Algorithms Algorithms

توضیحات

This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. ,Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated. , ,Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence. , ,An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center. , ,"Algorithms is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read." Tim Roughgarden Stanford University

-00
-11
-22
-33
-44
-55
-66
-77
-88
-99
-1010
-1111
-1212
-1313
-1414
-1515
-1616
-1717
-1818
-1919
{"title":"Algorithms","price":"۱۹","ebook_price":"۱۹","rent_3_price":"۱۵","rent_6_price":"۶","rent_12_price":"-۱","print_price":"-۱","front_cover":{"thumbnail":"/storage/files/styles/thumbnail/books/4f1eb51f4f5b6edb/front.jpg","medium":"/storage/files/styles/medium/books/4f1eb51f4f5b6edb/front.jpg","medium_rounded":"/storage/files/styles/medium_rounded/books/4f1eb51f4f5b6edb/front.png","large":"/storage/files/styles/large/books/4f1eb51f4f5b6edb/front.jpg","medium_trans":"/storage/files/styles/medium_trans/books/4f1eb51f4f5b6edb/front.png","medium_zoom_fit":"/storage/files/styles/medium_zoom_fit/books/4f1eb51f4f5b6edb/front.png"},"back_cover":{"thumbnail":"/storage/files/styles/thumbnail/books/4f1eb51f4f5b6edb/back.jpg","medium":"/storage/files/styles/medium/books/4f1eb51f4f5b6edb/back.jpg","medium_rounded":"/storage/files/styles/medium_rounded/books/4f1eb51f4f5b6edb/back.png","large":"/storage/files/styles/large/books/4f1eb51f4f5b6edb/back.jpg","medium_trans":"/storage/files/styles/medium_trans/books/4f1eb51f4f5b6edb/back.png","medium_zoom_fit":"/storage/files/styles/medium_zoom_fit/books/4f1eb51f4f5b6edb/back.png"},"print_book":false,"isbn":"9780073523408","lang":"null","cover_type":"null","dimension":"null","year":"۲۰۰۶","nobat_chap":1,"description":["This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal.\r","Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated.\r","\r","Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.\r","\r","An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center.\r","\r","\"Algorithms is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read.\" Tim Roughgarden Stanford University"],"pages_count":336,"token":"4f1eb51f4f5b6edb","deleted_at":null,"published_at":"2017-12-12 14:28:41","available_for_web":true,"publisher_title":"McGraw-Hill","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":1050,"title":"Sanjoy Dasgupta","meta_title":"Sanjoy Dasgupta","meta_description":"Sanjoy Dasgupta - 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":"Sanjoy","lastname":"Dasgupta","token":"fec7344359024485","national_code":null,"pivot":{"book_id":572,"author_id":1050,"created_at":"2017-12-09 19:21:20","updated_at":"2019-03-12 15:00:29","role":"writer"}},{"id":1052,"title":"Christos Papadimitriou","meta_title":"Christos Papadimitriou","meta_description":"Christos Papadimitriou - 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":"Christos","lastname":"Papadimitriou","token":"6e1b698e69d999c1","national_code":null,"pivot":{"book_id":572,"author_id":1052,"created_at":"2017-12-09 19:21:20","updated_at":"2019-03-12 15:00:29","role":"writer"}},{"id":1054,"title":"Umesh Vazirani","meta_title":"Umesh Vazirani","meta_description":"Umesh Vazirani - 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":"Umesh","lastname":"Vazirani","token":"0b7141b41bc46fa6","national_code":null,"pivot":{"book_id":572,"author_id":1054,"created_at":"2017-12-09 19:21:20","updated_at":"2019-03-12 15:00:29","role":"writer"}}],"translator_authors":[],"available_e_book":true,"dir":true,"vitrines":[{"title":"کتاب‌های مشابه","url":"/api/bookstore/vitrines/similar-books/4f1eb51f4f5b6edb","type":"books","books":[]},{"title":"کتاب‌های دیگر ناشر","url":"/api/bookstore/vitrines/publisher-books/4f1eb51f4f5b6edb","type":"books","books":[]}],"authors":[{"id":1050,"title":"Sanjoy Dasgupta","meta_title":"Sanjoy Dasgupta","meta_description":"Sanjoy Dasgupta - 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":"Sanjoy","lastname":"Dasgupta","token":"fec7344359024485","national_code":null,"pivot":{"book_id":572,"author_id":1050,"created_at":"2017-12-09 19:21:20","updated_at":"2019-03-12 15:00:29","role":"writer"}},{"id":1052,"title":"Christos Papadimitriou","meta_title":"Christos Papadimitriou","meta_description":"Christos Papadimitriou - 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":"Christos","lastname":"Papadimitriou","token":"6e1b698e69d999c1","national_code":null,"pivot":{"book_id":572,"author_id":1052,"created_at":"2017-12-09 19:21:20","updated_at":"2019-03-12 15:00:29","role":"writer"}},{"id":1054,"title":"Umesh Vazirani","meta_title":"Umesh Vazirani","meta_description":"Umesh Vazirani - 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":"Umesh","lastname":"Vazirani","token":"0b7141b41bc46fa6","national_code":null,"pivot":{"book_id":572,"author_id":1054,"created_at":"2017-12-09 19:21:20","updated_at":"2019-03-12 15:00:29","role":"writer"}}],"e_book":{"toc":[],"pages_count":336,"version":"6.15.2","dir":"ltr","state":"converting","token":"4f1eb51f4f5b6edb","status":"SUCCEED","pages_count_fa":"۳۳۶"},"publisher":{"id":103,"title":"McGraw-Hill","description":null,"logo":null,"token":"f1da1800d6e8795b","slug":"McGraw-Hill"},"tags":[{"title":"algorithms","token":"cd7cf7ad54e27c11","pivot":{"taggable_id":572,"tag_id":2731}},{"title":"طراحی الگوریتم","token":"2cce625e6845ad2d","pivot":{"taggable_id":572,"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":"Algorithms","ebook_price_en":19,"urlify":"Algorithms","pages_count_fa":"۳۳۶","authorTitle":"Sanjoy Dasgupta, Christos Papadimitriou, Umesh Vazirani","tocStr":"","url":"/preview/4f1eb51f4f5b6edb/Algorithms"}
{"toc":[],"pages_count":336,"version":"6.15.2","dir":"ltr","state":"converting","token":"4f1eb51f4f5b6edb","status":"SUCCEED","pages":[{"token":null,"index":0,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/ee690f996d6c75525c256e96b979f234.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/9b5f8911d974d0cb2785e128ebde3f75.jpg"},"info":{"width":612,"height":792,"margin":[0.1798,0.38831,0.18028,0.49158]},"elements":[{"words":[{"str":"Algorithms","boundary":[0.42705882352941177,0.3883132058080808,0.5729959071895425,0.41004982196969697],"dir":"ltr"}],"boundary":[0.42706,0.38831,0.573,0.41005],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Copyright","boundary":[0.17980392156862748,0.4549901414141414,0.2698976836601308,0.4700850909090909],"dir":"ltr"},{"str":"c","boundary":[0.2809803921568628,0.4545355833333333,0.28959516862745105,0.4696305328282828],"dir":"ltr"},{"str":"2006","boundary":[0.29508331699346413,0.4549901414141414,0.3382158032679739,0.4700850909090909],"dir":"ltr"},{"str":"S","boundary":[0.3439019444444445,0.4549901414141414,0.35703216143790856,0.4700850909090909],"dir":"ltr"},{"str":"Dasgupta,","boundary":[0.3664428921568628,0.4549901414141414,0.458919880392157,0.4700850909090909],"dir":"ltr"},{"str":"C","boundary":[0.4644097222222223,0.4549901414141414,0.47929806993464064,0.4700850909090909],"dir":"ltr"},{"str":"H.","boundary":[0.488708774509804,0.4549901414141414,0.5104703640522876,0.4700850909090909],"dir":"ltr"},{"str":"Papadimitriou,","boundary":[0.5157643300653595,0.4549901414141414,0.6509801633986928,0.4700850909090909],"dir":"ltr"},{"str":"and","boundary":[0.656862091503268,0.4549901414141414,0.6907742274509805,0.4700850909090909],"dir":"ltr"},{"str":".","boundary":[0.7101850980392158,0.4549901414141414,0.7103802816993465,0.4700850909090909],"dir":"ltr"},{"str":"U","boundary":[0.6962642156862746,0.4549901414141414,0.7141066588235295,0.4700850909090909],"dir":"ltr"},{"str":".","boundary":[0.7327194444444446,0.4549901414141414,0.7329146281045753,0.4700850909090909],"dir":"ltr"},{"str":"V","boundary":[0.7209683823529413,0.4549901414141414,0.7374253411764706,0.4700850909090909],"dir":"ltr"},{"str":"Vazirani","boundary":[0.74350272875817,0.4549901414141414,0.8197210000000001,0.4700850909090909],"dir":"ltr"},{"str":"July","boundary":[0.4398044117647061,0.4933234747474748,0.4785987104575165,0.5084184242424242],"dir":"ltr"},{"str":"18,","boundary":[0.4840888071895426,0.4933234747474748,0.5111442843137256,0.5084184242424242],"dir":"ltr"},{"str":"2006","boundary":[0.5166343954248367,0.4933234747474748,0.5597668816993465,0.5084184242424242],"dir":"ltr"}],"boundary":[0.1798,0.45454,0.81972,0.50842],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":1,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/f9068ab8bc4d074298c19cd02065dfe1.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/f455e88187c7a554c5a5ce68d6618f07.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11765,0.89621]},"elements":[{"words":[{"str":"2","boundary":[0.11764705882352941,0.09001376073232323,0.12762924183006535,0.10378787689393938],"dir":"ltr"}],"boundary":[0.11765,0.09001,0.12763,0.10379],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Algorithms","boundary":[0.7899820261437909,0.08979153426128839,0.8823528696078432,0.10356565042290454],"dir":"ltr"}],"boundary":[0.78998,0.08979,0.88235,0.10357],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":2,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/1588d89455b39e56b8c00ca248b1f502.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/c3935a13679c614043cd881211157399.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.20788,0.11631,0.09318]},"elements":[{"words":[{"str":"Contents","boundary":[0.11764705882352941,0.2078834261363636,0.30711446699346406,0.23918026957070707],"dir":"ltr"}],"boundary":[0.11765,0.20788,0.30711,0.23918],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Preface","boundary":[0.11764705882352941,0.31129475189393935,0.18850273284313726,0.32506886805555546],"dir":"ltr"},{"str":"0","boundary":[0.11764705882352931,0.342961418560606,0.12782532042483652,0.3567355347222222],"dir":"ltr"},{"str":"Prologue","boundary":[0.14429591503267963,0.342961418560606,0.22846710816993457,0.3567355347222222],"dir":"ltr"},{"str":"0.1","boundary":[0.14431388888888894,0.36137739709595956,0.1691623944444445,0.3751515132575758],"dir":"ltr"},{"str":"Books","boundary":[0.18524068627450985,0.36137739709595956,0.23456336552287588,0.3751515132575758],"dir":"ltr"},{"str":"and","boundary":[0.23966127450980396,0.36137739709595956,0.27078429509803925,0.3751515132575758],"dir":"ltr"},{"str":"algorithms","boundary":[0.27568611111111113,0.36137739709595956,0.3651157756535948,0.3751515132575758],"dir":"ltr"},{"str":"0.2","boundary":[0.14431424836601275,0.3789531546717172,0.16916275392156832,0.39272727083333336],"dir":"ltr"},{"str":"Enter","boundary":[0.1852410457516337,0.3789531546717172,0.2326029390522873,0.39272727083333336],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.23770084967320232,0.3789531546717172,0.31616792696078405,0.39272727083333336],"dir":"ltr"},{"str":"0.3","boundary":[0.14431459150326725,0.3965289122474748,0.16916309705882282,0.41030302840909094],"dir":"ltr"},{"str":"Big-O","boundary":[0.1852413888888882,0.3965289122474748,0.23279939183006465,0.4160192866161616],"dir":"ltr"},{"str":"notation","boundary":[0.23828959150326726,0.3965289122474748,0.3071666542483653,0.41030302840909094],"dir":"ltr"},{"str":"Exercises","boundary":[0.144314999999999,0.41425618497474753,0.22219385277777678,0.4280303011363637],"dir":"ltr"},{"str":"1","boundary":[0.11764859477124046,0.4452341458333334,0.12782685637254765,0.45900826199494954],"dir":"ltr"},{"str":"Algorithms","boundary":[0.1442974509803908,0.4452341458333334,0.24764869575163262,0.45900826199494954],"dir":"ltr"},{"str":"with","boundary":[0.25255055555555417,0.4452341458333334,0.2948322307189529,0.45900826199494954],"dir":"ltr"},{"str":"numbers","boundary":[0.29993013071895286,0.4452341458333334,0.3811779702614365,0.45900826199494954],"dir":"ltr"},{"str":"1.1","boundary":[0.14431575163398552,0.4634986092171718,0.1691642571895411,0.47727272537878795],"dir":"ltr"},{"str":"Basic","boundary":[0.18524254901960643,0.4634986092171718,0.22985934199346267,0.47727272537878795],"dir":"ltr"},{"str":"arithmetic","boundary":[0.2347611764705868,0.4634986092171718,0.32105358349673063,0.47727272537878795],"dir":"ltr"},{"str":"1.2","boundary":[0.1443163071895407,0.48122588194444454,0.16916481274509626,0.4949999981060607],"dir":"ltr"},{"str":"Modular","boundary":[0.1852431045751616,0.48122588194444454,0.25551054281045577,0.4949999981060607],"dir":"ltr"},{"str":"arithmetic","boundary":[0.26041238562091323,0.48122588194444454,0.34670479264705706,0.4949999981060607],"dir":"ltr"},{"str":"1.3","boundary":[0.1443167973856188,0.4988016395202021,0.16916530294117438,0.5125757556818183],"dir":"ltr"},{"str":"Primality","boundary":[0.18524359477123972,0.4988016395202021,0.26429891911764497,0.5125757556818183],"dir":"ltr"},{"str":"testing","boundary":[0.2690047058823508,0.4988016395202021,0.3259387996732005,0.5125757556818183],"dir":"ltr"},{"str":"1.4","boundary":[0.14431730392156616,0.5163773970959598,0.16916580947712173,0.5301515132575759],"dir":"ltr"},{"str":"Cryptography","boundary":[0.1852441013071871,0.5163773970959598,0.2995400967320237,0.5301515132575759],"dir":"ltr"},{"str":"1.5","boundary":[0.14431763071895154,0.5341046698232325,0.16916613627450708,0.5478787859848486],"dir":"ltr"},{"str":"Universal","boundary":[0.18524442810457245,0.5341046698232325,0.26645661699346135,0.5478787859848486],"dir":"ltr"},{"str":"hashing","boundary":[0.27135848039215416,0.5341046698232325,0.3377043467320234,0.5478787859848486],"dir":"ltr"},{"str":"Exercises","boundary":[0.1443181372548989,0.55168042739899,0.22219699003267668,0.5654545435606062],"dir":"ltr"},{"str":"Randomized","boundary":[0.11765173202614045,0.582809903409091,0.233748085457513,0.5965840195707073],"dir":"ltr"},{"str":"algorithms:","boundary":[0.238453856209147,0.582809903409091,0.34414021879084633,0.5965840195707073],"dir":"ltr"},{"str":"a","boundary":[0.35021856209149993,0.582809903409091,0.35608312581699014,0.5965840195707073],"dir":"ltr"},{"str":"virtual","boundary":[0.3662791503267941,0.582809903409091,0.4300759949346372,0.5965840195707073],"dir":"ltr"},{"str":"chapter","boundary":[0.43497784313725163,0.582809903409091,0.507009988725487,0.5965840195707073],"dir":"ltr"},{"str":"2","boundary":[0.11765267973855877,0.6144765700757577,0.12783094133986597,0.6282506862373739],"dir":"ltr"},{"str":"Divide-and-conquer","boundary":[0.1443015359477091,0.6144765700757577,0.32849063774509474,0.6282506862373739],"dir":"ltr"},{"str":"algorithms","boundary":[0.3333930392156829,0.6144765700757577,0.43419526225489863,0.6282506862373739],"dir":"ltr"},{"str":"2.1","boundary":[0.1443195098039182,0.6328925486111112,0.16916801535947376,0.6466666647727273],"dir":"ltr"},{"str":"Multiplication","boundary":[0.1852463071895391,0.6328925486111112,0.30283998807189205,0.6466666647727273],"dir":"ltr"},{"str":"2.2","boundary":[0.14432008169934288,0.6504683061868689,0.16916858725489844,0.664242422348485],"dir":"ltr"},{"str":"Recurrence","boundary":[0.18524687908496382,0.6504683061868689,0.27781380114378734,0.664242422348485],"dir":"ltr"},{"str":"relations","boundary":[0.2831078267973821,0.6504683061868689,0.35588863611110766,0.664242422348485],"dir":"ltr"},{"str":"2.3","boundary":[0.14431929738561697,0.6680440637626264,0.16916780294117253,0.6818181799242425],"dir":"ltr"},{"str":"Mergesort","boundary":[0.18524609477123788,0.6680440637626264,0.2688112267973817,0.6818181799242425],"dir":"ltr"},{"str":"2.4","boundary":[0.14431941176470164,0.6857713364898992,0.1691679173202572,0.6995454526515154],"dir":"ltr"},{"str":"Medians","boundary":[0.18524620915032255,0.6857713364898992,0.25590580457515916,0.6995454526515154],"dir":"ltr"},{"str":"2.5","boundary":[0.14431941176470145,0.7033470940656568,0.16916791732025702,0.7171212102272728],"dir":"ltr"},{"str":"Matrix","boundary":[0.18524620915032236,0.7033470940656568,0.24200204967319822,0.7171212102272728],"dir":"ltr"},{"str":"multiplication","boundary":[0.24690388888888445,0.7033470940656568,0.3635171767973812,0.7171212102272728],"dir":"ltr"},{"str":"2.6","boundary":[0.14431862745097554,0.7209228516414142,0.16916713300653108,0.7346969678030304],"dir":"ltr"},{"str":"The","boundary":[0.18524542483659645,0.7209228516414142,0.21695668120914546,0.7346969678030304],"dir":"ltr"},{"str":"fast","boundary":[0.22185849673202127,0.7209228516414142,0.252767613398688,0.7346969678030304],"dir":"ltr"},{"str":"Fourier","boundary":[0.2578656862745049,0.7209228516414142,0.318721374019603,0.7346969678030304],"dir":"ltr"},{"str":"transform","boundary":[0.323819297385616,0.7209228516414142,0.40601187924836113,0.7346969678030304],"dir":"ltr"},{"str":"Exercises","boundary":[0.14431787581698807,0.7386501243686869,0.22219672859476586,0.7524242405303031],"dir":"ltr"},{"str":"3","boundary":[0.11765147058822964,0.7696280852272728,0.12782973218953683,0.7834022013888889],"dir":"ltr"},{"str":"Decompositions","boundary":[0.14430032679737997,0.7696280852272728,0.2920901112745041,0.7834022013888889],"dir":"ltr"},{"str":"of","boundary":[0.29679575163398125,0.7696280852272728,0.3146032531045695,0.7834022013888889],"dir":"ltr"},{"str":"graphs","boundary":[0.3197013071895368,0.7696280852272728,0.3837120557189486,0.7834022013888889],"dir":"ltr"},{"str":"3.1","boundary":[0.14431732026143215,0.7880440637626264,0.16916582581698772,0.8018181799242424],"dir":"ltr"},{"str":"Why","boundary":[0.1852441176470531,0.7880440637626264,0.22322988905228186,0.8018181799242424],"dir":"ltr"},{"str":"graphs?","boundary":[0.22813169934639949,0.7880440637626264,0.29271285833332755,0.8018181799242424],"dir":"ltr"},{"str":"3.2","boundary":[0.14431732026143188,0.8056198213383838,0.16916582581698744,0.8193939375],"dir":"ltr"},{"str":"Depth-\u0002rst","boundary":[0.18524411764705281,0.8056198213383838,0.2756541751633927,0.8193939375],"dir":"ltr"},{"str":"search","boundary":[0.28094820261437303,0.8056198213383838,0.32927257026143186,0.8193939375],"dir":"ltr"},{"str":"in","boundary":[0.3394685947712358,0.8056198213383838,0.3560996246731966,0.8193939375],"dir":"ltr"},{"str":"undirected","boundary":[0.36080552287581097,0.8056198213383838,0.44886263725489595,0.8193939375],"dir":"ltr"},{"str":"graphs","boundary":[0.4539605882352881,0.8056198213383838,0.5107164287581639,0.8193939375],"dir":"ltr"},{"str":"3.3","boundary":[0.14431717320260817,0.8231955789141415,0.16916567875816374,0.8369696950757577],"dir":"ltr"},{"str":"Depth-\u0002rst","boundary":[0.18524397058822908,0.8231955789141415,0.27565402810456896,0.8369696950757577],"dir":"ltr"},{"str":"search","boundary":[0.28094805555554936,0.8231955789141415,0.3292724232026082,0.8369696950757577],"dir":"ltr"},{"str":"in","boundary":[0.3394684477124121,0.8231955789141415,0.3560994776143729,0.8369696950757577],"dir":"ltr"},{"str":"directed","boundary":[0.36080537581698724,0.8231955789141415,0.42693733823528796,0.8369696950757577],"dir":"ltr"},{"str":"graphs","boundary":[0.43223135620914416,0.8231955789141415,0.48898719673201996,0.8369696950757577],"dir":"ltr"},{"str":"3.4","boundary":[0.14431707516339218,0.8409228516414142,0.16916558071894774,0.8546969678030303],"dir":"ltr"},{"str":"Strongly","boundary":[0.1852438725490131,0.8409228516414142,0.25568956405228105,0.8546969678030303],"dir":"ltr"},{"str":"connected","boundary":[0.26078749999999346,0.8409228516414142,0.34180361029411116,0.8546969678030303],"dir":"ltr"},{"str":"components","boundary":[0.3470976307189477,0.8409228516414142,0.444370439052281,0.8546969678030303],"dir":"ltr"},{"str":"Exercises","boundary":[0.14431661764705178,0.8584986092171719,0.22219547042482957