,0.8250229282842305,0.8846714363869617],"dir":"ltr"},{"str":"k)","boundary":[0.8294171465944219,0.8667261721230165,0.84754354421226,0.8819987374540338],"dir":"ltr"},{"str":"!","boundary":[0.8467528616553205,0.8661152695097758,0.8533352939418418,0.8813878348407931],"dir":"ltr"},{"str":"3.","boundary":[0.2391054098217451,0.8841674417310382,0.2539307077643607,0.8994400070620555],"dir":"ltr"},{"str":"Number","boundary":[0.2746841481776303,0.8841674417310382,0.34608278306926715,0.8994400070620555],"dir":"ltr"},{"str":"of","boundary":[0.351024549050139,0.8841674417310382,0.36859746887811945,0.8994400070620555],"dir":"ltr"},{"str":"subsets","boundary":[0.3735392348589913,0.8841674417310382,0.4350543377888844,0.8994400070620555],"dir":"ltr"},{"str":"of","boundary":[0.4399961037697563,0.8841674417310382,0.4575690235977367,0.8994400070620555],"dir":"ltr"},{"str":"an","boundary":[0.4625107895786085,0.8841674417310382,0.48338480908181136,0.8994400070620555],"dir":"ltr"},{"str":"n-element","boundary":[0.4883285517690756,0.8841674417310382,0.5748687576261039,0.9000509096752962],"dir":"ltr"},{"str":"set:","boundary":[0.5798105236069758,0.8841674417310382,0.6089076417023493,0.8994400070620555],"dir":"ltr"},{"str":"2n","boundary":[0.6138494076832213,0.8818125634937598,0.6319524542688035,0.8994400070620555],"dir":"ltr"},{"str":"475","boundary":[0.8940253964965859,0.9329341022884333,0.9269968591209631,0.9482066676194506],"dir":"ltr"}],"boundary":[0.2391,0.46582,0.92728,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":505,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/24f3ca2af19cd4d6c65e6d4ba63f2e10.jpg","blurred":"/storage/books/4a8b03583f119702/pages/fc8f389bca91c5a3869d8e08533e38c6.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.11749,0.07296,0.05179]},"elements":[{"words":[{"str":"APPENDIX","boundary":[0.14421784044919886,0.1174858063376417,0.30406291377915085,0.13886748978046087],"dir":"ltr"},{"str":"B","boundary":[0.31327835862313874,0.1174858063376417,0.3332589927893827,0.13886748978046087],"dir":"ltr"},{"str":"Short","boundary":[0.14421784044919886,0.17365916009947602,0.27676819691359156,0.2103134088733125],"dir":"ltr"},{"str":"Tutorial","boundary":[0.2925660740441008,0.17365916009947602,0.478819724537732,0.2103134088733125],"dir":"ltr"},{"str":"on","boundary":[0.49461760166824126,0.17365916009947602,0.5550575279873666,0.2103134088733125],"dir":"ltr"},{"str":"Recurrence","boundary":[0.5708554051178758,0.17365916009947602,0.8412220770901644,0.2103134088733125],"dir":"ltr"},{"str":"Relations","boundary":[0.14421784044919886,0.21336670779617312,0.3659574131458958,0.2500209565700096],"dir":"ltr"}],"boundary":[0.14422,0.11749,0.84122,0.25002],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Sequences","boundary":[0.23910077902799318,0.3703671865887813,0.36168902297337147,0.3886943876251953],"dir":"ltr"},{"str":"and","boundary":[0.368283359625232,0.3703671865887813,0.41045864943461335,0.3886943876251953],"dir":"ltr"},{"str":"Recurrence","boundary":[0.41705298608647384,0.3703671865887813,0.5436025761500561,0.3886943876251953],"dir":"ltr"},{"str":"Relations","boundary":[0.5501969128019167,0.3703671865887813,0.6556588579608084,0.3886943876251953],"dir":"ltr"},{"str":"DEFINITION","boundary":[0.23910077902799318,0.4000637417206819,0.35114049734632036,0.4153363070516992],"dir":"ltr"},{"str":"A","boundary":[0.3709095379762002,0.4001706496779989,0.3874743375440827,0.41544321500901626],"dir":"ltr"},{"str":"(numerical)","boundary":[0.3924161035249546,0.4001706496779989,0.4934653343018227,0.41544321500901626],"dir":"ltr"},{"str":"sequence","boundary":[0.49840907698908693,0.4001706496779989,0.5741762330078145,0.41544321500901626],"dir":"ltr"},{"str":"is","boundary":[0.5798493803538555,0.4001706496779989,0.5930340119908216,0.41544321500901626],"dir":"ltr"},{"str":"an","boundary":[0.5979757779716935,0.4001706496779989,0.6188497974748962,0.41544321500901626],"dir":"ltr"},{"str":"ordered","boundary":[0.6237915634557681,0.4001706496779989,0.6919088657361062,0.41544321500901626],"dir":"ltr"},{"str":"list","boundary":[0.6968506317169779,0.4001706496779989,0.7221129394111949,0.41544321500901626],"dir":"ltr"},{"str":"of","boundary":[0.7270547053920668,0.4001706496779989,0.7446276252200472,0.41544321500901626],"dir":"ltr"},{"str":"numbers.","boundary":[0.7495693912009191,0.4001706496779989,0.8281237032328586,0.41544321500901626],"dir":"ltr"},{"str":"Examples:","boundary":[0.24044889278757492,0.4458600561222703,0.32995415823312635,0.46113262145328765],"dir":"ltr"},{"str":"2","boundary":[0.3348959242139982,0.4458600561222703,0.344779456175742,0.46113262145328765],"dir":"ltr"},{"str":",","boundary":[0.3449178256232064,0.446470958735511,0.35146072378188076,0.46174352406652835],"dir":"ltr"},{"str":"4","boundary":[0.3558529653856797,0.4458600561222703,0.3657364973474235,0.46113262145328765],"dir":"ltr"},{"str":",","boundary":[0.36577800818166273,0.446470958735511,0.3723209063403371,0.46174352406652835],"dir":"ltr"},{"str":"6","boundary":[0.376713147944136,0.4458600561222703,0.3865966799058798,0.46113262145328765],"dir":"ltr"},{"str":",","boundary":[0.3865373787141093,0.446470958735511,0.3930802768727837,0.46174352406652835],"dir":"ltr"},{"str":"8","boundary":[0.39747449518297495,0.4458600561222703,0.4073580271447187,0.46113262145328765],"dir":"ltr"},{"str":",","boundary":[0.40727895888902477,0.446470958735511,0.4138218570476991,0.46174352406652835],"dir":"ltr"},{"str":"10","boundary":[0.41821409865149806,0.4458600561222703,0.4379811625749856,0.46113262145328765],"dir":"ltr"},{"str":",","boundary":[0.43808197460099535,0.446470958735511,0.4446248727596697,0.46174352406652835],"dir":"ltr"},{"str":"12","boundary":[0.44901711436346864,0.4458600561222703,0.4687841782869562,0.46113262145328765],"dir":"ltr"},{"str":",...","boundary":[0.46892254773442055,0.446470958735511,0.5093422400451678,0.46174352406652835],"dir":"ltr"},{"str":"(positive","boundary":[0.5247190390712487,0.4458600561222703,0.599418773638108,0.46113262145328765],"dir":"ltr"},{"str":"even","boundary":[0.6043605396189798,0.4458600561222703,0.6450016230456701,0.46113262145328765],"dir":"ltr"},{"str":"integers)","boundary":[0.649943389026542,0.4458600561222703,0.7257303121091931,0.46113262145328765],"dir":"ltr"},{"str":"0","boundary":[0.33490185433317526,0.4700517996066018,0.344785386294919,0.4853243649376191],"dir":"ltr"},{"str":",","boundary":[0.34488422161453647,0.47066270221984247,0.3514271197732108,0.4859352675508598],"dir":"ltr"},{"str":"1","boundary":[0.35581936137700976,0.4700517996066018,0.3657028933387535,0.4853243649376191],"dir":"ltr"},{"str":",","boundary":[0.36475407427042605,0.47066270221984247,0.3712969724291004,0.4859352675508598],"dir":"ltr"},{"str":"1","boundary":[0.3756911907392917,0.4700517996066018,0.3855747227010355,0.4853243649376191],"dir":"ltr"},{"str":",","boundary":[0.38462590363270804,0.47066270221984247,0.3911688017913824,0.4859352675508598],"dir":"ltr"},{"str":"2","boundary":[0.39556104339518133,0.4700517996066018,0.40544457535692513,0.4853243649376191],"dir":"ltr"},{"str":",","boundary":[0.4055829448043895,0.47066270221984247,0.41212584296306387,0.4859352675508598],"dir":"ltr"},{"str":"3","boundary":[0.41652006127325514,0.4700517996066018,0.4264035932349989,0.4853243649376191],"dir":"ltr"},{"str":",","boundary":[0.42588964957298825,0.47066270221984247,0.43243254773166256,0.4859352675508598],"dir":"ltr"},{"str":"5","boundary":[0.43682478933546154,0.4700517996066018,0.4467083212972053,0.4853243649376191],"dir":"ltr"},{"str":",","boundary":[0.4462734458908886,0.47066270221984247,0.45281634404956295,0.4859352675508598],"dir":"ltr"},{"str":"8","boundary":[0.4572105623597542,0.4700517996066018,0.467094094321498,0.4853243649376191],"dir":"ltr"},{"str":",...","boundary":[0.46701502606580403,0.47066270221984247,0.5074347183765513,0.4859352675508598],"dir":"ltr"},{"str":"(the","boundary":[0.5247210157776411,0.4700517996066018,0.5598668554336019,0.4853243649376191],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.5648086214144737,0.4700517996066018,0.6475535509981925,0.4853243649376191],"dir":"ltr"},{"str":"numbers)","boundary":[0.6524953169790644,0.4700517996066018,0.7348844394121603,0.4853243649376191],"dir":"ltr"},{"str":"0","boundary":[0.33490383103956767,0.49424354309093327,0.3447873630013114,0.5095161084219506],"dir":"ltr"},{"str":",","boundary":[0.3448861983209288,0.494854445704174,0.3514290964796032,0.5101270110351913],"dir":"ltr"},{"str":"1","boundary":[0.35582133808340216,0.49424354309093327,0.3657048700451459,0.5095161084219506],"dir":"ltr"},{"str":",","boundary":[0.36475605097681846,0.494854445704174,0.37129894913549283,0.5101270110351913],"dir":"ltr"},{"str":"3","boundary":[0.3756931674456841,0.49424354309093327,0.3855766994074279,0.5095161084219506],"dir":"ltr"},{"str":",","boundary":[0.3850627557454172,0.494854445704174,0.3916056539040915,0.5101270110351913],"dir":"ltr"},{"str":"6","boundary":[0.3959978955078905,0.49424354309093327,0.4058814274696343,0.5095161084219506],"dir":"ltr"},{"str":",","boundary":[0.40582410298425614,0.494854445704174,0.41236700114293046,0.5101270110351913],"dir":"ltr"},{"str":"10","boundary":[0.41675924274672943,0.49424354309093327,0.43652630667021697,0.5095161084219506],"dir":"ltr"},{"str":",","boundary":[0.4366271186962267,0.494854445704174,0.44317001685490104,0.5101270110351913],"dir":"ltr"},{"str":"15","boundary":[0.4475622584587,0.49424354309093327,0.46732932238218755,0.5095161084219506],"dir":"ltr"},{"str":",...","boundary":[0.4668944469758708,0.494854445704174,0.5073141392866181,0.5101270110351913],"dir":"ltr"},{"str":"(numbers","boundary":[0.5247249691904258,0.49424354309093327,0.6071140916235217,0.5095161084219506],"dir":"ltr"},{"str":"of","boundary":[0.6120558576043936,0.49424354309093327,0.629628777432374,0.5095161084219506],"dir":"ltr"},{"str":"key","boundary":[0.6345705434132458,0.49424354309093327,0.6653280948781924,0.5095161084219506],"dir":"ltr"},{"str":"comparisons","boundary":[0.6702698608590644,0.49424354309093327,0.7779212909863772,0.5095161084219506],"dir":"ltr"},{"str":"in","boundary":[0.7828630569672491,0.49424354309093327,0.7993487882794377,0.5095161084219506],"dir":"ltr"},{"str":"selection","boundary":[0.8042905542603096,0.49424354309093327,0.8800774773429607,0.5095161084219506],"dir":"ltr"},{"str":"sort)","boundary":[0.8850192433238326,0.49424354309093327,0.9256603267505229,0.5095161084219506],"dir":"ltr"},{"str":"A","boundary":[0.2746933543286247,0.5215478353897259,0.2912581538965073,0.5368204007207433],"dir":"ltr"},{"str":"sequence","boundary":[0.29791965443872254,0.5215478353897259,0.377007677196596,0.5368204007207433],"dir":"ltr"},{"str":"is","boundary":[0.3836691777388113,0.5215478353897259,0.3968538093757775,0.5368204007207433],"dir":"ltr"},{"str":"usually","boundary":[0.4035153099179928,0.5215478353897259,0.4639432243320941,0.5368204007207433],"dir":"ltr"},{"str":"denoted","boundary":[0.4706047248743094,0.5215478353897259,0.5409161712501545,0.5368204007207433],"dir":"ltr"},{"str":"by","boundary":[0.5475776717923697,0.5215478353897259,0.5684516912955725,0.5368204007207433],"dir":"ltr"},{"str":"a","boundary":[0.5751131918377879,0.5215478353897259,0.5849967237995316,0.5368204007207433],"dir":"ltr"},{"str":"letter","boundary":[0.5916582243417469,0.5215478353897259,0.6377747844752433,0.5368204007207433],"dir":"ltr"},{"str":"(such","boundary":[0.6444362850174585,0.5215478353897259,0.6905726122148784,0.5368204007207433],"dir":"ltr"},{"str":"as","boundary":[0.6972341127570937,0.5215478353897259,0.714807032585074,0.5368204007207433],"dir":"ltr"},{"str":"x","boundary":[0.7213953949907724,0.5221587380029666,0.7312789269525161,0.537431303333984],"dir":"ltr"},{"str":"or","boundary":[0.7391185445045713,0.5215478353897259,0.7577984199122669,0.5368204007207433],"dir":"ltr"},{"str":"a","boundary":[0.7644520136289128,0.5221587380029666,0.7743355455906565,0.537431303333984],"dir":"ltr"},{"str":")","boundary":[0.7752250634672135,0.5215478353897259,0.7829144513334502,0.5368204007207433],"dir":"ltr"},{"str":"with","boundary":[0.7895759518756655,0.5215478353897259,0.8269159356271334,0.5368204007207433],"dir":"ltr"},{"str":"a","boundary":[0.8335774361693487,0.5215478353897259,0.8434609681310924,0.5368204007207433],"dir":"ltr"},{"str":"subindex","boundary":[0.8501224686733078,0.5215478353897259,0.9270361143995977,0.5368204007207433],"dir":"ltr"},{"str":"(such","boundary":[0.23911263926634713,0.5398749137869469,0.28524896646376696,0.5551474791179641],"dir":"ltr"},{"str":"as","boundary":[0.2893605157598524,0.5398749137869469,0.3069334355878328,0.5551474791179641],"dir":"ltr"},{"str":"n","boundary":[0.31106079853505697,0.5404858164001874,0.32183384837335766,0.5557583817312048],"dir":"ltr"},{"str":"or","boundary":[0.3259533044950125,0.5398749137869469,0.34463317990270814,0.5551474791179641],"dir":"ltr"},{"str":"i","boundary":[0.34875263602436296,0.5404858164001874,0.3548408917127971,0.5557583817312048],"dir":"ltr"},{"str":")","boundary":[0.35602691554820637,0.5398749137869469,0.363716303414443,0.5551474791179641],"dir":"ltr"},{"str":"written","boundary":[0.3678278527105284,0.5398749137869469,0.42932318857649804,0.5551474791179641],"dir":"ltr"},{"str":"in","boundary":[0.4334347378725834,0.5398749137869469,0.449920469184772,0.5551474791179641],"dir":"ltr"},{"str":"curly","boundary":[0.4540320184808574,0.5398749137869469,0.4968672460030548,0.5551474791179641],"dir":"ltr"},{"str":"brackets,","boundary":[0.5009787952991402,0.5398749137869469,0.577319196171649,0.5551474791179641],"dir":"ltr"},{"str":"e.g.,","boundary":[0.5816086490430459,0.5398749137869469,0.6151138223933572,0.5551474791179641],"dir":"ltr"},{"str":"{","boundary":[0.6194250190350697,0.5431585153331155,0.6267388326867601,0.5584310806641329],"dir":"ltr"},{"str":"xn","boundary":[0.6267388326867601,0.5404858164001874,0.6446907481976155,0.557953113969467],"dir":"ltr"},{"str":"}.","boundary":[0.645186105351284,0.5398735536569743,0.6574416849838464,0.5584297205341604],"dir":"ltr"},{"str":"We","boundary":[0.6615532342799316,0.5398735536569743,0.6897410674348249,0.5551461189879916],"dir":"ltr"},{"str":"use","boundary":[0.6938526167309104,0.5398735536569743,0.7224160241003498,0.5551461189879916],"dir":"ltr"},{"str":"the","boundary":[0.7265275733964351,0.5398735536569743,0.7539840251861593,0.5551461189879916],"dir":"ltr"},{"str":"alternative","boundary":[0.7580955744822446,0.5398735536569743,0.8503484618131608,0.5551461189879916],"dir":"ltr"},{"str":"notation","boundary":[0.8544600111092463,0.5398735536569743,0.9269656015805985,0.5551461189879916],"dir":"ltr"},{"str":"x","boundary":[0.23910340434551083,0.5588130619239688,0.2489869363072546,0.5740856272549861],"dir":"ltr"},{"str":"(n)","boundary":[0.2501729601426639,0.5588130619239688,0.2756922396678862,0.5740856272549861],"dir":"ltr"},{"str":".","boundary":[0.2756922396678862,0.5582021593107281,0.28063400564875807,0.5734747246417454],"dir":"ltr"},{"str":"This","boundary":[0.2861885506112581,0.5582021593107281,0.32275761886971,0.5734747246417454],"dir":"ltr"},{"str":"notation","boundary":[0.32831216383220996,0.5582021593107281,0.4008177543035621,0.5734747246417454],"dir":"ltr"},{"str":"stresses","boundary":[0.4063722992660621,0.5582021593107281,0.4711687348072542,0.5734747246417454],"dir":"ltr"},{"str":"the","boundary":[0.47672327976975415,0.5582021593107281,0.5041797315594783,0.5734747246417454],"dir":"ltr"},{"str":"fact","boundary":[0.5097342765219783,0.5582021593107281,0.5415592494387932,0.5734747246417454],"dir":"ltr"},{"str":"that","boundary":[0.547113794401293,0.5582021593107281,0.5811526784775385,0.5734747246417454],"dir":"ltr"},{"str":"a","boundary":[0.5867072234400386,0.5582021593107281,0.5965907554017823,0.5734747246417454],"dir":"ltr"},{"str":"sequence","boundary":[0.6021453003642824,0.5582021593107281,0.6812333231221559,0.5734747246417454],"dir":"ltr"},{"str":"is","boundary":[0.686787868084656,0.5582021593107281,0.6999724997216221,0.5734747246417454],"dir":"ltr"},{"str":"a","boundary":[0.7055270446841221,0.5582021593107281,0.7154105766458657,0.5734747246417454],"dir":"ltr"},{"str":"function:","boundary":[0.7209651216083658,0.5582021593107281,0.7973055224808745,0.5734747246417454],"dir":"ltr"},{"str":"its","boundary":[0.8028600674433746,0.5582021593107281,0.822627131366862,0.5734747246417454],"dir":"ltr"},{"str":"argument","boundary":[0.828181676329362,0.5582021593107281,0.9105510316985345,0.5734747246417454],"dir":"ltr"},{"str":"n","boundary":[0.9162320858701448,0.5588130619239688,0.9270051357084456,0.5740856272549861],"dir":"ltr"},{"str":"indicates","boundary":[0.2391034043455109,0.576529237707949,0.314890327428162,0.5918018030389663],"dir":"ltr"},{"str":"a","boundary":[0.31989139460080435,0.576529237707949,0.3297749265625481,0.5918018030389663],"dir":"ltr"},{"str":"position","boundary":[0.33477599373519046,0.576529237707949,0.4040002515952437,0.5918018030389663],"dir":"ltr"},{"str":"of","boundary":[0.40900131876788604,0.576529237707949,0.42657423859586646,0.5918018030389663],"dir":"ltr"},{"str":"a","boundary":[0.4315753057685087,0.576529237707949,0.4414588377302525,0.5918018030389663],"dir":"ltr"},{"str":"number","boundary":[0.44645990490289483,0.576529237707949,0.5134702516035174,0.5918018030389663],"dir":"ltr"},{"str":"in","boundary":[0.5184713187761598,0.576529237707949,0.5349570500883484,0.5918018030389663],"dir":"ltr"},{"str":"the","boundary":[0.5399581172609907,0.576529237707949,0.5674145690507149,0.5918018030389663],"dir":"ltr"},{"str":"list,","boundary":[0.5724156362233572,0.576529237707949,0.6026197098984462,0.5918018030389663],"dir":"ltr"},{"str":"while","boundary":[0.607640544135012,0.576529237707949,0.6537768713324318,0.5918018030389663],"dir":"ltr"},{"str":"the","boundary":[0.6587779385050742,0.576529237707949,0.6862343902947983,0.5918018030389663],"dir":"ltr"},{"str":"function’s","boundary":[0.6912354574674406,0.576529237707949,0.7754629168454209,0.5918018030389663],"dir":"ltr"},{"str":"value","boundary":[0.7804639840180632,0.576529237707949,0.826600311215483,0.5918018030389663],"dir":"ltr"},{"str":"x","boundary":[0.8315895181497713,0.5771401403211897,0.841473050111515,0.5924127056522069],"dir":"ltr"},{"str":"(n)","boundary":[0.8426590739469243,0.5771401403211897,0.8681783534721467,0.5924127056522069],"dir":"ltr"},{"str":"stands","boundary":[0.873179420644789,0.576529237707949,0.9270051357084454,0.5918018030389663],"dir":"ltr"},{"str":"for","boundary":[0.2391034043455109,0.5948563161051698,0.264365712039728,0.6101288814361872],"dir":"ltr"},{"str":"that","boundary":[0.2693074780205998,0.5948563161051698,0.30334636209684523,0.6101288814361872],"dir":"ltr"},{"str":"number","boundary":[0.30828812807771716,0.5948563161051698,0.37529847477833983,0.6101288814361872],"dir":"ltr"},{"str":"itself.","boundary":[0.3802402407592117,0.5948563161051698,0.42592192548639135,0.6101288814361872],"dir":"ltr"},{"str":"x","boundary":[0.4308656681736555,0.5954672187184105,0.4407492001353993,0.6107397840494279],"dir":"ltr"},{"str":"(n)","boundary":[0.44193522397080853,0.5954672187184105,0.4674545034960309,0.6107397840494279],"dir":"ltr"},{"str":"is","boundary":[0.4723962694769028,0.5948563161051698,0.4855809011138689,0.6101288814361872],"dir":"ltr"},{"str":"called","boundary":[0.4905226670947408,0.5948563161051698,0.5410472824831748,0.6101288814361872],"dir":"ltr"},{"str":"the","boundary":[0.5459890484640467,0.5948563161051698,0.5734455002537708,0.6101288814361872],"dir":"ltr"},{"str":"generic","boundary":[0.5783912196474275,0.5948563161051698,0.6395900495545448,0.6101288814361872],"dir":"ltr"},{"str":"term","boundary":[0.6450852933252742,0.5948563161051698,0.6845996541083258,0.6101288814361872],"dir":"ltr"},{"str":"of","boundary":[0.6892073567088908,0.5948563161051698,0.7067802765368711,0.6101288814361872],"dir":"ltr"},{"str":"the","boundary":[0.7117220425177431,0.5948563161051698,0.7391784943074672,0.6101288814361872],"dir":"ltr"},{"str":"sequence.","boundary":[0.7441202602883391,0.5948563161051698,0.8274186676619155,0.6101288814361872],"dir":"ltr"},{"str":"There","boundary":[0.2746860961141807,0.6131833945023905,0.32552698452539053,0.6284559598334079],"dir":"ltr"},{"str":"are","boundary":[0.33046875050626245,0.6131833945023905,0.3579252022959866,0.6284559598334079],"dir":"ltr"},{"str":"two","boundary":[0.36286696827685844,0.6131833945023905,0.3947117082575968,0.6284559598334079],"dir":"ltr"},{"str":"principal","boundary":[0.3996534742384687,0.6131833945023905,0.4754601643850433,0.6284559598334079],"dir":"ltr"},{"str":"ways","boundary":[0.4804019303659152,0.6131833945023905,0.5221302023083974,0.6284559598334079],"dir":"ltr"},{"str":"to","boundary":[0.5270719682892692,0.6131833945023905,0.5446448881172495,0.6284559598334079],"dir":"ltr"},{"str":"define","boundary":[0.5495866540981215,0.6131833945023905,0.6023251806459862,0.6284559598334079],"dir":"ltr"},{"str":"a","boundary":[0.607266946626858,0.6131833945023905,0.6171504785886017,0.6284559598334079],"dir":"ltr"},{"str":"sequence:","boundary":[0.6220922445694735,0.6131833945023905,0.706122033308219,0.6284559598334079],"dir":"ltr"},{"str":"by","boundary":[0.27468212901091943,0.6407596199884791,0.29555614851412226,0.6560321853194964],"dir":"ltr"},{"str":"an","boundary":[0.30328507050820586,0.6407596199884791,0.3241590900114087,0.6560321853194964],"dir":"ltr"},{"str":"explicit","boundary":[0.3318880120054923,0.6407596199884791,0.3944903034511772,0.6560321853194964],"dir":"ltr"},{"str":"formula","boundary":[0.4022192254452608,0.6407596199884791,0.47031676066167527,0.6560321853194964],"dir":"ltr"},{"str":"expressing","boundary":[0.4780456826557589,0.6407596199884791,0.5681241929550915,0.6560321853194964],"dir":"ltr"},{"str":"its","boundary":[0.5758531149491751,0.6407596199884791,0.5956201788726626,0.6560321853194964],"dir":"ltr"},{"str":"generic","boundary":[0.6033491008667463,0.6407596199884791,0.6659513923124313,0.6560321853194964],"dir":"ltr"},{"str":"term","boundary":[0.6736803143065148,0.6407596199884791,0.7143016306692815,0.6560321853194964],"dir":"ltr"},{"str":"as","boundary":[0.7220305526633651,0.6407596199884791,0.7396034724913455,0.6560321853194964],"dir":"ltr"},{"str":"a","boundary":[0.7473323944854292,0.6407596199884791,0.757215926447173,0.6560321853194964],"dir":"ltr"},{"str":"function","boundary":[0.7649448484412565,0.6407596199884791,0.8363434833328934,0.6560321853194964],"dir":"ltr"},{"str":"of","boundary":[0.8440724053269769,0.6407596199884791,0.8616453251549574,0.6560321853194964],"dir":"ltr"},{"str":"n","boundary":[0.8693584334979022,0.6413705226017198,0.880131483336203,0.6566430879327371],"dir":"ltr"},{"str":",","boundary":[0.8801295066298105,0.6407596199884791,0.8850712726106824,0.6560321853194964],"dir":"ltr"},{"str":"e.g.,","boundary":[0.8934920418420881,0.6407596199884791,0.9269972151923995,0.6560321853194964],"dir":"ltr"},{"str":"x","boundary":[0.27468015230452697,0.6596991282554736,0.28456368426627077,0.674971693586491],"dir":"ltr"},{"str":"(n)","boundary":[0.28574970810168,0.6596991282554736,0.31126898762690236,0.674971693586491],"dir":"ltr"},{"str":"=","boundary":[0.3156612292307013,0.6623718271884017,0.3310795390910215,0.6776443925194191],"dir":"ltr"},{"str":"2n","boundary":[0.3354717806948204,0.6590882256422329,0.3562667319423293,0.674971693586491],"dir":"ltr"},{"str":"for","boundary":[0.36120849792320114,0.6590882256422329,0.3864708056174182,0.6743607909732503],"dir":"ltr"},{"str":"n","boundary":[0.39141257159829,0.6596991282554736,0.40218562143659076,0.674971693586491],"dir":"ltr"},{"str":"≥","boundary":[0.4065778630403897,0.6623718271884017,0.4214822292386992,0.6776443925194191],"dir":"ltr"},{"str":"0","boundary":[0.42587644754889054,0.6590882256422329,0.4357599795106343,0.6743607909732503],"dir":"ltr"},{"str":"by","boundary":[0.27468212901091943,0.6804686577667038,0.29555614851412226,0.6957412230977211],"dir":"ltr"},{"str":"an","boundary":[0.3022176490563375,0.6804686577667038,0.32309166855954036,0.6957412230977211],"dir":"ltr"},{"str":"equation","boundary":[0.32975316910175567,0.6804686577667038,0.4055598592483302,0.6957412230977211],"dir":"ltr"},{"str":"relating","boundary":[0.41222135979054547,0.6804686577667038,0.4781247509114528,0.6957412230977211],"dir":"ltr"},{"str":"its","boundary":[0.4847862514536681,0.6804686577667038,0.5045533153771556,0.6957412230977211],"dir":"ltr"},{"str":"generic","boundary":[0.5112148159193709,0.6804686577667038,0.5738171073650559,0.6957412230977211],"dir":"ltr"},{"str":"term","boundary":[0.5804786079072711,0.6804686577667038,0.6210999242700379,0.6957412230977211],"dir":"ltr"},{"str":"to","boundary":[0.6277614248122533,0.6804686577667038,0.6453343446402336,0.6957412230977211],"dir":"ltr"},{"str":"one","boundary":[0.6519958451824489,0.6804686577667038,0.6838603522271107,0.6957412230977211],"dir":"ltr"},{"str":"or","boundary":[0.690521852769326,0.6804686577667038,0.7092017281770217,0.6957412230977211],"dir":"ltr"},{"str":"more","boundary":[0.715863228719237,0.6804686577667038,0.7608926003369415,0.6957412230977211],"dir":"ltr"},{"str":"other","boundary":[0.7675541008791568,0.6804686577667038,0.8136904280765767,0.6957412230977211],"dir":"ltr"},{"str":"terms","boundary":[0.8203519286187918,0.6804686577667038,0.8686626328477953,0.6957412230977211],"dir":"ltr"},{"str":"of","boundary":[0.8753241333900107,0.6804686577667038,0.8928970532179911,0.6957412230977211],"dir":"ltr"},{"str":"the","boundary":[0.8995585537602062,0.6804686577667038,0.9270150055499303,0.6957412230977211],"dir":"ltr"},{"str":"sequence,","boundary":[0.27468212901091943,0.6987957361639245,0.3579805363844958,0.7140683014949419],"dir":"ltr"},{"str":"combined","boundary":[0.3658675948899673,0.6987957361639245,0.4504508614185703,0.7140683014949419],"dir":"ltr"},{"str":"with","boundary":[0.45774490800633727,0.6987957361639245,0.4950848917578051,0.7140683014949419],"dir":"ltr"},{"str":"one","boundary":[0.502378938345572,0.6987957361639245,0.5342434453902338,0.7140683014949419],"dir":"ltr"},{"str":"or","boundary":[0.5415374919780008,0.6987957361639245,0.5602173673856964,0.7140683014949419],"dir":"ltr"},{"str":"more","boundary":[0.5675114139734634,0.6987957361639245,0.6125407855911679,0.7140683014949419],"dir":"ltr"},{"str":"explicit","boundary":[0.6198348321789348,0.6987957361639245,0.6824371236246196,0.7140683014949419],"dir":"ltr"},{"str":"values","boundary":[0.6897311702123866,0.6987957361639245,0.743556885276043,0.7140683014949419],"dir":"ltr"},{"str":"for","boundary":[0.7508509318638099,0.6987957361639245,0.7761132395580269,0.7140683014949419],"dir":"ltr"},{"str":"the","boundary":[0.7834072861457937,0.6987957361639245,0.8108637379355178,0.7140683014949419],"dir":"ltr"},{"str":"first","boundary":[0.8181577845232848,0.6987957361639245,0.8511094800837384,0.7140683014949419],"dir":"ltr"},{"str":"term(s),","boundary":[0.8584035266715054,0.6987957361639245,0.927034772613854,0.7140683014949419],"dir":"ltr"},{"str":"e.","boundary":[0.27468212901091943,0.7171228145611453,0.288044664223197,0.7323953798921626],"dir":"ltr"},{"str":"g","boundary":[0.28877604558836606,0.7171228145611453,0.29792819618494076,0.7323953798921626],"dir":"ltr"},{"str":".","boundary":[0.298303770399487,0.7171228145611453,0.30251415501518986,0.7323953798921626],"dir":"ltr"},{"str":",","boundary":[0.3032455363803589,0.7171228145611453,0.3074559209960617,0.7323953798921626],"dir":"ltr"},{"str":"x","boundary":[0.4673536777795445,0.744396561729276,0.47723720974128825,0.7596691270602934],"dir":"ltr"},{"str":"(n)","boundary":[0.4784232335766975,0.744396561729276,0.5039425131019198,0.7596691270602934],"dir":"ltr"},{"str":"=","boundary":[0.5083367314121111,0.7470692606622041,0.5237550412724313,0.7623418259932215],"dir":"ltr"},{"str":"x(n","boundary":[0.528145306169838,0.744396561729276,0.5585470504841618,0.7596691270602934],"dir":"ltr"},{"str":"−","boundary":[0.5617552449589438,0.7470692606622041,0.577173554819264,0.7623418259932215],"dir":"ltr"},{"str":"1","boundary":[0.5815638197166707,0.7437856591160353,0.5914473516784143,0.7590582244470527],"dir":"ltr"},{"str":")","boundary":[0.5904985326100871,0.744396561729276,0.5978716474535479,0.7596691270602934],"dir":"ltr"},{"str":"+","boundary":[0.6022638890573468,0.7470692606622041,0.6176821989176671,0.7623418259932215],"dir":"ltr"},{"str":"n","boundary":[0.622074440521466,0.744396561729276,0.6328474903597667,0.7596691270602934],"dir":"ltr"},{"str":"for","boundary":[0.6526145542832542,0.7437856591160353,0.6778768619774712,0.7590582244470527],"dir":"ltr"},{"str":"n>0","boundary":[0.6828186279583431,0.7437856591160353,0.7276780028263056,0.7596691270602934],"dir":"ltr"},{"str":",","boundary":[0.7277768381459231,0.744396561729276,0.7343197363045975,0.7596691270602934],"dir":"ltr"},{"str":"(B.1)","boundary":[0.8832428191977599,0.7437856591160353,0.9269873316604379,0.7590582244470527],"dir":"ltr"},{"str":"x(0","boundary":[0.46813843021730706,0.7666181442859062,0.49646463281966463,0.7825016122301643],"dir":"ltr"},{"str":")","boundary":[0.49656346813928204,0.767229046899147,0.5039365829827429,0.7825016122301643],"dir":"ltr"},{"str":"=","boundary":[0.5083288245865418,0.769901745832075,0.523747134446862,0.7851743111630924],"dir":"ltr"},{"str":"0","boundary":[0.5281373993442686,0.7666181442859062,0.5380209313060124,0.7818907096169236],"dir":"ltr"},{"str":".","boundary":[0.5381197666256299,0.767229046899147,0.5435557092045888,0.7825016122301643],"dir":"ltr"},{"str":"(B.2)","boundary":[0.8832408424913676,0.7666181442859062,0.9269853549540454,0.7818907096169236],"dir":"ltr"},{"str":"It","boundary":[0.27467422218535015,0.7925326331395766,0.28894604233810817,0.8078051984705937],"dir":"ltr"},{"str":"is","boundary":[0.2944215190449142,0.7925326331395766,0.30760615068188035,0.8078051984705937],"dir":"ltr"},{"str":"the","boundary":[0.3130816273886864,0.7925326331395766,0.3405380791784105,0.8078051984705937],"dir":"ltr"},{"str":"latter","boundary":[0.3460135558852166,0.7925326331395766,0.39213011601871295,0.8078051984705937],"dir":"ltr"},{"str":"method","boundary":[0.397605592725519,0.7925326331395766,0.4635089838464263,0.8078051984705937],"dir":"ltr"},{"str":"that","boundary":[0.4689844605532324,0.7925326331395766,0.5030233446294778,0.8078051984705937],"dir":"ltr"},{"str":"is","boundary":[0.5084988213362839,0.7925326331395766,0.52168345297325,0.8078051984705937],"dir":"ltr"},{"str":"particularly","boundary":[0.527158929680056,0.7925326331395766,0.626014016361417,0.8078051984705937],"dir":"ltr"},{"str":"important","boundary":[0.6314894930682231,0.7925326331395766,0.7171599481126179,0.8078051984705937],"dir":"ltr"},{"str":"for","boundary":[0.722635424819424,0.7925326331395766,0.747897732513641,0.8078051984705937],"dir":"ltr"},{"str":"analysis","boundary":[0.7533732092204471,0.7925326331395766,0.8203835559210697,0.8078051984705937],"dir":"ltr"},{"str":"of","boundary":[0.8258590326278757,0.7925326331395766,0.8434319524558561,0.8078051984705937],"dir":"ltr"},{"str":"recursive","boundary":[0.8489074291626623,0.7925326331395766,0.9268884963408205,0.8078051984705937],"dir":"ltr"},{"str":"algorithms","boundary":[0.23909350712307265,0.8108597115367975,0.330259205938197,0.8261322768678147],"dir":"ltr"},{"str":"(see","boundary":[0.3352009719190689,0.8108597115367975,0.37034681157502963,0.8261322768678147],"dir":"ltr"},{"str":"Section","boundary":[0.37528857755590156,0.8108597115367975,0.43899782458130177,0.8261322768678147],"dir":"ltr"},{"str":"2.4","boundary":[0.44393959056217364,0.8108597115367975,0.468648420466533,0.8261322768678147],"dir":"ltr"},{"str":"for","boundary":[0.4735901864474049,0.8108597115367975,0.49885249414162197,0.8261322768678147],"dir":"ltr"},{"str":"a","boundary":[0.5037942601224938,0.8108597115367975,0.5136777920842376,0.8261322768678147],"dir":"ltr"},{"str":"detailed","boundary":[0.5186195580651095,0.8108597115367975,0.5878240488612392,0.8261322768678147],"dir":"ltr"},{"str":"discussion","boundary":[0.592765814842111,0.8108597115367975,0.6795629925301446,0.8261322768678147],"dir":"ltr"},{"str":"of","boundary":[0.6845047585110167,0.8108597115367975,0.702077678338997,0.8261322768678147],"dir":"ltr"},{"str":"this","boundary":[0.7070194443198689,0.8108597115367975,0.7377769957848155,0.8261322768678147],"dir":"ltr"},{"str":"topic).","boundary":[0.7427187617656873,0.8108597115367975,0.7981851431349931,0.8261322768678147],"dir":"ltr"},{"str":"An","boundary":[0.27467422218535015,0.8291867899340182,0.3022295092946918,0.8444593552650355],"dir":"ltr"},{"str":"equation","boundary":[0.3071910423394871,0.8291867899340182,0.38299773248606167,0.8444593552650355],"dir":"ltr"},{"str":"such","boundary":[0.3879592655308571,0.8291867899340182,0.4264062048620403,0.8444593552650355],"dir":"ltr"},{"str":"as","boundary":[0.43136773790683564,0.8291867899340182,0.44894065773481606,0.8444593552650355],"dir":"ltr"},{"str":"(B.1)","boundary":[0.45390219077961136,0.8291867899340182,0.4969153218771201,0.8444593552650355],"dir":"ltr"},{"str":"is","boundary":[0.5018768549219156,0.8291867899340182,0.5150614865588817,0.8444593552650355],"dir":"ltr"},{"str":"called","boundary":[0.5200230196036771,0.8291867899340182,0.5705476349921111,0.8444593552650355],"dir":"ltr"},{"str":"a","boundary":[0.5755091680369064,0.8291867899340182,0.5853926999986502,0.8444593552650355],"dir":"ltr"},{"str":"recurrence","boundary":[0.5903285358603451,0.8291867899340182,0.6792605564521154,0.8444593552650355],"dir":"ltr"},{"str":"equation","boundary":[0.6847755672867682,0.8291867899340182,0.7616694459491348,0.8444593552650355],"dir":"ltr"},{"str":"or","boundary":[0.7671824800773954,0.8291867899340182,0.7858623554850911,0.8444593552650355],"dir":"ltr"},{"str":"recurrence","boundary":[0.7908199351171018,0.8291867899340182,0.8797519557088721,0.8444593552650355],"dir":"ltr"},{"str":"rela-","boundary":[0.885266966543525,0.8291867899340182,0.9269952384860072,0.8444593552650355],"dir":"ltr"},{"str":"tion","boundary":[0.23909350712307265,0.8475138683312389,0.27423934677903344,0.8627864336622562],"dir":"ltr"},{"str":"(or","boundary":[0.2781472953167069,0.8475138683312389,0.30451655859063925,0.8627864336622562],"dir":"ltr"},{"str":"simply","boundary":[0.30803509596902,0.8475138683312389,0.3640549551281836,0.8627864336622562],"dir":"ltr"},{"str":"a","boundary":[0.36757349250656435,0.8475138683312389,0.37745702446830814,0.8627864336622562],"dir":"ltr"},{"str":"recurrence","boundary":[0.38096567831472716,0.8475138683312389,0.4698976989064974,0.8627864336622562],"dir":"ltr"},{"str":"),","boundary":[0.47063105697805885,0.8475138683312389,0.4832622108251673,0.8627864336622562],"dir":"ltr"},{"str":"and","boundary":[0.4870574870984769,0.8475138683312389,0.5189219941431388,0.8627864336622562],"dir":"ltr"},{"str":"an","boundary":[0.5224405315215196,0.8475138683312389,0.5433145510247224,0.8627864336622562],"dir":"ltr"},{"str":"equation","boundary":[0.5468330884031031,0.8475138683312389,0.6226397785496777,0.8627864336622562],"dir":"ltr"},{"str":"such","boundary":[0.6261583159280585,0.8475138683312389,0.6646052552592416,0.8627864336622562],"dir":"ltr"},{"str":"as","boundary":[0.6681237926376224,0.8475138683312389,0.6856967124656029,0.8627864336622562],"dir":"ltr"},{"str":"(B.2)","boundary":[0.6892152498439837,0.8475138683312389,0.7322283809414926,0.8627864336622562],"dir":"ltr"},{"str":"is","boundary":[0.7357469183198734,0.8475138683312389,0.7489315499568395,0.8627864336622562],"dir":"ltr"},{"str":"called","boundary":[0.7524500873352203,0.8475138683312389,0.8029747027236545,0.8627864336622562],"dir":"ltr"},{"str":"its","boundary":[0.8064932401020352,0.8475138683312389,0.8262603040255226,0.8627864336622562],"dir":"ltr"},{"str":"initial","boundary":[0.829749190808018,0.8475138683312389,0.8846423273235428,0.8627864336622562],"dir":"ltr"},{"str":"con-","boundary":[0.8885562059803934,0.8475138683312389,0.9270031453115766,0.8627864336622562],"dir":"ltr"},{"str":"dition","boundary":[0.23909350712307265,0.8658409467284596,0.2918122666070138,0.8811135120594769],"dir":"ltr"},{"str":".","boundary":[0.2916738971595494,0.8658409467284596,0.29661566314042126,0.8811135120594769],"dir":"ltr"},{"str":"An","boundary":[0.2997981604321028,0.8658409467284596,0.32735344754144435,0.8811135120594769],"dir":"ltr"},{"str":"initial","boundary":[0.33053594483312587,0.8658409467284596,0.3799733717057681,0.8811135120594769],"dir":"ltr"},{"str":"condition","boundary":[0.3831558689974496,0.8658409467284596,0.4644578029147537,0.8811135120594769],"dir":"ltr"},{"str":"can","boundary":[0.4676403002064352,0.8658409467284596,0.49729089609166643,0.8811135120594769],"dir":"ltr"},{"str":"be","boundary":[0.500473393383348,0.8658409467284596,0.5213474128865507,0.8811135120594769],"dir":"ltr"},{"str":"given","boundary":[0.5245299101782321,0.8658409467284596,0.570666237375652,0.8811135120594769],"dir":"ltr"},{"str":"for","boundary":[0.5738487346673335,0.8658409467284596,0.5991110423615505,0.8811135120594769],"dir":"ltr"},{"str":"a","boundary":[0.6022935396532321,0.8658409467284596,0.6121770716149757,0.8811135120594769],"dir":"ltr"},{"str":"value","boundary":[0.6153595689066573,0.8658409467284596,0.6614958961040772,0.8811135120594769],"dir":"ltr"},{"str":"of","boundary":[0.6646783933957586,0.8658409467284596,0.682251313223739,0.8811135120594769],"dir":"ltr"},{"str":"n","boundary":[0.685504971945545,0.8664518493417003,0.6962780217838458,0.8817244146727176],"dir":"ltr"},{"str":"other","boundary":[0.699464472488312,0.8658409467284596,0.7456007996857318,0.8811135120594769],"dir":"ltr"},{"str":"than","boundary":[0.7487832969774133,0.8658409467284596,0.7872302363085965,0.8811135120594769],"dir":"ltr"},{"str":"0","boundary":[0.790412733600278,0.8658409467284596,0.8002962655620217,0.8811135120594769],"dir":"ltr"},{"str":"(e.g.,","boundary":[0.8034787628537032,0.8658409467284596,0.8446733240702512,0.8811135120594769],"dir":"ltr"},{"str":"for","boundary":[0.8482116285125555,0.8658409467284596,0.8734739362067725,0.8811135120594769],"dir":"ltr"},{"str":"n","boundary":[0.8766841073879469,0.8664518493417003,0.8874571572262476,0.8817244146727176],"dir":"ltr"},{"str":"=","boundary":[0.8913631290575287,0.8691245482746283,0.9067814389178489,0.8843971136056454],"dir":"ltr"},{"str":"1","boundary":[0.9106893874555224,0.8658409467284596,0.9205729194172662,0.8811135120594769],"dir":"ltr"},{"str":")","boundary":[0.9196241003489388,0.8664518493417003,0.9269972151923997,0.8817244146727176],"dir":"ltr"},{"str":"and","boundary":[0.23909350712307276,0.8841680251256805,0.27095801416773463,0.8994405904566978],"dir":"ltr"},{"str":"for","boundary":[0.27831136194727196,0.8841680251256805,0.303573669641489,0.8994405904566978],"dir":"ltr"},{"str":"some","boundary":[0.3109270174210263,0.8841680251256805,0.35595638903873084,0.8994405904566978],"dir":"ltr"},{"str":"recurrences","boundary":[0.3633097368182682,0.8841680251256805,0.4632520120154211,0.8994405904566978],"dir":"ltr"},{"str":"(e.g.,","boundary":[0.4706053597949584,0.8841680251256805,0.5117999210115063,0.8994405904566978],"dir":"ltr"},{"str":"for","boundary":[0.5197462807087483,0.8841680251256805,0.5450085884029653,0.8994405904566978],"dir":"ltr"},{"str":"the","boundary":[0.5523619361825027,0.8841680251256805,0.5798183879722268,0.8994405904566978],"dir":"ltr"},{"str":"recurrence","boundary":[0.5871717357517642,0.8841680251256805,0.6794246230826804,0.8994405904566978],"dir":"ltr"},{"str":"F","boundary":[0.6867463435599402,0.8847789277389212,0.6992391279595842,0.9000514930699385],"dir":"ltr"},{"str":"(n)","boundary":[0.7020065169088725,0.8847789277389212,0.727525796434095,0.9000514930699385],"dir":"ltr"},{"str":"=","boundary":[0.7321868701072533,0.8874516266718492,0.7476051799675735,0.9027241920028664],"dir":"ltr"},{"str":"F(n","boundary":[0.7522662536407319,0.8847789277389212,0.788439980620714,0.9000514930699385],"dir":"ltr"},{"str":"−","boundary":[0.790333665344584,0.8874516266718492,0.8057519752049044,0.9027241920028664],"dir":"ltr"},{"str":"1","boundary":[0.8104130488780626,0.8841680251256805,0.8202965808398064,0.8994405904566978],"dir":"ltr"},{"str":")","boundary":[0.819347761771479,0.8847789277389212,0.8267208766149399,0.9000514930699385],"dir":"ltr"},{"str":"+","boundary":[0.8313819502880982,0.8874516266718492,0.8468002601484185,0.9027241920028664],"dir":"ltr"},{"str":"F(n","boundary":[0.8514613338215768,0.8847789277389212,0.887635060801559,0.9000514930699385],"dir":"ltr"},{"str":"−","boundary":[0.889528745525429,0.8874516266718492,0.9049470553857493,0.9027241920028664],"dir":"ltr"},{"str":"2","boundary":[0.9096081290589076,0.8841680251256805,0.9194916610206514,0.8994405904566978],"dir":"ltr"},{"str":")","boundary":[0.9196300304681158,0.8847789277389212,0.9270031453115767,0.9000514930699385],"dir":"ltr"},{"str":"479","boundary":[0.8940237758616302,0.9329333262276187,0.9269952384860073,0.9482058915586359],"dir":"ltr"}],"boundary":[0.23909,0.37037,0.92704,0.94821],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":519,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/52c2626c76b231ac70a3ec460729bfbf.jpg","blurred":"/storage/books/4a8b03583f119702/pages/b066afe5fcbd59ecef5d8de33253ed46.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.16303,0.07296,0.0518]},"elements":[{"words":[{"str":"References","boundary":[0.14421784044919886,0.16302940802619442,0.4093185533779842,0.19968365680003092],"dir":"ltr"}],"boundary":[0.14422,0.16303,0.40932,0.19968],"dir":"ltr","type":"paragraph"},{"words":[{"str":"[Ade62]","boundary":[0.23910077902799318,0.3251905799265899,0.3094715265956087,0.34046314525760724],"dir":"ltr"}],"boundary":[0.2391,0.32519,0.30947,0.34046],"dir":"ltr","type":"paragraph"},{"words":[{"str":"[Adl94]","boundary":[0.23910275573438539,0.38600288056163473,0.3050852151109867,0.401275445892652],"dir":"ltr"},{"str":"[Agr04]","boundary":[0.23910275573438539,0.42848810279945865,0.3061724036267785,0.443760668130476],"dir":"ltr"},{"str":"[Aho74]","boundary":[0.23910275573438539,0.4709733250372827,0.3105804588817162,0.4862458903683],"dir":"ltr"},{"str":"[Aho83]","boundary":[0.23910275573438544,0.5134585472751066,0.31058045888171626,0.528731112606124],"dir":"ltr"},{"str":"[Ahu93]","boundary":[0.23910077902799318,0.5559437695129307,0.310578482175324,0.571216334843948],"dir":"ltr"},{"str":"[App]","boundary":[0.23909880232160088,0.5984289917507547,0.2908094415454442,0.613701557081772],"dir":"ltr"},{"str":"[App07]","boundary":[0.23909880232160094,0.6409142139885786,0.3105765054689318,0.656186779319596],"dir":"ltr"}],"boundary":[0.2391,0.386,0.31058,0.65619],"dir":"ltr","type":"paragraph"},{"words":[{"str":"[Arb93]","boundary":[0.23909880232160088,0.7017265146236233,0.3072754057937093,0.7169990799546407],"dir":"ltr"},{"str":"[Aro09]","boundary":[0.23909880232160088,0.7442117368614473,0.3072754057937093,0.7594843021924647],"dir":"ltr"},{"str":"[Ata09]","boundary":[0.23909880232160083,0.7866969590992713,0.3050614946342787,0.8019695244302886],"dir":"ltr"}],"boundary":[0.2391,0.70173,0.30728,0.80197],"dir":"ltr","type":"paragraph"},{"words":[{"str":"[Avi07]","boundary":[0.23909880232160077,0.8475092597343162,0.3025115433881487,0.8627818250653334],"dir":"ltr"}],"boundary":[0.2391,0.84751,0.30251,0.86278],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Adelson-Velsky,","boundary":[0.34584292421482576,0.3251905799265899,0.4856949014735,0.34046314525760724],"dir":"ltr"},{"str":"G.M.","boundary":[0.4922773337600212,0.3251905799265899,0.5358241755834642,0.34046314525760724],"dir":"ltr"},{"str":"and","boundary":[0.5420705677832863,0.3251905799265899,0.5739350748279481,0.34046314525760724],"dir":"ltr"},{"str":"Landis,","boundary":[0.5801814670277702,0.3251905799265899,0.6422698148114444,0.34046314525760724],"dir":"ltr"},{"str":"E.M.","boundary":[0.6488522470979659,0.3251905799265899,0.6916677075562397,0.34046314525760724],"dir":"ltr"},{"str":"An","boundary":[0.6979140997560617,0.3251905799265899,0.7254693868654033,0.34046314525760724],"dir":"ltr"},{"str":"algorithm","boundary":[0.7317157790652253,0.3251905799265899,0.815192090014113,0.34046314525760724],"dir":"ltr"},{"str":"for","boundary":[0.8214384822139351,0.3251905799265899,0.8467007899081521,0.34046314525760724],"dir":"ltr"},{"str":"organi-","boundary":[0.852947182107974,0.3251905799265899,0.9144622850378672,0.34046314525760724],"dir":"ltr"},{"str":"zation","boundary":[0.3458429242148257,0.3435176583238107,0.3985616836987669,0.35879022365482804],"dir":"ltr"},{"str":"of","boundary":[0.405460389008064,0.3435176583238107,0.42303330883604445,0.35879022365482804],"dir":"ltr"},{"str":"information.","boundary":[0.4299320141453416,0.3435176583238107,0.5370299664827969,0.35879022365482804],"dir":"ltr"},{"str":"Soviet","boundary":[0.5439108814345628,0.3435176583238107,0.5951866452520894,0.35879022365482804],"dir":"ltr"},{"str":"Mathematics","boundary":[0.6020853505613866,0.3435176583238107,0.7096972465608525,0.35879022365482804],"dir":"ltr"},{"str":"Doklady","boundary":[0.7165959518701497,0.3435176583238107,0.7912956864370091,0.35879022365482804],"dir":"ltr"},{"str":",","boundary":[0.79108615555942,0.3435176583238107,0.7960279215402919,0.35879022365482804],"dir":"ltr"},{"str":"vol.","boundary":[0.8034010363837527,0.3435176583238107,0.8347120656385569,0.35879022365482804],"dir":"ltr"},{"str":"3,","boundary":[0.8416107709478541,0.3435176583238107,0.8564360688904696,0.35879022365482804],"dir":"ltr"},{"str":"1962,","boundary":[0.8638091837339306,0.3435176583238107,0.9082850775617773,0.35879022365482804],"dir":"ltr"},{"str":"1259–1263.","boundary":[0.34584490092121795,0.3618447367210315,0.4397384545577836,0.37711730205204885],"dir":"ltr"},{"str":"Adleman,","boundary":[0.345844900921218,0.38600288056163473,0.4310607134953726,0.401275445892652],"dir":"ltr"},{"str":"L.M.","boundary":[0.43497459215222317,0.38600288056163473,0.47670286409470525,0.401275445892652],"dir":"ltr"},{"str":"Molecular","boundary":[0.4803597709205505,0.38600288056163473,0.5682243700604523,0.401275445892652],"dir":"ltr"},{"str":"computation","boundary":[0.5718812768862976,0.38600288056163473,0.6806198955294025,0.401275445892652],"dir":"ltr"},{"str":"of","boundary":[0.6842768023552476,0.38600288056163473,0.701849722183228,0.401275445892652],"dir":"ltr"},{"str":"solutions","boundary":[0.7055066290090731,0.38600288056163473,0.782420274735363,0.401275445892652],"dir":"ltr"},{"str":"to","boundary":[0.7860771815612081,0.38600288056163473,0.8036501013891886,0.401275445892652],"dir":"ltr"},{"str":"combinatorial","boundary":[0.8073070082150338,0.38600288056163473,0.9270361143995975,0.401275445892652],"dir":"ltr"},{"str":"problems.","boundary":[0.34584490092121795,0.4043299589588555,0.4298944567238869,0.4196025242898728],"dir":"ltr"},{"str":"Science,","boundary":[0.43978194209841526,0.4043299589588555,0.5068120558629614,0.4196025242898728],"dir":"ltr"},{"str":"vol.","boundary":[0.5117518451374409,0.4043299589588555,0.5430628743922452,0.4196025242898728],"dir":"ltr"},{"str":"266,","boundary":[0.5480046403731169,0.4043299589588555,0.5825970022392201,0.4196025242898728],"dir":"ltr"},{"str":"1994,","boundary":[0.587538768220092,0.4043299589588555,0.6320146620479389,0.4196025242898728],"dir":"ltr"},{"str":"1021–1024.","boundary":[0.6369564280288108,0.4043299589588555,0.7308499816653764,0.4196025242898728],"dir":"ltr"},{"str":"Agrawal,","boundary":[0.345844900921218,0.42848810279945865,0.4244585141449278,0.443760668130476],"dir":"ltr"},{"str":"M.,","boundary":[0.43027003093843313,0.42848810279945865,0.45881367124394906,0.443760668130476],"dir":"ltr"},{"str":"Kayal,","boundary":[0.46462518803745445,0.42848810279945865,0.5200915694067604,0.443760668130476],"dir":"ltr"},{"str":"N.,","boundary":[0.5259030862002657,0.42848810279945865,0.5497026311641446,0.443760668130476],"dir":"ltr"},{"str":"and","boundary":[0.55551414795765,0.42848810279945865,0.5873786550023118,0.443760668130476],"dir":"ltr"},{"str":"Saxena,","boundary":[0.5930122682205058,0.42848810279945865,0.6594691371312708,0.443760668130476],"dir":"ltr"},{"str":"N.","boundary":[0.6652806539247761,0.42848810279945865,0.6841384329077832,0.443760668130476],"dir":"ltr"},{"str":"PRIMES","boundary":[0.6897720461259771,0.42848810279945865,0.768840301819927,0.443760668130476],"dir":"ltr"},{"str":"is","boundary":[0.774473915038121,0.42848810279945865,0.7876585466750872,0.443760668130476],"dir":"ltr"},{"str":"in","boundary":[0.7932921598932812,0.42848810279945865,0.8097778912054697,0.443760668130476],"dir":"ltr"},{"str":"P.","boundary":[0.8154549919642953,0.42848810279945865,0.8310314383360035,0.443760668130476],"dir":"ltr"},{"str":"Annals","boundary":[0.8366650515541973,0.42848810279945865,0.8970929659682987,0.443760668130476],"dir":"ltr"},{"str":"of","boundary":[0.9027265791864926,0.42848810279945865,0.9202994990144729,0.443760668130476],"dir":"ltr"},{"str":"Mathematics","boundary":[0.3458449009212179,0.4468151811966795,0.4534567969206839,0.4620877465276968],"dir":"ltr"},{"str":",","boundary":[0.4535002844613155,0.4468151811966795,0.4584420504421874,0.4620877465276968],"dir":"ltr"},{"str":"vol.","boundary":[0.4633838164230593,0.4468151811966795,0.4946948456778635,0.4620877465276968],"dir":"ltr"},{"str":"160,","boundary":[0.4996366116587354,0.4468151811966795,0.5342289735248386,0.4620877465276968],"dir":"ltr"},{"str":"no.","boundary":[0.5391707395057104,0.4468151811966795,0.5653027980125609,0.4620877465276968],"dir":"ltr"},{"str":"2,","boundary":[0.5702445639934328,0.4468151811966795,0.5850698619360484,0.4620877465276968],"dir":"ltr"},{"str":"2004,","boundary":[0.5900116279169202,0.4468151811966795,0.6344875217447671,0.4620877465276968],"dir":"ltr"},{"str":"781–793.","boundary":[0.639429287725639,0.4468151811966795,0.7135557774387172,0.4620877465276968],"dir":"ltr"},{"str":"Aho,","boundary":[0.345844900921218,0.4709733250372827,0.388541758995951,0.4862458903683],"dir":"ltr