,0.872272725378788],"dir":"ltr"},{"str":"3","boundary":[0.4951011764705809,0.8930440637626264,0.5050833594771169,0.9068181799242424],"dir":"ltr"}],"boundary":[0.11765,0.31129,0.51072,0.90682],"dir":"ltr","type":"paragraph"},{"words":[{"str":"9","boundary":[0.872032679738562,0.31129475189393935,0.8822109413398692,0.32506886805555546],"dir":"ltr"},{"str":"11","boundary":[0.861800816993464,0.342961418560606,0.8821573401960784,0.3567355347222222],"dir":"ltr"},{"str":"11","boundary":[0.8615495424836603,0.36137739709595956,0.8815139084967323,0.3751515132575758],"dir":"ltr"},{"str":"12","boundary":[0.861567859477124,0.3789531546717172,0.881532225490196,0.39272727083333336],"dir":"ltr"},{"str":"15","boundary":[0.8615682679738556,0.3965289122474748,0.8815326339869276,0.41030302840909094],"dir":"ltr"},{"str":"18","boundary":[0.8615865032679729,0.41425618497474753,0.8815508692810449,0.4280303011363637],"dir":"ltr"},{"str":"21","boundary":[0.8615706535947698,0.4452341458333334,0.8819271767973842,0.45900826199494954],"dir":"ltr"},{"str":"21","boundary":[0.8615516013071882,0.4634986092171718,0.8815159673202603,0.47727272537878795],"dir":"ltr"},{"str":"25","boundary":[0.8615520915032664,0.48122588194444454,0.8815164575163383,0.4949999981060607],"dir":"ltr"},{"str":"33","boundary":[0.8615525980392138,0.4988016395202021,0.8815169640522857,0.5125757556818183],"dir":"ltr"},{"str":"39","boundary":[0.8615888725490173,0.5163773970959598,0.8815532385620892,0.5301515132575759],"dir":"ltr"},{"str":"43","boundary":[0.8615534313725465,0.5341046698232325,0.8815177973856184,0.5478787859848486],"dir":"ltr"},{"str":"48","boundary":[0.8615896405228729,0.55168042739899,0.8815540065359448,0.5654545435606062],"dir":"ltr"},{"str":"39","boundary":[0.8613242483660097,0.582809903409091,0.8816807715686241,0.5965840195707073],"dir":"ltr"},{"str":"55","boundary":[0.8614502287581666,0.6144765700757577,0.881806751960781,0.6282506862373739],"dir":"ltr"},{"str":"55","boundary":[0.8615553758169903,0.6328925486111112,0.8815197418300622,0.6466666647727273],"dir":"ltr"},{"str":"58","boundary":[0.8615382516339837,0.6504683061868689,0.8815026176470556,0.664242422348485],"dir":"ltr"},{"str":"60","boundary":[0.8615906535947674,0.6680440637626264,0.8815550196078393,0.6818181799242425],"dir":"ltr"},{"str":"64","boundary":[0.8616086274509763,0.6857713364898992,0.8815729934640483,0.6995454526515154],"dir":"ltr"},{"str":"66","boundary":[0.861519607843133,0.7033470940656568,0.8814839738562049,0.7171212102272728],"dir":"ltr"},{"str":"68","boundary":[0.8615188562091456,0.7209228516414142,0.8814832222222175,0.7346969678030304],"dir":"ltr"},{"str":"83","boundary":[0.861589379084962,0.7386501243686869,0.8815537450980341,0.7524242405303031],"dir":"ltr"},{"str":"91","boundary":[0.8615542483660074,0.7696280852272728,0.8819107715686217,0.7834022013888889],"dir":"ltr"},{"str":"91","boundary":[0.8616065359477068,0.7880440637626264,0.8815709019607787,0.8018181799242424],"dir":"ltr"},{"str":"93","boundary":[0.861464232026138,0.8056198213383838,0.8814285980392099,0.8193939375],"dir":"ltr"},{"str":"98","boundary":[0.8614641339869221,0.8231955789141415,0.8814284999999942,0.8369696950757577],"dir":"ltr"},{"str":"101","boundary":[0.8536564869280983,0.8409228516414142,0.8836030359477061,0.8546969678030303],"dir":"ltr"},{"str":"106","boundary":[0.8537449673202546,0.8584986092171719,0.8836915163398624,0.872272725378788],"dir":"ltr"}],"boundary":[0.85366,0.31129,0.88369,0.87227],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":3,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/cdfd93093eab09b7a01725af5f9359a7.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/bce288d4f863691ac96b10f653d218a3.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11629,0.12773]},"elements":[{"words":[{"str":"4","boundary":[0.11764705882352941,0.09001376073232323,0.12762924183006535,0.10378787689393938],"dir":"ltr"},{"str":"4","boundary":[0.11764705882352941,0.12811293371212124,0.1278253204248366,0.1418870498737374],"dir":"ltr"},{"str":"Paths","boundary":[0.14429591503267974,0.12811293371212124,0.19636368267973855,0.1418870498737374],"dir":"ltr"},{"str":"in","boundary":[0.20146174836601308,0.12811293371212124,0.2202496428104575,0.1418870498737374],"dir":"ltr"},{"str":"graphs","boundary":[0.2253476960784314,0.12811293371212124,0.2893584446078431,0.1418870498737374],"dir":"ltr"},{"str":"4.1","boundary":[0.14431501633986926,0.1469834577020202,0.16916352189542483,0.16075757386363637],"dir":"ltr"},{"str":"Distances","boundary":[0.18524181372549017,0.1469834577020202,0.26566968823529413,0.16075757386363637],"dir":"ltr"},{"str":"4.2","boundary":[0.14431522875816946,0.16516527588383836,0.16916373431372503,0.1789393920454545],"dir":"ltr"},{"str":"Breadth-\u0002rst","boundary":[0.1852420261437904,0.16516527588383836,0.29247919215686224,0.1789393920454545],"dir":"ltr"},{"str":"search","boundary":[0.29757715686274466,0.16516527588383836,0.34452894281045704,0.1789393920454545],"dir":"ltr"},{"str":"4.3","boundary":[0.14431436274509715,0.18319557891414134,0.16916286830065272,0.1969696950757575],"dir":"ltr"},{"str":"Lengths","boundary":[0.1852411601307181,0.18319557891414134,0.25256741944444355,0.1969696950757575],"dir":"ltr"},{"str":"on","boundary":[0.2574692647058815,0.18319557891414134,0.2772375521241821,0.1969696950757575],"dir":"ltr"},{"str":"edges","boundary":[0.28213936274509716,0.18319557891414134,0.32773654869280955,0.1969696950757575],"dir":"ltr"},{"str":"4.4","boundary":[0.14431439542483526,0.2013773970959595,0.16916290098039083,0.21515151325757567],"dir":"ltr"},{"str":"Dijkstra's","boundary":[0.1852411928104562,0.2013773970959595,0.26016102973856076,0.21515151325757567],"dir":"ltr"},{"str":"algorithm","boundary":[0.2699648039215673,0.2013773970959595,0.3511769928104562,0.21515151325757567],"dir":"ltr"},{"str":"4.5","boundary":[0.14431364379084782,0.21955921527777766,0.1691621493464034,0.2333333314393938],"dir":"ltr"},{"str":"Priority","boundary":[0.18524044117646873,0.21955921527777766,0.249411617647057,0.2333333314393938],"dir":"ltr"},{"str":"queue","boundary":[0.25450955882352755,0.21955921527777766,0.3040283166666648,0.2333333314393938],"dir":"ltr"},{"str":"implementations","boundary":[0.30893014705882166,0.21955921527777766,0.4480746480392138,0.2333333314393938],"dir":"ltr"},{"str":"4.6","boundary":[0.14431318627450734,0.23774103345959582,0.1691616918300629,0.25151514962121196],"dir":"ltr"},{"str":"Shortest","boundary":[0.18523998366012825,0.23774103345959582,0.2547052821895401,0.25151514962121196],"dir":"ltr"},{"str":"paths","boundary":[0.26019537581699104,0.23774103345959582,0.30638079754901715,0.25151514962121196],"dir":"ltr"},{"str":"in","boundary":[0.3112826307189518,0.23774103345959582,0.3279136606209126,0.25151514962121196],"dir":"ltr"},{"str":"the","boundary":[0.33261955882352695,0.23774103345959582,0.3592327717320237,0.25151514962121196],"dir":"ltr"},{"str":"presence","boundary":[0.3643308333333309,0.23774103345959582,0.43575691781045506,0.25151514962121196],"dir":"ltr"},{"str":"of","boundary":[0.4410509313725466,0.23774103345959582,0.45062311862744847,0.25151514962121196],"dir":"ltr"},{"str":"negative","boundary":[0.46081923202614133,0.23774103345959582,0.5310688449346381,0.25151514962121196],"dir":"ltr"},{"str":"edges","boundary":[0.5359707026143766,0.23774103345959582,0.5815678885620892,0.25151514962121196],"dir":"ltr"},{"str":"4.7","boundary":[0.14431352941176193,0.255922851641414,0.1691620349673175,0.2696969678030301],"dir":"ltr"},{"str":"Shortest","boundary":[0.18524032679738286,0.255922851641414,0.25470562532679464,0.2696969678030301],"dir":"ltr"},{"str":"paths","boundary":[0.26019571895424565,0.255922851641414,0.30638114068627176,0.2696969678030301],"dir":"ltr"},{"str":"in","boundary":[0.3112829738562064,0.255922851641414,0.3279140037581672,0.2696969678030301],"dir":"ltr"},{"str":"dags","boundary":[0.33261990196078156,0.255922851641414,0.37058784803921296,0.2696969678030301],"dir":"ltr"},{"str":"Exercises","boundary":[0.14431406862744758,0.2741046698232321,0.22219292140522537,0.2878787859848483],"dir":"ltr"},{"str":"5","boundary":[0.11764764705881982,0.3059917215909088,0.12782590866012702,0.319765837752525],"dir":"ltr"},{"str":"Greedy","boundary":[0.14429650326797014,0.3059917215909088,0.21164058790849302,0.319765837752525],"dir":"ltr"},{"str":"algorithms","boundary":[0.21673849673202242,0.3059917215909088,0.3175407197712381,0.319765837752525],"dir":"ltr"},{"str":"5.1","boundary":[0.14431529411764338,0.32486224558080784,0.16916379967319892,0.338636361742424],"dir":"ltr"},{"str":"Minimum","boundary":[0.1852420915032643,0.32486224558080784,0.2670781668300617,0.338636361742424],"dir":"ltr"},{"str":"spanning","boundary":[0.2717839215686238,0.32486224558080784,0.34830804950980027,0.338636361742424],"dir":"ltr"},{"str":"trees","boundary":[0.35281774509803554,0.32486224558080784,0.3933168875816957,0.338636361742424],"dir":"ltr"},{"str":"5.2","boundary":[0.14431581699345977,0.343044063762626,0.16916432254901534,0.3568181799242422],"dir":"ltr"},{"str":"Huffman","boundary":[0.1852426143790807,0.343044063762626,0.2596277031045709,0.3568181799242422],"dir":"ltr"},{"str":"encoding","boundary":[0.26433346405228336,0.343044063762626,0.3371320986928062,0.3568181799242422],"dir":"ltr"},{"str":"5.3","boundary":[0.14431625816993,0.3612258819444441,0.16916476372548556,0.37499999810606033],"dir":"ltr"},{"str":"Horn","boundary":[0.18524305555555093,0.3612258819444441,0.22772080931372088,0.37499999810606033],"dir":"ltr"},{"str":"formulas","boundary":[0.23281887254901498,0.3612258819444441,0.30600966437908034,0.37499999810606033],"dir":"ltr"},{"str":"5.4","boundary":[0.14431656862744602,0.3792561849747471,0.16916507418300158,0.39303030113636334],"dir":"ltr"},{"str":"Set","boundary":[0.18524336601306693,0.3792561849747471,0.21205265751633492,0.39303030113636334],"dir":"ltr"},{"str":"cover","boundary":[0.21734663398692314,0.3792561849747471,0.2601987196078382,0.39303030113636334],"dir":"ltr"},{"str":"Exercises","boundary":[0.14431637254901422,0.3974380031565653,0.222195225326792,0.41121211931818147],"dir":"ltr"},{"str":"6","boundary":[0.11764995098038634,0.42947657007575724,0.12782821258169355,0.4432506862373734],"dir":"ltr"},{"str":"Dynamic","boundary":[0.14429880718953667,0.42947657007575724,0.22711527549019028,0.4432506862373734],"dir":"ltr"},{"str":"programming","boundary":[0.23182102941175892,0.42947657007575724,0.3592721160130661,0.4432506862373734],"dir":"ltr"},{"str":"6.1","boundary":[0.1443161274509747,0.448195578914141,0.16916463300653026,0.4619696950757572],"dir":"ltr"},{"str":"Shortest","boundary":[0.1852429248365956,0.448195578914141,0.2547082233660074,0.4619696950757572],"dir":"ltr"},{"str":"paths","boundary":[0.26019831699345836,0.448195578914141,0.3063837387254845,0.4619696950757572],"dir":"ltr"},{"str":"in","boundary":[0.31128557189541917,0.448195578914141,0.32791660179737997,0.4619696950757572],"dir":"ltr"},{"str":"dags","boundary":[0.3326224999999943,0.448195578914141,0.37059044607842573,0.4619696950757572],"dir":"ltr"},{"str":"revisited","boundary":[0.37998436274509234,0.448195578914141,0.45158870049019034,0.4619696950757572],"dir":"ltr"},{"str":"6.2","boundary":[0.1443158496731964,0.46637739709595916,0.16916435522875198,0.4801515132575754],"dir":"ltr"},{"str":"Longest","boundary":[0.18524264705881732,0.46637739709595916,0.25041204183005916,0.4801515132575754],"dir":"ltr"},{"str":"increasing","boundary":[0.2555099673202552,0.46637739709595916,0.3410180599673141,0.4801515132575754],"dir":"ltr"},{"str":"subsequences","boundary":[0.34572385620914414,0.46637739709595916,0.45747082990195465,0.4801515132575754],"dir":"ltr"},{"str":"6.3","boundary":[0.14431558823528745,0.48455921527777734,0.16916409379084302,0.4983333314393935],"dir":"ltr"},{"str":"Edit","boundary":[0.18524238562090836,0.48455921527777734,0.22085738856208487,0.4983333314393935],"dir":"ltr"},{"str":"distance","boundary":[0.22595545751633322,0.48455921527777734,0.2944403630718888,0.4983333314393935],"dir":"ltr"},{"str":"6.4","boundary":[0.14431602941175767,0.5027410334595955,0.16916453496731323,0.5165151496212117],"dir":"ltr"},{"str":"Knapsack","boundary":[0.18524282679737858,0.5027410334595955,0.258825821241823,0.5165151496212117],"dir":"ltr"},{"str":"6.5","boundary":[0.14431583333332595,0.5209228516414136,0.16916433888888152,0.5346969678030298],"dir":"ltr"},{"str":"Chain","boundary":[0.18524263071894687,0.5209228516414136,0.23574178153594033,0.5346969678030298],"dir":"ltr"},{"str":"matrix","boundary":[0.2404475326797312,0.5209228516414136,0.2962229802287508,0.5346969678030298],"dir":"ltr"},{"str":"multiplication","boundary":[0.300928741830058,0.5209228516414136,0.41754202973855475,0.5346969678030298],"dir":"ltr"},{"str":"6.6","boundary":[0.14431532679737777,0.5391046698232318,0.1691638323529333,0.552878785984848],"dir":"ltr"},{"str":"Shortest","boundary":[0.18524212418299868,0.5391046698232318,0.2547074227124105,0.552878785984848],"dir":"ltr"},{"str":"paths","boundary":[0.26019751633986143,0.5391046698232318,0.3063829380718876,0.552878785984848],"dir":"ltr"},{"str":"6.7","boundary":[0.14431563725489369,0.5571349728535347,0.16916414281044925,0.570909089015151],"dir":"ltr"},{"str":"Independent","boundary":[0.1852424346405146,0.5571349728535347,0.2891640898692728,0.570909089015151],"dir":"ltr"},{"str":"sets","boundary":[0.29445812091502443,0.5571349728535347,0.32654370915031855,0.570909089015151],"dir":"ltr"},{"str":"in","boundary":[0.3316416176470506,0.5571349728535347,0.3482726475490114,0.570909089015151],"dir":"ltr"},{"str":"trees","boundary":[0.35297854575162574,0.5571349728535347,0.3934776882352859,0.570909089015151],"dir":"ltr"},{"str":"Exercises","boundary":[0.14431490196077557,0.5753167910353529,0.22219375473855335,0.5890909071969691],"dir":"ltr"},{"str":"7","boundary":[0.1176484803921477,0.6073553579545449,0.1278267419934549,0.621129474116161],"dir":"ltr"},{"str":"Linear","boundary":[0.14429733660129804,0.6073553579545449,0.20634729918299738,0.621129474116161],"dir":"ltr"},{"str":"programming","boundary":[0.21144521241829145,0.6073553579545449,0.33889629901959867,0.621129474116161],"dir":"ltr"},{"str":"and","boundary":[0.34340599673201694,0.6073553579545449,0.3784505892156771,0.621129474116161],"dir":"ltr"},{"str":"reductions","boundary":[0.38354864379084047,0.6073553579545449,0.48317439526142875,0.621129474116161],"dir":"ltr"},{"str":"7.1","boundary":[0.1443149836601214,0.6260743667929287,0.16916348921567695,0.6398484829545449],"dir":"ltr"},{"str":"An","boundary":[0.18524178104574232,0.6260743667929287,0.20912771895423907,0.6398484829545449],"dir":"ltr"},{"str":"introduction","boundary":[0.21402952614378154,0.6260743667929287,0.31538433431371615,0.6398484829545449],"dir":"ltr"},{"str":"to","boundary":[0.3204823039215593,0.6260743667929287,0.3361329408496639,0.6398484829545449],"dir":"ltr"},{"str":"linear","boundary":[0.34123099673201684,0.6260743667929287,0.39014369346404304,0.6398484829545449],"dir":"ltr"},{"str":"programming","boundary":[0.39484946078430444,0.6260743667929287,0.5070064169934548,0.6398484829545449],"dir":"ltr"},{"str":"7.2","boundary":[0.14431472222221253,0.6442561849747468,0.1691632277777681,0.658030301136363],"dir":"ltr"},{"str":"Flows","boundary":[0.18524151960783347,0.6442561849747468,0.2337798844771145,0.658030301136363],"dir":"ltr"},{"str":"in","boundary":[0.23868171568626484,0.6442561849747468,0.25531274558822564,0.658030301136363],"dir":"ltr"},{"str":"networks","boundary":[0.26021455882351974,0.6442561849747468,0.3361504509803825,0.658030301136363],"dir":"ltr"},{"str":"7.3","boundary":[0.14431496732025131,0.662438003156565,0.16916347287580688,0.6762121193181811],"dir":"ltr"},{"str":"Bipartite","boundary":[0.18524176470587225,0.662438003156565,0.2599833599673102,0.6762121193181811],"dir":"ltr"},{"str":"matching","boundary":[0.2650813071895324,0.662438003156565,0.3425858539215585,0.6762121193181811],"dir":"ltr"},{"str":"7.4","boundary":[0.14431393790848623,0.6806198213383833,0.1691624434640418,0.6943939374999994],"dir":"ltr"},{"str":"Duality","boundary":[0.18524073529410717,0.6806198213383833,0.2478611083333228,0.6943939374999994],"dir":"ltr"},{"str":"7.5","boundary":[0.14431392156861672,0.6988016395202015,0.1691624271241723,0.7125757556818175],"dir":"ltr"},{"str":"Zero-sum","boundary":[0.18524071895423766,0.6988016395202015,0.26254916127449907,0.7125757556818175],"dir":"ltr"},{"str":"games","boundary":[0.2676470915032572,0.6988016395202015,0.3201070282679631,0.7125757556818175],"dir":"ltr"},{"str":"7.6","boundary":[0.14431405228757047,0.7169834577020195,0.16916255784312603,0.7307575738636357],"dir":"ltr"},{"str":"The","boundary":[0.18524084967319138,0.7169834577020195,0.2169521060457404,0.7307575738636357],"dir":"ltr"},{"str":"simplex","boundary":[0.2218539215686162,0.7169834577020195,0.28584684477123057,0.7307575738636357],"dir":"ltr"},{"str":"algorithm","boundary":[0.2907486928104463,0.7169834577020195,0.37196088169933517,0.7307575738636357],"dir":"ltr"},{"str":"7.7","boundary":[0.1443145915032562,0.7350137607323226,0.16916309705881177,0.7487878768939387],"dir":"ltr"},{"str":"Postscript:","boundary":[0.18524138888887712,0.7350137607323226,0.2719081331699229,0.7487878768939387],"dir":"ltr"},{"str":"circuit","boundary":[0.27837864379083793,0.7350137607323226,0.33099900849672026,0.7487878768939387],"dir":"ltr"},{"str":"evaluation","boundary":[0.33609694444443267,0.7350137607323226,0.4233697444444327,0.7487878768939387],"dir":"ltr"},{"str":"Exercises","boundary":[0.14431450980390917,0.7531955789141409,0.22219336258168695,0.766969695075757],"dir":"ltr"},{"str":"8","boundary":[0.1176480882352813,0.7852341458333326,0.1278263498365885,0.7990082619949488],"dir":"ltr"},{"str":"NP-complete","boundary":[0.14429694444443164,0.7852341458333326,0.262924494281033,0.7990082619949488],"dir":"ltr"},{"str":"problems","boundary":[0.26782635620913753,0.7852341458333326,0.3539583352941048,0.7990082619949488],"dir":"ltr"},{"str":"8.1","boundary":[0.14431491830064072,0.8039531546717166,0.1691634238561963,0.8177272708333326],"dir":"ltr"},{"str":"Search","boundary":[0.18524171568626166,0.8039531546717166,0.23631119771240544,0.8177272708333326],"dir":"ltr"},{"str":"problems","boundary":[0.24689934640521594,0.8039531546717166,0.32224700277776497,0.8177272708333326],"dir":"ltr"},{"str":"8.2","boundary":[0.14431521241828751,0.8221349728535348,0.16916371797384308,0.8359090890151508],"dir":"ltr"},{"str":"NP-complete","boundary":[0.18524200980390843,0.8221349728535348,0.2903401366012941,0.8359090890151508],"dir":"ltr"},{"str":"problems","boundary":[0.29563416666665354,0.8221349728535348,0.3709818230392026,0.8359090890151508],"dir":"ltr"},{"str":"8.3","boundary":[0.14431424836599957,0.840316791035353,0.16916275392155514,0.8540909071969691],"dir":"ltr"},{"str":"The","boundary":[0.18524104575162048,0.840316791035353,0.21695230212416952,0.8540909071969691],"dir":"ltr"},{"str":"reductions","boundary":[0.22185411764704532,0.840316791035353,0.30795044607841787,0.8540909071969691],"dir":"ltr"},{"str":"Exercises","boundary":[0.1443145098039076,0.8584986092171711,0.22219336258168537,0.8722727253787873],"dir":"ltr"}],"boundary":[0.11765,0.09001,0.58157,0.87227],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Algorithms","boundary":[0.7899820261437909,0.08979153426128839,0.8823528696078432,0.10356565042290454],"dir":"ltr"},{"str":"115","boundary":[0.8513199183006536,0.12811293371212124,0.8818547031045751,0.1418870498737374],"dir":"ltr"},{"str":"115","boundary":[0.8537433333333334,0.1469834577020202,0.8836898823529412,0.16075757386363637],"dir":"ltr"},{"str":"116","boundary":[0.8536901797385618,0.16516527588383836,0.8836367287581695,0.1789393920454545],"dir":"ltr"},{"str":"118","boundary":[0.8537424999999991,0.18319557891414134,0.8836890490196069,0.1969696950757575],"dir":"ltr"},{"str":"119","boundary":[0.8536714869281035,0.2013773970959595,0.8836180359477113,0.21515151325757567],"dir":"ltr"},{"str":"126","boundary":[0.8536350816993448,0.21955921527777766,0.8835816307189525,0.2333333314393938],"dir":"ltr"},{"str":"128","boundary":[0.8535815032679714,0.23774103345959582,0.8835280522875792,0.25151514962121196],"dir":"ltr"},{"str":"130","boundary":[0.8537062254901935,0.255922851641414,0.8836527745098013,0.2696969678030301],"dir":"ltr"},{"str":"132","boundary":[0.8537424183006502,0.2741046698232321,0.883688967320258,0.2878787859848483],"dir":"ltr"},{"str":"139","boundary":[0.8512662745098002,0.3059917215909088,0.8818010593137218,0.319765837752525],"dir":"ltr"},{"str":"139","boundary":[0.8537079738562057,0.32486224558080784,0.8836545228758135,0.338636361742424],"dir":"ltr"},{"str":"153","boundary":[0.8537263888888847,0.343044063762626,0.8836729379084926,0.3568181799242422],"dir":"ltr"},{"str":"157","boundary":[0.8537446732026098,0.3612258819444441,0.8836912222222176,0.37499999810606033],"dir":"ltr"},{"str":"158","boundary":[0.8537624509803873,0.3792561849747471,0.8837089999999951,0.39303030113636334],"dir":"ltr"},{"str":"161","boundary":[0.853744722222217,0.3974380031565653,0.8836912712418248,0.41121211931818147],"dir":"ltr"},{"str":"169","boundary":[0.8512327941176413,0.42947657007575724,0.8817675789215629,0.4432506862373734],"dir":"ltr"},{"str":"169","boundary":[0.8536377450980338,0.448195578914141,0.8835842941176415,0.4619696950757572],"dir":"ltr"},{"str":"170","boundary":[0.8536374836601246,0.46637739709595916,0.8835840326797324,0.4801515132575754],"dir":"ltr"},{"str":"174","boundary":[0.8537261601307125,0.48455921527777734,0.8836727091503203,0.4983333314393935],"dir":"ltr"},{"str":"181","boundary":[0.8537619117646991,0.5027410334595955,0.8837084607843068,0.5165151496212117],"dir":"ltr"},{"str":"184","boundary":[0.8536551960784242,0.5209228516414136,0.883601745098032,0.5346969678030298],"dir":"ltr"},{"str":"186","boundary":[0.8537257679738485,0.5391046698232318,0.8836723169934563,0.552878785984848],"dir":"ltr"},{"str":"189","boundary":[0.8536727450980313,0.5571349728535347,0.883619294117639,0.570909089015151],"dir":"ltr"},{"str":"191","boundary":[0.8537432516339784,0.5753167910353529,0.8836898006535862,0.5890909071969691],"dir":"ltr"},{"str":"201","boundary":[0.8510175980392064,0.6073553579545449,0.8815523828431279,0.621129474116161],"dir":"ltr"},{"str":"201","boundary":[0.8536366176470497,0.6260743667929287,0.8835831666666575,0.6398484829545449],"dir":"ltr"},{"str":"211","boundary":[0.8537250980392062,0.6442561849747468,0.8836716470588138,0.658030301136363],"dir":"ltr"},{"str":"219","boundary":[0.85370772875816,0.662438003156565,0.8836542777777677,0.6762121193181811],"dir":"ltr"},{"str":"220","boundary":[0.8537599999999896,0.6806198213383833,0.8837065490195974,0.6943939374999994],"dir":"ltr"},{"str":"224","boundary":[0.8537421568627346,0.6988016395202015,0.8836887058823424,0.7125757556818175],"dir":"ltr"},{"str":"227","boundary":[0.8537067483660021,0.7169834577020195,0.8836532973856098,0.7307575738636357],"dir":"ltr"},{"str":"236","boundary":[0.8536184313725373,0.7350137607323226,0.8835649803921451,0.7487878768939387],"dir":"ltr"},{"str":"239","boundary":[0.8537428594771119,0.7531955789141409,0.8836894084967197,0.766969695075757],"dir":"ltr"},{"str":"247","boundary":[0.8512136111110983,0.7852341458333326,0.8817483959150197,0.7990082619949488],"dir":"ltr"},{"str":"247","boundary":[0.8537253431372424,0.8039531546717166,0.88367189215685,0.8177272708333326],"dir":"ltr"},{"str":"257","boundary":[0.8537080392156733,0.8221349728535348,0.8836545882352811,0.8359090890151508],"dir":"ltr"},{"str":"262","boundary":[0.8537246405228623,0.840316791035353,0.8836711895424701,0.8540909071969691],"dir":"ltr"},{"str":"278","boundary":[0.8537428594771105,0.8584986092171711,0.8836894084967182,0.8722727253787873],"dir":"ltr"}],"boundary":[0.78998,0.08979,0.88371,0.87227],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":4,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/dad94edd0cb15f276cbdeb142f426bfc.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/560b2209826c4362b54a1e34737aec83.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11629,0.56023]},"elements":[{"words":[{"str":"S","boundary":[0.11764705882352941,0.08979153426128839,0.1293939594771242,0.10356565042290454],"dir":"ltr"},{"str":"Dasgupta,","boundary":[0.13800351307189543,0.08979153426128839,0.2225490380718954,0.10356565042290454],"dir":"ltr"},{"str":"C.H.","boundary":[0.22745089869281046,0.08979153426128839,0.26443845637254904,0.10356565042290454],"dir":"ltr"},{"str":"Papadimitriou,","boundary":[0.2693402777777778,0.08979153426128839,0.3932084790849673,0.10356565042290454],"dir":"ltr"},{"str":"and","boundary":[0.39771821895424836,0.08979153426128839,0.42884123954248365,0.10356565042290454],"dir":"ltr"},{"str":"U.V","boundary":[0.43374305555555553,0.08979153426128839,0.4664347251633986,0.10356565042290454],"dir":"ltr"},{"str":"Vazirani","boundary":[0.47190697712418295,0.08979153426128839,0.5419605168300654,0.10356565042290454],"dir":"ltr"},{"str":"9","boundary":[0.11764705882352941,0.12811293371212124,0.1278253204248366,0.1418870498737374],"dir":"ltr"},{"str":"Coping","boundary":[0.14429591503267974,0.12811293371212124,0.21085568529411766,0.1418870498737374],"dir":"ltr"},{"str":"with","boundary":[0.21575751633986928,0.12811293371212124,0.25803919150326793,0.1418870498737374],"dir":"ltr"},{"str":"NP-completeness","boundary":[0.2629410130718954,0.12811293371212124,0.4214972949346405,0.1418870498737374],"dir":"ltr"},{"str":"9.1","boundary":[0.1443135620915033,0.1459228516414141,0.16916206764705885,0.15969696780303025],"dir":"ltr"},{"str":"Intelligent","boundary":[0.18524035947712422,0.1459228516414141,0.2722992555555556,0.15969696780303025],"dir":"ltr"},{"str":"exhaustive","boundary":[0.2772011437908497,0.1459228516414141,0.3666308083333334,0.15969696780303025],"dir":"ltr"},{"str":"search","boundary":[0.37153267973856213,0.1459228516414141,0.4249550596405229,0.15969696780303025],"dir":"ltr"},{"str":"9.2","boundary":[0.1443133169934635,0.16304406376262615,0.16916182254901904,0.1768181799242423],"dir":"ltr"},{"str":"Approximation","boundary":[0.18524011437908441,0.16304406376262615,0.3085378998366008,0.1768181799242423],"dir":"ltr"},{"str":"algorithms","boundary":[0.3134397875816988,0.16304406376262615,0.40286945212418246,0.1768181799242423],"dir":"ltr"},{"str":"9.3","boundary":[0.14431277777777682,0.1801652758838382,0.16916128333333239,0.19393939204545435],"dir":"ltr"},{"str":"Local","boundary":[0.18523957516339773,0.1801652758838382,0.22946421094771147,0.19393939204545435],"dir":"ltr"},{"str":"search","boundary":[0.23436604575163306,0.1801652758838382,0.2826904133986919,0.19393939204545435],"dir":"ltr"},{"str":"heuristics","boundary":[0.2928864379084958,0.1801652758838382,0.3738847228758161,0.19393939204545435],"dir":"ltr"},{"str":"Exercises","boundary":[0.14431197712418148,0.19728648800505025,0.22219082990195924,0.21106060416666642],"dir":"ltr"},{"str":"10","boundary":[0.11764555555555359,0.22735535795454523,0.13800207875816797,0.24112947411616137],"dir":"ltr"},{"str":"Quantum","boundary":[0.14427660130718759,0.22735535795454523,0.23140679869280853,0.24112947411616137],"dir":"ltr"},{"str":"algorithms","boundary":[0.236504705882351,0.22735535795454523,0.33730692892156666,0.24112947411616137],"dir":"ltr"},{"str":"10.1","boundary":[0.14431189542483472,0.24516527588383807,0.17914258398692623,0.25893939204545424],"dir":"ltr"},{"str":"Qubits","boundary":[0.1852210457516321,0.24516527588383807,0.24080041470588048,0.25893939204545424],"dir":"ltr"},{"str":"superposition,","boundary":[0.25019418300653407,0.24516527588383807,0.3662192351307171,0.25893939204545424],"dir":"ltr"},{"str":"and","boundary":[0.3713172222222203,0.24516527588383807,0.4024402428104556,0.25893939204545424],"dir":"ltr"},{"str":"measurement","boundary":[0.40734205882352753,0.24516527588383807,0.5202833294117628,0.25893939204545424],"dir":"ltr"},{"str":"10.2","boundary":[0.14431220588235064,0.26228648800505017,0.17914289444444215,0.2760606041666663],"dir":"ltr"},{"str":"The","boundary":[0.18522135620914804,0.26228648800505017,0.21693261258169705,0.2760606041666663],"dir":"ltr"},{"str":"plan","boundary":[0.22183442810457288,0.26228648800505017,0.2586259026143768,0.2760606041666663],"dir":"ltr"},{"str":"10.3","boundary":[0.14431238562091245,0.2794077001262622,0.179143074183004,0.29318181628787837],"dir":"ltr"},{"str":"The","boundary":[0.18522153594770985,0.2794077001262622,0.2169327923202589,0.29318181628787837],"dir":"ltr"},{"str":"quantum","boundary":[0.2218346078431347,0.2794077001262622,0.29739616813725234,0.29318181628787837],"dir":"ltr"},{"str":"Fourier","boundary":[0.3021019281045726,0.2794077001262622,0.3629576158496707,0.29318181628787837],"dir":"ltr"},{"str":"transform","boundary":[0.3678594607843112,0.2794077001262622,0.45005204264705634,0.29318181628787837],"dir":"ltr"},{"str":"10.4","boundary":[0.1443118627450951,0.29652891224747424,0.17914255130718665,0.3103030284090904],"dir":"ltr"},{"str":"Periodicity","boundary":[0.1852210130718925,0.29652891224747424,0.27345638611110823,0.3103030284090904],"dir":"ltr"},{"str":"10.5","boundary":[0.14431259803921248,0.3136501243686863,0.17914328660130402,0.32742424053030245],"dir":"ltr"},{"str":"Quantum","boundary":[0.18522174836600988,0.3136501243686863,0.26470488055555236,0.32742424053030245],"dir":"ltr"},{"str":"circuits","boundary":[0.2694106372548988,0.3136501243686863,0.33024847761437587,0.32742424053030245],"dir":"ltr"},{"str":"10.6","boundary":[0.14431328431372187,0.33077133648989837,0.17914397287581338,0.3445454526515146],"dir":"ltr"},{"str":"Factoring","boundary":[0.18522243464051924,0.33077133648989837,0.26349343415032317,0.3445454526515146],"dir":"ltr"},{"str":"as","boundary":[0.268591372549016,0.33077133648989837,0.2867910312091467,0.3445454526515146],"dir":"ltr"},{"str":"periodicity","boundary":[0.2914967647058787,0.33077133648989837,0.37855566078431013,0.3445454526515146],"dir":"ltr"},{"str":"10.7","boundary":[0.14431290849672784,0.3478925486111105,0.17914359705881938,0.3616666647727267],"dir":"ltr"},{"str":"The","boundary":[0.18522205882352524,0.3478925486111105,0.21693331519607428,0.3616666647727267],"dir":"ltr"},{"str":"quantum","boundary":[0.22183513071895009,0.3478925486111105,0.29739669101306776,0.3616666647727267],"dir":"ltr"},{"str":"algorithm","boundary":[0.302102450980388,0.3478925486111105,0.3833146398692769,0.3616666647727267],"dir":"ltr"},{"str":"for","boundary":[0.38802042483659716,0.3478925486111105,0.4105159872548978,0.3616666647727267],"dir":"ltr"},{"str":"factoring","boundary":[0.41561405228757753,0.3478925486111105,0.4889830973856168,0.3616666647727267],"dir":"ltr"},{"str":"Exercises","boundary":[0.1443129084967274,0.36501388699494886,0.22219176127450516,0.3787880031565651],"dir":"ltr"},{"str":"Historical","boundary":[0.11764648692809952,0.39523427209595896,0.2102134089869231,0.4090083882575752],"dir":"ltr"},{"str":"notes","boundary":[0.21491919934640016,0.39523427209595896,0.26463403578430866,0.4090083882575752],"dir":"ltr"},{"str":"and","boundary":[0.26992802287581197,0.39523427209595896,0.30497261535947207,0.4090083882575752],"dir":"ltr"},{"str":"further","boundary":[0.3098744281045701,0.39523427209595896,0.37720068741829565,0.4090083882575752],"dir":"ltr"},{"str":"reading","boundary":[0.3826907679738512,0.39523427209595896,0.4547229135620865,0.4090083882575752],"dir":"ltr"},{"str":"Index","boundary":[0.11764665032679238,0.4259918478535348,0.170694822875812,0.43976596401515095],"dir":"ltr"}],"boundary":[0.11765,0.08979,0.54196,0.43977],"dir":"ltr","type":"paragraph"},{"words":[{"str":"5","boundary":[0.8715686274509804,0.09001376073232323,0.8815508104575164,0.10378787689393938],"dir":"ltr"},{"str":"283","boundary":[0.8511044117647059,0.12811293371212124,0.8816391965686274,0.1418870498737374],"dir":"ltr"},{"str":"284","boundary":[0.8536352124183009,0.1459228516414141,0.8835817614379087,0.15969696780303025],"dir":"ltr"},{"str":"290","boundary":[0.8536706209150323,0.16304406376262615,0.88361716993464,0.1768181799242423],"dir":"ltr"},{"str":"297","boundary":[0.8536698202614373,0.1801652758838382,0.883616369281045,0.19393939204545435],"dir":"ltr"},{"str":"306","boundary":[0.8537403267973842,0.19728648800505025,0.883686875816992,0.21106060416666642],"dir":"ltr"},{"str":"311","boundary":[0.8512285620915013,0.22735535795454523,0.8817633468954229,0.24112947411616137],"dir":"ltr"},{"str":"311","boundary":[0.8535981535947695,0.24516527588383807,0.8835447026143773,0.25893939204545424],"dir":"ltr"},{"str":"315","boundary":[0.8537584640522854,0.26228648800505017,0.8837050130718931,0.2760606041666663],"dir":"ltr"},{"str":"316","boundary":[0.8536697058823506,0.2794077001262622,0.8836162549019584,0.29318181628787837],"dir":"ltr"},{"str":"318","boundary":[0.853704754901958,0.29652891224747424,0.8836513039215658,0.3103030284090904],"dir":"ltr"},{"str":"321","boundary":[0.8537054411764674,0.3136501243686863,0.8836519901960751,0.32742424053030245],"dir":"ltr"},{"str":"324","boundary":[0.8536348039215652,0.33077133648989837,0.883581352941173,0.3445454526515146],"dir":"ltr"},{"str":"326","boundary":[0.8536168300653554,0.3478925486111105,0.8835633790849632,0.3616666647727267],"dir":"ltr"},{"str":"329","boundary":[0.8537412581699302,0.36501388699494886,0.8836878071895379,0.3787880031565651],"dir":"ltr"},{"str":"331","boundary":[0.8509979575163348,0.39523427209595896,0.8815327423202564,0.4090083882575752],"dir":"ltr"},{"str":"333","boundary":[0.8514783496731977,0.4259918478535348,0.8820131344771193,0.43976596401515095],"dir":"ltr"}],"boundary":[0.851,0.09001,0.88371,0.43977],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":5,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/8d5caa8c1d5c1cc8aec593cb8938c4df.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/8f30e94ee7e011d21087250568675d30.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11765,0.89621]},"elements":[{"words":[{"str":"6","boundary":[0.11764705882352941,0.09001376073232323,0.12762924183006535,0.10378787689393938],"dir":"ltr"}],"boundary":[0.11765,0.09001,0.12763,0.10379],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Algorithms","boundary":[0.7899820261437909,0.08979153426128839,0.8823528696078432,0.10356565042290454],"dir":"ltr"}],"boundary":[0.78998,0.08979,0.88235,0.10357],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":6,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/993629d6089abf3432d88423d15c7d78.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/75acaf3e8e8f5bef7eb374eabe724674.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.20758,0.11628,0.09318]},"elements":[{"words":[{"str":"List","boundary":[0.11764705882352941,0.2075803958333333,0.19913667516339867,0.23887723926767673],"dir":"ltr"},{"str":"of","boundary":[0.21090130718954248,0.2075803958333333,0.2512410973856209,0.23887723926767673],"dir":"ltr"},{"str":"boxes","boundary":[0.26300571895424835,0.2075803958333333,0.38208100326797384,0.23887723926767673],"dir":"ltr"},{"str":"Bases","boundary":[0.14431372549019605,0.2972864880050505,0.19245993316993465,0.31106060416666664],"dir":"ltr"},{"str":"and","boundary":[0.19736176470588235,0.2972864880050505,0.22848478529411761,0.31106060416666664],"dir":"ltr"},{"str":"logs","boundary":[0.23338660130718952,0.2972864880050505,0.26566826813725486,0.31106060416666664],"dir":"ltr"},{"str":"Two's","boundary":[0.14431375816993428,0.3147107304292928,0.18559732058823492,0.328484846590909],"dir":"ltr"},{"str":"complement","boundary":[0.19540109477124146,0.3147107304292928,0.29502684624182973,0.328484846590909],"dir":"ltr"},{"str":"Is","boundary":[0.1443142973856202,0.3319834577020201,0.15976885571895355,0.34575757386363626],"dir":"ltr"},{"str":"your","boundary":[0.16486691176470517,0.3319834577020201,0.20205054346405157,0.34575757386363626],"dir":"ltr"},{"str":"social","boundary":[0.20695236928104502,0.3319834577020201,0.25311996568627376,0.34575757386363626],"dir":"ltr"},{"str":"security","boundary":[0.2580218137254895,0.3319834577020201,0.32376161895424765,0.34575757386363626],"dir":"ltr"},{"str":"number","boundary":[0.3288595588235287,0.3319834577020201,0.3932624645424829,0.34575757386363626],"dir":"ltr"},{"str":"a","boundary":[0.3981642973856202,0.3319834577020201,0.4034406568627444,0.34575757386363626],"dir":"ltr"},{"str":"prime?","boundary":[0.4128523039215679,0.3319834577020201,0.46901990866013005,0.34575757386363626],"dir":"ltr"},{"str":"Hey","boundary":[0.14431390522875706,0.3494077001262625,0.177593790359476,0.3631818162878787],"dir":"ltr"},{"str":"that","boundary":[0.18541910130718844,0.3494077001262625,0.22005371127450868,0.3631818162878787],"dir":"ltr"},{"str":"was","boundary":[0.2249555392156852,0.3494077001262625,0.2566667828431362,0.3631818162878787],"dir":"ltr"},{"str":"group","boundary":[0.2615685947712408,0.3494077001262625,0.3089304880718943,0.3631818162878787],"dir":"ltr"},{"str":"theory!","boundary":[0.31383232026143687,0.3494077001262625,0.37194288562091393,0.3631818162878787],"dir":"ltr"},{"str":"Carmichael","boundary":[0.14431282679738425,0.3666804273989898,0.23962472499999862,0.380454543560606],"dir":"ltr"},{"str":"numbers","boundary":[0.24452655228758036,0.3666804273989898,0.31714693366012936,0.380454543560606],"dir":"ltr"},{"str":"Randomized","boundary":[0.14431318627450818,0.3839531546717171,0.24629188088235132,0.39772727083333326],"dir":"ltr"},{"str":"algorithms:","boundary":[0.2511937418300637,0.3839531546717171,0.3455075459150311,0.39772727083333326],"dir":"ltr"},{"str":"a","boundary":[0.3515858986928088,0.3839531546717171,0.356862258169933,0.39772727083333326],"dir":"ltr"},{"str":"virtual","boundary":[0.3662739052287565,0.3839531546717171,0.4228158418300637,0.39772727083333326],"dir":"ltr"},{"str":"chapter","boundary":[0.42771769607842974,0.3839531546717171,0.4899459040849657,0.39772727083333326],"dir":"ltr"},{"str":"An","boundary":[0.14431325163398495,0.4013773970959595,0.1681991895424817,0.4151515132575757],"dir":"ltr"},{"str":"application","boundary":[0.17310099673202417,0.4013773970959595,0.26486577908496534,0.4151515132575757],"dir":"ltr"},{"str":"of","boundary":[0.26957158496731826,0.4013773970959595,0.27914377222222025,0.4151515132575757],"dir":"ltr"},{"str":"number","boundary":[0.289339885620913,0.4013773970959595,0.35374279133986725,0.4151515132575757],"dir":"ltr"},{"str":"theory?","boundary":[0.3586446241830045,0.4013773970959595,0.41930421127450784,0.4151515132575757],"dir":"ltr"},{"str":"Binary","boundary":[0.1443126797385597,0.4313773970959595,0.20126459885620676,0.4451515132575757],"dir":"ltr"},{"str":"search","boundary":[0.20597035947712178,0.4313773970959595,0.2593927393790825,0.4451515132575757],"dir":"ltr"},{"str":"An","boundary":[0.14431279411764428,0.4486501243686868,0.16819873202614102,0.46242424053030295],"dir":"ltr"},{"str":"n","boundary":[0.1731005392156835,0.45436638257575745,0.18386703660130443,0.4681404987373736],"dir":"ltr"},{"str":"log","boundary":[0.18680815359476846,0.45436638257575745,0.20930371601306913,0.4681404987373736],"dir":"ltr"},{"str":"n","boundary":[0.21263707516339592,0.45436638257575745,0.22340357254901683,0.4681404987373736],"dir":"ltr"},{"str":"lower","boundary":[0.22830547385620636,0.4486501243686868,0.27331442401960504,0.46242424053030295],"dir":"ltr"},{"str":"bound","boundary":[0.27841233660130443,0.4486501243686868,0.3293036446078404,0.46242424053030295],"dir":"ltr"},{"str":"for","boundary":[0.3340093954248338,0.4486501243686868,0.35650495784313446,0.46242424053030295],"dir":"ltr"},{"str":"sorting","boundary":[0.36179910130718673,0.4486501243686868,0.4197135880718926,0.46242424053030295],"dir":"ltr"},{"str":"The","boundary":[0.14431192810457197,0.46592285164141406,0.176023184477121,0.4796969678030303],"dir":"ltr"},{"str":"Unix","boundary":[0.1809249999999968,0.46592285164141406,0.2216380464052256,0.4796969678030303],"dir":"ltr"},{"str":"command","boundary":[0.2741155228758138,0.46592285164141406,0.35359865506535626,0.4796969678030303],"dir":"ltr"},{"str":"sort","boundary":[0.22653986928104256,0.4750826388888888,0.26932065359476803,0.48885675505050497],"dir":"ltr"},{"str":"Why","boundary":[0.14431184640522524,0.4833470940656565,0.18229761781045398,0.4971212102272727],"dir":"ltr"},{"str":"multiply","boundary":[0.18719942810457163,0.4833470940656565,0.2576451196078396,0.4971212102272727],"dir":"ltr"},{"str":"polynomials?","boundary":[0.26235089869280687,0.4833470940656565,0.3695880647058788,0.4971212102272727],"dir":"ltr"},{"str":"The","boundary":[0.1443110620914993,0.5006198213383838,0.1760223184640483,0.5143939375],"dir":"ltr"},{"str":"slow","boundary":[0.18092413398692414,0.5006198213383838,0.21751952990195683,0.5143939375],"dir":"ltr"},{"str":"spread","boundary":[0.22242135620914638,0.5006198213383838,0.27760856797385225,0.5143939375],"dir":"ltr"},{"str":"of","boundary":[0.28290256535947317,0.5006198213383838,0.29247475261437517,0.5143939375],"dir":"ltr"},{"str":"a","boundary":[0.3026708660130679,0.5006198213383838,0.3079472254901921,0.5143939375],"dir":"ltr"},{"str":"fast","boundary":[0.3173588725490156,0.5006198213383838,0.3482679892156823,0.5143939375],"dir":"ltr"},{"str":"algorithm","boundary":[0.35336606209149934,0.5006198213383838,0.43457825098038816,0.5143939375],"dir":"ltr"},{"str":"How","boundary":[0.14431049019607414,0.5306198213383838,0.18190410441176041,0.5443939375],"dir":"ltr"},{"str":"big","boundary":[0.187001993464048,0.5306198213383838,0.21224265620914604,0.5443939375],"dir":"ltr"},{"str":"is","boundary":[0.21694839869280616,0.5306198213383838,0.22593251274509377,0.5443939375],"dir":"ltr"},{"str":"your","boundary":[0.23573614379084537,0.5306198213383838,0.27291977549019175,0.5443939375],"dir":"ltr"},{"str":"graph?","boundary":[0.27782160130718525,0.5306198213383838,0.33418528464051855,0.5443939375],"dir":"ltr"},{"str":"Crawling","boundary":[0.14431050653594318,0.547892548611111,0.22063857499999548,0.5616666647727272],"dir":"ltr"},{"str":"fast","boundary":[0.22534433006535493,0.547892548611111,0.2562534467320216,0.5616666647727272],"dir":"ltr"},{"str":"Which","boundary":[0.1443107189542433,0.5778925486111111,0.19206485784313224,0.5916666647727272],"dir":"ltr"},{"str":"heap","boundary":[0.2018686601307139,0.5778925486111111,0.2417973921568577,0.5916666647727272],"dir":"ltr"},{"str":"is","boundary":[0.24669921568626943,0.5778925486111111,0.255683329738557,0.5916666647727272],"dir":"ltr"},{"str":"best?","boundary":[0.26548696078430867,0.5778925486111111,0.3071625748365962,0.5916666647727272],"dir":"ltr"},{"str":"Trees","boundary":[0.14431099673202066,0.6078925486111111,0.18990818267973308,0.6216666647727273],"dir":"ltr"},{"str":"A","boundary":[0.1443108169934583,0.6251652758838383,0.1523322140522818,0.6389393920454545],"dir":"ltr"},{"str":"randomized","boundary":[0.1621361437908439,0.6251652758838383,0.25901679493463475,0.6389393920454545],"dir":"ltr"},{"str":"algorithm","boundary":[0.2639186601307132,0.6251652758838383,0.34513084901960206,0.6389393920454545],"dir":"ltr"},{"str":"for","boundary":[0.35003271241829487,0.6251652758838383,0.3725282748365955,0.6389393920454545],"dir":"ltr"},{"str":"minimum","boundary":[0.37762633986927524,0.6251652758838383,0.45848202222221646,0.6389393920454545],"dir":"ltr"},{"str":"cut","boundary":[0.46299169934639944,0.6251652758838383,0.48862451928103995,0.6389393920454545],"dir":"ltr"},{"str":"Entropy","boundary":[0.1443105392156801,0.6425895183080806,0.21144071993463434,0.6563636344696968],"dir":"ltr"},{"str":"Recursion?","boundary":[0.14431050653594116,0.6724380031565657,0.23413232826796732,0.6862121193181818],"dir":"ltr"},{"str":"No","boundary":[0.2404067483660065,0.6724380031565657,0.26370445049018953,0.6862121193181818],"dir":"ltr"},{"str":"thanks","boundary":[0.27349053921567973,0.6724380031565657,0.3310306941176405,0.6862121193181818],"dir":"ltr"},{"str":"Programming?","boundary":[0.14430973856208446,0.689862245580808,0.26605672058822827,0.7036363617424242],"dir":"ltr"},{"str":"Common","boundary":[0.14431003267973116,0.7071349728535353,0.2175364751633913,0.7209090890151515],"dir":"ltr"},{"str":"subproblems","boundary":[0.22243830065358738,0.7071349728535353,0.32694819166665934,0.7209090890151515],"dir":"ltr"},{"str":"Of","boundary":[0.14431044117646272,0.7245592152777778,0.16407872859476336,0.7383333314393938],"dir":"ltr"},{"str":"mice","boundary":[0.16917678104574374,0.7245592152777778,0.20734080571894636,0.7383333314393938],"dir":"ltr"},{"str":"and","boundary":[0.21224263071894636,0.7245592152777778,0.24336565130718166,0.7383333314393938],"dir":"ltr"},{"str":"men","boundary":[0.24826746732025357,0.7245592152777778,0.28390029558822744,0.7383333314393938],"dir":"ltr"},{"str":"Memoization","boundary":[0.14431031045750806,0.7418319425505051,0.25117314460783485,0.7556060587121212],"dir":"ltr"},{"str":"On","boundary":[0.14431057189541607,0.7592561849747475,0.169176902777769,0.7730303011363636],"dir":"ltr"},{"str":"time","boundary":[0.174078709150318,0.7592561849747475,0.21126234084966442,0.7730303011363636],"dir":"ltr"},{"str":"and","boundary":[0.21616416666665791,0.7592561849747475,0.2472871872548932,0.7730303011363636],"dir":"ltr"},{"str":"memory","boundary":[0.2521890032679651,0.7592561849747475,0.3189448521241742,0.7730303011363636],"dir":"ltr"},{"str":"A","boundary":[0.14431042483659218,0.7891046698232322,0.1523318218954157,0.8028787859848484],"dir":"ltr"},{"str":"magic","boundary":[0.16213575163397778,0.7891046698232322,0.21106627369280132,0.8028787859848484],"dir":"ltr"},{"str":"trick","boundary":[0.21596810457515425,0.7891046698232322,0.2494085173202523,0.8028787859848484],"dir":"ltr"},{"str":"called","boundary":[0.25960447712417384,0.7891046698232322,0.307732859477115,0.8028787859848484],"dir":"ltr"},{"str":"duality","boundary":[0.31263470588234377,0.7891046698232322,0.3715295856209059,0.8028787859848484],"dir":"ltr"},{"str":"Reductions","boundary":[0.14430972222221264,0.8065289122474748,0.23550409411763745,0.820303028409091],"dir":"ltr"},{"str":"Matrix-vector","boundary":[0.14430995098038216,0.823801639520202,0.256627335130709,0.8375757556818181],"dir":"ltr"},{"str":"notation","boundary":[0.26192138888887895,0.823801639520202,0.330798451633977,0.8375757556818181],"dir":"ltr"},{"str":"Visualizing","boundary":[0.14430937908495692,0.8412258819444444,0.2378388568627347,0.8549999981060605],"dir":"ltr"},{"str":"duality","boundary":[0.24215249999998958,0.8412258819444444,0.30104737973855167,0.8549999981060605],"dir":"ltr"},{"str":"Gaussian","boundary":[0.14430852941175404,0.8584986092171717,0.2222052075163292,0.8722727253787879],"dir":"ltr"},{"str":"elimination","boundary":[0.22671490196077365,0.8584986092171717,0.32161694183005474,0.8722727253787879],"dir":"ltr"},{"str":"7","boundary":[0.49509207516338755,0.8930440637626264,0.5050742581699236,0.9068181799242424],"dir":"ltr"}],"boundary":[0.11765,0.20758,0.50507,0.90682],"dir":"ltr","type":"paragraph"},{"words":[{"str":"21","boundary":[0.861585,0.2972864880050505,0.881549366013072,0.31106060416666664],"dir":"ltr"},{"str":"27","boundary":[0.8615675653594768,0.3147107304292928,0.8815319313725487,0.328484846590909],"dir":"ltr"},{"str":"33","boundary":[0.8614789379084962,0.3319834577020201,0.8814433039215681,0.34575757386363626],"dir":"ltr"},{"str":"36","boundary":[0.8615317810457508,0.3494077001262625,0.8814961470588227,0.3631818162878787],"dir":"ltr"},{"str":"37","boundary":[0.8615664542483648,0.3666804273989898,0.8815308202614367,0.380454543560606],"dir":"ltr"},{"str":"39","boundary":[0.8614423366013058,0.3839531546717171,0.8814067026143777,0.39772727083333326],"dir":"ltr"},{"str":"40","boundary":[0.861495686274508,0.4013773970959595,0.88146005228758,0.4151515132575757],"dir":"ltr"},{"str":"60","boundary":[0.86158403594771,0.4313773970959595,0.881548401960782,0.4451515132575757],"dir":"ltr"},{"str":"62","boundary":[0.8615129084967292,0.4486501243686868,0.8814772745098012,0.46242424053030295],"dir":"ltr"},{"str":"66","boundary":[0.8616010620915003,0.46592285164141406,0.8815654281045723,0.4796969678030303],"dir":"ltr"},{"str":"68","boundary":[0.861530016339866,0.4833470940656565,0.881494382352938,0.4971212102272727],"dir":"ltr"},{"str":"82","boundary":[0.8614934967320224,0.5006198213383838,0.8814578627450944,0.5143939375],"dir":"ltr"},{"str":"93","boundary":[0.8615637745097998,0.5306198213383838,0.8815281405228718,0.5443939375],"dir":"ltr"},{"str":"105","boundary":[0.8537388235294073,0.547892548611111,0.883685372549015,0.5616666647727272],"dir":"ltr"},{"str":"125","boundary":[0.8537211274509755,0.5778925486111111,0.8836676764705832,0.5916666647727272],"dir":"ltr"},{"str":"140","boundary":[0.8537748692810404,0.6078925486111111,0.8837214183006481,0.6216666647727273],"dir":"ltr"},{"str":"150","boundary":[0.8536504084967264,0.6251652758838383,0.8835969575163342,0.6389393920454545],"dir":"ltr"},{"str":"155","boundary":[0.8537565849673142,0.6425895183080806,0.883703133986922,0.6563636344696968],"dir":"ltr"},{"str":"173","boundary":[0.8536855555555493,0.6724380031565657,0.883632104575157,0.6862121193181818],"dir":"ltr"},{"str":"173","boundary":[0.853738137254895,0.689862245580808,0.8836846862745027,0.7036363617424242],"dir":"ltr"},{"str":"177","boundary":[0.8537385457516267,0.7071349728535353,0.8836850947712345,0.7209090890151515],"dir":"ltr"},{"str":"179","boundary":[0.8537563888888813,0.7245592152777778,0.8837029379084891,0.7383333314393938],"dir":"ltr"},{"str":"183","boundary":[0.8537386764705801,0.7418319425505051,0.8836852254901878,0.7556060587121212],"dir":"ltr"},{"str":"189","boundary":[0.8537565032679653,0.7592561849747475,0.8837030522875731,0.7730303011363636],"dir":"ltr"},{"str":"205","boundary":[0.8536675653594681,0.7891046698232322,0.8836141143790759,0.8028787859848484],"dir":"ltr"},{"str":"209","boundary":[0.8537380555555462,0.8065289122474748,0.883684604575154,0.820303028409091],"dir":"ltr"},{"str":"211","boundary":[0.8536672222222124,0.823801639520202,0.8836137712418202,0.8375757556818181],"dir":"ltr"},{"str":"222","boundary":[0.8536843464052186,0.8412258819444444,0.8836308954248264,0.8549999981060605],"dir":"ltr"},{"str":"234","boundary":[0.8536835784313621,0.8584986092171717,0.8836301274509699,0.8722727253787879],"dir":"ltr"}],"boundary":[0.85365,0.29729,0.88372,0.87227],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":7,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/24f212ab287914363d2904d026fec9e3.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/d616759368b00f8d8f5a59e75909f33c.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11626,0.69545]},"elements":[{"words":[{"str":"8","boundary":[0.11764705882352941,0.09001376073232323,0.12762924183006535,0.10378787689393938],"dir":"ltr"}],"boundary":[0.11765,0.09001,0.12763,0.10379],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Linear","boundary":[0.14431372549019605,0.12880163952020204,0.19950093725490195,0.1425757556818182],"dir":"ltr"},{"str":"programming","boundary":[0.20440277777777777,0.12880163952020204,0.3165597339869281,0.1425757556818182],"dir":"ltr"},{"str":"in","boundary":[0.321265522875817,0.12880163952020204,0.3378965527777778,0.1425757556818182],"dir":"ltr"},{"str":"polynomial","boundary":[0.3427983660130719,0.12880163952020204,0.43399273790849674,0.1425757556818182],"dir":"ltr"},{"str":"time","boundary":[0.4386985294117647,0.12880163952020204,0.4758821611111111,0.1425757556818182],"dir":"ltr"},{"str":"The","boundary":[0.14431338235294064,0.15849860921717174,0.17602463872548965,0.17227272537878788],"dir":"ltr"},{"str":"story","boundary":[0.18092645424836548,0.15849860921717174,0.22220991111111055,0.17227272537878788],"dir":"ltr"},{"str":"of","boundary":[0.22750390522875763,0.15849860921717174,0.2370760924836596,0.17227272537878788],"dir":"ltr"},{"str":"Sissa","boundary":[0.24727220588235238,0.15849860921717174,0.2905164486928099,0.17227272537878788],"dir":"ltr"},{"str":"and","boundary":[0.2954182843137249,0.15849860921717174,0.3265413049019602,0.17227272537878788],"dir":"ltr"},{"str":"Moore","boundary":[0.33124704248365955,0.15849860921717174,0.38233442908496673,0.17227272537878788],"dir":"ltr"},{"str":"Why","boundary":[0.1443137908496722,0.17561982133838377,0.18229956225490093,0.18939393749999994],"dir":"ltr"},{"str":"P","boundary":[0.18720137254901859,0.17493111553030297,0.2007129702614369,0.1887052316919191],"dir":"ltr"},{"str":"and","boundary":[0.20561477124182906,0.17561982133838377,0.23673779183006435,0.18939393749999994],"dir":"ltr"},{"str":"NP","boundary":[0.24163960784313623,0.17493111553030297,0.2700353534313716,0.1887052316919191],"dir":"ltr"},{"str":"The","boundary":[0.1443133823529399,0.19274103345959584,0.1760246387254889,0.20651514962121198],"dir":"ltr"},{"str":"two","boundary":[0.18092645424836473,0.19274103345959584,0.2104808460784301,0.20651514962121198],"dir":"ltr"},{"str":"ways","boundary":[0.2155789052287569,0.19274103345959584,0.25668408643790724,0.20651514962121198],"dir":"ltr"},{"str":"to","boundary":[0.2615858986928092,0.19274103345959584,0.2772365356209137,0.20651514962121198],"dir":"ltr"},{"str":"use","boundary":[0.2823345915032667,0.19274103345959584,0.3103203545751621,0.20651514962121198],"dir":"ltr"},{"str":"reductions","boundary":[0.31522217320261303,0.19274103345959584,0.40131850163398564,0.20651514962121198],"dir":"ltr"},{"str":"Unsolvable","boundary":[0.14431248366012903,0.20986224558080788,0.23648724852941008,0.22363636174242404],"dir":"ltr"},{"str":"problems","boundary":[0.24119303921568455,0.20986224558080788,0.3165406955882336,0.22363636174242404],"dir":"ltr"},{"str":"Entanglement","boundary":[0.14431310457516114,0.23955921527777754,0.26253067189542256,0.25333333143939374],"dir":"ltr"},{"str":"The","boundary":[0.14431344771241564,0.2565289122474746,0.17602470408496465,0.27030302840909076],"dir":"ltr"},{"str":"Fourier","boundary":[0.18092651960784048,0.2565289122474746,0.24178220735293854,0.27030302840909076],"dir":"ltr"},{"str":"transform","boundary":[0.24688013071895157,0.2565289122474746,0.3290727125816967,0.27030302840909076],"dir":"ltr"},{"str":"of","boundary":[0.33417065359476855,0.2565289122474746,0.3437428408496705,0.27030302840909076],"dir":"ltr"},{"str":"a","boundary":[0.3539389542483633,0.2565289122474746,0.3590192352941149,0.27030302840909076],"dir":"ltr"},{"str":"periodic","boundary":[0.36882303921568355,0.2565289122474746,0.43377853006535677,0.27030302840909076],"dir":"ltr"},{"str":"vector","boundary":[0.4388764705882326,0.2565289122474746,0.4885734816993438,0.27030302840909076],"dir":"ltr"},{"str":"Setting","boundary":[0.14431348039215358,0.27365012436868663,0.20418875310457188,0.2874242405303028],"dir":"ltr"},{"str":"up","boundary":[0.20928668300653264,0.27365012436868663,0.23042752058823202,0.2874242405303028],"dir":"ltr"},{"str":"a","boundary":[0.23532933006535617,0.27365012436868663,0.2404096111111078,0.2874242405303028],"dir":"ltr"},{"str":"periodic","boundary":[0.2502134150326764,0.27365012436868663,0.31516890588234964,0.2874242405303028],"dir":"ltr"},{"str":"superposition","boundary":[0.32026684640522546,0.27365012436868663,0.43140775898692485,0.2874242405303028],"dir":"ltr"},{"str":"Quantum","boundary":[0.144313300653591,0.2907713364898987,0.2237964328431335,0.30454545265151484],"dir":"ltr"},{"str":"physics","boundary":[0.22850218954247986,0.2907713364898987,0.2891617766339831,0.30454545265151484],"dir":"ltr"},{"str":"meets","boundary":[0.29406362745097664,0.2907713364898987,0.3426019923202577,0.30454545265151484],"dir":"ltr"},{"str":"computation","boundary":[0.34769990196078054,0.2907713364898987,0.4504450856209113,0.30454545265151484],"dir":"ltr"}],"boundary":[0.14431,0.1288,0.48857,0.30455],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Algorithms","boundary":[0.7899820261437909,0.08979153426128839,0.8823528696078432,0.10356565042290454],"dir":"ltr"},{"str":"236","boundary":[0.8536352777777778,0.12880163952020204,0.8835818267973856,0.1425757556818182],"dir":"ltr"},{"str":"247","boundary":[0.8537059477124179,0.15849860921717174,0.8836524967320256,0.17227272537878788],"dir":"ltr"},{"str":"258","boundary":[0.8537954084967313,0.17561982133838377,0.883741957516339,0.18939393749999994],"dir":"ltr"},{"str":"259","boundary":[0.8536883006535936,0.19274103345959584,0.8836348496732014,0.20651514962121198],"dir":"ltr"},{"str":"276","boundary":[0.853705261437907,0.20986224558080788,0.8836518104575148,0.22363636174242404],"dir":"ltr"},{"str":"314","boundary":[0.8537415522875794,0.23955921527777754,0.8836881013071872,0.25333333143939374],"dir":"ltr"},{"str":"320","boundary":[0.8535994281045725,0.2565289122474746,0.8835459771241803,0.27030302840909076],"dir":"ltr"},{"str":"325","boundary":[0.853617222222219,0.27365012436868663,0.8835637712418267,0.2874242405303028],"dir":"ltr"},{"str":"327","boundary":[0.8536706045751598,0.2907713364898987,0.8836171535947674,0.30454545265151484],"dir":"ltr"}],"boundary":[0.78998,0.08979,0.88374,0.30455],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":8,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/b0b04eccde006146062b25f8f76a3515.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/c5f9bcfbab0c52694c3e878a7f1847d0.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.21031,0.11861,0.09318]},"elements":[{"words":[{"str":"Preface","boundary":[0.11764705882352941,0.21030766856060598,0.27892521601307196,0.24160451199494942],"dir":"ltr"},{"str":"This","boundary":[0.11764705882352941,0.3025895183080807,0.15443853333333332,0.31636363446969684],"dir":"ltr"},{"str":"book","boundary":[0.15875212418300655,0.3025895183080807,0.19691614885620914,0.31636363446969684],"dir":"ltr"},{"str":"evolved","boundary":[0.2016218954248366,0.3025895183080807,0.26306579689542486,0.31636363446969684],"dir":"ltr"},{"str":"over","boundary":[0.26796764705882353,0.3025895183080807,0.3029944142156863,0.31636363446969684],"dir":"ltr"},{"str":"the","boundary":[0.3077001633986928,0.3025895183080807,0.33431337630718955,0.31636363446969684],"dir":"ltr"},{"str":"past","boundary":[0.33901911764705883,0.3025895183080807,0.3742419633986928,0.31636363446969684],"dir":"ltr"},{"str":"ten","boundary":[0.37894771241830066,0.3025895183080807,0.4055609253267974,0.31636363446969684],"dir":"ltr"},{"str":"years","boundary":[0.41026666666666667,0.3025895183080807,0.4546873810457517,0.31636363446969684],"dir":"ltr"},{"str":"from","boundary":[0.45939313725490194,0.3025895183080807,0.4977532405228758,0.31636363446969684],"dir":"ltr"},{"str":"a","boundary":[0.5024589869281045,0.3025895183080807,0.507931408496732,0.31636363446969684],"dir":"ltr"},{"str":"set","boundary":[0.516950931372549,0.3025895183080807,0.5408190439542484,0.31636363446969684],"dir":"ltr"},{"str":"of","boundary":[0.5457208660130718,0.3025895183080807,0.5556852101307189,0.31636363446969684],"dir":"ltr"},{"str":"lecture","boundary":[0.5650970098039215,0.3025895183080807,0.621835025,0.31636363446969684],"dir":"ltr"},{"str":"notes","boundary":[0.6267368790849672,0.3025895183080807,0.6703732790849672,0.31636363446969684],"dir":"ltr"},{"str":"developed","boundary":[0.6750790359477123,0.3025895183080807,0.7560951462418299,0.31636363446969684],"dir":"ltr"},{"str":"while","boundary":[0.7611932516339869,0.3025895183080807,0.8062022017973856,0.31636363446969684],"dir":"ltr"},{"str":"teaching","boundary":[0.8105158006535947,0.3025895183080807,0.8809613604575165,0.31636363446969684],"dir":"ltr"},{"str":"the","boundary":[0.11764700980392159,0.3197107304292927,0.14426022271241834,0.3334848465909089],"dir":"ltr"},{"str":"undergraduate","boundary":[0.15014243464052293,0.3197107304292927,0.2730480629084968,0.3334848465909089],"dir":"ltr"},{"str":"Algorithms","boundary":[0.27893017973856216,0.3197107304292927,0.37130102320261443,0.3334848465909089],"dir":"ltr"},{"str":"course","boundary":[0.376987205882353,0.3197107304292927,0.4294293173202615,0.3334848465909089],"dir":"ltr"},{"str":"at","boundary":[0.4355076307189543,0.3197107304292927,0.45233473921568634,0.3334848465909089],"dir":"ltr"},{"str":"Berkeley","boundary":[0.4582169444444445,0.3197107304292927,0.5312116576797387,0.3334848465909089],"dir":"ltr"},{"str":"and","boundary":[0.5372899836601308,0.3197107304292927,0.568413004248366,0.3334848465909089],"dir":"ltr"},{"str":"U.C","boundary":[0.5740991339869281,0.3197107304292927,0.605222127124183,0.3334848465909089],"dir":"ltr"},{"str":"San","boundary":[0.6148121241830066,0.3197107304292927,0.6469155377450981,0.3334848465909089],"dir":"ltr"},{"str":"Diego","boundary":[0.6526016666666667,0.3197107304292927,0.6993753241830066,0.3334848465909089],"dir":"ltr"},{"str":"Our","boundary":[0.7128867647058824,0.3197107304292927,0.7455784140522876,0.3334848465909089],"dir":"ltr"},{"str":"way","boundary":[0.7512645424836601,0.3197107304292927,0.7782700189542484,0.3334848465909089],"dir":"ltr"},{"str":"of","boundary":[0.7900345424836601,0.3197107304292927,0.8047047864379085,0.3334848465909089],"dir":"ltr"},{"str":"teaching","boundary":[0.8105869934640524,0.3197107304292927,0.881032553267974,0.3334848465909089],"dir":"ltr"},{"str":"this","boundary":[0.11764630718954262,0.3366804273989898,0.14933973823529426,0.350454543560606],"dir":"ltr"},{"str":"course","boundary":[0.15365349673202627,0.3366804273989898,0.20609560816993477,0.350454543560606],"dir":"ltr"},{"str":"evolved","boundary":[0.21060529411764717,0.3366804273989898,0.2720491955882354,0.350454543560606],"dir":"ltr"},{"str":"tremendously","boundary":[0.27655888888888897,0.3366804273989898,0.3890901769607844,0.350454543560606],"dir":"ltr"},{"str":"over","boundary":[0.3935999019607844,0.3366804273989898,0.4286266691176472,0.350454543560606],"dir":"ltr"},{"str":"these","boundary":[0.43313633986928113,0.3366804273989898,0.4767727398692811,0.350454543560606],"dir":"ltr"},{"str":"years","boundary":[0.48128241830065366,0.3366804273989898,0.5257031326797386,0.350454543560606],"dir":"ltr"},{"str":"in","boundary":[0.5300167320261439,0.3366804273989898,0.5466477619281046,0.350454543560606],"dir":"ltr"},{"str":"a","boundary":[0.5509615032679739,0.3366804273989898,0.5568260653594771,0.350454543560606],"dir":"ltr"},{"str":"number","boundary":[0.5650613071895425,0.3366804273989898,0.6294642129084967,0.350454543560606],"dir":"ltr"},{"str":"of","boundary":[0.6337778104575164,0.3366804273989898,0.6441343114379086,0.350454543560606],"dir":"ltr"},{"str":",","boundary":[0.7331717647058824,0.3366804273989898,0.7333500274509803,0.350454543560606],"dir":"ltr"},{"str":"directions","boundary":[0.6527617973856209,0.3366804273989898,0.73356400375817,0.350454543560606],"dir":"ltr"},{"str":"partly","boundary":[0.7427617810457516,0.3366804273989898,0.7928509493464052,0.350454543560606],"dir":"ltr"},{"str":"to","boundary":[0.7971645588235293,0.3366804273989898,0.812815195751634,0.350454543560606],"dir":"ltr"},{"str":"address","boundary":[0.8173248529411764,0.3366804273989898,0.8807295403594769,0.350454543560606],"dir":"ltr"},{"str":"our","boundary":[0.11764674836601302,0.35380163952020194,0.14524035424836595,0.3675757556818181],"dir":"ltr"},{"str":"students'","boundary":[0.15112256535947707,0.35380163952020194,0.22586416062091502,0.3675757556818181],"dir":"ltr"},{"str":"background","boundary":[0.23155034313725487,0.35380163952020194,0.32803885866013066,0.3675757556818181],"dir":"ltr"},{"str":"(undeveloped","boundary":[0.33372501633986923,0.35380163952020194,0.44253081111111114,0.3675757556818181],"dir":"ltr"},{"str":"formal","boundary":[0.44860916666666667,0.35380163952020194,0.5026199068627452,0.3675757556818181],"dir":"ltr"},{"str":"skills","boundary":[0.5083060620915032,0.35380163952020194,0.5523167939542484,0.3675757556818181],"dir":"ltr"},{"str":"outside","boundary":[0.5578068790849673,0.35380163952020194,0.6172899946078431,0.3675757556818181],"dir":"ltr"},{"str":"of","boundary":[0.6231722385620915,0.35380163952020194,0.6378424825163398,0.3675757556818181],"dir":"ltr"},{"str":"programming),","boundary":[0.6437246895424836,0.35380163952020194,0.7666303178104575,0.3675757556818181],"dir":"ltr"},{"str":"and","boundary":[0.7725124346405229,0.35380163952020194,0.8036354552287581,0.3675757556818181],"dir":"ltr"},{"str":"partly","boundary":[0.8093215849673202,0.35380163952020194,0.8594107532679739,0.3675757556818181],"dir":"ltr"},{"str":"to","boundary":[0.8650969117647058,0.35380163952020194,0.8807475486928105,0.3675757556818181],"dir":"ltr"},{"str":"re\u0003ect","boundary":[0.11764593137254899,0.37092285164141403,0.1687154926470588,0.38469696780303025],"dir":"ltr"},{"str":"the","boundary":[0.1742055718954248,0.37092285164141403,0.20081878480392154,0.38469696780303025],"dir":"ltr"},{"str":"maturing","boundary":[0.20611276143790844,0.37092285164141403,0.2838133609477124,0.38469696780303025],"dir":"ltr"},{"str":"of","boundary":[0.28891129084967315,0.37092285164141403,0.30358153480392147,0.38469696780303025],"dir":"ltr"},{"str":"the","boundary":[0.30887566993464044,0.37092285164141403,0.3354888828431372,0.38469696780303025],"dir":"ltr"},{"str":"\u0002eld","boundary":[0.34097893790849665,0.37092285164141403,0.3765939408496731,0.38469696780303025],"dir":"ltr"},{"str":"in","boundary":[0.3816920098039215,0.37092285164141403,0.3983230397058823,0.38469696780303025],"dir":"ltr"},{"str":"general,","boundary":[0.4034210947712418,0.37092285164141403,0.46994521437908493,0.38469696780303025],"dir":"ltr"},{"str":"as","boundary":[0.47523923202614377,0.37092285164141403,0.49343889068627445,0.38469696780303025],"dir":"ltr"},{"str":"we","boundary":[0.4987328594771242,0.37092285164141403,0.5214423258169936,0.38469696780303025],"dir":"ltr"},{"str":"have","boundary":[0.526736454248366,0.37092285164141403,0.5658808843137254,0.38469696780303025],"dir":"ltr"},{"str":"come","boundary":[0.5709789379084966,0.37092285164141403,0.6122802200980392,0.38469696780303025],"dir":"ltr"},{"str":"to","boundary":[0.6177702777777777,0.37092285164141403,0.6334209147058824,0.38469696780303025],"dir":"ltr"},{"str":"see","boundary":[0.6389111274509803,0.37092285164141403,0.6647400259803922,0.38469696780303025],"dir":"ltr"},{"str":"it.","boundary":[0.6700341666666666,0.37092285164141403,0.687431685620915,0.38469696780303025],"dir":"ltr"},{"str":"The","boundary":[0.6944903758169935,0.37092285164141403,0.7262016321895425,0.38469696780303025],"dir":"ltr"},{"str":"notes","boundary":[0.7314956045751634,0.37092285164141403,0.7751320045751633,0.38469696780303025],"dir":"ltr"},{"str":"increasingly","boundary":[0.7806220751633987,0.37092285164141403,0.8813886475490196,0.38469696780303025],"dir":"ltr"},{"str":"crystallized","boundary":[0.11764658496732025,0.3880440637626262,0.21253079950980394,0.40181817992424235],"dir":"ltr"},{"str":"into","boundary":[0.21958955882352937,0.3880440637626262,0.2518712256535947,0.40181817992424235],"dir":"ltr"},{"str":"a","boundary":[0.25892991830065354,0.3880440637626262,0.26185327124183005,0.40181817992424235],"dir":"ltr"},{"str":"narrative","boundary":[0.275970931372549,0.3880440637626262,0.35345762696078437,0.40181817992424235],"dir":"ltr"},{"str":"and","boundary":[0.3657925980392157,0.3880440637626262,0.396915618627451,0.40181817992424235],"dir":"ltr"},{"str":"we","boundary":[0.40377821895424837,0.3880440637626262,0.4264876852941176,0.40181817992424235],"dir":"ltr"},{"str":"progressively","boundary":[0.43374259803921567,0.3880440637626262,0.5425305674836601,0.40181817992424235],"dir":"ltr"},{"str":"structured","boundary":[0.549785408496732,0.3880440637626262,0.6360778155228758,0.40181817992424235],"dir":"ltr"},{"str":"the","boundary":[0.6435287091503268,0.3880440637626262,0.6701419220588235,0.40181817992424235],"dir":"ltr"},{"str":"course","boundary":[0.6773966830065359,0.3880440637626262,0.7298387944444444,0.40181817992424235],"dir":"ltr"},{"str":"to","boundary":[0.7372896568627451,0.3880440637626262,0.7529402937908496,0.40181817992424235],"dir":"ltr"},{"str":"emphasize","boundary":[0.7601952124183006,0.3880440637626262,0.8472897591503267,0.40181817992424235],"dir":"ltr"},{"str":"the","boundary":[0.8543484803921566,0.3880440637626262,0.8809616933006534,0.40181817992424235],"dir":"ltr"},{"str":"ìstory","boundary":[0.11764586601307166,0.4051654021464645,0.16577424836601284,0.41893951830808074],"dir":"ltr"},{"str":"lineî","boundary":[0.1716564869281043,0.4051654021464645,0.2096066076797383,0.41893951830808074],"dir":"ltr"},{"str":"implicit","boundary":[0.21529276143790824,0.4051654021464645,0.2786796235294115,0.41893951830808074],"dir":"ltr"},{"str":"in","boundary":[0.284169722222222,0.4051654021464645,0.3008007521241828,0.41893951830808074],"dir":"ltr"},{"str":"the","boundary":[0.30629096405228734,0.4051654021464645,0.33290417696078406,0.41893951830808074],"dir":"ltr"},{"str":"progression","boundary":[0.3387863888888886,0.4051654021464645,0.43368842875816976,0.41893951830808074],"dir":"ltr"},{"str":"of","boundary":[0.4395707026143788,0.4051654021464645,0.4542409465686272,0.41893951830808074],"dir":"ltr"},{"str":"the","boundary":[0.46012315359477096,0.4051654021464645,0.4867363665032677,0.41893951830808074],"dir":"ltr"},{"str":"material.","boundary":[0.4924224999999997,0.4051654021464645,0.5679484096405226,0.41893951830808074],"dir":"ltr"},{"str":"As","boundary":[0.5761836111111108,0.4051654021464645,0.5973244486928101,0.41893951830808074],"dir":"ltr"},{"str":"a","boundary":[0.6030105718954245,0.4051654021464645,0.6075026013071892,0.41893951830808074],"dir":"ltr"},{"str":"result,","boundary":[0.6184829084967317,0.4051654021464645,0.6716915089869278,0.41893951830808074],"dir":"ltr"},{"str":"the","boundary":[0.6777698366013069,0.4051654021464645,0.7043830495098036,0.41893951830808074],"dir":"ltr"},{"str":"topics","boundary":[0.7100693464052283,0.4051654021464645,0.7576094929738558,0.41893951830808074],"dir":"ltr"},{"str":"were","boundary":[0.7634917320261434,0.4051654021464645,0.8028322282679735,0.41893951830808074],"dir":"ltr"},{"str":"carefully","boundary":[0.8087144444444441,0.4051654021464645,0.8809070179738558,0.41893951830808074],"dir":"ltr"},{"str":"selected","boundary":[0.11764581699346366,0.42228661426767666,0.1827973864379081,0.43606073042929283],"dir":"ltr"},{"str":"and","boundary":[0.18848356209150288,0.42228661426767666,0.21960658267973818,0.43606073042929283],"dir":"ltr"},{"str":"clustered.","boundary":[0.22470464052287545,0.42228661426767666,0.30452644607843105,0.43606073042929283],"dir":"ltr"},{"str":"No","boundary":[0.3117812581699343,0.42228661426767666,0.33507896029411727,0.43606073042929283],"dir":"ltr"},{"str":"attempt","boundary":[0.3405691666666663,0.42228661426767666,0.4059346400326794,0.43606073042929283],"dir":"ltr"},{"str":"was","boundary":[0.4114247222222219,0.42228661426767666,0.44313596584967274,0.43606073042929283],"dir":"ltr"},{"str":"made","boundary":[0.4482340196078427,0.42228661426767666,0.4930647165032676,0.43606073042929283],"dir":"ltr"},{"str":"to","boundary":[0.49835869281045714,0.42228661426767666,0.5140093297385617,0.43606073042929283],"dir":"ltr"},{"str":"be","boundary":[0.5193034640522872,0.42228661426767666,0.5380913584967316,0.43606073042929283],"dir":"ltr"},{"str":"encyclopedic","boundary":[0.5433854901960781,0.42228661426767666,0.6453284076797382,0.43606073042929283],"dir":"ltr"},{"str":"and","boundary":[0.655702581699346,0.42228661426767666,0.6868256022875814,0.43606073042929283],"dir":"ltr"},{"str":"this","boundary":[0.6919236601307186,0.42228661426767666,0.7236170911764702,0.43606073042929283],"dir":"ltr"},{"str":"freed","boundary":[0.7287151633986925,0.42228661426767666,0.7701946988562087,0.43606073042929283],"dir":"ltr"},{"str":"us","boundary":[0.7756847712418298,0.42228661426767666,0.7948648228758166,0.43606073042929283],"dir":"ltr"},{"str":"to","boundary":[0.8001589542483657,0.42228661426767666,0.8158095911764703,0.43606073042929283],"dir":"ltr"},{"str":"include","boundary":[0.8211037254901957,0.42228661426767666,0.8809790225490193,0.43606073042929283],"dir":"ltr"},{"str":"topics","boundary":[0.11764669934640493,0.43940782638888876,0.16518684591503238,0.453181942550505],"dir":"ltr"},{"str":"traditionally","boundary":[0.17028477124182978,0.43940782638888876,0.27397469722222195,0.453181942550505],"dir":"ltr"},{"str":"de-emphasized","boundary":[0.27868052287581674,0.43940782638888876,0.40080183676470565,0.453181942550505],"dir":"ltr"},{"str":"or","boundary":[0.4058998039215684,0.43940782638888876,0.42253083382352913,0.453181942550505],"dir":"ltr"},{"str":"omitted","boundary":[0.42762888888888867,0.43940782638888876,0.4906414191176468,0.453181942550505],"dir":"ltr"},{"str":"from","boundary":[0.4959354248366011,0.43940782638888876,0.5342955281045749,0.453181942550505],"dir":"ltr"},{"str":"most","boundary":[0.5393934313725488,0.43940782638888876,0.5791260848039214,0.453181942550505],"dir":"ltr"},{"str":"Algorithms","boundary":[0.5842241503267971,0.43940782638888876,0.6765949937908494,0.453181942550505],"dir":"ltr"},{"str":"books","boundary":[0.6814968627450978,0.43940782638888876,0.7278783630718951,0.453181942550505],"dir":"ltr"},{"str":".","boundary":[0.727486241830065,0.43940782638888876,0.7323703813725487,0.453181942550505],"dir":"ltr"},{"str":"Playing","boundary":[0.14529343137254863,0.4594078263888888,0.20850206192810422,0.47318194255050494],"dir":"ltr"},{"str":"on","boundary":[0.21536467320261402,0.4594078263888888,0.23513296062091463,0.47318194255050494],"dir":"ltr"},{"str":"the","boundary":[0.24238787581699306,0.4594078263888888,0.26900108872548983,0.47318194255050494],"dir":"ltr"},{"str":"strengths","boundary":[0.2762558496732022,0.4594078263888888,0.3545268596405225,0.47318194255050494],"dir":"ltr"},{"str":"of","boundary":[0.3619777450980388,0.4594078263888888,0.3766479890522872,0.47318194255050494],"dir":"ltr"},{"str":"our","boundary":[0.38390290849673164,0.4594078263888888,0.4114965143790846,0.47318194255050494],"dir":"ltr"},{"str":"students","boundary":[0.4189473529411761,0.4594078263888888,0.48998128022875775,0.47318194255050494],"dir":"ltr"},{"str":"(shared","boundary":[0.49723607843137224,0.4594078263888888,0.5590721370915029,0.47318194255050494],"dir":"ltr"},{"str":"by","boundary":[0.5665230065359473,0.4594078263888888,0.5860952153594767,0.47318194255050494],"dir":"ltr"},{"str":"most","boundary":[0.5931540522875813,0.4594078263888888,0.6328867057189539,0.47318194255050494],"dir":"ltr"},{"str":"of","boundary":[0.640141470588235,0.4594078263888888,0.6548117145424833,0.47318194255050494],"dir":"ltr"},{"str":"today's","boundary":[0.6622627124183004,0.4594078263888888,0.7117457846405226,0.47318194255050494],"dir":"ltr"},{"str":"undergraduates","boundary":[0.7262555718954246,0.4594078263888888,0.8573786758169932,0.47318194255050494],"dir":"ltr"},{"str":"in","boundary":[0.8646335130718951,0.4594078263888888,0.8812645429738558,0.47318194255050494],"dir":"ltr"},{"str":"Computer","boundary":[0.11764658496731988,0.47637752335858574,0.19985699215686237,0.4901516395202019],"dir":"ltr"},{"str":"Science),","boundary":[0.20671962418300616,0.47637752335858574,0.27852004052287543,0.4901516395202019],"dir":"ltr"},{"str":"instead","boundary":[0.28597093137254864,0.47637752335858574,0.3466305184640519,0.4901516395202019],"dir":"ltr"},{"str":"of","boundary":[0.3532970751633983,0.47637752335858574,0.3679673191176467,0.4901516395202019],"dir":"ltr"},{"str":"dwelling","boundary":[0.3748299183006532,0.47637752335858574,0.44527560980392117,0.4901516395202019],"dir":"ltr"},{"str":"on","boundary":[0.4517460947712415,0.47637752335858574,0.47151438218954217,0.4901516395202019],"dir":"ltr"},{"str":"formal","boundary":[0.47818089869281005,0.47637752335858574,0.5321916388888885,0.4901516395202019],"dir":"ltr"},{"str":"proofs","boundary":[0.5390542647058819,0.47637752335858574,0.588751275816993,0.4901516395202019],"dir":"ltr"},{"str":"we","boundary":[0.5958099836601304,0.47637752335858574,0.6185194499999997,0.4901516395202019],"dir":"ltr"},{"str":"distilled","boundary":[0.6251859640522872,0.47637752335858574,0.6920844155228755,0.4901516395202019],"dir":"ltr"},{"str":"in","boundary":[0.6987509967320258,0.47637752335858574,0.7153820266339865,0.4901516395202019],"dir":"ltr"},{"str":"each","boundary":[0.7220485457516336,0.47637752335858574,0.75276160620915,0.4901516395202019],"dir":"ltr"},{"str":"case","boundary":[0.7660949509803918,0.47637752335858574,0.8009256395424833,0.4901516395202019],"dir":"ltr"},{"str":"the","boundary":[0.8077882516339866,0.47637752335858574,0.8344014645424833,0.4901516395202019],"dir":"ltr"},{"str":"crisp","boundary":[0.8410681535947708,0.47637752335858574,0.8807829816993459,0.4901516395202019],"dir":"ltr"},{"str":"mathematical","boundary":[0.11764658496731988,0.49349873547979783,0.2319425803921565,0.507272851641414],"dir":"ltr"},{"str":"idea","boundary":[0.23645230392156827,0.49349873547979783,0.27108691388888856,0.507272851641414],"dir":"ltr"},{"str":"that","boundary":[0.27579266339869246,0.49349873547979783,0.3104272733660127,0.507272851641414],"dir":"ltr"},{"str":"makes","boundary":[0.3149369444444441,0.49349873547979783,0.36837727418300614,0.507272851641414],"dir":"ltr"},{"str":"the","boundary":[0.37308302287581663,0.49349873547979783,0.39969623578431335,0.507272851641414],"dir":"ltr"},{"str":"algorithm","boundary":[0.40459805555555517,0.49349873547979783,0.48581024444444415,0.507272851641414],"dir":"ltr"},{"str":"work.","boundary":[0.49031995098039177,0.49349873547979783,0.5363092941176467,0.507272851641414],"dir":"ltr"},{"str":"In","boundary":[0.5423875980392153,0.49349873547979783,0.5605872566993461,0.507272851641414],"dir":"ltr"},{"str":"other","boundary":[0.565292990196078,0.49349873547979783,0.6085372330065356,0.507272851641414],"dir":"ltr"},{"str":"words","boundary":[0.6134390686274506,0.49349873547979783,0.6623695906862741,0.507272851641414],"dir":"ltr"},{"str":"we","boundary":[0.6717633496732023,0.49349873547979783,0.6944728160130715,0.507272851641414],"dir":"ltr"},{"str":"emphasized","boundary":[0.6993746241830061,0.49349873547979783,0.7966474325163395,0.507272851641414],"dir":"ltr"},{"str":"rigor","boundary":[0.8011571405228755,0.49349873547979783,0.8408719686274506,0.