"},{"str":"A.V.,","boundary":[0.3930091154426592,0.4709733250372827,0.4372280374395007,0.4862458903683],"dir":"ltr"},{"str":"Hopcroft,","boundary":[0.44169539388620893,0.4709733250372827,0.5257054155610308,0.4862458903683],"dir":"ltr"},{"str":"J.E.,","boundary":[0.530172772007739,0.4709733250372827,0.5662278966041803,0.4862458903683],"dir":"ltr"},{"str":"and","boundary":[0.5706952530508884,0.4709733250372827,0.6025597600955502,0.4862458903683],"dir":"ltr"},{"str":"Ullman,","boundary":[0.6069085141587176,0.4709733250372827,0.6766467156807816,0.4862458903683],"dir":"ltr"},{"str":"J.D.","boundary":[0.6811140721274895,0.4709733250372827,0.712958812108228,0.4862458903683],"dir":"ltr"},{"str":"The","boundary":[0.7173253565289263,0.4709733250372827,0.75027705208938,0.4862458903683],"dir":"ltr"},{"str":"Design","boundary":[0.7546258061525472,0.4709733250372827,0.8139269979230096,0.4862458903683],"dir":"ltr"},{"str":"and","boundary":[0.818275751986177,0.4709733250372827,0.8501402590308388,0.4862458903683],"dir":"ltr"},{"str":"Analysis","boundary":[0.8544890130940062,0.4709733250372827,0.9269946035653583,0.4862458903683],"dir":"ltr"},{"str":"of","boundary":[0.34584490092121795,0.4893004034345035,0.3634178207491984,0.5045729687655208],"dir":"ltr"},{"str":"Computer","boundary":[0.3683595867300702,0.4893004034345035,0.4540300417744651,0.5045729687655208],"dir":"ltr"},{"str":"Algorithms","boundary":[0.4589718077553369,0.4893004034345035,0.5545455618253989,0.5045729687655208],"dir":"ltr"},{"str":".","boundary":[0.5545870726596385,0.4893004034345035,0.5595288386405103,0.5045729687655208],"dir":"ltr"},{"str":"Addison-Wesley,","boundary":[0.569412370602254,0.4893004034345035,0.7139689090747182,0.5045729687655208],"dir":"ltr"},{"str":"1974.","boundary":[0.7189106750555901,0.4893004034345035,0.7633865688834369,0.5045729687655208],"dir":"ltr"},{"str":"Aho,","boundary":[0.34584490092121806,0.5134585472751066,0.38854175899595106,0.528731112606124],"dir":"ltr"},{"str":"A.V.,","boundary":[0.3958753397115649,0.5134585472751066,0.44009426170840643,0.528731112606124],"dir":"ltr"},{"str":"Hopcroft,","boundary":[0.44742784242402034,0.5134585472751066,0.5314378640988422,0.528731112606124],"dir":"ltr"},{"str":"J.E.,","boundary":[0.5387714448144562,0.5134585472751066,0.5748265694108973,0.528731112606124],"dir":"ltr"},{"str":"and","boundary":[0.5821601501265112,0.5134585472751066,0.614024657171173,0.528731112606124],"dir":"ltr"},{"str":"Ullman,","boundary":[0.6208838283526233,0.5134585472751066,0.6906220298746872,0.528731112606124],"dir":"ltr"},{"str":"J.D.","boundary":[0.697955610590301,0.5134585472751066,0.7298003505710394,0.528731112606124],"dir":"ltr"},{"str":"Data","boundary":[0.7366931257611594,0.5134585472751066,0.7784213977036416,0.528731112606124],"dir":"ltr"},{"str":"Structures","boundary":[0.7852805688850917,0.5134585472751066,0.8698638354136947,0.528731112606124],"dir":"ltr"},{"str":"and","boundary":[0.8767230065951449,0.5134585472751066,0.9085875136398067,0.528731112606124],"dir":"ltr"},{"str":"Algorithms","boundary":[0.34584292421482565,0.5317856256723275,0.4414166782848878,0.5470581910033449],"dir":"ltr"},{"str":".","boundary":[0.4414581891191271,0.5317856256723275,0.44639995509999897,0.5470581910033449],"dir":"ltr"},{"str":"Addison-Wesley,","boundary":[0.4562834870617427,0.5317856256723275,0.6008400255342069,0.5470581910033449],"dir":"ltr"},{"str":"1983.","boundary":[0.6057817915150788,0.5317856256723275,0.6502576853429256,0.5470581910033449],"dir":"ltr"},{"str":"Ahuja,","boundary":[0.34584292421482576,0.5559437695129307,0.4047092405789716,0.571216334843948],"dir":"ltr"},{"str":"R.K.,","boundary":[0.40953240417630254,0.5559437695129307,0.45511525358386473,0.571216334843948],"dir":"ltr"},{"str":"Magnanti,","boundary":[0.45993841718119566,0.5559437695129307,0.5472495385312399,0.571216334843948],"dir":"ltr"},{"str":"T.L.,","boundary":[0.5520727021285708,0.5559437695129307,0.5914486934641581,0.571216334843948],"dir":"ltr"},{"str":"and","boundary":[0.596271857061489,0.5559437695129307,0.6281363641061508,0.571216334843948],"dir":"ltr"},{"str":"Orlin,","boundary":[0.6329397606395584,0.5559437695129307,0.6840178538178502,0.571216334843948],"dir":"ltr"},{"str":"J.B.","boundary":[0.688841017415181,0.5559437695129307,0.7184916133004122,0.571216334843948],"dir":"ltr"},{"str":"Network","boundary":[0.7232950098338197,0.5559437695129307,0.7968877888209637,0.571216334843948],"dir":"ltr"},{"str":"Flows","boundary":[0.8016911853543711,0.5559437695129307,0.8518599935921825,0.571216334843948],"dir":"ltr"},{"str":":","boundary":[0.8518935976008523,0.5559437695129307,0.8568353635817242,0.571216334843948],"dir":"ltr"},{"str":"Theory,","boundary":[0.8616288765831699,0.5559437695129307,0.9269985569781432,0.571216334843948],"dir":"ltr"},{"str":"Algorithms,","boundary":[0.3458409475084334,0.5742708479101515,0.4452692790435756,0.5895434132411688],"dir":"ltr"},{"str":"and","boundary":[0.4502110450244474,0.5742708479101515,0.4820755520691093,0.5895434132411688],"dir":"ltr"},{"str":"Applications","boundary":[0.48701731804998116,0.5742708479101515,0.5946885152412177,0.5895434132411688],"dir":"ltr"},{"str":".","boundary":[0.5947320027818493,0.5742708479101515,0.5996737687627212,0.5895434132411688],"dir":"ltr"},{"str":"Prentice","boundary":[0.604615534743593,0.5742708479101515,0.6759944025713064,0.5895434132411688],"dir":"ltr"},{"str":"Hall,","boundary":[0.6809361685521783,0.5742708479101515,0.723217918284518,0.5895434132411688],"dir":"ltr"},{"str":"1993.","boundary":[0.7281596842653899,0.5742708479101515,0.7726355780932368,0.5895434132411688],"dir":"ltr"},{"str":"Applegate,","boundary":[0.34584094750843347,0.5984289917507547,0.4402089106791628,0.613701557081772],"dir":"ltr"},{"str":"D.L.,","boundary":[0.44853084459095105,0.5984289917507547,0.49154397568845987,0.613701557081772],"dir":"ltr"},{"str":"Bixby,","boundary":[0.4998659096002481,0.5984289917507547,0.5535137210885932,0.613701557081772],"dir":"ltr"},{"str":"R.E.,","boundary":[0.5618356550003815,0.5984289917507547,0.6063115488282284,0.613701557081772],"dir":"ltr"},{"str":"Chvatal,","boundary":[0.6146334827400166,0.5984289917507547,0.6865895488342958,0.613701557081772],"dir":"ltr"},{"str":"V.,","boundary":[0.694911482746084,0.5984289917507547,0.7176238391941713,0.613701557081772],"dir":"ltr"},{"str":"and","boundary":[0.7259457731059594,0.5984289917507547,0.7578102801506212,0.613701557081772],"dir":"ltr"},{"str":"Cook,","boundary":[0.765460133889011,0.5984289917507547,0.817645182647018,0.613701557081772],"dir":"ltr"},{"str":"W.J.","boundary":[0.8259671165588062,0.5984289917507547,0.860381574849598,0.613701557081772],"dir":"ltr"},{"str":"The","boundary":[0.8680492189455188,0.5984289917507547,0.9010009145059725,0.613701557081772],"dir":"ltr"},{"str":"Traveling","boundary":[0.3458409475084335,0.6167560701479754,0.42566035163147603,0.6320286354789927],"dir":"ltr"},{"str":"Salesman","boundary":[0.43060211761234796,0.6167560701479754,0.5107773288860132,0.6320286354789927],"dir":"ltr"},{"str":"Problems","boundary":[0.5157190948668852,0.6167560701479754,0.5970012617202658,0.6320286354789927],"dir":"ltr"},{"str":".","boundary":[0.5970447492608973,0.6167560701479754,0.6019865152417693,0.6320286354789927],"dir":"ltr"},{"str":"www.tsp.gatech.edu/index.html.","boundary":[0.6069282812226411,0.6167560701479754,0.8798521328142332,0.6320286354789927],"dir":"ltr"},{"str":"Applegate,","boundary":[0.3458409475084336,0.6409142139885786,0.4402089106791629,0.656186779319596],"dir":"ltr"},{"str":"D.L.,","boundary":[0.44853084459095116,0.6409142139885786,0.49154397568846,0.656186779319596],"dir":"ltr"},{"str":"Bixby,","boundary":[0.49986590960024824,0.6409142139885786,0.5535137210885933,0.656186779319596],"dir":"ltr"},{"str":"R.E.,","boundary":[0.5618356550003815,0.6409142139885786,0.6063115488282284,0.656186779319596],"dir":"ltr"},{"str":"Chvatal,","boundary":[0.6146334827400166,0.6409142139885786,0.6865895488342958,0.656186779319596],"dir":"ltr"},{"str":"V.,","boundary":[0.694911482746084,0.6409142139885786,0.7176238391941713,0.656186779319596],"dir":"ltr"},{"str":"and","boundary":[0.7259457731059594,0.6409142139885786,0.7578102801506212,0.656186779319596],"dir":"ltr"},{"str":"Cook,","boundary":[0.765460133889011,0.6409142139885786,0.817645182647018,0.656186779319596],"dir":"ltr"},{"str":"W.J.","boundary":[0.8259671165588062,0.6409142139885786,0.860381574849598,0.656186779319596],"dir":"ltr"},{"str":"The","boundary":[0.8680492189455188,0.6409142139885786,0.9010009145059725,0.656186779319596],"dir":"ltr"},{"str":"Traveling","boundary":[0.3458409475084335,0.6592412923857994,0.42566035163147603,0.6745138577168167],"dir":"ltr"},{"str":"Salesman","boundary":[0.43275672758000805,0.6592412923857994,0.5129319388536733,0.6745138577168167],"dir":"ltr"},{"str":"Problem:","boundary":[0.5200283148022053,0.6592412923857994,0.5985628597702213,0.6745138577168167],"dir":"ltr"},{"str":"A","boundary":[0.6056592357187532,0.6592412923857994,0.6210380114512265,0.6745138577168167],"dir":"ltr"},{"str":"Computational","boundary":[0.6281343873997586,0.6592412923857994,0.7555726485144827,0.6745138577168167],"dir":"ltr"},{"str":"Study","boundary":[0.7626690244630147,0.6592412923857994,0.811019262819865,0.6745138577168167],"dir":"ltr"},{"str":".","boundary":[0.8108196154742376,0.6592412923857994,0.8157613814551096,0.6745138577168167],"dir":"ltr"},{"str":"Princeton","boundary":[0.8228577574036415,0.6592412923857994,0.9063340683525294,0.6745138577168167],"dir":"ltr"},{"str":"University","boundary":[0.34584094750843347,0.6775683707830201,0.43589969074384255,0.6928409361140374],"dir":"ltr"},{"str":"Press,","boundary":[0.4408414567247144,0.6775683707830201,0.489725405807499,0.6928409361140374],"dir":"ltr"},{"str":"2007.","boundary":[0.4946671717883709,0.6775683707830201,0.5391430656162177,0.6928409361140374],"dir":"ltr"},{"str":"Arbel,","boundary":[0.3458409475084335,0.7017265146236233,0.4014061641973569,0.7169990799546407],"dir":"ltr"},{"str":"A.","boundary":[0.4058932877079885,0.7017265146236233,0.4273998532567429,0.7169990799546407],"dir":"ltr"},{"str":"Exploring","boundary":[0.43179407156693417,0.7017265146236233,0.5174842936752525,0.7169990799546407],"dir":"ltr"},{"str":"Interior-Point","boundary":[0.5218725818662667,0.7017265146236233,0.6376087411382861,0.7169990799546407],"dir":"ltr"},{"str":"Linear","boundary":[0.6419970293293003,0.7017265146236233,0.6991040770042557,0.7169990799546407],"dir":"ltr"},{"str":"Programming:","boundary":[0.7034923651952699,0.7017265146236233,0.8270562817809903,0.7169990799546407],"dir":"ltr"},{"str":"Algorithms","boundary":[0.8314445699720046,0.7017265146236233,0.9270183240420667,0.7169990799546407],"dir":"ltr"},{"str":"and","boundary":[0.34584094750843347,0.7200535930208442,0.37770545455309534,0.7353261583518614],"dir":"ltr"},{"str":"Software","boundary":[0.38264722053396716,0.7200535930208442,0.457327188036903,0.7353261583518614],"dir":"ltr"},{"str":"(Foundations","boundary":[0.4622689540177749,0.7200535930208442,0.5754551620436643,0.7353261583518614],"dir":"ltr"},{"str":"of","boundary":[0.5803969280245362,0.7200535930208442,0.5979698478525166,0.7353261583518614],"dir":"ltr"},{"str":"Computing)","boundary":[0.6029116138333884,0.7200535930208442,0.7061747557696871,0.7353261583518614],"dir":"ltr"},{"str":".","boundary":[0.7048938500274452,0.7200535930208442,0.7098356160083171,0.7353261583518614],"dir":"ltr"},{"str":"MIT","boundary":[0.7147773819891888,0.7200535930208442,0.7543115098361639,0.7353261583518614],"dir":"ltr"},{"str":"Press,","boundary":[0.7592532758170358,0.7200535930208442,0.8081372248998204,0.7353261583518614],"dir":"ltr"},{"str":"1993.","boundary":[0.8130789908806924,0.7200535930208442,0.8575548847085391,0.7353261583518614],"dir":"ltr"},{"str":"Arora,","boundary":[0.3458409475084335,0.7442117368614473,0.40360030829286403,0.7594843021924647],"dir":"ltr"},{"str":"S.","boundary":[0.41186294101288173,0.7442117368614473,0.4266091706998034,0.7594843021924647],"dir":"ltr"},{"str":"and","boundary":[0.4342194903103461,0.7442117368614473,0.46608399735500805,0.7594843021924647],"dir":"ltr"},{"str":"Barak,","boundary":[0.47369431696555064,0.7442117368614473,0.5313548424303637,0.7594843021924647],"dir":"ltr"},{"str":"B.","boundary":[0.5396174751503815,0.7442117368614473,0.5573682985536733,0.7594843021924647],"dir":"ltr"},{"str":"Computational","boundary":[0.5649924551089623,0.7442117368614473,0.6924307162236862,0.7594843021924647],"dir":"ltr"},{"str":"Complexity:","boundary":[0.7000410358342289,0.7442117368614473,0.8027309329167466,0.7594843021924647],"dir":"ltr"},{"str":"A","boundary":[0.8103412525272893,0.7442117368614473,0.8257200282597625,0.7594843021924647],"dir":"ltr"},{"str":"Modern","boundary":[0.8333303478703052,0.7442117368614473,0.9014278830867197,0.7594843021924647],"dir":"ltr"},{"str":"Approach.","boundary":[0.3458409475084334,0.7625388152586681,0.43623573083054173,0.7778113805896855],"dir":"ltr"},{"str":"Cambridge","boundary":[0.4393609036368451,0.7625388152586681,0.5349148906429837,0.7778113805896855],"dir":"ltr"},{"str":"University","boundary":[0.5398566566238556,0.7625388152586681,0.6299153998592647,0.7778113805896855],"dir":"ltr"},{"str":"Press,","boundary":[0.6348571658401366,0.7625388152586681,0.6837411149229211,0.7778113805896855],"dir":"ltr"},{"str":"2009.","boundary":[0.688682880903793,0.7625388152586681,0.7331587747316399,0.7778113805896855],"dir":"ltr"},{"str":"Atallah,","boundary":[0.34584094750843347,0.7866969590992713,0.4156779843501148,0.8019695244302886],"dir":"ltr"},{"str":"M.J.","boundary":[0.4243557254125258,0.7866969590992713,0.4598573722191094,0.8019695244302886],"dir":"ltr"},{"str":"and","boundary":[0.4677839648524279,0.7866969590992713,0.4996484718970898,0.8019695244302886],"dir":"ltr"},{"str":"Blanton,","boundary":[0.5075750645304082,0.7866969590992713,0.5817213213074098,0.8019695244302886],"dir":"ltr"},{"str":"M.,","boundary":[0.5903990623698209,0.7866969590992713,0.6189427026753368,0.8019695244302886],"dir":"ltr"},{"str":"eds.","boundary":[0.6276204437377477,0.7866969590992713,0.6600384285722672,0.8019695244302886],"dir":"ltr"},{"str":"Algorithms","boundary":[0.6679828115631169,0.7866969590992713,0.763556565633179,0.8019695244302886],"dir":"ltr"},{"str":"and","boundary":[0.7714831582664975,0.7866969590992713,0.8033476653111593,0.8019695244302886],"dir":"ltr"},{"str":"Theory","boundary":[0.8112742579444778,0.7866969590992713,0.872789360874371,0.8019695244302886],"dir":"ltr"},{"str":"of","boundary":[0.8807159535076895,0.7866969590992713,0.8982888733356699,0.8019695244302886],"dir":"ltr"},{"str":"Computation","boundary":[0.34584094750843336,0.8050240374964922,0.457900432890684,0.8202966028275095],"dir":"ltr"},{"str":"Handbook","boundary":[0.4638503191316538,0.8050240374964922,0.556142740590417,0.8202966028275095],"dir":"ltr"},{"str":",","boundary":[0.5566547075460352,0.8050240374964922,0.5615964735269071,0.8202966028275095],"dir":"ltr"},{"str":"2nd","boundary":[0.5677835645349587,0.8050240374964922,0.5996480715796205,0.8202966028275095],"dir":"ltr"},{"str":"ed.","boundary":[0.6055979578205903,0.8050240374964922,0.631413743304665,0.8202966028275095],"dir":"ltr"},{"str":"(two-volume","boundary":[0.6373636295456347,0.8050240374964922,0.7471894367045313,0.8202966028275095],"dir":"ltr"},{"str":"set),","boundary":[0.7531393229455011,0.8050240374964922,0.7899258289071114,0.8202966028275095],"dir":"ltr"},{"str":"Chapman","boundary":[0.796112919915163,0.8050240374964922,0.8795892308640506,0.8202966028275095],"dir":"ltr"},{"str":"and","boundary":[0.8855391171050204,0.8050240374964922,0.9174036241496822,0.8202966028275095],"dir":"ltr"},{"str":"Hall/CRC,","boundary":[0.34584094750843336,0.8233511158937129,0.4370461804514047,0.8386236812247302],"dir":"ltr"},{"str":"2009.","boundary":[0.4419879464322765,0.8233511158937129,0.4864638402601234,0.8386236812247302],"dir":"ltr"},{"str":"Avidan,","boundary":[0.34584094750843336,0.8475092597343162,0.4131280331039848,0.8627818250653334],"dir":"ltr"},{"str":"S.","boundary":[0.41973023245442964,0.8475092597343162,0.43447646214135127,0.8627818250653334],"dir":"ltr"},{"str":"and","boundary":[0.44074262140509685,0.8475092597343162,0.4726071284497587,0.8627818250653334],"dir":"ltr"},{"str":"Shamir,","boundary":[0.4788732877135043,0.8475092597343162,0.5449743494736465,0.8627818250653334],"dir":"ltr"},{"str":"A.","boundary":[0.5515765488240914,0.8475092597343162,0.5730831143728459,0.8627818250653334],"dir":"ltr"},{"str":"Seam","boundary":[0.5793492736365912,0.8475092597343162,0.6265727893498029,0.8627818250653334],"dir":"ltr"},{"str":"carving","boundary":[0.6328389486135485,0.8475092597343162,0.6954412400592334,0.8627818250653334],"dir":"ltr"},{"str":"for","boundary":[0.7017073993229789,0.8475092597343162,0.7269697070171959,0.8627818250653334],"dir":"ltr"},{"str":"content-aware","boundary":[0.7332358662809415,0.8475092597343162,0.8562265380128807,0.8627818250653334],"dir":"ltr"},{"str":"image","boundary":[0.8624926972766263,0.8475092597343162,0.9141045011808522,0.8627818250653334],"dir":"ltr"},{"str":"resizing.","boundary":[0.34584094750843336,0.8658363381315369,0.41633029745958977,0.8811089034625542],"dir":"ltr"},{"str":"ACM","boundary":[0.42258261977858885,0.8658363381315369,0.46943056127725424,0.8811089034625542],"dir":"ltr"},{"str":"Transactions","boundary":[0.47567695347707634,0.8658363381315369,0.5829725764537665,0.8811089034625542],"dir":"ltr"},{"str":"on","boundary":[0.5892189686535886,0.8658363381315369,0.6111999437365068,0.8811089034625542],"dir":"ltr"},{"str":"Graphics","boundary":[0.6174463359363288,0.8658363381315369,0.695427403114487,0.8811089034625542],"dir":"ltr"},{"str":",","boundary":[0.6954867043062573,0.8658363381315369,0.7004284702871292,0.8811089034625542],"dir":"ltr"},{"str":"vol.","boundary":[0.7070109025736505,0.8658363381315369,0.7383219318284548,0.8811089034625542],"dir":"ltr"},{"str":"26,","boundary":[0.7445683240282768,0.8658363381315369,0.7692771539326362,0.8811089034625542],"dir":"ltr"},{"str":"no.","boundary":[0.7758595862191575,0.8658363381315369,0.801991644726008,0.8811089034625542],"dir":"ltr"},{"str":"3,","boundary":[0.8082380369258301,0.8658363381315369,0.8230633348684456,0.8811089034625542],"dir":"ltr"},{"str":"article","boundary":[0.829645767154967,0.8658363381315369,0.8834517151547,0.8811089034625542],"dir":"ltr"},{"str":"10,","boundary":[0.889698107354522,0.8658363381315369,0.9144069372588814,0.8811089034625542],"dir":"ltr"},{"str":"July","boundary":[0.34583699409564855,0.8841634165287576,0.379994480555435,0.8994359818597749],"dir":"ltr"},{"str":"2007,","boundary":[0.3849362465363068,0.8841634165287576,0.4294121403641537,0.8994359818597749],"dir":"ltr"},{"str":"9","boundary":[0.4343539063450256,0.8841634165287576,0.44423743830676937,0.8994359818597749],"dir":"ltr"},{"str":"pages.","boundary":[0.4491792042876412,0.8841634165287576,0.5013642530456482,0.8994359818597749],"dir":"ltr"}],"boundary":[0.34584,0.32519,0.92704,0.89944],"dir":"ltr","type":"paragraph"},{"words":[{"str":"493","boundary":[0.8940172108218041,0.9329287176306958,0.9269886734461813,0.948201282961713],"dir":"ltr"}],"boundary":[0.89402,0.93293,0.92699,0.9482],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":529,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/6d3859960f6e224dc7b04d90b05c93bb.jpg","blurred":"/storage/books/4a8b03583f119702/pages/cd65ac2d3d9c458a1cbb4a0b099e76d7.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.16303,0.07296,0.0518]},"elements":[{"words":[{"str":"Hints","boundary":[0.14421784044919886,0.16302940802619442,0.268892978884569,0.19968365680003092],"dir":"ltr"},{"str":"to","boundary":[0.28469085601507815,0.16302940802619442,0.3345514231747334,0.19968365680003092],"dir":"ltr"},{"str":"Exercises","boundary":[0.35034930030524264,0.16302940802619442,0.5747455730599232,0.19968365680003092],"dir":"ltr"}],"boundary":[0.14422,0.16303,0.57475,0.19968],"dir":"ltr","type":"paragraph"},{"words":[{"str":"CHAPTER","boundary":[0.23910077902799318,0.32287822498997637,0.36166530233793315,0.34120542602639037],"dir":"ltr"},{"str":"1","boundary":[0.36956427393890273,0.32287822498997637,0.38538593777628033,0.34120542602639037],"dir":"ltr"},{"str":"Exercises","boundary":[0.23910077902799318,0.371885350345499,0.3357739347093517,0.38868523352921464],"dir":"ltr"},{"str":"1.1","boundary":[0.34181872492064674,0.371885350345499,0.3720426759771219,0.38868523352921464],"dir":"ltr"},{"str":"1.","boundary":[0.2499737951383169,0.3975308410437055,0.2647990930809325,0.41280340637472285],"dir":"ltr"},{"str":"It","boundary":[0.27468262504267627,0.3975308410437055,0.2889544451954343,0.41280340637472285],"dir":"ltr"},{"str":"is","boundary":[0.2942322512630054,0.3975308410437055,0.3074168828999716,0.41280340637472285],"dir":"ltr"},{"str":"probably","boundary":[0.31269468896754277,0.3975308410437055,0.3896083346938326,0.41280340637472285],"dir":"ltr"},{"str":"faster","boundary":[0.3948861407614038,0.3975308410437055,0.44319684499040723,0.41280340637472285],"dir":"ltr"},{"str":"to","boundary":[0.44847465105797846,0.3975308410437055,0.46604757088595883,0.41280340637472285],"dir":"ltr"},{"str":"do","boundary":[0.47132537695352994,0.3975308410437055,0.49330635203644807,0.41280340637472285],"dir":"ltr"},{"str":"this","boundary":[0.49858415810401924,0.3975308410437055,0.5293417095689659,0.41280340637472285],"dir":"ltr"},{"str":"by","boundary":[0.534619515636537,0.3975308410437055,0.5554935351397398,0.41280340637472285],"dir":"ltr"},{"str":"searching","boundary":[0.560771341207311,0.3975308410437055,0.6420535080606916,0.41280340637472285],"dir":"ltr"},{"str":"the","boundary":[0.6473313141282627,0.3975308410437055,0.6747877659179868,0.41280340637472285],"dir":"ltr"},{"str":"Web,","boundary":[0.6800655719855581,0.3975308410437055,0.7234542772976131,0.41280340637472285],"dir":"ltr"},{"str":"but","boundary":[0.7288111516208783,0.3975308410437055,0.7573745589903178,0.41280340637472285],"dir":"ltr"},{"str":"your","boundary":[0.7626523650578888,0.3975308410437055,0.8022062599687874,0.41280340637472285],"dir":"ltr"},{"str":"library","boundary":[0.8074840660363585,0.3975308410437055,0.8646108807752374,0.41280340637472285],"dir":"ltr"},{"str":"should","boundary":[0.8698886868428085,0.3975308410437055,0.9270352686456109,0.41280340637472285],"dir":"ltr"},{"str":"be","boundary":[0.27468262504267627,0.4158594466974594,0.2955566445458791,0.43113201202847673],"dir":"ltr"},{"str":"able","boundary":[0.30049841052675097,0.4158594466974594,0.33675120576242706,0.43113201202847673],"dir":"ltr"},{"str":"to","boundary":[0.34169297174329893,0.4158594466974594,0.3592658915712793,0.43113201202847673],"dir":"ltr"},{"str":"help,","boundary":[0.3642076575521512,0.4158594466974594,0.40571849179147496,0.43113201202847673],"dir":"ltr"},{"str":"too.","boundary":[0.4106602577723468,0.4158594466974594,0.4433747485657187,0.43113201202847673],"dir":"ltr"},{"str":"2.","boundary":[0.2499737951383169,0.44404191150278566,0.2647990930809325,0.45931447683380294],"dir":"ltr"},{"str":"One","boundary":[0.27468262504267627,0.44404191150278566,0.3120226087941442,0.45931447683380294],"dir":"ltr"},{"str":"can","boundary":[0.31854573988889506,0.44404191150278566,0.3481963357741263,0.45931447683380294],"dir":"ltr"},{"str":"find","boundary":[0.3547194668688772,0.44404191150278566,0.38769092949325434,0.45931447683380294],"dir":"ltr"},{"str":"arguments","boundary":[0.39421406058800523,0.44404191150278566,0.4842728038234143,0.45931447683380294],"dir":"ltr"},{"str":"supporting","boundary":[0.49079593491816514,0.44404191150278566,0.5830883563769284,0.45931447683380294],"dir":"ltr"},{"str":"either","boundary":[0.5896114874716794,0.44404191150278566,0.6401361028601135,0.45931447683380294],"dir":"ltr"},{"str":"view.","boundary":[0.6466592339548641,0.44404191150278566,0.689672365052373,0.45931447683380294],"dir":"ltr"},{"str":"There","boundary":[0.6961954961471238,0.44404191150278566,0.7470363845583337,0.45931447683380294],"dir":"ltr"},{"str":"is","boundary":[0.7535595156530844,0.44404191150278566,0.7667441472900507,0.45931447683380294],"dir":"ltr"},{"str":"a","boundary":[0.7732672783848016,0.44404191150278566,0.7831508103465453,0.45931447683380294],"dir":"ltr"},{"str":"well-established","boundary":[0.7896739414412961,0.44404191150278566,0.9269759674538404,0.45931447683380294],"dir":"ltr"},{"str":"principle","boundary":[0.27468262504267627,0.4623705171565395,0.35048931518925086,0.4776430824875568],"dir":"ltr"},{"str":"pertinent","boundary":[0.3588507832288861,0.4623705171565395,0.4379388059867596,0.4776430824875568],"dir":"ltr"},{"str":"to","boundary":[0.4463002740263948,0.4623705171565395,0.46387319385437525,0.4776430824875568],"dir":"ltr"},{"str":"the","boundary":[0.47223466189401037,0.4623705171565395,0.49969111368373453,0.4776430824875568],"dir":"ltr"},{"str":"matter,","boundary":[0.5080525817233698,0.4623705171565395,0.5697258211646506,0.4776430824875568],"dir":"ltr"},{"str":"though:","boundary":[0.578937272952996,0.4623705171565395,0.6443069533479692,0.4776430824875568],"dir":"ltr"},{"str":"scientific","boundary":[0.6526684213876043,0.4623705171565395,0.7273483888905401,0.4776430824875568],"dir":"ltr"},{"str":"facts","boundary":[0.7357098569301752,0.4623705171565395,0.7752242177132267,0.4776430824875568],"dir":"ltr"},{"str":"or","boundary":[0.783585685752862,0.4623705171565395,0.8022655611605576,0.4776430824875568],"dir":"ltr"},{"str":"mathematical","boundary":[0.8106270292001927,0.4623705171565395,0.9270155015816872,0.4776430824875568],"dir":"ltr"},{"str":"expressions","boundary":[0.27468262504267627,0.48069912281029337,0.3735574787879608,0.4959716881413107],"dir":"ltr"},{"str":"of","boundary":[0.3788155177916085,0.48069912281029337,0.3963884376195889,0.4959716881413107],"dir":"ltr"},{"str":"them","boundary":[0.40164647662323655,0.48069912281029337,0.4455688926612258,0.4959716881413107],"dir":"ltr"},{"str":"are","boundary":[0.4508269316648735,0.48069912281029337,0.47828338345459764,0.4959716881413107],"dir":"ltr"},{"str":"not","boundary":[0.4835414224582453,0.48069912281029337,0.5121048298276848,0.4959716881413107],"dir":"ltr"},{"str":"patentable.","boundary":[0.5173628688313324,0.48069912281029337,0.6127389522621596,0.4959716881413107],"dir":"ltr"},{"str":"(Why","boundary":[0.6179969912658074,0.48069912281029337,0.6659716554081115,0.4959716881413107],"dir":"ltr"},{"str":"do","boundary":[0.6712296944117592,0.48069912281029337,0.6932106694946774,0.4959716881413107],"dir":"ltr"},{"str":"you","boundary":[0.698468708498325,0.48069912281029337,0.7303332155429868,0.4959716881413107],"dir":"ltr"},{"str":"think","boundary":[0.7355912545466345,0.48069912281029337,0.7806403932282625,0.4959716881413107],"dir":"ltr"},{"str":"this","boundary":[0.7858984322319102,0.48069912281029337,0.8166559836968569,0.4959716881413107],"dir":"ltr"},{"str":"is","boundary":[0.8219140227005045,0.48069912281029337,0.8350986543374707,0.4959716881413107],"dir":"ltr"},{"str":"the","boundary":[0.8403566933411183,0.48069912281029337,0.8678131451308424,0.4959716881413107],"dir":"ltr"},{"str":"case?)","boundary":[0.8730711841344903,0.48069912281029337,0.9268771321342232,0.4959716881413107],"dir":"ltr"},{"str":"But","boundary":[0.27468262504267627,0.4990262012075142,0.3065273650234147,0.5142987665385315],"dir":"ltr"},{"str":"should","boundary":[0.3114691310042865,0.4990262012075142,0.36861571280708894,0.5142987665385315],"dir":"ltr"},{"str":"this","boundary":[0.3735574787879608,0.4990262012075142,0.4043150302529074,0.5142987665385315],"dir":"ltr"},{"str":"preclude","boundary":[0.40925679623377925,0.4990262012075142,0.4839565308006385,0.5142987665385315],"dir":"ltr"},{"str":"granting","boundary":[0.48889829678151037,0.4990262012075142,0.5602969316731472,0.5142987665385315],"dir":"ltr"},{"str":"patents","boundary":[0.5652386976540192,0.4990262012075142,0.6278409890997041,0.5142987665385315],"dir":"ltr"},{"str":"for","boundary":[0.6327827550805759,0.4990262012075142,0.6580450627747929,0.5142987665385315],"dir":"ltr"},{"str":"all","boundary":[0.6629868287556648,0.4990262012075142,0.6838608482588676,0.5142987665385315],"dir":"ltr"},{"str":"algorithms?","boundary":[0.6888026142397395,0.4990262012075142,0.7898518450166075,0.5142987665385315],"dir":"ltr"},{"str":"3.","boundary":[0.2499737951383169,0.5272101932693736,0.2647990930809325,0.5424827586003909],"dir":"ltr"},{"str":"You","boundary":[0.27468262504267627,0.5272101932693736,0.3102238059771068,0.5424827586003909],"dir":"ltr"},{"str":"may","boundary":[0.31390047986687547,0.5272101932693736,0.3501335080386281,0.5424827586003909],"dir":"ltr"},{"str":"assume","boundary":[0.35381018192839675,0.5272101932693736,0.41641247337408166,0.5424827586003909],"dir":"ltr"},{"str":"that","boundary":[0.4200891472638504,0.5272101932693736,0.45412803134009583,0.5424827586003909],"dir":"ltr"},{"str":"you","boundary":[0.4578047052298645,0.5272101932693736,0.4896692122745264,0.5424827586003909],"dir":"ltr"},{"str":"are","boundary":[0.4933458861642951,0.5272101932693736,0.5208023379540192,0.5424827586003909],"dir":"ltr"},{"str":"writing","boundary":[0.5244790118437879,0.5272101932693736,0.5848871591939656,0.5424827586003909],"dir":"ltr"},{"str":"your","boundary":[0.5885638330837344,0.5272101932693736,0.628117727994633,0.5424827586003909],"dir":"ltr"},{"str":"algorithms","boundary":[0.6317944018844015,0.5272101932693736,0.7229601006995259,0.5424827586003909],"dir":"ltr"},{"str":"for","boundary":[0.7266367745892945,0.5272101932693736,0.7518990822835115,0.5424827586003909],"dir":"ltr"},{"str":"a","boundary":[0.7555757561732802,0.5272101932693736,0.7654592881350238,0.5424827586003909],"dir":"ltr"},{"str":"human","boundary":[0.7691359620247926,0.5272101932693736,0.8284569208591787,0.5424827586003909],"dir":"ltr"},{"str":"rather","boundary":[0.8321335947489474,0.5272101932693736,0.8848523542328887,0.5424827586003909],"dir":"ltr"},{"str":"than","boundary":[0.8885290281226573,0.5272101932693736,0.9269759674538405,0.5424827586003909],"dir":"ltr"},{"str":"a","boundary":[0.27468262504267627,0.5455372716665944,0.28456615700442006,0.5608098369976117],"dir":"ltr"},{"str":"machine.","boundary":[0.2888951440036638,0.5455372716665944,0.3655913520267953,0.5608098369976117],"dir":"ltr"},{"str":"Still,","boundary":[0.3699203390260391,0.5455372716665944,0.40892075614707996,0.5608098369976117],"dir":"ltr"},{"str":"make","boundary":[0.4133881125937881,0.5455372716665944,0.46061162830699975,0.5608098369976117],"dir":"ltr"},{"str":"sure","boundary":[0.46494061530624353,0.5455372716665944,0.5011934105419196,0.5608098369976117],"dir":"ltr"},{"str":"that","boundary":[0.5055223975411633,0.5455372716665944,0.5395612816174089,0.5608098369976117],"dir":"ltr"},{"str":"your","boundary":[0.5438902686166526,0.5455372716665944,0.5834441635275511,0.5608098369976117],"dir":"ltr"},{"str":"descriptions","boundary":[0.5877731505267949,0.5455372716665944,0.6910362924630936,0.5608098369976117],"dir":"ltr"},{"str":"do","boundary":[0.6953652794623374,0.5455372716665944,0.7173462545452555,0.5608098369976117],"dir":"ltr"},{"str":"not","boundary":[0.7216752415444992,0.5455372716665944,0.7502386489139388,0.5608098369976117],"dir":"ltr"},{"str":"contain","boundary":[0.7545676359131824,0.5455372716665944,0.8182768829385827,0.5608098369976117],"dir":"ltr"},{"str":"obvious","boundary":[0.8226058699378264,0.5455372716665944,0.8896359837023725,0.5608098369976117],"dir":"ltr"},{"str":"am-","boundary":[0.8939649707016164,0.5455372716665944,0.9268968991981467,0.5608098369976117],"dir":"ltr"},{"str":"biguities.","boundary":[0.27468262504267627,0.5638643500638152,0.35104279297910856,0.5791369153948325],"dir":"ltr"},{"str":"Knuth","boundary":[0.3553322458505053,0.5638643500638152,0.41026491649387714,0.5791369153948325],"dir":"ltr"},{"str":"provides","boundary":[0.4145543693652739,0.5638643500638152,0.48816691541634133,0.5791369153948325],"dir":"ltr"},{"str":"an","boundary":[0.4924563682877382,0.5638643500638152,0.513330387790941,0.5791369153948325],"dir":"ltr"},{"str":"interesting","boundary":[0.5176198406623378,0.5638643500638152,0.6087855394774622,0.5791369153948325],"dir":"ltr"},{"str":"comparison","boundary":[0.6130749923488589,0.5638643500638152,0.7130370346099352,0.5791369153948325],"dir":"ltr"},{"str":"between","boundary":[0.717326487481332,0.5638643500638152,0.7898123108887607,0.5791369153948325],"dir":"ltr"},{"str":"cooking","boundary":[0.7941017637601575,0.5638643500638152,0.8622190660404955,0.5791369153948325],"dir":"ltr"},{"str":"recipes","boundary":[0.8665085189118922,0.5638643500638152,0.92691666626207,0.5791369153948325],"dir":"ltr"},{"str":"and","boundary":[0.27468262504267627,0.582191428461036,0.3065471320873382,0.5974639937920534],"dir":"ltr"},{"str":"algorithms","boundary":[0.31148889806821,0.582191428461036,0.4026545968833344,0.5974639937920534],"dir":"ltr"},{"str":"[KnuI,","boundary":[0.40759636286420625,0.582191428461036,0.46416969981322753,0.5974639937920534],"dir":"ltr"},{"str":"p.","boundary":[0.4691114657940994,0.582191428461036,0.48425303675949083,0.5974639937920534],"dir":"ltr"},{"str":"6].","boundary":[0.4891948027403627,0.582191428461036,0.5106025329694996,0.5974639937920534