507272851641414],"dir":"ltr"},{"str":"over","boundary":[0.8457738071895421,0.49349873547979783,0.8808005743464049,0.507272851641414],"dir":"ltr"},{"str":"formalism.","boundary":[0.11764635620914997,0.5106199476010099,0.20629170637254868,0.5243940637626262],"dir":"ltr"},{"str":"We","boundary":[0.21609553921568592,0.5106199476010099,0.23527562222222184,0.5243940637626262],"dir":"ltr"},{"str":"found","boundary":[0.2474324346405225,0.5106199476010099,0.2942060921568624,0.5243940637626262],"dir":"ltr"},{"str":"that","boundary":[0.30048047385620874,0.5106199476010099,0.335115083823529,0.5243940637626262],"dir":"ltr"},{"str":"our","boundary":[0.34119354575163363,0.5106199476010099,0.36878715163398657,0.5243940637626262],"dir":"ltr"},{"str":"students","boundary":[0.3750615196078428,0.5106199476010099,0.4460954468954245,0.5243940637626262],"dir":"ltr"},{"str":"were","boundary":[0.4523698529411761,0.5106199476010099,0.49171034918300616,0.5243940637626262],"dir":"ltr"},{"str":"much","boundary":[0.4979847222222218,0.5106199476010099,0.5373252336601303,0.5243940637626262],"dir":"ltr"},{"str":"more","boundary":[0.5494821078431368,0.5106199476010099,0.5907833900326793,0.5243940637626262],"dir":"ltr"},{"str":"receptive","boundary":[0.5970577614379081,0.5106199476010099,0.6714071995098035,0.5243940637626262],"dir":"ltr"},{"str":"to","boundary":[0.6780737745098034,0.5106199476010099,0.6937244114379081,0.5243940637626262],"dir":"ltr"},{"str":"mathematical","boundary":[0.6999989379084963,0.5106199476010099,0.8142949333333329,0.5243940637626262],"dir":"ltr"},{"str":"rigor","boundary":[0.8201770424836597,0.5106199476010099,0.8598918705882349,0.5243940637626262],"dir":"ltr"},{"str":"of","boundary":[0.866166421568627,0.5106199476010099,0.8808366655228755,0.5243940637626262],"dir":"ltr"},{"str":"this","boundary":[0.1176468137254898,0.5277411597222221,0.14934024477124144,0.5415152758838383],"dir":"ltr"},{"str":"form.","boundary":[0.15424207516339827,0.5277411597222221,0.1974863179738558,0.5415152758838383],"dir":"ltr"},{"str":"It","boundary":[0.20376070261437867,0.5277411597222221,0.21274465359477082,0.5415152758838383],"dir":"ltr"},{"str":"is","boundary":[0.22294076797385579,0.5277411597222221,0.2319248820261434,0.5415152758838383],"dir":"ltr"},{"str":"this","boundary":[0.241728513071895,0.5277411597222221,0.27342194411764664,0.5415152758838383],"dir":"ltr"},{"str":"progression","boundary":[0.2783237745098035,0.5277411597222221,0.37322581437908453,0.5415152758838383],"dir":"ltr"},{"str":"of","boundary":[0.378519852941176,0.5277411597222221,0.388092040196078,0.5415152758838383],"dir":"ltr"},{"str":"crisp","boundary":[0.39828815359477077,0.5277411597222221,0.43800298169934593,0.5415152758838383],"dir":"ltr"},{"str":"ideas","boundary":[0.44310089869281,0.5277411597222221,0.485952984313725,0.5415152758838383],"dir":"ltr"},{"str":"that","boundary":[0.4908548202614374,0.5277411597222221,0.5254894302287576,0.5415152758838383],"dir":"ltr"},{"str":"helps","boundary":[0.5303912581699342,0.5277411597222221,0.5742237367647054,0.5415152758838383],"dir":"ltr"},{"str":"weave","boundary":[0.5791255718954244,0.5277411597222221,0.6300168973856204,0.5415152758838383],"dir":"ltr"},{"str":"the","boundary":[0.6349188725490191,0.5277411597222221,0.6615320854575159,0.5415152758838383],"dir":"ltr"},{"str":"story","boundary":[0.6666301470588231,0.5277411597222221,0.7079136039215681,0.5415152758838383],"dir":"ltr"},{"str":".","boundary":[0.7057567810457511,0.5277411597222221,0.7106409205882348,0.5415152758838383],"dir":"ltr"},{"str":"Once","boundary":[0.14529436274509755,0.547741159722222,0.18679172352941126,0.5615152758838382],"dir":"ltr"},{"str":"you","boundary":[0.1920858660130714,0.547741159722222,0.2214441792483655,0.5615152758838382],"dir":"ltr"},{"str":"think","boundary":[0.22673831699346353,0.547741159722222,0.2717472671568622,0.5615152758838382],"dir":"ltr"},{"str":"about","boundary":[0.27704125816993413,0.547741159722222,0.32361883709150274,0.5615152758838382],"dir":"ltr"},{"str":"Algorithms","boundary":[0.32871674836601256,0.547741159722222,0.42108759183006483,0.5615152758838382],"dir":"ltr"},{"str":"in","boundary":[0.4263816176470583,0.547741159722222,0.4430126475490191,0.5615152758838382],"dir":"ltr"},{"str":"this","boundary":[0.4481107026143786,0.547741159722222,0.4798041336601302,0.5615152758838382],"dir":"ltr"},{"str":"way","boundary":[0.485098284313725,0.547741159722222,0.5201428947712413,0.5615152758838382],"dir":"ltr"},{"str":"it","boundary":[0.5260073202614374,0.547741159722222,0.5332265627450975,0.5615152758838382],"dir":"ltr"},{"str":"makes","boundary":[0.5438148366013067,0.547741159722222,0.5972551663398687,0.5615152758838382],"dir":"ltr"},{"str":"sense","boundary":[0.6025491503267969,0.547741159722222,0.6475581004901956,0.5615152758838382],"dir":"ltr"},{"str":"to","boundary":[0.65304816993464,0.547741159722222,0.6686988068627445,0.5615152758838382],"dir":"ltr"},{"str":"start","boundary":[0.6741890196078426,0.547741159722222,0.7139038477124178,0.5615152758838382],"dir":"ltr"},{"str":"at","boundary":[0.7193939215686268,0.547741159722222,0.7362210300653589,0.5615152758838382],"dir":"ltr"},{"str":"the","boundary":[0.7415149999999994,0.547741159722222,0.7681282129084961,0.5615152758838382],"dir":"ltr"},{"str":"historical","boundary":[0.7736182679738556,0.547741159722222,0.8510871382352936,0.5615152758838382],"dir":"ltr"},{"str":"be-","boundary":[0.8563811764705876,0.547741159722222,0.8810336034313719,0.5615152758838382],"dir":"ltr"},{"str":"ginning","boundary":[0.11764751633986868,0.5648623718434341,0.18105220375816933,0.5786364880050504],"dir":"ltr"},{"str":"of","boundary":[0.18654228758169875,0.5648623718434341,0.20121253153594712,0.5786364880050504],"dir":"ltr"},{"str":"it","boundary":[0.20729098039215627,0.5648623718434341,0.21392198758169875,0.5786364880050504],"dir":"ltr"},{"str":"all,","boundary":[0.2256867320261432,0.5648623718434341,0.2518899624183001,0.5786364880050504],"dir":"ltr"},{"str":"where","boundary":[0.25796826797385564,0.5648623718434341,0.3082713401960778,0.5786364880050504],"dir":"ltr"},{"str":"in","boundary":[0.3192339052287576,0.5648623718434341,0.3358649351307184,0.5786364880050504],"dir":"ltr"},{"str":"addition,","boundary":[0.34174714052287525,0.5648623718434341,0.41492010702614324,0.5786364880050504],"dir":"ltr"},{"str":"the","boundary":[0.42099844771241773,0.5648623718434341,0.44761166062091445,0.5786364880050504],"dir":"ltr"},{"str":"characters","boundary":[0.4536901143790844,0.5648623718434341,0.5395903563725485,0.5786364880050504],"dir":"ltr"},{"str":"are","boundary":[0.5456686928104569,0.5648623718434341,0.5722819057189537,0.5786364880050504],"dir":"ltr"},{"str":"familiar","boundary":[0.5783603594771236,0.5648623718434341,0.6448844790849667,0.5786364880050504],"dir":"ltr"},{"str":"and","boundary":[0.6505706535947706,0.5648623718434341,0.681693674183006,0.5786364880050504],"dir":"ltr"},{"str":"the","boundary":[0.6875758823529405,0.5648623718434341,0.7141890952614373,0.5786364880050504],"dir":"ltr"},{"str":"contrasts","boundary":[0.7200714705882346,0.5648623718434341,0.7955973802287575,0.5786364880050504],"dir":"ltr"},{"str":"dramatic:","boundary":[0.8018717973856203,0.5648623718434341,0.8809271217320255,0.5786364880050504],"dir":"ltr"},{"str":"numbers","boundary":[0.11764794117646994,0.5819835839646463,0.19026832254901896,0.5957577001262625],"dir":"ltr"},{"str":"primality","boundary":[0.20201506535947647,0.5819835839646463,0.2793056823529405,0.5957577001262625],"dir":"ltr"},{"str":"and","boundary":[0.28909166666666597,0.5819835839646463,0.32021468725490126,0.5957577001262625],"dir":"ltr"},{"str":"factoring","boundary":[0.3268812091503261,0.5819835839646463,0.4002502542483653,0.5957577001262625],"dir":"ltr"},{"str":"This","boundary":[0.4167029411764699,0.5819835839646463,0.45349441568627386,0.5957577001262625],"dir":"ltr"},{"str":"is","boundary":[0.4601609477124176,0.5819835839646463,0.47404687728758105,0.5957577001262625],"dir":"ltr"},{"str":"the","boundary":[0.48071339869280977,0.5819835839646463,0.5073266116013065,0.5957577001262625],"dir":"ltr"},{"str":"subject","boundary":[0.5143854575163392,0.5819835839646463,0.572299944281045,0.5957577001262625],"dir":"ltr"},{"str":"of","boundary":[0.5791625816993458,0.5819835839646463,0.5938328256535941,0.5957577001262625],"dir":"ltr"},{"str":"Part","boundary":[0.6006954248366007,0.5819835839646463,0.6367025903594765,0.5957577001262625],"dir":"ltr"},{"str":"I","boundary":[0.6435651960784307,0.5819835839646463,0.6439396065359471,0.5957577001262625],"dir":"ltr"},{"str":"of","boundary":[0.6576649509803915,0.5819835839646463,0.6723351949346399,0.5957577001262625],"dir":"ltr"},{"str":"the","boundary":[0.6791977941176465,0.5819835839646463,0.7058110070261432,0.5957577001262625],"dir":"ltr"},{"str":"book,","boundary":[0.7128698529411759,0.5819835839646463,0.7559180171568621,0.5957577001262625],"dir":"ltr"},{"str":"which","boundary":[0.763368872549019,0.5819835839646463,0.8058286650326791,0.5957577001262625],"dir":"ltr"},{"str":"also","boundary":[0.819162009803921,0.5819835839646463,0.8518358338235289,0.5957577001262625],"dir":"ltr"},{"str":"in-","boundary":[0.8586984477124175,0.5819835839646463,0.8811940101307182,0.5957577001262625],"dir":"ltr"},{"str":"cludes","boundary":[0.11764779411764632,0.5991047960858584,0.16910950473856134,0.6128789122474746],"dir":"ltr"},{"str":"the","boundary":[0.1751878104575156,0.5991047960858584,0.2018010233660123,0.6128789122474746],"dir":"ltr"},{"str":"RSA","boundary":[0.2076832352941169,0.5991047960858584,0.24468861372548942,0.6128789122474746],"dir":"ltr"},{"str":"cryptosystem,","boundary":[0.2505708169934633,0.5991047960858584,0.36406467271241755,0.6128789122474746],"dir":"ltr"},{"str":"and","boundary":[0.3705351960784306,0.5991047960858584,0.4016582166666659,0.6128789122474746],"dir":"ltr"},{"str":"divide-and-conquer","boundary":[0.407344346405228,0.5991047960858584,0.5654549950980384,0.6128789122474746],"dir":"ltr"},{"str":"algorithms","boundary":[0.5713378104575155,0.5991047960858584,0.6607674749999992,0.6128789122474746],"dir":"ltr"},{"str":"for","boundary":[0.6666497385620906,0.5991047960858584,0.6891453009803914,0.6128789122474746],"dir":"ltr"},{"str":"integer","boundary":[0.6952237581699339,0.5991047960858584,0.7537264807189534,0.6128789122474746],"dir":"ltr"},{"str":"multiplication,","boundary":[0.7596087254901952,0.5991047960858584,0.8811061529411757,0.6128789122474746],"dir":"ltr"},{"str":"sorting","boundary":[0.11764794117646975,0.6162260082070705,0.17556242794117563,0.6300001243686868],"dir":"ltr"},{"str":"and","boundary":[0.17987604575163313,0.6162260082070705,0.21099906633986842,0.6300001243686868],"dir":"ltr"},{"str":"median","boundary":[0.2149204901960776,0.6162260082070705,0.2763822169934632,0.6300001243686868],"dir":"ltr"},{"str":"\u0002nding","boundary":[0.2803036601307181,0.6162260082070705,0.33862812941176385,0.6300001243686868],"dir":"ltr"},{"str":",","boundary":[0.33823584967320175,0.6162260082070705,0.33900236405228673,0.6300001243686868],"dir":"ltr"},{"str":"as","boundary":[0.3472376143790841,0.6162260082070705,0.36543727303921486,0.6300001243686868],"dir":"ltr"},{"str":"well","boundary":[0.369554934640522,0.6162260082070705,0.40360130882352857,0.6300001243686868],"dir":"ltr"},{"str":"as","boundary":[0.4075227450980384,0.6162260082070705,0.4257224037581691,0.6300001243686868],"dir":"ltr"},{"str":"the","boundary":[0.4298400653594763,0.6162260082070705,0.456453278267973,0.6300001243686868],"dir":"ltr"},{"str":"fast","boundary":[0.46076686274509715,0.6162260082070705,0.4916759794117638,0.6300001243686868],"dir":"ltr"},{"str":"Fourier","boundary":[0.4957936601307181,0.6162260082070705,0.5566493478758161,0.6300001243686868],"dir":"ltr"},{"str":"transform.","boundary":[0.5609629575163391,0.6162260082070705,0.6480396789215678,0.6300001243686868],"dir":"ltr"},{"str":"There","boundary":[0.6541180228758161,0.6162260082070705,0.702460309150326,0.6300001243686868],"dir":"ltr"},{"str":"are","boundary":[0.7067740686274502,0.6162260082070705,0.7333872815359469,0.6300001243686868],"dir":"ltr"},{"str":"three","boundary":[0.7375047875816986,0.6162260082070705,0.780749030392156,0.6300001243686868],"dir":"ltr"},{"str":"other","boundary":[0.7852587091503259,0.6162260082070705,0.8285029519607835,0.6300001243686868],"dir":"ltr"},{"str":"parts:","boundary":[0.8328165522875808,0.6162260082070705,0.8807488560457507,0.6300001243686868],"dir":"ltr"},{"str":"Part","boundary":[0.11764825163398605,0.6331957051767675,0.15365541715686187,0.6469698213383835],"dir":"ltr"},{"str":"II,","boundary":[0.158753480392156,0.6331957051767675,0.17811178529411678,0.6469698213383835],"dir":"ltr"},{"str":"the","boundary":[0.18340593137254815,0.6331957051767675,0.21001914428104487,0.6469698213383835],"dir":"ltr"},{"str":"most","boundary":[0.21531312091503182,0.6331957051767675,0.2550457743464044,0.6469698213383835],"dir":"ltr"},{"str":"traditional","boundary":[0.26033975490195993,0.6331957051767675,0.34877120114379,0.6469698213383835],"dir":"ltr"},{"str":"section","boundary":[0.3538691666666658,0.6331957051767675,0.4109993390522867,0.6469698213383835],"dir":"ltr"},{"str":"of","boundary":[0.4164894281045743,0.6331957051767675,0.43115967205882266,0.6469698213383835],"dir":"ltr"},{"str":"the","boundary":[0.4364538071895417,0.6331957051767675,0.4630670200980384,0.6469698213383835],"dir":"ltr"},{"str":"book,","boundary":[0.4683609967320253,0.6331957051767675,0.5114091609477116,0.6469698213383835],"dir":"ltr"},{"str":"concentrates","boundary":[0.516899232026143,0.6331957051767675,0.6206069833333325,0.6469698213383835],"dir":"ltr"},{"str":"on","boundary":[0.6260971078431364,0.6331957051767675,0.645865395261437,0.6469698213383835],"dir":"ltr"},{"str":"data","boundary":[0.6511595261437899,0.6331957051767675,0.6881470792483652,0.6469698213383835],"dir":"ltr"},{"str":"structures","boundary":[0.6932451470588226,0.6331957051767675,0.777576768137254,0.6469698213383835],"dir":"ltr"},{"str":"and","boundary":[0.7830668790849664,0.6331957051767675,0.8141898996732018,0.6469698213383835],"dir":"ltr"},{"str":"graphs;","boundary":[0.8192877941176462,0.6331957051767675,0.8809277741830057,0.6469698213383835],"dir":"ltr"},{"str":"the","boundary":[0.11764890522875722,0.6503169172979797,0.14426211813725395,0.6640910334595957],"dir":"ltr"},{"str":"contrast","boundary":[0.14936017973856114,0.6503169172979797,0.21666861372548926,0.6640910334595957],"dir":"ltr"},{"str":"here","boundary":[0.22176655228758074,0.6503169172979797,0.2581658696078422,0.6640910334595957],"dir":"ltr"},{"str":"is","boundary":[0.263263774509803,0.6503169172979797,0.2722478885620906,0.6640910334595957],"dir":"ltr"},{"str":"between","boundary":[0.2820515196078422,0.6503169172979797,0.3501620933006526,0.6640910334595957],"dir":"ltr"},{"str":"the","boundary":[0.35526001633986837,0.6503169172979797,0.3818732292483651,0.6640910334595957],"dir":"ltr"},{"str":"intricate","boundary":[0.38697129084967224,0.6503169172979797,0.4573991570261428,0.6640910334595957],"dir":"ltr"},{"str":"structure","boundary":[0.4624971078431363,0.6503169172979797,0.5386112532679729,0.6640910334595957],"dir":"ltr"},{"str":"of","boundary":[0.5437091993464043,0.6503169172979797,0.5532813866013062,0.6640910334595957],"dir":"ltr"},{"str":"the","boundary":[0.5634774999999991,0.6503169172979797,0.5900907129084958,0.6640910334595957],"dir":"ltr"},{"str":"underlying","boundary":[0.595188774509803,0.6503169172979797,0.6854027534313717,0.6640910334595957],"dir":"ltr"},{"str":"problems","boundary":[0.690108545751633,0.6503169172979797,0.7654562021241821,0.6640910334595957],"dir":"ltr"},{"str":"and","boundary":[0.7705541339869272,0.6503169172979797,0.8016771545751625,0.6640910334595957],"dir":"ltr"},{"str":"the","boundary":[0.8063828921568619,0.6503169172979797,0.8329961050653586,0.6640910334595957],"dir":"ltr"},{"str":"short","boundary":[0.8380941666666658,0.6503169172979797,0.8807501736928095,0.6640910334595957],"dir":"ltr"},{"str":"and","boundary":[0.11764972222222135,0.6674381294191919,0.14877274281045666,0.681212245580808],"dir":"ltr"},{"str":"crisp","boundary":[0.15524334967320175,0.6674381294191919,0.1949581777777769,0.681212245580808],"dir":"ltr"},{"str":"pieces","boundary":[0.20162472222222136,0.6674381294191919,0.25112565473856124,0.681212245580808],"dir":"ltr"},{"str":"of","boundary":[0.2579882843137246,0.6674381294191919,0.272658528267973,0.681212245580808],"dir":"ltr"},{"str":"pseudocode","boundary":[0.2795211274509795,0.6674381294191919,0.37228412810457434,0.681212245580808],"dir":"ltr"},{"str":"that","boundary":[0.3793428594771233,0.6674381294191919,0.4139774694444436,0.681212245580808],"dir":"ltr"},{"str":"solve","boundary":[0.42044792483660043,0.6674381294191919,0.46153530310457436,0.681212245580808],"dir":"ltr"},{"str":"them.","boundary":[0.4683979248366004,0.6674381294191919,0.515759818137254,0.681212245580808],"dir":"ltr"},{"str":"Instructors","boundary":[0.5269361601307181,0.6674381294191919,0.618504863888888,0.681212245580808],"dir":"ltr"},{"str":"wishing","boundary":[0.6253675326797377,0.6674381294191919,0.6903408488562083,0.681212245580808],"dir":"ltr"},{"str":"to","boundary":[0.6966152450980383,0.6674381294191919,0.7122658820261429,0.681212245580808],"dir":"ltr"},{"str":"teach","boundary":[0.7189325653594762,0.6674381294191919,0.7562943186274501,0.681212245580808],"dir":"ltr"},{"str":"a","boundary":[0.770019820261437,0.6674381294191919,0.773531571895424,0.681212245580808],"dir":"ltr"},{"str":"more","boundary":[0.786472434640522,0.6674381294191919,0.8277737168300644,0.681212245580808],"dir":"ltr"},{"str":"tradi-","boundary":[0.8346363235294109,0.6674381294191919,0.8809999985294108,0.681212245580808],"dir":"ltr"},{"str":"tional","boundary":[0.11764939542483571,0.6845593415404039,0.16558169918300567,0.69833345770202],"dir":"ltr"},{"str":"course","boundary":[0.17166001633986838,0.6845593415404039,0.22410212777777685,0.69833345770202],"dir":"ltr"},{"str":"can","boundary":[0.23037651960784222,0.6845593415404039,0.2591465970588226,0.69833345770202],"dir":"ltr"},{"str":"simply","boundary":[0.2652248856209141,0.6845593415404039,0.32041209738562,0.69833345770202],"dir":"ltr"},{"str":"start","boundary":[0.3264904084967311,0.6845593415404039,0.3662052366013063,0.69833345770202],"dir":"ltr"},{"str":"with","boundary":[0.3724796241830056,0.6845593415404039,0.40985933447712325,0.69833345770202],"dir":"ltr"},{"str":"Part","boundary":[0.41593763071895334,0.6845593415404039,0.45194479624182915,0.69833345770202],"dir":"ltr"},{"str":"II,","boundary":[0.458023251633986,0.6845593415404039,0.4773815565359468,0.69833345770202],"dir":"ltr"},{"str":"which","boundary":[0.4836560947712409,0.6845593415404039,0.5269002009803911,0.69833345770202],"dir":"ltr"},{"str":"is","boundary":[0.5386649183006526,0.6845593415404039,0.552550847875816,0.69833345770202],"dir":"ltr"},{"str":"self-contained","boundary":[0.5588253758169925,0.6845593415404039,0.6732817991830056,0.69833345770202],"dir":"ltr"},{"str":"(following","boundary":[0.6795560947712409,0.6845593415404039,0.7603583011437899,0.69833345770202],"dir":"ltr"},{"str":"the","boundary":[0.7664366503267965,0.6845593415404039,0.7930498632352933,0.69833345770202],"dir":"ltr"},{"str":"prologue),","boundary":[0.7993242320261429,0.6845593415404039,0.8807146741830056,0.69833345770202],"dir":"ltr"},{"str":"and","boundary":[0.11764939542483571,0.701680553661616,0.148772416013071,0.715454669823232],"dir":"ltr"},{"str