],"dir":"ltr"},{"str":"4.","boundary":[0.2499737951383169,0.6103754205228954,0.2647990930809325,0.6256479858539127],"dir":"ltr"},{"str":"There","boundary":[0.27468262504267627,0.6103754205228954,0.3255235134538862,0.6256479858539127],"dir":"ltr"},{"str":"is","boundary":[0.33376637910998047,0.6103754205228954,0.3469510107469466,0.6256479858539127],"dir":"ltr"},{"str":"a","boundary":[0.3551938764030409,0.6103754205228954,0.36507740836478464,0.6256479858539127],"dir":"ltr"},{"str":"quite","boundary":[0.3733202740208789,0.6103754205228954,0.41726245712279164,0.6256479858539127],"dir":"ltr"},{"str":"straightforward","boundary":[0.4255053227788859,0.6103754205228954,0.5583992935364924,0.6256479858539127],"dir":"ltr"},{"str":"algorithm","boundary":[0.5666421591925866,0.6103754205228954,0.6501184701414744,0.6256479858539127],"dir":"ltr"},{"str":"for","boundary":[0.6583613357975687,0.6103754205228954,0.6836236434917857,0.6256479858539127],"dir":"ltr"},{"str":"this","boundary":[0.6918665091478801,0.6103754205228954,0.7226240606128266,0.6256479858539127],"dir":"ltr"},{"str":"problem","boundary":[0.730866926268921,0.6103754205228954,0.8033725167402732,0.6256479858539127],"dir":"ltr"},{"str":"based","boundary":[0.8116153823963674,0.6103754205228954,0.8610528092690097,0.6256479858539127],"dir":"ltr"},{"str":"on","boundary":[0.869295674925104,0.6103754205228954,0.891276650008022,0.6256479858539127],"dir":"ltr"},{"str":"the","boundary":[0.8995195156641165,0.6103754205228954,0.9269759674538406,0.6256479858539127],"dir":"ltr"},{"str":"√","boundary":[0.39332651941784064,0.6208722546749037,0.4100494554971111,0.636144820005921],"dir":"ltr"},{"str":"definition","boundary":[0.27468262504267627,0.6287024989201162,0.3570915145396957,0.6439750642511335],"dir":"ltr"},{"str":"of","boundary":[0.3620332805205676,0.6287024989201162,0.37960620034854803,0.6439750642511335],"dir":"ltr"},{"str":"\u000e","boundary":[0.3845499430358122,0.631986100466285,0.39332651941784064,0.6472586657973023],"dir":"ltr"},{"str":"n","boundary":[0.41004919545742285,0.6293120239272992,0.42082224529572354,0.6445845892583166],"dir":"ltr"},{"str":"\u000f.","boundary":[0.42082026858933125,0.6287011213140585,0.43454058765862386,0.6472572881912446],"dir":"ltr"},{"str":"5.","boundary":[0.24997353509862869,0.6568851133759178,0.2647988330412443,0.6721576787069352],"dir":"ltr"},{"str":"Try","boundary":[0.2746823650029881,0.6568851133759178,0.30324577237242756,0.6721576787069352],"dir":"ltr"},{"str":"to","boundary":[0.3081875383532994,0.6568851133759178,0.3257604581812798,0.6721576787069352],"dir":"ltr"},{"str":"design","boundary":[0.33070222416215167,0.6568851133759178,0.38563489480552343,0.6721576787069352],"dir":"ltr"},{"str":"an","boundary":[0.3905766607863953,0.6568851133759178,0.41145068028959814,0.6721576787069352],"dir":"ltr"},{"str":"algorithm","boundary":[0.41639244627047,0.6568851133759178,0.49986875721935775,0.6721576787069352],"dir":"ltr"},{"str":"that","boundary":[0.5048105232002296,0.6568851133759178,0.538849407276475,0.6721576787069352],"dir":"ltr"},{"str":"always","boundary":[0.5437911732573469,0.6568851133759178,0.6008982209323024,0.6721576787069352],"dir":"ltr"},{"str":"makes","boundary":[0.6058399869131743,0.6568851133759178,0.6607528904926226,0.6721576787069352],"dir":"ltr"},{"str":"less","boundary":[0.6656946564734944,0.6568851133759178,0.6964522079384409,0.6721576787069352],"dir":"ltr"},{"str":"than","boundary":[0.7013939739193128,0.6568851133759178,0.739840913250496,0.6721576787069352],"dir":"ltr"},{"str":"mn","boundary":[0.7447886093505449,0.6574960159891585,0.7709997361130894,0.6727685813201759],"dir":"ltr"},{"str":"comparisons.","boundary":[0.7759434788003536,0.6568851133759178,0.8874494863927467,0.6721576787069352],"dir":"ltr"},{"str":"6.","boundary":[0.24997551180502098,0.6850691054377773,0.2648008097476366,0.7003416707687946],"dir":"ltr"},{"str":"a.","boundary":[0.27468434170938033,0.6850691054377773,0.28950963965199594,0.7003416707687946],"dir":"ltr"},{"str":"Just","boundary":[0.3003795481035218,0.6850691054377773,0.3334300789835929,0.7003416707687946],"dir":"ltr"},{"str":"follow","boundary":[0.33837184496446476,0.6850691054377773,0.39219756002812123,0.7003416707687946],"dir":"ltr"},{"str":"Euclid’s","boundary":[0.39713932600899315,0.6850691054377773,0.46598800965450016,0.7003416707687946],"dir":"ltr"},{"str":"algorithm","boundary":[0.470929775635372,0.6850691054377773,0.5544060865842597,0.7003416707687946],"dir":"ltr"},{"str":"as","boundary":[0.5593478525651316,0.6850691054377773,0.576920772393112,0.7003416707687946],"dir":"ltr"},{"str":"described","boundary":[0.5818625383739839,0.6850691054377773,0.6642516608070799,0.7003416707687946],"dir":"ltr"},{"str":"in","boundary":[0.6691934267879517,0.6850691054377773,0.6856791581001402,0.7003416707687946],"dir":"ltr"},{"str":"the","boundary":[0.6906209240810122,0.6850691054377773,0.7180773758707363,0.7003416707687946],"dir":"ltr"},{"str":"text.","boundary":[0.7230191418516081,0.6850691054377773,0.7608928363290102,0.7003416707687946],"dir":"ltr"},{"str":"b.","boundary":[0.27468236500298804,0.7079779534343033,0.29021927724684915,0.7232505187653205],"dir":"ltr"},{"str":"Compare","boundary":[0.3003795481035218,0.7079779534343033,0.3805547593771871,0.7232505187653205],"dir":"ltr"},{"str":"the","boundary":[0.38549652535805895,0.7079779534343033,0.4129529771477831,0.7232505187653205],"dir":"ltr"},{"str":"number","boundary":[0.417894743128655,0.7079779534343033,0.4849050898292776,0.7232505187653205],"dir":"ltr"},{"str":"of","boundary":[0.48984685581014953,0.7079779534343033,0.5074197756381299,0.7232505187653205],"dir":"ltr"},{"str":"divisions","boundary":[0.5123615416190018,0.7079779534343033,0.5870810432497846,0.7232505187653205],"dir":"ltr"},{"str":"made","boundary":[0.5920228092306564,0.7079779534343033,0.6392463249438681,0.7232505187653205],"dir":"ltr"},{"str":"by","boundary":[0.6441880909247399,0.7079779534343033,0.6650621104279427,0.7232505187653205],"dir":"ltr"},{"str":"the","boundary":[0.6700038764088146,0.7079779534343033,0.6974603281985388,0.7232505187653205],"dir":"ltr"},{"str":"two","boundary":[0.7024020941794107,0.7079779534343033,0.734246834160149,0.7232505187653205],"dir":"ltr"},{"str":"algorithms.","boundary":[0.739188600141021,0.7079779534343033,0.8342088764212253,0.7232505187653205],"dir":"ltr"},{"str":"7.","boundary":[0.24997551180502098,0.7361619454961627,0.2648008097476366,0.7514345108271799],"dir":"ltr"},{"str":"Prove","boundary":[0.27468434170938033,0.7361619454961627,0.3252089570978144,0.7514345108271799],"dir":"ltr"},{"str":"that","boundary":[0.3296565464805991,0.7361619454961627,0.36369543055684456,0.7514345108271799],"dir":"ltr"},{"str":"if","boundary":[0.3681430199396293,0.7361619454961627,0.3802206959968802,0.7514345108271799],"dir":"ltr"},{"str":"d","boundary":[0.38469991268194237,0.7367728481094034,0.39458344464368617,0.7520454134404206],"dir":"ltr"},{"str":"divides","boundary":[0.40052344735269413,0.7361619454961627,0.4609513617667954,0.7514345108271799],"dir":"ltr"},{"str":"both","boundary":[0.46539895114958013,0.7361619454961627,0.5049528460604786,0.7514345108271799],"dir":"ltr"},{"str":"m","boundary":[0.5094221792135791,0.7367728481094034,0.5248602561378228,0.7520454134404206],"dir":"ltr"},{"str":"and","boundary":[0.5293177290525692,0.7361619454961627,0.5611822360972311,0.7514345108271799],"dir":"ltr"},{"str":"n","boundary":[0.5656397090119776,0.7367728481094034,0.5764127588502783,0.7520454134404206],"dir":"ltr"},{"str":"(i.e.,","boundary":[0.5808722084714171,0.7361619454961627,0.6180342886475736,0.7514345108271799],"dir":"ltr"},{"str":"m","boundary":[0.6225886201755451,0.7367728481094034,0.6380266970997889,0.7520454134404206],"dir":"ltr"},{"str":"=","boundary":[0.6422825459625157,0.7394455470423315,0.6577008558228359,0.7547181123733487],"dir":"ltr"},{"str":"sd","boundary":[0.6619586813919551,0.7367728481094034,0.681903648890754,0.7520454134404206],"dir":"ltr"},{"str":"and","boundary":[0.6866576277643529,0.7361619454961627,0.7185221348090147,0.7514345108271799],"dir":"ltr"},{"str":"n","boundary":[0.7229815844301535,0.7367728481094034,0.7337546342684542,0.7520454134404206],"dir":"ltr"},{"str":"=","boundary":[0.738010483131181,0.7394455470423315,0.7534287929915012,0.7547181123733487],"dir":"ltr"},{"str":"td","boundary":[0.7576866185606205,0.7367728481094034,0.7766234657993216,0.7520454134404206],"dir":"ltr"},{"str":"for","boundary":[0.7807844327552157,0.7361619454961627,0.8060467404494327,0.7514345108271799],"dir":"ltr"},{"str":"some","boundary":[0.8104943298322175,0.7361619454961627,0.855523701449922,0.7514345108271799],"dir":"ltr"},{"str":"positive","boundary":[0.8599712908327066,0.7361619454961627,0.9269816375333293,0.7514345108271799],"dir":"ltr"},{"str":"integers","boundary":[0.2746823650029881,0.7544890238933835,0.3427799002194025,0.7697615892244007],"dir":"ltr"},{"str":"s","boundary":[0.34800235850798794,0.7550999265066242,0.35569174637422457,0.7703724918376414],"dir":"ltr"},{"str":"and","boundary":[0.3621022052046116,0.7544890238933835,0.3939667122492735,0.7697615892244007],"dir":"ltr"},{"str":"t)","boundary":[0.3991871938314665,0.7550999265066242,0.4156136239518846,0.7703724918376414],"dir":"ltr"},{"str":",","boundary":[0.41383656490516313,0.7544890238933835,0.41877833088603494,0.7697615892244007],"dir":"ltr"},{"str":"then","boundary":[0.42407590401752965,0.7544890238933835,0.4625228433487128,0.7697615892244007],"dir":"ltr"},{"str":"it","boundary":[0.4677413482245135,0.7544890238933835,0.47981902428176443,0.7697615892244007],"dir":"ltr"},{"str":"also","boundary":[0.4850375291575651,0.7544890238933835,0.5190961802977341,0.7697615892244007],"dir":"ltr"},{"str":"divides","boundary":[0.5243146851735347,0.7544890238933835,0.584742599587636,0.7697615892244007],"dir":"ltr"},{"str":"both","boundary":[0.5899611044634369,0.7544890238933835,0.6295149993743353,0.7697615892244007],"dir":"ltr"},{"str":"n","boundary":[0.6347473411948824,0.7550999265066242,0.6455203910331831,0.7703724918376414],"dir":"ltr"},{"str":"and","boundary":[0.6507408726153763,0.7544890238933835,0.6826053796600381,0.7697615892244007],"dir":"ltr"},{"str":"r","boundary":[0.6878278379486236,0.7550999265066242,0.6955172258148601,0.7703724918376414],"dir":"ltr"},{"str":"=","boundary":[0.7015224598348156,0.7577726254395523,0.7169407696951359,0.7730451907705695],"dir":"ltr"},{"str":"m","boundary":[0.7213666153076048,0.7550999265066242,0.7368046922318485,0.7703724918376414],"dir":"ltr"},{"str":"mod","boundary":[0.741228561137925,0.7544890238933835,0.7796755004691082,0.7697615892244007],"dir":"ltr"},{"str":"n","boundary":[0.7841982046948022,0.7550999265066242,0.7949712545331029,0.7703724918376414],"dir":"ltr"},{"str":"and","boundary":[0.8001937128216883,0.7544890238933835,0.8320582198663501,0.7697615892244007],"dir":"ltr"},{"str":"vice","boundary":[0.8372767247421508,0.7544890238933835,0.8713156088183962,0.7697615892244007],"dir":"ltr"},{"str":"versa","boundary":[0.8765341136941971,0.7544890238933835,0.9215634853119016,0.7697615892244007],"dir":"ltr"},{"str":".","boundary":[0.9215713921374709,0.7550999265066242,0.9270073347164299,0.7703724918376414],"dir":"ltr"},{"str":"Use","boundary":[0.2746863184157729,0.7728161022906042,0.3087252024920184,0.7880886676216216],"dir":"ltr"},{"str":"the","boundary":[0.3163552891664846,0.7728161022906042,0.34381174095620876,0.7880886676216216],"dir":"ltr"},{"str":"formula","boundary":[0.35144182763067494,0.7728161022906042,0.41953936284708937,0.7880886676216216],"dir":"ltr"},{"str":"m","boundary":[0.4271813097599096,0.7734270049038449,0.44261938668415335,0.7886995702348623],"dir":"ltr"},{"str":"=","boundary":[0.4473120876595893,0.776099703836773,0.4627303975199095,0.7913722691677904],"dir":"ltr"},{"str":"qn","boundary":[0.46742309849534547,0.7734270049038449,0.49084706924467814,0.7886995702348623],"dir":"ltr"},{"str":"+","boundary":[0.49415805245186234,0.776099703836773,0.5095763623121826,0.7913722691677904],"dir":"ltr"},{"str":"r(0","boundary":[0.5142690632876186,0.7728161022906042,0.5484305031601896,0.7886995702348623],"dir":"ltr"},{"str":"≤","boundary":[0.5532220394552431,0.776099703836773,0.5681264056535528,0.7913722691677904],"dir":"ltr"},{"str":"r<n)","boundary":[0.5728191066289886,0.7734270049038449,0.6313217090169422,0.7886995702348623],"dir":"ltr"},{"str":"and","boundary":[0.6326717994829164,0.7728161022906042,0.6645363065275782,0.7880886676216216],"dir":"ltr"},{"str":"the","boundary":[0.6721663932020445,0.7728161022906042,0.6996228449917686,0.7880886676216216],"dir":"ltr"},{"str":"fact","boundary":[0.7072529316662348,0.7728161022906042,0.7390779045830497,0.7880886676216216],"dir":"ltr"},{"str":"that","boundary":[0.7467079912575159,0.7728161022906042,0.7807468753337613,0.7880886676216216],"dir":"ltr"},{"str":"if","boundary":[0.7883769620082275,0.7728161022906042,0.8004546380654783,0.7880886676216216],"dir":"ltr"},{"str":"d","boundary":[0.808104491803868,0.7734270049038449,0.8179880237656117,0.7886995702348623],"dir":"ltr"},{"str":"divides","boundary":[0.8271045936471242,0.7728161022906042,0.8875325080612254,0.7880886676216216],"dir":"ltr"},{"str":"two","boundary":[0.8951625947356916,0.7728161022906042,0.9270073347164299,0.7880886676216216],"dir":"ltr"},{"str":"integers","boundary":[0.27469224853495,0.7911447079443582,0.34278978375136443,0.8064172732753755],"dir":"ltr"},{"str":"u","boundary":[0.3477315497322363,0.7917556105575989,0.35866273608192484,0.8070281758886162],"dir":"ltr"},{"str":"and","boundary":[0.36360450206279676,0.7911447079443582,0.39546900910745864,0.8064172732753755],"dir":"ltr"},{"str":"v,","boundary":[0.4004107750883305,0.7917556105575989,0.41816159849162227,0.8070281758886162],"dir":"ltr"},{"str":"it","boundary":[0.42231268191555466,0.7911447079443582,0.4343903579728055,0.8064172732753755],"dir":"ltr"},{"str":"also","boundary":[0.4393321239536774,0.7911447079443582,0.47339077509384636,0.8064172732753755],"dir":"ltr"},{"str":"divides","boundary":[0.47833254107471823,0.7911447079443582,0.5387604554888196,0.8064172732753755],"dir":"ltr"},{"str":"u","boundary":[0.5437041981760838,0.7917556105575989,0.5546353845257724,0.8070281758886162],"dir":"ltr"},{"str":"+","boundary":[0.5590276261295714,0.7944283094905268,0.5744459359898916,0.8097008748215441],"dir":"ltr"},{"str":"v","boundary":[0.5788401543000828,0.7917556105575989,0.5884667144308213,0.8070281758886162],"dir":"ltr"},{"str":"and","boundary":[0.5941971862622403,0.7911447079443582,0.6260616933069021,0.8064172732753755],"dir":"ltr"},{"str":"u","boundary":[0.6310054359941665,0.7917556105575989,0.6419366223438551,0.8070281758886162],"dir":"ltr"},{"str":"−","boundary":[0.646328863947654,0.7944283094905268,0.6617471738079742,0.8097008748215441],"dir":"ltr"},{"str":"v","boundary":[0.6661374387053809,0.7917556105575989,0.6757639988361193,0.8070281758886162],"dir":"ltr"},{"str":"(why?).","boundary":[0.6814964473739307,0.7911447079443582,0.7468463607049803,0.8064172732753755],"dir":"ltr"},{"str":"8.","boundary":[0.24998144192419844,0.8193271727496845,0.2648067398668141,0.8345997380807018],"dir":"ltr"},{"str":"Perform","boundary":[0.2746902718285578,0.8193271727496845,0.34606913965627123,0.8345997380807018],"dir":"ltr"},{"str":"one","boundary":[0.3536399251389669,0.8193271727496845,0.3855044321836288,0.8345997380807018],"dir":"ltr"},{"str":"iteration","boundary":[0.3930752176663245,0.8193271727496845,0.4666679966534685,0.8345997380807018],"dir":"ltr"},{"str":"of","boundary":[0.4742387821361642,0.8193271727496845,0.4918117019641446,0.8345997380807018],"dir":"ltr"},{"str":"the","boundary":[0.49938248744684033,0.8193271727496845,0.5268389392365644,0.8345997380807018],"dir":"ltr"},{"str":"algorithm","boundary":[0.5344097247192602,0.8193271727496845,0.6178860356681478,0.8345997380807018],"dir":"ltr"},{"str":"for","boundary":[0.6254568211508434,0.8193271727496845,0.6507191288450604,0.8345997380807018],"dir":"ltr"},{"str":"two","boundary":[0.6582899143277562,0.8193271727496845,0.6901346543084945,0.8345997380807018],"dir":"ltr"},{"str":"arbitrarily","boundary":[0.6977054397911904,0.8193271727496845,0.7844828504153005,0.8345997380807018],"dir":"ltr"},{"str":"chosen","boundary":[0.7920536358979962,0.8193271727496845,0.8513745947323822,0.8345997380807018],"dir":"ltr"},{"str":"integers","boundary":[0.8589453802150779,0.8193271727496845,0.9270429154314924,0.8345997380807018],"dir":"ltr"},{"str":"m<n.","boundary":[0.2746902718285578,0.8382666810166789,0.334936329254563,0.8535392463476962],"dir":"ltr"},{"str":"9.","boundary":[0.24998144192419844,0.8658397704652977,0.2648067398668141,0.881112335796315],"dir":"ltr"},{"str":"The","boundary":[0.2746902718285578,0.8658397704652977,0.3079582404117873,0.881112335796315],"dir":"ltr"},{"str":"answer","boundary":[0.3134930183103638,0.8658397704652977,0.3739011656605416,0.881112335796315],"dir":"ltr"},{"str":"to","boundary":[0.37943594355911814,0.8658397704652977,0.3970088633870985,0.881112335796315],"dir":"ltr"},{"str":"part","boundary":[0.402543641285675,0.8658397704652977,0.4376894809416358,0.881112335796315],"dir":"ltr"},{"str":"(a)","boundary":[0.4432242588402123,0.8658397704652977,0.4684865665344294,0.881112335796315],"dir":"ltr"},{"str":"can","boundary":[0.47402134443300586,0.8658397704652977,0.503671940318237,0.881112335796315],"dir":"ltr"},{"str":"be","boundary":[0.5092067182168136,0.8658397704652977,0.5300807377200164,0.881112335796315],"dir":"ltr"},{"str":"given","boundary":[0.5356155156185929,0.8658397704652977,0.5817518428160128,0.881112335796315],"dir":"ltr"},{"str":"immediately,","boundary":[0.5872866207145893,0.8658397704652977,0.6969345242981744,0.881112335796315],"dir":"ltr"},{"str":"the","boundary":[0.7026274387081387,0.8658397704652977,0.7300838904978628,0.881112335796315],"dir":"ltr"},{"str":"answer","boundary":[0.7356186683964395,0.8658397704652977,0.7960268157466173,0.881112335796315],"dir":"ltr"},{"str":"to","boundary":[0.8015615936451939,0.8658397704652977,0.8191345134731742,0.881112335796315],"dir":"ltr"},{"str":"part","boundary":[0.8246692913717507,0.8658397704652977,0.8598151310277115,0.881112335796315],"dir":"ltr"},{"str":"(b)","boundary":[0.865349908926288,0.8658397704652977,0.8917191722002203,0.881112335796315],"dir":"ltr"},{"str":"can","boundary":[0.8972539500987968,0.8658397704652977,0.926904545984028,0.881112335796315],"dir":"ltr"},{"str":"be","boundary":[0.2746902718285578,0.8841668488625184,0.29556429133176065,0.8994394141935357],"dir":"ltr"},{"str":"given","boundary":[0.2995177041164581,0.8841668488625184,0.3456540313138779,0.8994394141935357],"dir":"ltr"},{"str":"by","boundary":[0.34960744409857547,0.8841668488625184,0.37048146360177825,0.8994394141935357],"dir":"ltr"},{"str":"checking","boundary":[0.37443487638647577,0.8841668488625184,0.4502217994691269,0.8994394141935357],"dir":"ltr"},{"str":"the","boundary":[0.45417521225382435,0.8841668488625184,0.4816316640435485,0.8994394141935357],"dir":"ltr"},{"str":"algorithm’s","boundary":[0.4855850768282459,0.8841668488625184,0.581890212263477,0.8994394141935357],"dir":"ltr"},{"str":"performance","boundary":[0.5858436250481746,0.8841668488625184,0.6956694322070711,0.8994394141935357],"dir":"ltr"},{"str":"on","boundary":[0.6996228449917686,0.8841668488625184,0.7216038200746867,0.8994394141935357],"dir":"ltr"},{"str":"all","boundary":[0.7255572328593841,0.8841668488625184,0.7464312523625869,0.8994394141935357],"dir":"ltr"},{"str":"pairs","boundary":[0.7503846651472844,0.8841668488625184,0.7921327041536901,0.8994394141935357],"dir":"ltr"},{"str":"1","boundary":[0.7960861169383876,0.8841668488625184,0.8059696489001313,0.8994394141935357],"dir":"ltr"},{"str":"<m<n","boundary":[0.8091640064301671,0.8847777514757591,0.8826895773999711,0.9000503168067764],"dir":"ltr"},{"str":"≤","boundary":[0.8826876006935789,0.8874504504086871,0.8975919668918885,0.9027230157397043],"dir":"ltr"},{"str":"10","boundary":[0.9017114230135433,0.8841668488625184,0.9214784869370308,0.8994394141935357],"dir":"ltr"},{"str":".","boundary":[0.9215773222566482,0.8847777514757591,0.9270132648356072,0.9000503168067764],"dir":"ltr"},{"str":"503","boundary":[0.8940338953856607,0.9329321499644566,0.9270053580100379,0.9482047152954738],"dir":"ltr"}],"boundary":[0.2391,0.32288,0.92704,0.9482],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":573,"image":{"jpeg":"/storage/books/4a8b03583f119702/pages/93d8a48181ac8fbfb171252902ff21d6.jpg","blurred":"/storage/books/4a8b03583f119702/pages/00b3d0dcab5e79dbf7ed5d9f3e229215.jpg"},"info":{"width":503.999989,"height":652.3200119999999,"margin":[0.14422,0.16303,0.07299,0.05179]},"elements":[{"words":[{"str":"Index","boundary":[0.14421784044919886,0.16302940802619442,0.274158937928072,0.19968365680003092],"dir":"ltr"},{"str":"The","boundary":[0.23910077902799318,0.2518814691829508,0.27236874761122265,0.26715403451396813],"dir":"ltr"},{"str":"index","boundary":[0.27831863385219235,0.2518814691829508,0.32556191662932754,0.26715403451396813],"dir":"ltr"},{"str":"covers","boundary":[0.3315118028702973,0.2518814691829508,0.3864247064497456,0.26715403451396813],"dir":"ltr"},{"str":"the","boundary":[0.3923745926907153,0.2518814691829508,0.41983104448043945,0.26715403451396813],"dir":"ltr"},{"str":"main","boundary":[0.42578093072140916,0.2518814691829508,0.4686161582436066,0.26715403451396813],"dir":"ltr"},{"str":"text,","boundary":[0.47456604448457634,0.2518814691829508,0.5124397389619784,0.26715403451396813],"dir":"ltr"},{"str":"the","boundary":[0.5186268299700301,0.2518814691829508,0.5460832817597542,0.26715403451396813],"dir":"ltr"},{"str":"exercises,","boundary":[0.5520331680007239,0.2518814691829508,0.6327618570642468,0.26715403451396813],"dir":"ltr"},{"str":"the","boundary":[0.6389489480722984,0.2518814691829508,0.6664053998620225,0.26715403451396813],"dir":"ltr"},{"str":"epilogue,","boundary":[0.6723552861029923,0.2518814691829508,0.7501782167697626,0.26715403451396813],"dir":"ltr"},{"str":"and","boundary":[0.7563653077778142,0.2518814691829508,0.788229814822476,0.26715403451396813],"dir":"ltr"},{"str":"the","boundary":[0.7941797010634459,0.2518814691829508,0.82163615285317,0.26715403451396813],"dir":"ltr"},{"str":"appendices.","boundary":[0.8275860390941396,0.2518814691829508,0.9270143706292818,0.26715403451396813],"dir":"ltr"},{"str":"The","boundary":[0.23910077902799318,0.27020854758017165,0.27236874761122265,0.28548111291118894],"dir":"ltr"},{"str":"following","boundary":[0.276559365163002,0.27020854758017165,0.3567543435005908,0.28548111291118894],"dir":"ltr"},{"str":"indicators","boundary":[0.3609449610523702,0.27020854758017165,0.4455282275809732,0.28548111291118894],"dir":"ltr"},{"str":"are","boundary":[0.44971884513275256,0.27020854758017165,0.47717529692247673,0.28548111291118894],"dir":"ltr"},{"str":"used","boundary":[0.48136591447425603,0.27020854758017165,0.5209198093851546,0.28548111291118894],"dir":"ltr"},{"str":"after","boundary":[0.5251104269369339,0.27020854758017165,0.5657317432997008,0.28548111291118894],"dir":"ltr"},{"str":"page","boundary":[0.5699223608514801,0.27020854758017165,0.6105634442781703,0.28548111291118894],"dir":"ltr"},{"str":"numbers:","boundary":[0.6147540618299497,0.27020854758017165,0.6943955623776809,0.28548111291118894],"dir":"ltr"},{"str":"“ex”","boundary":[0.6985861799294604,0.27020854758017165,0.7381203077764353,0.28548111291118894],"dir":"ltr"},{"str":"for","boundary":[0.7423109253282146,0.27020854758017165,0.7675732330224316,0.28548111291118894],"dir":"ltr"},{"str":"exercises,","boundary":[0.7717638505742108,0.27020854758017165,0.8524925396377339,0.28548111291118894],"dir":"ltr"},{"str":"“fig”","boundary":[0.8568412937009011,0.27020854758017165,0.8974823771275915,0.28548111291118894],"dir":"ltr"},{"str":"for","boundary":[0.9016729946793708,0.27020854758017165,0.9269353023735878,0.28548111291118894],"dir":"ltr"},{"str":"figures,","boundary":[0.23910077902799318,0.28853562597739246,0.30008217123195213,0.3038081913084098],"dir":"ltr"},{"str":"“n”","boundary":[0.305023937212824,0.28853562597739246,0.3357814886777706,0.3038081913084098],"dir":"ltr"},{"str":"for","boundary":[0.3407232546586424,0.28853562597739246,0.36598556235285945,0.3038081913084098],"dir":"ltr"},{"str":"footnotes,","boundary":[0.3709273283337314,0.28853562597739246,0.4560640726521921,0.3038081913084098],"dir":"ltr"},{"str":"“sum”","boundary":[0.4610058386330639,0.28853562597739246,0.5159187422125122,0.3038081913084098],"dir":"ltr"},{"str":"for","boundary":[0.520860508193384,0.28853562597739246,0.546122815887601,0.3038081913084098],"dir":"ltr"},{"str":"summaries.","boundary":[0.5510645818684731,0.28853562597739246,0.6471720466644694,0.3038081913084098],"dir":"ltr"}],"boundary":[0.14422,0.16303,0.92701,0.30381],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Numbers","boundary":[0.23910077902799318,0.3832150426192966,0.32410367612131036,0.39696044339660713],"dir":"ltr"},{"str":"and","boundary":[0.3300279048220376,0.3832150426192966,0.36463038176772655,0.39696044339660713],"dir":"ltr"},{"str":"Symbols","boundary":[0.3705546104684538,0.3832150426192966,0.4516080217612861,0.39696044339660713],"dir":"ltr"},{"str":"2-approximation","boundary":[0.23910077902799318,0.400109514714689,0.36761918183295833,0.41385491549199954],"dir":"ltr"},{"str":"algorithm,","boundary":[0.37206680097764844,0.400109514714689,0.45164360271444376,0.41385491549199954],"dir":"ltr"},{"str":"447,","boundary":[0.45609122185913387,0.400109514714689,0.48722455587196456,0.41385491549199954],"dir":"ltr"},{"str":"458ex","boundary":[0.4916721750166546,0.400109514714689,0.5361483664635556,0.41385491549199954],"dir":"ltr"},{"str":"2-change,","boundary":[0.23910077902799318,0.41690914354471786,0.31273556158748245,0.43065454432202843],"dir":"ltr"},{"str":"450","boundary":[0.31718318073217255,0.41690914354471786,0.3438688956003132,0.43065454432202843],"dir":"ltr"},{"str":"2-colorable","boundary":[0.23910077902799318,0.4337087723747468,0.32609620949813156,0.4474541731520573],"dir":"ltr"},{"str":"graph,","boundary":[0.33057940959597915,0.4337087723747468,0.379521010664149,0.4474541731520573],"dir":"ltr"},{"str":"129ex.","boundary":[0.38400421076199664,0.4337087723747468,0.43292802135358777,0.4474541731520573],"dir":"ltr"},{"str":"See","boundary":[0.4373969890701723,0.4337087723747468,0.46308643724990234,0.4474541731520573],"dir":"ltr"},{"str":"also","boundary":[0.4675696373477499,0.4337087723747468,0.4982226284929541,0.4474541731520573],"dir":"ltr"},{"str":"bipartite","boundary":[0.5023535771545423,0.4337087723747468,0.5685875214572673,0.4474541731520573],"dir":"ltr"},{"str":"graph","boundary":[0.2924722087642743,0.45050702666469794,0.33696619068775413,0.4642524274420085],"dir":"ltr"},{"str":"2-node,","boundary":[0.23909899998033524,0.46730665549472683,0.2969358393378853,0.4810520562720374],"dir":"ltr"},{"str":"223","boundary":[0.3013834584825754,0.46730665549472683,0.328069173350716,0.4810520562720374],"dir":"ltr"},{"str":"2-opt,","boundary":[0.23909899998033524,0.4841062843247558,0.28407332477144154,0.4978516851020663],"dir":"ltr"},{"str":"449–450,","boundary":[0.2885209439161316,0.4841062843247558,0.3552352310864831,0.4978516851020663],"dir":"ltr"},{"str":"451fig,","boundary":[0.35968285023117325,0.4841062843247558,0.40928269893275726,0.4978516851020663],"dir":"ltr"},{"str":"453,","boundary":[0.41373031807744726,0.4841062843247558,0.444863652090278,0.4978516851020663],"dir":"ltr"},{"str":"469sum","boundary":[0.4493112712349681,0.4841062843247558,0.5076284534601447,0.4978516851020663],"dir":"ltr"},{"str":"2–3","boundary":[0.23909899998033524,0.5009059131547846,0.2657847148484758,0.5146513139320952],"dir":"ltr"},{"str":"tree,","boundary":[0.27023233399316593,0.5009059131547846,0.30531515380648144,0.5146513139320952],"dir":"ltr"},{"str":"218,","boundary":[0.3097627729511715,0.5009059131547846,0.34089610696400224,0.5146513139320952],"dir":"ltr"},{"str":"223–225,","boundary":[0.34534372610869235,0.5009059131547846,0.41205801327904384,0.5146513139320952],"dir":"ltr"},{"str":"226ex,","boundary":[0.41650563242373395,0.5009059131547846,0.4654294430153251,0.5146513139320952],"dir":"ltr"},{"str":"250sum","boundary":[0.4698770621600152,0.5009059131547846,0.5281942443851918,0.5146513139320952],"dir":"ltr"},{"str":"2–3-4","boundary":[0.23909899998033524,0.5177041674447358,0.2806041818385832,0.5314495682220464],"dir":"ltr"},{"str":"tree,","boundary":[0.2850518009832733,0.5177041674447358,0.32013462079658883,0.5314495682220464],"dir":"ltr"},{"str":"218","boundary":[0.32458223994127894,0.5177041674447358,0.3512679548094195,0.5314495682220464],"dir":"ltr"},{"str":"top-down,","boundary":[0.2568912556067535,0.5345037962747647,0.33548958113171695,0.5482491970520753],"dir":"ltr"},{"str":"279ex","boundary":[0.339937200276407,0.5345037962747647,0.384413391723308,0.5482491970520753],"dir":"ltr"},{"str":"3-change,","boundary":[0.23909899998033524,0.5513034251047936,0.31273378253982453,0.5650488258821041],"dir":"ltr"},{"str":"450,","boundary":[0.31718140168451464,0.5513034251047936,0.34831473569734533,0.5650488258821041],"dir":"ltr"},{"str":"452fig","boundary":[0.3527623548420354,0.5513034251047936,0.398234812977347,0.5650488258821041],"dir":"ltr"},{"str":"3-node,","boundary":[0.23909899998033524,0.5681030539348225,0.2969358393378853,0.5818484547121331],"dir":"ltr"},{"str":"223","boundary":[0.3013834584825754,0.5681030539348225,0.328069173350716,0.5818484547121331],"dir":"ltr"},{"str":"3-opt,","boundary":[0.23909899998033524,0.5849013082247737,0.28407332477144154,0.5986467090020843],"dir":"ltr"},{"str":"449,","boundary":[0.2885209439161316,0.5849013082247737,0.31965427792896234,0.5986467090020843],"dir":"ltr"},{"str":"450,","boundary":[0.32410189707365245,0.5849013082247737,0.35523523108648314,0.5986467090020843],"dir":"ltr"},{"str":"453,","boundary":[0.35968285023117325,0.5849013082247737,0.390816184244004,0.5986467090020843],"dir":"ltr"},{"str":"469sum","boundary":[0.39526380338869405,0.5849013082247737,0.4535809856138706,0.5986467090020843],"dir":"ltr"},{"str":"e,","boundary":[0.23909899998033524,0.602250753085895,0.25359823839202494,0.6159961538632056],"dir":"ltr"},{"str":"475","boundary":[0.25769004800513984,0.6017009370548025,0.2843757628732805,0.6154463378321131],"dir":"ltr"},{"str":"o","boundary":[0.23909899998033524,0.6190503819159239,0.24799423826971542,0.6327957826932344],"dir":"ltr"},{"str":".","boundary":[0.24817214303550306,0.6185005658848315,0.25261976218019316,0.6322459666621421],"dir":"ltr"},{"str":"See","boundary":[0.25706738132488327,0.6185005658848315,0.2827568295046133,0.6322459666621421],"dir":"ltr"},{"str":"little-oh","boundary":[0.2872934010321972,0.6185005658848315,0.3485815928460268,0.6322459666621421],"dir":"ltr"},{"str":"notation","boundary":[0.35302921199071685,0.6185005658848315,0.41828468008160996,0.6322459666621421],"dir":"ltr"},{"str":"O","boundary":[0.23909899998033524,0.6358500107459528,0.25318905743071346,0.6495954115232634],"dir":"ltr"},{"str":".","boundary":[0.25443439079122665,0.6353001947148604,0.25888200993591676,0.649045595492171],"dir":"ltr"},{"str":"See","boundary":[0.2633314081282647,0.6353001947148604,0.28902085630799473,0.649045595492171],"dir":"ltr"},{"str":"big-oh","boundary":[0.29355564878792073,0.6353001947148604,0.34299538320029593,0.649045595492171],"dir":"ltr"},{"str":"notation","boundary":[0.34744300234498604,0.6353001947148604,0.41269847043587915,0.649045595492171],"dir":"ltr"},{"str":"\u0003.","boundary":[0.23909899998033515,0.6520984490048116,0.2578145813411911,0.6663936658132146],"dir":"ltr"},{"str":"See","boundary":[0.262263979533539,0.6520984490048116,0.2879534277132691,0.6658438497821221],"dir":"ltr"},{"str":"big-theta","boundary":[0.29248822019319515,0.6520984490048116,0.3616753836079943,0.6658438497821221],"dir":"ltr"},{"str":"notation","boundary":[0.3661230027526844,0.6520984490048116,0.43137847084357756,0.6658438497821221],"dir":"ltr"},{"str":"\u0002.","boundary":[0.23909899998033515,0.6688980778348405,0.2573876099033009,0.6831932946432434],"dir":"ltr"},{"str":"See","boundary":[0.261835229047991,0.6688980778348405,0.287524677227721,0.682643478612151],"dir":"ltr"},{"str":"big-omega","boundary":[0.29206124875530487,0.6688980778348405,0.37311466004813726,0.682643478612151],"dir":"ltr"},{"str":"notation","boundary":[0.37756227919282737,0.6688980778348405,0.4428177472837205,0.682643478612151],"dir":"ltr"},{"str":"γ","boundary":[0.23909899998033515,0.6862475226959618,0.24802981922287287,0.6999929234732724],"dir":"ltr"},{"str":"(Euler’s","boundary":[0.2553256936678225,0.6856977066648694,0.317289923591645,0.69944310744218],"dir":"ltr"},{"str":"constant),","boundary":[0.3217375427363351,0.6856977066648694,0.3983433348844774,0.69944310744218],"dir":"ltr"},{"str":"476","boundary":[0.4027909540291675,0.6856977066648694,0.4294766688973081,0.69944310744218],"dir":"ltr"},{"str":"π,","boundary":[0.23909899998033515,0.7030471515259907,0.2568716860825168,0.7167925523033012],"dir":"ltr"},{"str":"17ex,","boundary":[0.26071442902352904,0.7024973354948982,0.3007430013257399,0.7162427362722088],"dir":"ltr"},{"str":"419ex","boundary":[0.30519062047043,0.7024973354948982,0.349666811917331,0.7162427362722088],"dir":"ltr"},{"str":"φ","