":"then","boundary":[0.15465462418300566,0.701680553661616,0.19223041307189453,0.715454669823232],"dir":"ltr"},{"str":"cover","boundary":[0.19811263071895335,0.701680553661616,0.2409647163398684,0.715454669823232],"dir":"ltr"},{"str":"Part","boundary":[0.24723910130718865,0.701680553661616,0.28324626683006443,0.715454669823232],"dir":"ltr"},{"str":"I","boundary":[0.28912848039215594,0.701680553661616,0.2902871718954239,0.715454669823232],"dir":"ltr"},{"str":"as","boundary":[0.30244395424836507,0.701680553661616,0.3206436129084958,0.715454669823232],"dir":"ltr"},{"str":"required.","boundary":[0.3265258169934631,0.701680553661616,0.4014634908496723,0.715454669823232],"dir":"ltr"},{"str":"In","boundary":[0.4108751633986919,0.701680553661616,0.4290748220588226,0.715454669823232],"dir":"ltr"},{"str":"Parts","boundary":[0.4349570261437899,0.701680553661616,0.4791816673202605,0.715454669823232],"dir":"ltr"},{"str":"I","boundary":[0.4850638888888879,0.701680553661616,0.48641869150326694,0.715454669823232],"dir":"ltr"},{"str":"and","boundary":[0.4981832516339859,0.701680553661616,0.5293062722222212,0.715454669823232],"dir":"ltr"},{"str":"II","boundary":[0.5351884803921558,0.701680553661616,0.549662645751633,0.715454669823232],"dir":"ltr"},{"str":"we","boundary":[0.5555450163398682,0.701680553661616,0.5782544826797376,0.715454669823232],"dir":"ltr"},{"str":"introduced","boundary":[0.5843329248366003,0.701680553661616,0.6723900392156853,0.715454669823232],"dir":"ltr"},{"str":"certain","boundary":[0.6786644607843126,0.701680553661616,0.7365789475490185,0.715454669823232],"dir":"ltr"},{"str":"techniques","boundary":[0.7424611928104564,0.701680553661616,0.831302646732025,0.715454669823232],"dir":"ltr"},{"str":"(such","boundary":[0.8373809640522866,0.701680553661616,0.881017396241829,0.715454669823232],"dir":"ltr"},{"str":"as","boundary":[0.11764959150326697,0.7188017657828282,0.1358492501633977,0.7325758819444442],"dir":"ltr"},{"str":"greedy","boundary":[0.14231968954248267,0.7188017657828282,0.19711474411764607,0.7325758819444442],"dir":"ltr"},{"str":"and","boundary":[0.2037812908496722,0.7188017657828282,0.23490431143790752,0.7325758819444442],"dir":"ltr"},{"str":"divide-and-conquer)","boundary":[0.24117883986928007,0.7188017657828282,0.4051540210784304,0.7325758819444442],"dir":"ltr"},{"str":"which","boundary":[0.4116249183006526,0.7188017657828282,0.45447686764705786,0.7325758819444442],"dir":"ltr"},{"str":"work","boundary":[0.46702589869280947,0.7188017657828282,0.5081311022875807,0.7325758819444442],"dir":"ltr"},{"str":"for","boundary":[0.5147976307189533,0.7188017657828282,0.537293193137254,0.7325758819444442],"dir":"ltr"},{"str":"special","boundary":[0.5439597222222212,0.7188017657828282,0.6003055802287572,0.7325758819444442],"dir":"ltr"},{"str":"kinds","boundary":[0.6067760620915024,0.7188017657828282,0.6523732480392147,0.7325758819444442],"dir":"ltr"},{"str":"of","boundary":[0.6586476307189534,0.7188017657828282,0.6733178746732017,0.7325758819444442],"dir":"ltr"},{"str":"problems;","boundary":[0.6799845588235285,0.7188017657828282,0.7602163547385612,0.7325758819444442],"dir":"ltr"},{"str":"Part","boundary":[0.7676672385620906,0.7188017657828282,0.8036743550653587,0.7325758819444442],"dir":"ltr"},{"str":"III","boundary":[0.8099487254901951,0.7188017657828282,0.8316599735294109,0.7325758819444442],"dir":"ltr"},{"str":"deals","boundary":[0.8381304248366004,0.7188017657828282,0.8809825104575155,0.7325758819444442],"dir":"ltr"},{"str":"with","boundary":[0.11765003267973764,0.7359229779040404,0.15502974297385527,0.7496970940656564],"dir":"ltr"},{"str":"the","boundary":[0.16110803921568537,0.7359229779040404,0.1877212521241821,0.7496970940656564],"dir":"ltr"},{"str":"ìsledgehammersî","boundary":[0.19399562091503178,0.7359229779040404,0.33647345800653505,0.7496970940656564],"dir":"ltr"},{"str":"of","boundary":[0.34294382352941083,0.7359229779040404,0.3576140674836592,0.7496970940656564],"dir":"ltr"},{"str":"the","boundary":[0.36388859477124086,0.7359229779040404,0.39050180767973763,0.7496970940656564],"dir":"ltr"},{"str":"trade","boundary":[0.39677617647058727,0.7359229779040404,0.4404125764705873,0.7496970940656564],"dir":"ltr"},{"str":"techniques","boundary":[0.4517672875816983,0.7359229779040404,0.540608741503267,0.7496970940656564],"dir":"ltr"},{"str":"that","boundary":[0.5466870588235284,0.7359229779040404,0.5813216687908486,0.7496970940656564],"dir":"ltr"},{"str":"are","boundary":[0.5875962091503257,0.7359229779040404,0.6142094220588226,0.7496970940656564],"dir":"ltr"},{"str":"powerful","boundary":[0.6204837908496722,0.7359229779040404,0.6924981111111101,0.7496970940656564],"dir":"ltr"},{"str":"and","boundary":[0.6987725163398684,0.7359229779040404,0.7298955369281036,0.7496970940656564],"dir":"ltr"},{"str":"general:","boundary":[0.7359739869281036,0.7359229779040404,0.8024981065359467,0.7496970940656564],"dir":"ltr"},{"str":"dynamic","boundary":[0.8111254575163389,0.7359229779040404,0.8811968171568618,0.7496970940656564],"dir":"ltr"},{"str":"programming","boundary":[0.1176499673202605,0.7530441900252524,0.22980692352941084,0.7668183061868685],"dir":"ltr"},{"str":"(a","boundary":[0.2364734967320252,0.7530441900252524,0.25232021225490103,0.7668183061868685],"dir":"ltr"},{"str":"novel","boundary":[0.25898673202614286,0.7530441900252524,0.3028192106209141,0.7668183061868685],"dir":"ltr"},{"str":"approach","boundary":[0.309485751633986,0.7530441900252524,0.37816662254901867,0.7668183061868685],"dir":"ltr"},{"str":"helps","boundary":[0.39189212418300556,0.7530441900252524,0.4357246027777768,0.7668183061868685],"dir":"ltr"},{"str":"clarify","boundary":[0.44239114379084876,0.7530441900252524,0.49461934346405134,0.7668183061868685],"dir":"ltr"},{"str":"this","boundary":[0.5014819771241821,0.7530441900252524,0.5331754081699337,0.7668183061868685],"dir":"ltr"},{"str":"traditional","boundary":[0.5398419444444434,0.7530441900252524,0.6282733906862736,0.7668183061868685],"dir":"ltr"},{"str":"stumbling","boundary":[0.6349399836601297,0.7530441900252524,0.7187011942810447,0.7668183061868685],"dir":"ltr"},{"str":"block","boundary":[0.7249756045751624,0.7530441900252524,0.7607688931372539,0.7668183061868685],"dir":"ltr"},{"str":"for","boundary":[0.7744940686274501,0.7530441900252524,0.7969896310457507,0.7668183061868685],"dir":"ltr"},{"str":"students)","boundary":[0.8038522385620905,0.7530441900252524,0.880750698366012,0.7668183061868685],"dir":"ltr"},{"str":"and","boundary":[0.11764962418300554,0.7701654021464645,0.14877264477124083,0.7839395183080805],"dir":"ltr"},{"str":"linear","boundary":[0.15485109477124084,0.7701654021464645,0.203763791503267,0.7839395183080805],"dir":"ltr"},{"str":"programming","boundary":[0.20984210784313628,0.7701654021464645,0.3219990640522866,0.7839395183080805],"dir":"ltr"},{"str":"(a","boundary":[0.3280774019607834,0.7701654021464645,0.34392411748365914,0.7839395183080805],"dir":"ltr"},{"str":"clean","boundary":[0.3501986437908487,0.7701654021464645,0.39324680016339775,0.7839395183080805],"dir":"ltr"},{"str":"and","boundary":[0.39932509803921473,0.7701654021464645,0.43044811862745,0.7839395183080805],"dir":"ltr"},{"str":"intuitive","boundary":[0.4367226470588226,0.7701654021464645,0.5077387490196068,0.7839395183080805],"dir":"ltr"},{"str":"treatment","boundary":[0.5136210130718944,0.7701654021464645,0.5964018307189534,0.7839395183080805],"dir":"ltr"},{"str":"of","boundary":[0.602872320261437,0.7701654021464645,0.6175425642156853,0.7839395183080805],"dir":"ltr"},{"str":"the","boundary":[0.6240131699346395,0.7701654021464645,0.6506263828431363,0.7839395183080805],"dir":"ltr"},{"str":"simplex","boundary":[0.656900751633986,0.7701654021464645,0.7208936748366003,0.7839395183080805],"dir":"ltr"},{"str":"algorithm,","boundary":[0.7269719934640514,0.7701654021464645,0.8130683218954239,0.7839395183080805],"dir":"ltr"},{"str":"duality","boundary":[0.8195388235294108,0.7701654021464645,0.8784337032679728,0.7839395183080805],"dir":"ltr"},{"str":",","boundary":[0.8762767320261428,0.7701654021464645,0.8811608715686264,0.7839395183080805],"dir":"ltr"},{"str":"and","boundary":[0.11764928104575066,0.7872866142676767,0.14877230163398597,0.8010607304292927],"dir":"ltr"},{"str":"reductions","boundary":[0.1550468300653585,0.7872866142676767,0.2411431584967311,0.8010607304292927],"dir":"ltr"},{"str":"to","boundary":[0.24761366013071798,0.7872866142676767,0.26326429705882254,0.8010607304292927],"dir":"ltr"},{"str":"the","boundary":[0.26993098039215585,0.7872866142676767,0.2965441933006526,0.8010607304292927],"dir":"ltr"},{"str":"basic","boundary":[0.3030146405228748,0.7872866142676767,0.3446902545751624,0.8010607304292927],"dir":"ltr"},{"str":"problem).","boundary":[0.35096464052287485,0.7872866142676767,0.42884349330065263,0.8010607304292927],"dir":"ltr"},{"str":"The","boundary":[0.4394316339869271,0.7872866142676767,0.47114289035947615,0.8010607304292927],"dir":"ltr"},{"str":"\u0002nal","boundary":[0.4774172549019598,0.7872866142676767,0.5149930437908486,0.8010607304292927],"dir":"ltr"},{"str":"Part","boundary":[0.5210715032679729,0.7872866142676767,0.5570786687908488,0.8010607304292927],"dir":"ltr"},{"str":"IV","boundary":[0.5633530392156854,0.7872866142676767,0.5835134838235285,0.8010607304292927],"dir":"ltr"},{"str":"is","boundary":[0.589787843137254,0.7872866142676767,0.6036737727124174,0.8010607304292927],"dir":"ltr"},{"str":"about","boundary":[0.6101443790849663,0.7872866142676767,0.656721958006535,0.8010607304292927],"dir":"ltr"},{"str":"ways","boundary":[0.66299633986928,0.7872866142676767,0.7041015537581689,0.8010607304292927],"dir":"ltr"},{"str":"of","boundary":[0.7103759150326786,0.7872866142676767,0.725046158986927,0.8010607304292927],"dir":"ltr"},{"str":"dealing","boundary":[0.7315166013071885,0.7872866142676767,0.792372266993463,0.8010607304292927],"dir":"ltr"},{"str":"with","boundary":[0.7986466666666656,0.7872866142676767,0.8360263769607833,0.8010607304292927],"dir":"ltr"},{"str":"hard","boundary":[0.8421046732026133,0.7872866142676767,0.8810530122549008,0.8010607304292927],"dir":"ltr"},{"str":"problems:","boundary":[0.11764879084967209,0.8044078263888889,0.19788058676470477,0.8181819425505049],"dir":"ltr"},{"str":"NP-completeness","boundary":[0.20552754901960674,0.8044078263888889,0.3468289145424826,0.8181819425505049],"dir":"ltr"},{"str":"various","boundary":[0.35739924836601195,0.8044078263888889,0.41845099264705776,0.8181819425505049],"dir":"ltr"},{"str":"heuristics","boundary":[0.4239410784313714,0.8044078263888889,0.5049393633986917,0.8181819425505049],"dir":"ltr"},{"str":"as","boundary":[0.5151174999999988,0.8044078263888889,0.5333171586601295,0.8181819425505049],"dir":"ltr"},{"str":"well","boundary":[0.5388072058823518,0.8044078263888889,0.5728535800653584,0.8181819425505049],"dir":"ltr"},{"str":"as","boundary":[0.5783436437908486,0.8044078263888889,0.5965433024509793,0.8181819425505049],"dir":"ltr"},{"str":"quantum","boundary":[0.602229428104574,0.8044078263888889,0.6777909883986918,0.8181819425505049],"dir":"ltr"},{"str":"algorithms","boundary":[0.6828889052287571,0.8044078263888889,0.7723185697712407,0.8181819425505049],"dir":"ltr"},{"str":"perhaps","boundary":[0.7824967320261428,0.8044078263888889,0.8486465197712408,0.8181819425505049],"dir":"ltr"},{"str":"the","boundary":[0.8543326797385611,0.8044078263888889,0.8809458926470578,0.8181819425505049],"dir":"ltr"},{"str":"most","boundary":[0.11764803921568528,0.8213775233585857,0.15738069264705784,0.8351516395202019],"dir":"ltr"},{"str":"advanced","boundary":[0.16326290849673106,0.8213775233585857,0.2407674294117637,0.8351516395202019],"dir":"ltr"},{"str":"and","boundary":[0.24645359477124085,0.8213775233585857,0.27757661535947614,0.8351516395202019],"dir":"ltr"},{"str":"modern","boundary":[0.2832627450980382,0.8213775233585857,0.34570486486928004,0.8351516395202019],"dir":"ltr"},{"str":"topic","boundary":[0.351587091503267,0.8213775233585857,0.3909097624182997,0.8351516395202019],"dir":"ltr"},{"str":"As","boundary":[0.40442137254901867,0.8213775233585857,0.425562210130718,0.8351516395202019],"dir":"ltr"},{"str":"it","boundary":[0.43124833333333235,0.8213775233585857,0.4378793405228748,0.8351516395202019],"dir":"ltr"},{"str":"happens","boundary":[0.4496440849673193,0.8213775233585857,0.5189311302287573,0.8351516395202019],"dir":"ltr"},{"str":"we","boundary":[0.5293052941176462,0.8213775233585857,0.5520147604575155,0.8351516395202019],"dir":"ltr"},{"str":"end","boundary":[0.5577008823529402,0.8213775233585857,0.5876474313725482,0.8351516395202019],"dir":"ltr"},{"str":"the","boundary":[0.5935296405228749,0.8213775233585857,0.6201428534313717,0.8351516395202019],"dir":"ltr"},{"str":"story","boundary":[0.6260250653594762,0.8213775233585857,0.6673085222222213,0.8351516395202019],"dir":"ltr"},{"str":"exactly","boundary":[0.673190751633986,0.8213775233585857,0.7314973955882343,0.8351516395202019],"dir":"ltr"},{"str":"where","boundary":[0.7373796405228749,0.8213775233585857,0.7876827127450972,0.8351516395202019],"dir":"ltr"},{"str":"we","boundary":[0.7935649346405219,0.8213775233585857,0.8162744009803913,0.8351516395202019],"dir":"ltr"},{"str":"started","boundary":[0.8221566013071887,0.8213775233585857,0.8808554024509796,0.8351516395202019],"dir":"ltr"},{"str":"it,","boundary":[0.11764679738561999,0.8384987354797979,0.13504431633986835,0.8522728516414141],"dir":"ltr"},{"str":"with","boundary":[0.14014238562091413,0.8384987354797979,0.17752209591503176,0.8522728516414141],"dir":"ltr"},{"str":"Shor's","boundary":[0.182227843137254,0.8384987354797979,0.22761124215686185,0.8522728516414141],"dir":"ltr"},{"str":"quantum","boundary":[0.2374150163398684,0.8384987354797979,0.31297657663398604,0.8522728516414141],"dir":"ltr"},{"str":"algorithm","boundary":[0.31768233660130635,0.8384987354797979,0.3988945254901952,0.8522728516414141],"dir":"ltr"},{"str":"for","boundary":[0.40360031045751543,0.8384987354797979,0.42609587287581613,0.8522728516414141],"dir":"ltr"},{"str":"factoring","boundary":[0.4311939379084958,0.8384987354797979,0.5045629830065351,0.8522728516414141],"dir":"ltr"},{"str":".","boundary":[0.5041707352941168,0.8384987354797979,0.5090548748366004,0.8522728516414141],"dir":"ltr"},{"str":"The","boundary":[0.1452932843137246,0.8584987354797978,0.1770045406862736,0.872272851641414],"dir":"ltr"},{"str":"book","boundary":[0.18269066993463964,0.8584987354797978,0.22085469460784224,0.872272851641414],"dir":"ltr"},{"str":"includes","boundary":[0.22654083333333244,0.8584987354797978,0.29463360604575073,0.872272851641414],"dir":"ltr"},{"str":"three","boundary":[0.3003197549019599,0.8584987354797978,0.3435639977124174,0.872272851641414],"dir":"ltr"},{"str":"additional","boundary":[0.3496423039215677,0.8584987354797978,0.4335817678104566,0.872272851641414],"dir":"ltr"},{"str":"undercurrents","boundary":[0.4390718790849664,0.8584987354797978,0.5570755424836593,0.872272851641414],"dir":"ltr"},{"str":"in","boundary":[0.567645866013071,0.8584987354797978,0.5842768959150317,0.872272851641414],"dir":"ltr"},{"str":"the","boundary":[0.5897671078431364,0.8584987354797978,0.6163803207516331,0.872272851641414],"dir":"ltr"},{"str":"form","boundary":[0.6222625326797376,0.8584987354797978,0.6606226359477115,0.872272851641414],"dir":"ltr"},{"str":"of","boundary":[0.6665048529411756,0.8584987354797978,0.681175096895424,0.872272851641414],"dir":"ltr"},{"str":"three","boundary":[0.6870573039215677,0.8584987354797978,0.7303015467320253,0.872272851641414],"dir":"ltr"},{"str":"series","boundary":[0.7361837745098031,0.8584987354797978,0.7837239210784306,0.872272851641414],"dir":"ltr"},{"str":"of","boundary":[0.7896061601307182,0.8584987354797978,0.8042764040849665,0.872272851641414],"dir":"ltr"},{"str":"separate","boundary":[0.8101586111111103,0.8584987354797978,0.8808003812091495,0.872272851641414],"dir":"ltr"},{"str":"9","boundary":[0.49509651960784234,0.8930441900252524,0.5050787026143783,0.9068183061868685],"dir":"ltr"}],"boundary":[0.11765,0.21031,0.88139,0.90682],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":9,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/f3f93c9f736f9bfccf54ba54eaa81a92.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/520fa8c42f77533acedb22d8ed63f55a.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11767,0.80606]},"elements":[{"words":[{"str":"10","boundary":[0.11764705882352941,0.09001376073232323,0.1376114248366013,0.10378787689393938],"dir":"ltr"},{"str":"Algorithms","boundary":[0.7899640522875817,0.08979153426128839,0.8823348957516342,0.10356565042290454],"dir":"ltr"},{"str":"ìboxes","boundary":[0.11764705882352941,0.12880163952020204,0.16989309166666666,0.1425757556818182],"dir":"ltr"},{"str":",","boundary":[0.16950081699346406,0.12880163952020204,0.17497318104575163,0.1425757556818182],"dir":"ltr"},{"str":"î","boundary":[0.17379673202614376,0.12880163952020204,0.1753475633986928,0.1425757556818182],"dir":"ltr"},{"str":"strengthening","boundary":[0.1859357516339869,0.12880163952020204,0.3019786290849673,0.1425757556818182],"dir":"ltr"},{"str":"the","boundary":[0.30707660130718956,0.12880163952020204,0.3336898142156863,0.1425757556818182],"dir":"ltr"},{"str":"narrative","boundary":[0.33878787581699343,0.12880163952020204,0.4162745714052288,0.1425757556818182],"dir":"ltr"},{"str":"(and","boundary":[0.4213725163398693,0.12880163952020204,0.45836006944444446,0.1425757556818182],"dir":"ltr"},{"str":"addressing","boundary":[0.4634579738562091,0.12880163952020204,0.553083716993464,0.1425757556818182],"dir":"ltr"},{"str":"variations","boundary":[0.5581816666666666,0.12880163952020204,0.6417289733660131,0.1425757556818182],"dir":"ltr"},{"str":"in","boundary":[0.6466308496732026,0.12880163952020204,0.6632618795751634,0.1425757556818182],"dir":"ltr"},{"str":"the","boundary":[0.6683599346405228,0.12880163952020204,0.6949731475490196,0.1425757556818182],"dir":"ltr"},{"str":"needs","boundary":[0.7000710457516339,0.12880163952020204,0.747040781862745,0.1425757556818182],"dir":"ltr"},{"str":"and","boundary":[0.75233477124183,0.12880163952020204,0.7834577918300653,0.1425757556818182],"dir":"ltr"},{"str":"interests","boundary":[0.7885558496732026,0.12880163952020204,0.8607484232026142,0.1425757556818182],"dir":"ltr"},{"str":"of","boundary":[0.8660424509803921,0.12880163952020204,0.8807126949346405,0.1425757556818182],"dir":"ltr"},{"str":"the","boundary":[0.11764702614379084,0.1459228516414141,0.14426023905228758,0.15969696780303025],"dir":"ltr"},{"str":"students)","boundary":[0.14818166666666666,0.1459228516414141,0.22508012647058828,0.15969696780303025],"dir":"ltr"},{"str":"while","boundary":[0.22939375816993465,0.1459228516414141,0.27440270833333336,0.15969696780303025],"dir":"ltr"},{"str":"keeping","boundary":[0.2781280718954248,0.1459228516414141,0.34270923088235294,0.15969696780303025],"dir":"ltr"},{"str":"the","boundary":[0.3466306862745098,0.1459228516414141,0.37324389918300654,0.15969696780303025],"dir":"ltr"},{"str":"\u0003ow","boundary":[0.3771653267973856,0.1459228516414141,0.41083736911764707,0.15969696780303025],"dir":"ltr"},{"str":"intact:","boundary":[0.4147587908496732,0.1459228516414141,0.46777131274509803,0.15969696780303025],"dir":"ltr"},{"str":"pieces","boundary":[0.47345748366013074,0.1459228516414141,0.5229584161764707,0.15969696780303025],"dir":"ltr"},{"str":"that","boundary":[0.5270759477124184,0.1459228516414141,0.5617105576797385,0.15969696780303025],"dir":"ltr"},{"str":"provide","boundary":[0.5656319934