boundary":[0.2390989999803351,0.7198454058159418,0.24936410496627986,0.7335908065932524],"dir":"ltr"},{"str":"(golden","boundary":[0.25470302698756586,0.7192955897848494,0.3140342663777318,0.73304099056216],"dir":"ltr"},{"str":"ratio),","boundary":[0.3184818855224219,0.7192955897848494,0.3664272199021812,0.73304099056216],"dir":"ltr"},{"str":"80","boundary":[0.3708748390468713,0.7192955897848494,0.38866531562563167,0.73304099056216],"dir":"ltr"},{"str":"A","boundary":[0.2390989999803351,0.7528000041795438,0.2539184669704425,0.7665454049568544],"dir":"ltr"},{"str":"Abel,","boundary":[0.2390989999803351,0.7696958508150139,0.28218753425409276,0.7834412515923245],"dir":"ltr"},{"str":"Niels,","boundary":[0.28663515339878287,0.7696958508150139,0.3296525257662255,0.7834412515923245],"dir":"ltr"},{"str":"460","boundary":[0.3341001449109156,0.7696958508150139,0.36078585977905625,0.7834412515923245],"dir":"ltr"},{"str":"absolute","boundary":[0.2390989999803351,0.786494105104965,0.30435446807122823,0.8002395058822755],"dir":"ltr"},{"str":"error,","boundary":[0.30880208721591834,0.786494105104965,0.3527979357951928,0.8002395058822755],"dir":"ltr"},{"str":"414,","boundary":[0.3572455549398829,0.786494105104965,0.38837888895271366,0.8002395058822755],"dir":"ltr"},{"str":"419ex,","boundary":[0.39282650809740377,0.786494105104965,0.4417503186889949,0.8002395058822755],"dir":"ltr"},{"str":"461,","boundary":[0.44619793783368494,0.786494105104965,0.47733127184651564,0.8002395058822755],"dir":"ltr"},{"str":"468ex","boundary":[0.48177889099120574,0.786494105104965,0.5262550824381067,0.8002395058822755],"dir":"ltr"},{"str":"abstract","boundary":[0.2390989999803351,0.803293733934994,0.3003694013175859,0.8170391347123046],"dir":"ltr"},{"str":"data","boundary":[0.30481702046227604,0.803293733934994,0.33842323071955444,0.8170391347123046],"dir":"ltr"},{"str":"type","boundary":[0.34287084986424454,0.803293733934994,0.37647706012152293,0.8170391347123046],"dir":"ltr"},{"str":"(ADT),","boundary":[0.38092467926621304,0.803293733934994,0.4408074234303206,0.8170391347123046],"dir":"ltr"},{"str":"37,","boundary":[0.44525504257501064,0.803293733934994,0.4674931382984611,0.8170391347123046],"dir":"ltr"},{"str":"39sum","boundary":[0.4719407574431512,0.803293733934994,0.5213627013789477,0.8170391347123046],"dir":"ltr"},{"str":"accuracy","boundary":[0.2390989999803351,0.8200933627650228,0.3059734014398955,0.8338387635423333],"dir":"ltr"},{"str":"ratio,","boundary":[0.3105811348737944,0.8200933627650228,0.3516059738644159,0.8338387635423333],"dir":"ltr"},{"str":"442–444,","boundary":[0.35624928825147234,0.8200933627650228,0.42296357542182383,0.8338387635423333],"dir":"ltr"},{"str":"446–447,","boundary":[0.42760688980888034,0.8200933627650228,0.49432117697923184,0.8338387635423333],"dir":"ltr"},{"str":"453,","boundary":[0.49896449136628823,0.8200933627650228,0.5300978253791189,0.8338387635423333],"dir":"ltr"},{"str":"455,","boundary":[0.5347411397661754,0.8200933627650228,0.5658744737790061,0.8338387635423333],"dir":"ltr"},{"str":"457ex","boundary":[0.2924722087642742,0.8368916170549741,0.3369484002111752,0.8506370178322846],"dir":"ltr"},{"str":"Adelson-Velsky,","boundary":[0.2390989999803351,0.8536912458850029,0.36496662177506495,0.8674366466623135],"dir":"ltr"},{"str":"G.","boundary":[0.36941424091975505,0.8536912458850029,0.3873648317877243,0.8674366466623135],"dir":"ltr"},{"str":"M.,","boundary":[0.39181245093241446,0.8536912458850029,0.41750189911214447,0.8674366466623135],"dir":"ltr"},{"str":"218","boundary":[0.4219495182568346,0.8536912458850029,0.44863523312497516,0.8674366466623135],"dir":"ltr"},{"str":"adjacency","boundary":[0.2390989999803351,0.8704908747150318,0.31488643020585444,0.8842362754923424],"dir":"ltr"},{"str":"lists,","boundary":[0.31933404935054455,0.8704908747150318,0.3534383929520282,0.8842362754923424],"dir":"ltr"},{"str":"29,","boundary":[0.35788601209671833,0.8704908747150318,0.3801241078201688,0.8842362754923424],"dir":"ltr"},{"str":"30,","boundary":[0.38457172696485886,0.8704908747150318,0.40680982268830934,0.8842362754923424],"dir":"ltr"},{"str":"37ex,","boundary":[0.41125744183299956,0.8704908747150318,0.4512860141352104,0.8842362754923424],"dir":"ltr"},{"str":"39sum,","boundary":[0.4557336332799005,0.8704908747150318,0.509603196360387,0.8842362754923424],"dir":"ltr"},{"str":"43n","boundary":[0.5140508155050771,0.8704908747150318,0.5417327970616284,0.8842362754923424],"dir":"ltr"}],"boundary":[0.2391,0.38322,0.56859,0.88424],"dir":"ltr","type":"paragraph"},{"words":[{"str":"adjacency","boundary":[0.5968850535034435,0.38329339140372715,0.6726724837289627,0.3970387921810377],"dir":"ltr"},{"str":"matrix,","boundary":[0.6771201028736529,0.38329339140372715,0.7319681421659712,0.3970387921810377],"dir":"ltr"},{"str":"29,","boundary":[0.7364157613106613,0.38329339140372715,0.7586538570341118,0.3970387921810377],"dir":"ltr"},{"str":"30,","boundary":[0.7631014761788019,0.38329339140372715,0.7853395719022525,0.3970387921810377],"dir":"ltr"},{"str":"37ex,","boundary":[0.7897871910469424,0.38329339140372715,0.8298157633491533,0.3970387921810377],"dir":"ltr"},{"str":"39sum","boundary":[0.8342633824938435,0.38329339140372715,0.8836853264296399,0.3970387921810377],"dir":"ltr"},{"str":"Adleman,","boundary":[0.5968850535034435,0.40009302023375604,0.6735797980344795,0.4138384210110666],"dir":"ltr"},{"str":"L.","boundary":[0.6780274171791696,0.40009302023375604,0.694341284201893,0.4138384210110666],"dir":"ltr"},{"str":"M.,","boundary":[0.6987889033465831,0.40009302023375604,0.7244783515263131,0.4138384210110666],"dir":"ltr"},{"str":"474","boundary":[0.7289259706710031,0.40009302023375604,0.7556116855391436,0.4138384210110666],"dir":"ltr"},{"str":"ADT.","boundary":[0.5968850535034435,0.416892649063785,0.6429268068892753,0.4306380498410955],"dir":"ltr"},{"str":"See","boundary":[0.6473744260339654,0.416892649063785,0.6730638742136954,0.4306380498410955],"dir":"ltr"},{"str":"abstract","boundary":[0.6776004457412793,0.416892649063785,0.7388708470785301,0.4306380498410955],"dir":"ltr"},{"str":"data","boundary":[0.7433184662232203,0.416892649063785,0.7769246764804987,0.4306380498410955],"dir":"ltr"},{"str":"type","boundary":[0.7813722956251887,0.416892649063785,0.8149785058824671,0.4306380498410955],"dir":"ltr"},{"str":"adversary","boundary":[0.5968868325511012,0.43369227789381387,0.6720160151432064,0.44743767867112444],"dir":"ltr"},{"str":"arguments,","boundary":[0.6781003581331425,0.43369227789381387,0.763601388570665,0.44743767867112444],"dir":"ltr"},{"str":"390–391,","boundary":[0.7700949125219124,0.43369227789381387,0.836809199692264,0.44743767867112444],"dir":"ltr"},{"str":"394ex,","boundary":[0.8433027236435116,0.43369227789381387,0.8922265342351027,0.44743767867112444],"dir":"ltr"},{"str":"420sum","boundary":[0.6502600413350403,0.450490532183765,0.7085772235602169,0.46423593296107557],"dir":"ltr"},{"str":"algorithm,","boundary":[0.5968868325511012,0.46729016101379395,0.6764636342878966,0.48103556179110446],"dir":"ltr"},{"str":"3–4,","boundary":[0.6809112534325866,0.46729016101379395,0.7120445874454173,0.48103556179110446],"dir":"ltr"},{"str":"38sum","boundary":[0.7164922065901074,0.46729016101379395,0.7659141505259037,0.48103556179110446],"dir":"ltr"},{"str":"analyzing","boundary":[0.6146790881775196,0.48408978984382284,0.6878335278693823,0.4978351906211334],"dir":"ltr"},{"str":"of,","boundary":[0.6922811470140724,0.48408978984382284,0.7125444998372804,0.4978351906211334],"dir":"ltr"},{"str":"14–15","boundary":[0.7169921189819707,0.48408978984382284,0.7614683104288716,0.4978351906211334],"dir":"ltr"},{"str":"approximation,","boundary":[0.6146790881775196,0.500888044133774,0.7328256431370674,0.5146334449110845],"dir":"ltr"},{"str":"11","boundary":[0.7372732622817575,0.500888044133774,0.7550637388605179,0.5146334449110845],"dir":"ltr"},{"str":"basic","boundary":[0.6146790881775196,0.5176876729638029,0.6532310509236934,0.5314330737411135],"dir":"ltr"},{"str":"operation","boundary":[0.6576786700683834,0.5176876729638029,0.7328256431370674,0.5314330737411135],"dir":"ltr"},{"str":"of,","boundary":[0.7372732622817575,0.5176876729638029,0.7575366151049655,0.5314330737411135],"dir":"ltr"},{"str":"44,","boundary":[0.7619842342496557,0.5176876729638029,0.7842223299731061,0.5314330737411135],"dir":"ltr"},{"str":"46","boundary":[0.7886699491177963,0.5176876729638029,0.8064604256965567,0.5314330737411135],"dir":"ltr"},{"str":"coding","boundary":[0.6146790881775196,0.5344873017938319,0.6660935654901371,0.5482327025711423],"dir":"ltr"},{"str":"of,","boundary":[0.6705411846348271,0.5344873017938319,0.6908045374580353,0.5482327025711423],"dir":"ltr"},{"str":"15–16","boundary":[0.6952521566027254,0.5344873017938319,0.7397283480496264,0.5482327025711423],"dir":"ltr"},{"str":"correctness","boundary":[0.6146790881775196,0.5512869306238607,0.7016567281710792,0.5650323314011713],"dir":"ltr"},{"str":"of,","boundary":[0.7061043473157693,0.5512869306238607,0.7263677001389773,0.5650323314011713],"dir":"ltr"},{"str":"13–14","boundary":[0.7308153192836675,0.5512869306238607,0.7752915107305685,0.5650323314011713],"dir":"ltr"},{"str":"efficiency","boundary":[0.6146790881775196,0.5680851849138119,0.6874955088143858,0.5818305856911224],"dir":"ltr"},{"str":"of,","boundary":[0.691943127959076,0.5680851849138119,0.7122064807822841,0.5818305856911224],"dir":"ltr"},{"str":"14","boundary":[0.7166540999269742,0.5680851849138119,0.7344445765057346,0.5818305856911224],"dir":"ltr"},{"str":"exact,","boundary":[0.6146790881775196,0.5848848137438408,0.6596356224920471,0.5986302145211513],"dir":"ltr"},{"str":"11","boundary":[0.6640832416367373,0.5848848137438408,0.6818737182154977,0.5986302145211513],"dir":"ltr"},{"str":"generality","boundary":[0.6146790881775196,0.6016844425738697,0.6917830136698672,0.6154298433511802],"dir":"ltr"},{"str":"of,","boundary":[0.6962306328145572,0.6016844425738697,0.7164939856377653,0.6154298433511802],"dir":"ltr"},{"str":"14","boundary":[0.7209416047824554,0.6016844425738697,0.7387320813612158,0.6154298433511802],"dir":"ltr"},{"str":"input","boundary":[0.6146790881775196,0.6184840714038986,0.6552235843005145,0.6322294721812092],"dir":"ltr"},{"str":"to,","boundary":[0.6596712034452046,0.6184840714038986,0.6799345562684127,0.6322294721812092],"dir":"ltr"},{"str":"9","boundary":[0.6843821754131028,0.6184840714038986,0.693277413702483,0.6322294721812092],"dir":"ltr"},{"str":"methods","boundary":[0.6146790881775196,0.6352823256938498,0.6809130324802445,0.6490277264711602],"dir":"ltr"},{"str":"of","boundary":[0.6853606516249346,0.6352823256938498,0.7011763853034526,0.6490277264711602],"dir":"ltr"},{"str":"specifying,","boundary":[0.7056240044481427,0.6352823256938498,0.7871755490851804,0.6490277264711602],"dir":"ltr"},{"str":"12–13","boundary":[0.7916231682298704,0.6352823256938498,0.8360993596767715,0.6490277264711602],"dir":"ltr"},{"str":"nondeterministic,","boundary":[0.6146790881775196,0.6520819545238786,0.7496198530274172,0.6658273553011892],"dir":"ltr"},{"str":"404","boundary":[0.7540674721721073,0.6520819545238786,0.7807531870402479,0.6658273553011892],"dir":"ltr"},{"str":"optimality","boundary":[0.6146790881775196,0.6688815833539076,0.6937577565701095,0.6826269841312181],"dir":"ltr"},{"str":"of,","boundary":[0.6982053757147996,0.6688815833539076,0.7184687285380077,0.6826269841312181],"dir":"ltr"},{"str":"16.","boundary":[0.7229163476826979,0.6688815833539076,0.7451544434061484,0.6826269841312181],"dir":"ltr"},{"str":"See","boundary":[0.7496002835031805,0.6688815833539076,0.7752897316829106,0.6826269841312181],"dir":"ltr"},{"str":"also","boundary":[0.7797373508276007,0.6688815833539076,0.8103903419728049,0.6826269841312181],"dir":"ltr"},{"str":"lower","boundary":[0.8144999420624984,0.6688815833539076,0.8579976572975676,0.6826269841312181],"dir":"ltr"},{"str":"bounds","boundary":[0.6502618203826982,0.6856812121839365,0.7066398406607899,0.699426612961247],"dir":"ltr"},{"str":"origin","boundary":[0.6146808672251775,0.7024794664738876,0.6601711158370678,0.7162248672511982],"dir":"ltr"},{"str":"of","boundary":[0.6646187349817578,0.7024794664738876,0.6804344686602758,0.7162248672511982],"dir":"ltr"},{"str":"word,","boundary":[0.684882087804966,0.7024794664738876,0.7288779363842404,0.7162248672511982],"dir":"ltr"},{"str":"7ex","boundary":[0.7333255555289306,0.7024794664738876,0.7600112703970712,0.7162248672511982],"dir":"ltr"},{"str":"parallel,","boundary":[0.6146808672251775,0.7192790953039165,0.677463459071623,0.7330244960812271],"dir":"ltr"},{"str":"10,","boundary":[0.681911078216313,0.7192790953039165,0.7041491739397636,0.7330244960812271],"dir":"ltr"},{"str":"472","boundary":[0.7085967930844536,0.7192790953039165,0.7352825079525942,0.7330244960812271],"dir":"ltr"},{"str":"patentability","boundary":[0.6146808672251775,0.7360787241339455,0.7125462788849385,0.7498241249112559],"dir":"ltr"},{"str":"of,","boundary":[0.7169938980296285,0.7360787241339455,0.7372572508528367,0.7498241249112559],"dir":"ltr"},{"str":"7ex","boundary":[0.7417048699975267,0.7360787241339455,0.7683905848656674,0.7498241249112559],"dir":"ltr"},{"str":"randomized,","boundary":[0.6146808672251775,0.7528783529639743,0.7110696693289014,0.7666237537412849],"dir":"ltr"},{"str":"180,","boundary":[0.7155172884735914,0.7528783529639743,0.7466506224864221,0.7666237537412849],"dir":"ltr"},{"str":"472","boundary":[0.7510982416311123,0.7528783529639743,0.7777839564992528,0.7666237537412849],"dir":"ltr"},{"str":"running","boundary":[0.6146808672251775,0.7696766072539255,0.675008373303754,0.7834220080312361],"dir":"ltr"},{"str":"time","boundary":[0.6794559924484441,0.7696766072539255,0.7140406789175544,0.7834220080312361],"dir":"ltr"},{"str":"of,","boundary":[0.7184882980622443,0.7696766072539255,0.7387516508854525,0.7834220080312361],"dir":"ltr"},{"str":"44–45","boundary":[0.7431992700301425,0.7696766072539255,0.7876754614770436,0.7834220080312361],"dir":"ltr"},{"str":"sequential,","boundary":[0.6146808672251775,0.7864762360839544,0.6982249452390363,0.8002216368612649],"dir":"ltr"},{"str":"10,","boundary":[0.7026725643837264,0.7864762360839544,0.724910660107177,0.8002216368612649],"dir":"ltr"},{"str":"473","boundary":[0.729358279251867,0.7864762360839544,0.7560439941200076,0.8002216368612649],"dir":"ltr"},{"str":"simplicity","boundary":[0.6146808672251775,0.8032758649139833,0.688813783128872,0.8170212656912939],"dir":"ltr"},{"str":"of,","boundary":[0.6932614022735621,0.8032758649139833,0.7135247550967702,0.8170212656912939],"dir":"ltr"},{"str":"14","boundary":[0.7179723742414603,0.8032758649139833,0.7357628508202207,0.8170212656912939],"dir":"ltr"},{"str":"space","boundary":[0.6146808672251775,0.8200754937440122,0.6571823157718361,0.8338208945213228],"dir":"ltr"},{"str":"efficiency","boundary":[0.6627151539878304,0.8200754937440122,0.7355315746246968,0.8338208945213228],"dir":"ltr"},{"str":"of,","boundary":[0.7410644128406914,0.8200754937440122,0.7613277656638994,0.8338208945213228],"dir":"ltr"},{"str":"14,","boundary":[0.7671274610285753,0.8200754937440122,0.7893655567520259,0.8338208945213228],"dir":"ltr"},{"str":"41–42,","boundary":[0.7951652521167017,0.8200754937440122,0.8440890627082929,0.8338208945213228],"dir":"ltr"},{"str":"94sum,","boundary":[0.8498887580729687,0.8200754937440122,0.9037583211534552,0.8338208945213228],"dir":"ltr"},{"str":"95sum","boundary":[0.6502618203826982,0.8368737480339634,0.6996837643184945,0.850619148811274],"dir":"ltr"},{"str":"time","boundary":[0.6146808672251775,0.8536733768639924,0.6492655536942877,0.8674187776413029],"dir":"ltr"},{"str":"efficiency","boundary":[0.655100830012121,0.8536733768639924,0.7279172506489874,0.8674187776413029],"dir":"ltr"},{"str":"of,","boundary":[0.7337525269668208,0.8536733768639924,0.7540158797900288,0.8674187776413029],"dir":"ltr"},{"str":"14,","boundary":[0.7601891751628588,0.8536733768639924,0.7824272708863094,0.8674187776413029],"dir":"ltr"},{"str":"41–42,","boundary":[0.7886005662591391,0.8536733768639924,0.8375243768507302,0.8674187776413029],"dir":"ltr"},{"str":"94sum,","boundary":[0.8436976722235601,0.8536733768639924,0.8975672353040465,0.8674187776413029],"dir":"ltr"},{"str":"95sum","boundary":[0.6502618203826982,0.8704730056940213,0.6996837643184945,0.8842184064713318],"dir":"ltr"}],"boundary":[0.59689,0.38329,0.90376,0.88422],"dir":"ltr","type":"paragraph"},{"words":[{"str":"547","boundary":[0.8940253964965859,0.9329341022884333,0.9269968591209631,0.9482066676194506],"dir":"ltr"}],"boundary":[0.89403,0.93293,0.927,0.94821],"dir":"ltr","type":"paragraph"}]}],"words":[]}