640524,0.1459228516414141,0.6266837377450981,0.15969696780303025],"dir":"ltr"},{"str":"historical","boundary":[0.6308012745098039,0.1459228516414141,0.7082701447712418,0.15969696780303025],"dir":"ltr"},{"str":"context;","boundary":[0.7121916339869281,0.1459228516414141,0.7767549676470589,0.15969696780303025],"dir":"ltr"},{"str":"descriptions","boundary":[0.781460751633987,0.1459228516414141,0.880658695261438,0.15969696780303025],"dir":"ltr"},{"str":"of","boundary":[0.11764702614379084,0.16304406376262615,0.128003527124183,0.1768181799242423],"dir":"ltr"},{"str":"how","boundary":[0.13663101307189543,0.16304406376262615,0.17030305539215684,0.1768181799242423],"dir":"ltr"},{"str":"the","boundary":[0.17442055555555555,0.16304406376262615,0.20103376846405227,0.1768181799242423],"dir":"ltr"},{"str":"explained","boundary":[0.20534735294117645,0.16304406376262615,0.28518699166666667,0.1768181799242423],"dir":"ltr"},{"str":"algorithms","boundary":[0.2893045424836601,0.16304406376262615,0.3787342070261438,0.1768181799242423],"dir":"ltr"},{"str":"are","boundary":[0.38265568627450974,0.16304406376262615,0.4092688991830065,0.1768181799242423],"dir":"ltr"},{"str":"used","boundary":[0.4135824836601307,0.16304406376262615,0.4517465083333333,0.1768181799242423],"dir":"ltr"},{"str":"in","boundary":[0.45586401960784306,0.16304406376262615,0.4724950495098038,0.1768181799242423],"dir":"ltr"},{"str":"practice","boundary":[0.47661271241830055,0.16304406376262615,0.5415682032679737,0.1768181799242423],"dir":"ltr"},{"str":"(with","boundary":[0.5458818300653594,0.16304406376262615,0.5891260728758169,0.1768181799242423],"dir":"ltr"},{"str":"emphasis","boundary":[0.5932435947712418,0.16304406376262615,0.671140272875817,0.1768181799242423],"dir":"ltr"},{"str":"on","boundary":[0.6752578104575163,0.16304406376262615,0.6950260978758169,0.1768181799242423],"dir":"ltr"},{"str":"internet","boundary":[0.6991437581699346,0.16304406376262615,0.765863956372549,0.1768181799242423],"dir":"ltr"},{"str":"applications);","boundary":[0.7701775816993464,0.16304406376262615,0.8809085117647059,0.1768181799242423],"dir":"ltr"},{"str":"and","boundary":[0.11764653594771235,0.1801652758838382,0.14876955653594764,0.19393939204545435],"dir":"ltr"},{"str":"excursions","boundary":[0.15367137254901955,0.1801652758838382,0.24055201535947707,0.19393939204545435],"dir":"ltr"},{"str":"for","boundary":[0.2454538888888888,0.1801652758838382,0.26794945130718945,0.19393939204545435],"dir":"ltr"},{"str":"the","boundary":[0.2732435947712417,0.1801652758838382,0.2998568076797385,0.19393939204545435],"dir":"ltr"},{"str":"mathematically","boundary":[0.30475862745098026,0.1801652758838382,0.43431310261437894,0.19393939204545435],"dir":"ltr"},{"str":"sophisticated.","boundary":[0.43901875816993446,0.1801652758838382,0.5521026313725489,0.19393939204545435],"dir":"ltr"}],"boundary":[0.11765,0.08979,0.88233,0.19394],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":10,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/97b854c6df0802b4cc877712044efa0e.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/3bebfbbf035bc1ca03f9661f7a692293.jpg"},"info":{"width":612,"height":792,"margin":[0.11764,0.20785,0.11854,0.09318]},"elements":[{"words":[{"str":"Chapter","boundary":[0.11764705882352941,0.20784714772727275,0.2612048614379085,0.23393628914141415],"dir":"ltr"},{"str":"0","boundary":[0.27100849673202615,0.20784714772727275,0.2903881248366013,0.23393628914141415],"dir":"ltr"},{"str":"Prologue","boundary":[0.11764705882352941,0.2648531231060606,0.30865353529411765,0.29614996654040404],"dir":"ltr"},{"str":"Look","boundary":[0.11764705882352941,0.3545592152777778,0.15777186944444443,0.36833333143939395],"dir":"ltr"},{"str":"around","boundary":[0.16208545751633988,0.3545592152777778,0.2208020839869281,0.36833333143939395],"dir":"ltr"},{"str":"you.","boundary":[0.2251156862745098,0.3545592152777778,0.25935813905228755,0.36833333143939395],"dir":"ltr"},{"str":"Computers","boundary":[0.2652403594771242,0.3545592152777778,0.35566824232026145,0.36833333143939395],"dir":"ltr"},{"str":"and","boundary":[0.36017794117647056,0.3545592152777778,0.39130096176470586,0.36833333143939395],"dir":"ltr"},{"str":"networks","boundary":[0.3954186274509804,0.3545592152777778,0.4713545196078431,0.36833333143939395],"dir":"ltr"},{"str":"are","boundary":[0.4758642156862745,0.3545592152777778,0.5024774285947713,0.36833333143939395],"dir":"ltr"},{"str":"everywhere","boundary":[0.5067910130718954,0.3545592152777778,0.6017108782679739,0.36833333143939395],"dir":"ltr"},{"str":"enabling","boundary":[0.6111046732026145,0.3545592152777778,0.6827268362745099,0.36833333143939395],"dir":"ltr"},{"str":"an","boundary":[0.686648300653595,0.3545592152777778,0.707593059640523,0.36833333143939395],"dir":"ltr"},{"str":"intricate","boundary":[0.7117105555555557,0.3545592152777778,0.7821384217320263,0.36833333143939395],"dir":"ltr"},{"str":"web","boundary":[0.7864520588235295,0.3545592152777778,0.8191437081699348,0.36833333143939395],"dir":"ltr"},{"str":"of","boundary":[0.823261209150327,0.3545592152777778,0.8334217950980394,0.36833333143939395],"dir":"ltr"},{"str":"com-","boundary":[0.8424411111111112,0.3545592152777778,0.880801214379085,0.36833333143939395],"dir":"ltr"},{"str":"plex","boundary":[0.11764699346405236,0.37168042739898993,0.15188944624183015,0.3854545435606061],"dir":"ltr"},{"str":"human","boundary":[0.15659519607843145,0.37168042739898993,0.21532964787581704,0.3854545435606061],"dir":"ltr"},{"str":"activities:","boundary":[0.2196432352941177,0.37168042739898993,0.29964330196078437,0.3854545435606061],"dir":"ltr"},{"str":"education,","boundary":[0.3057216666666667,0.37168042739898993,0.39064152352941184,0.3854545435606061],"dir":"ltr"},{"str":"commerce","boundary":[0.395347320261438,0.37168042739898993,0.4769694916666667,0.3854545435606061],"dir":"ltr"},{"str":"entertainment,","boundary":[0.48675545751634,0.37168042739898993,0.6108197320261439,0.3854545435606061],"dir":"ltr"},{"str":"research,","boundary":[0.6157214705882353,0.37168042739898993,0.6906590357843138,0.3854545435606061],"dir":"ltr"},{"str":"manufacturing","boundary":[0.6957570915032679,0.37168042739898993,0.8190548769607844,0.3854545435606061],"dir":"ltr"},{"str":",","boundary":[0.8186626470588234,0.37168042739898993,0.8192331320261437,0.3854545435606061],"dir":"ltr"},{"str":"health","boundary":[0.8278604411764705,0.37168042739898993,0.8810868669934641,0.3854545435606061],"dir":"ltr"},{"str":"management,","boundary":[0.11764638888888881,0.388801639520202,0.23019550228758162,0.40257575568181825],"dir":"ltr"},{"str":"human","boundary":[0.23431305555555548,0.388801639520202,0.2930475073529411,0.40257575568181825],"dir":"ltr"},{"str":"communication,","boundary":[0.2967728594771241,0.388801639520202,0.4276998848039215,0.40257575568181825],"dir":"ltr"},{"str":"even","boundary":[0.43181746732026144,0.388801639520202,0.46998149199346406,0.40257575568181825],"dir":"ltr"},{"str":"war","boundary":[0.4740990032679739,0.388801639520202,0.5071827970588235,0.40257575568181825],"dir":"ltr"},{"str":"Of","boundary":[0.514419820261438,0.388801639520202,0.5341881076797386,0.40257575568181825],"dir":"ltr"},{"str":"the","boundary":[0.5383057679738563,0.388801639520202,0.564918980882353,0.40257575568181825],"dir":"ltr"},{"str":"two","boundary":[0.5690366503267975,0.388801639520202,0.5985910421568629,0.40257575568181825],"dir":"ltr"},{"str":"main","boundary":[0.6027087091503269,0.388801639520202,0.6451864629084968,0.40257575568181825],"dir":"ltr"},{"str":"technological","boundary":[0.6491078921568628,0.388801639520202,0.7563272580065361,0.40257575568181825],"dir":"ltr"},{"str":"underpinnings","boundary":[0.760444820261438,0.388801639520202,0.8813896625816995,0.40257575568181825],"dir":"ltr"},{"str":"of","boundary":[0.11764580065359488,0.4059229779040404,0.13231604460784324,0.4196970940656566],"dir":"ltr"},{"str":"this","boundary":[0.1383944934640524,0.4059229779040404,0.170087924509804,0.4196970940656566],"dir":"ltr"},{"str":"amazing","boundary":[0.17597014705882366,0.4059229779040404,0.24662974248366026,0.4196970940656566],"dir":"ltr"},{"str":"proliferation,","boundary":[0.25211982026143803,0.4059229779040404,0.35990957140522895,0.4196970940656566],"dir":"ltr"},{"str":"one","boundary":[0.3663799509803923,0.4059229779040404,0.3949539498366014,0.4196970940656566],"dir":"ltr"},{"str":"is","boundary":[0.40103240196078443,0.4059229779040404,0.40903612385620924,0.4196970940656566],"dir":"ltr"},{"str":"obvious:","boundary":[0.42080053921568644,0.4059229779040404,0.48771681601307204,0.4196970940656566],"dir":"ltr"},{"str":"the","boundary":[0.4957559313725492,0.4059229779040404,0.522369144281046,0.4196970940656566],"dir":"ltr"},{"str":"breathtaking","boundary":[0.5284475980392158,0.4059229779040404,0.6364690784313727,0.4196970940656566],"dir":"ltr"},{"str":"pace","boundary":[0.6421552777777779,0.4059229779040404,0.6789467522875818,0.4196970940656566],"dir":"ltr"},{"str":"with","boundary":[0.6850252124183007,0.4059229779040404,0.7224049227124184,0.4196970940656566],"dir":"ltr"},{"str":"which","boundary":[0.7280910620915033,0.4059229779040404,0.7713353316993464,0.4196970940656566],"dir":"ltr"},{"str":"advances","boundary":[0.7830997222222222,0.4059229779040404,0.8586434571895425,0.4196970940656566],"dir":"ltr"},{"str":"in","boundary":[0.8645257026143791,0.4059229779040404,0.8811567325163399,0.4196970940656566],"dir":"ltr"},{"str":"microelectronics","boundary":[0.11764498366013075,0.4230441900252525,0.2508893014705883,0.43681830618686873],"dir":"ltr"},{"str":"and","boundary":[0.25637929738562093,0.4230441900252525,0.2875023179738562,0.43681830618686873],"dir":"ltr"},{"str":"chip","boundary":[0.29220805555555557,0.4230441900252525,0.32664657908496736,0.43681830618686873],"dir":"ltr"},{"str":"design","boundary":[0.33174447712418303,0.4230441900252525,0.38516698153594775,0.43681830618686873],"dir":"ltr"},{"str":"have","boundary":[0.3900688235294118,0.4230441900252525,0.42921325359477125,0.43681830618686873],"dir":"ltr"},{"str":"been","boundary":[0.43391915032679734,0.4230441900252525,0.47247533218954246,0.43681830618686873],"dir":"ltr"},{"str":"bringing","boundary":[0.47757339869281046,0.4230441900252525,0.5478230116013072,0.43681830618686873],"dir":"ltr"},{"str":"us","boundary":[0.5523327124183006,0.4230441900252525,0.5715127640522876,0.43681830618686873],"dir":"ltr"},{"str":"faster","boundary":[0.5764145751633987,0.4230441900252525,0.6239547217320262,0.43681830618686873],"dir":"ltr"},{"str":"and","boundary":[0.6290526470588235,0.4230441900252525,0.6601756676470588,0.43681830618686873],"dir":"ltr"},{"str":"faster","boundary":[0.6650774836601306,0.4230441900252525,0.7126176302287581,0.43681830618686873],"dir":"ltr"},{"str":"hardware","boundary":[0.7177155555555554,0.4230441900252525,0.7967887357843136,0.43681830618686873],"dir":"ltr"},{"str":".","boundary":[0.7963966013071895,0.4230441900252525,0.8012807408496732,0.43681830618686873],"dir":"ltr"},{"str":"This","boundary":[0.14529202614379078,0.44046843244949496,0.1820835006535947,0.45424254861111113],"dir":"ltr"},{"str":"book","boundary":[0.1883578758169934,0.44046843244949496,0.226521900490196,0.45424254861111113],"dir":"ltr"},{"str":"tells","boundary":[0.23318843137254894,0.44046843244949496,0.2683934517973855,0.45424254861111113],"dir":"ltr"},{"str":"the","boundary":[0.2748639215686274,0.44046843244949496,0.3014771344771241,0.45424254861111113],"dir":"ltr"},{"str":"story","boundary":[0.30814366013071887,0.44046843244949496,0.34942711699346396,0.45424254861111113],"dir":"ltr"},{"str":"of","boundary":[0.3560936601307189,0.44046843244949496,0.37076390408496723,0.45424254861111113],"dir":"ltr"},{"str":"the","boundary":[0.3774305882352941,0.44046843244949496,0.4040438011437908,0.45424254861111113],"dir":"ltr"},{"str":"other","boundary":[0.41071032679738556,0.44046843244949496,0.4539545696078431,0.45424254861111113],"dir":"ltr"},{"str":"intellectual","boundary":[0.4608171895424836,0.44046843244949496,0.5545249325163398,0.45424254861111113],"dir":"ltr"},{"str":"enterprise","boundary":[0.5607993790849672,0.44046843244949496,0.6447388429738562,0.45424254861111113],"dir":"ltr"},{"str":"that","boundary":[0.6516015032679738,0.44046843244949496,0.686236113235294,0.45424254861111113],"dir":"ltr"},{"str":"is","boundary":[0.6927067320261437,0.44046843244949496,0.7065926616013072,0.45424254861111113],"dir":"ltr"},{"str":"crucially","boundary":[0.7130631045751633,0.44046843244949496,0.7840792065359476,0.45424254861111113],"dir":"ltr"},{"str":"fueling","boundary":[0.7903537908496732,0.44046843244949496,0.8478761204248365,0.45424254861111113],"dir":"ltr"},{"str":"the","boundary":[0.8543466013071894,0.44046843244949496,0.8809598142156861,0.45424254861111113],"dir":"ltr"},{"str":"computer","boundary":[0.1176456209150326,0.45758964457070705,0.1947579846405228,0.4713637607323233],"dir":"ltr"},{"str":"revolution:","boundary":[0.2000519934640522,0.45758964457070705,0.28887559689542475,0.4713637607323233],"dir":"ltr"},{"str":"ef\u0002cient","boundary":[0.2951500326797385,0.45758964457070705,0.3585368947712418,0.4713637607323233],"dir":"ltr"},{"str":"algorithms","boundary":[0.36363483660130713,0.45758964457070705,0.4526723439542483,0.4713637607323233],"dir":"ltr"},{"str":".","boundary":[0.451691862745098,0.45758964457070705,0.45657600228758166,0.4713637607323233],"dir":"ltr"},{"str":"It","boundary":[0.4630465522875816,0.45758964457070705,0.47222674509803914,0.4713637607323233],"dir":"ltr"},{"str":"is","boundary":[0.4820303758169935,0.45758964457070705,0.49101448986928103,0.4713637607323233],"dir":"ltr"},{"str":"a","boundary":[0.5008181209150326,0.45758964457070705,0.5058984019607843,0.4713637607323233],"dir":"ltr"},{"str":"fascinating","boundary":[0.5157022058823528,0.45758964457070705,0.6072709096405228,0.4713637607323233],"dir":"ltr"},{"str":"story","boundary":[0.6119767156862745,0.45758964457070705,0.6532601725490197,0.4713637607323233],"dir":"ltr"},{"str":".","boundary":[0.6511033496732026,0.45758964457070705,0.6559874892156863,0.4713637607323233],"dir":"ltr"},{"str":"Gather","boundary":[0.1452928921568628,0.4751654021464647,0.20224481127450988,0.48893951830808086],"dir":"ltr"},{"str":"'round","boundary":[0.20734272875817,0.4751654021464647,0.2605691545751635,0.48893951830808086],"dir":"ltr"},{"str":"and","boundary":[0.26527491830065364,0.4751654021464647,0.29737833186274515,0.48893951830808086],"dir":"ltr"},{"str":"listen","boundary":[0.302084068627451,0.4751654021464647,0.34668303627450986,0.48893951830808086],"dir":"ltr"},{"str":"close","boundary":[0.35178096405228765,0.4751654021464647,0.3899271633986929,0.48893951830808086],"dir":"ltr"},{"str":".","boundary":[0.38933880718954256,0.4751654021464647,0.3942229467320262,0.48893951830808086],"dir":"ltr"},{"str":"0.1","boundary":[0.11764599673202618,0.5092038724747475,0.15116734640522878,0.5273177613636364],"dir":"ltr"},{"str":"Books","boundary":[0.17450073529411766,0.5092038724747475,0.24873997614379087,0.5273177613636364],"dir":"ltr"},{"str":"and","boundary":[0.25540678104575165,0.5092038724747475,0.3014458934640523,0.5273177613636364],"dir":"ltr"},{"str":"algorithms","boundary":[0.3081126633986928,0.5092038724747475,0.4403227418300654,0.5273177613636364],"dir":"ltr"},{"str":"Two","boundary":[0.11764534313725492,0.5498623718434344,0.15229777843137257,0.5636364880050506],"dir":"ltr"},{"str":"ideas","boundary":[0.15857214052287583,0.5498623718434344,0.20142422614379088,0.5636364880050506],"dir":"ltr"},{"str":"changed","boundary":[0.2075025326797386,0.5498623718434344,0.27561309852941185,0.5636364880050506],"dir":"ltr"},{"str":"the","boundary":[0.2818874836601308,0.5498623718434344,0.3085006965686275,0.5636364880050506],"dir":"ltr"},{"str":"world.","boundary":[0.31477506535947714,0.5498623718434344,0.3660407052287582,0.5636364880050506],"dir":"ltr"},{"str":"In","boundary":[0.37623666666666666,0.5498623718434344,0.3944363253267974,0.5636364880050506],"dir":"ltr"},{"str":"1448","boundary":[0.4005147712418301,0.5498623718434344,0.4404435032679739,0.5636364880050506],"dir":"ltr"},{"str":"in","boundary":[0.4463257189542484,0.5498623718434344,0.46295674885620913,0.5636364880050506],"dir":"ltr"},{"str":"the","boundary":[0.46903519607843136,0.5498623718434344,0.4956484089869281,0.5636364880050506],"dir":"ltr"},{"str":"German","boundary":[0.5021188562091503,0.5498623718434344,0.5694629408496732,0.5636364880050506],"dir":"ltr"},{"str":"city","boundary":[0.5755412418300654,0.5498623718434344,0.6054699655228759,0.5636364880050506],"dir":"ltr"},{"str":"of","boundary":[0.6117443464052288,0.5498623718434344,0.6264145903594771,0.5636364880050506],"dir":"ltr"},{"str":"Mainz","boundary":[0.6328851960784314,0.5498623718434344,0.6849529756535948,0.5636364880050506],"dir":"ltr"},{"str":"a","boundary":[0.6908351960784314,0.5498623718434344,0.6947389411764706,0.5636364880050506],"dir":"ltr"},{"str":"goldsmith","boundary":[0.706895816993464,0.5498623718434344,0.7886962416666666,0.5636364880050506],"dir":"ltr"},{"str":"named","boundary":[0.7949706535947711,0.5498623718434344,0.8507639264705882,0.5636364880050506],"dir":"ltr"},{"str":"Jo-","boundary":[0.8568422222222222,0.5498623718434344,0.8811024825163399,0.5636364880050506],"dir":"ltr"},{"str":"hann","boundary":[0.11764465686274513,0.5669835839646465,0.16051456781045756,0.5807577001262627],"dir":"ltr"},{"str":"Gutenberg","boundary":[0.16502423202614383,0.5669835839646465,0.2527070145424837,0.5807577001262627],"dir":"ltr"},{"str":"discovered","boundary":[0.2574127941176471,0.5669835839646465,0.34331304395424844,0.5807577001262627],"dir":"ltr"},{"str":"a","boundary":[0.3484109967320262,0.5669835839646465,0.35368735620915037,0.5807577001262627],"dir":"ltr"},{"str":"way","boundary":[0.3630990032679739,0.5669835839646465,0.3912809013071896,0.5807577001262627],"dir":"ltr"},{"str":"to","boundary":[0.40069251633986935,0.5669835839646465,0.41634315326797394,0.5807577001262627],"dir":"ltr"},{"str":"print","boundary":[0.4212449673202615,0.5669835839646465,0.4627245027777778,0.5807577001262627],"dir":"ltr"},{"str":"books","boundary":[0.46762633986928115,0.5669835839646465,0.5140078401960786,0.5807577001262627],"dir":"ltr"},{"str":"by","boundary":[0.5189096732026145,0.5669835839646465,0.5384818820261439,0.5807577001262627],"dir":"ltr"},{"str":"putting","boundary":[0.5429916993464053,0.5669835839646465,0.6040434436274511,0.5807577001262627],"dir":"ltr"},{"str":"together","boundary":[0.6087492156862746,0.5669835839646465,0.6772341212418302,0.5807577001262627],"dir":"ltr"},{"str":"movable","boundary":[0.6823320588235295,0.5669835839646465,0.7510308683006537,0.5807577001262627],"dir":"ltr"},{"str":"metallic","boundary":[0.7557366339869283,0.5669835839646465,0.8220646750000001,0.5807577001262627],"dir":"ltr"},{"str":"pieces","boundary":[0.82677045751634,0.5669835839646465,0.87627139003268,0.5807577001262627],"dir":"ltr"},{"str":".","boundary":[0.875879117647059,0.5669835839646465,0.8807632571895426,0.5807577001262627],"dir":"ltr"},{"str":"Literacy","boundary":[0.11764382352941186,0.5839532809343435,0.18612872908496741,0.5977273970959597],"dir":"ltr"},{"str":"spread,","boundary":[0.1922070588235295,0.5839532809343435,0.25227841013071906,0.5977273970959597],"dir":"ltr"},{"str":"the","boundary":[0.25894496732026157,0.5839532809343435,0.2855581802287583,0.5977273970959597],"dir":"ltr"},{"str":"Dark","boundary":[0.29163663398692824,0.5839532809343435,0.33391830915032694,0.5977273970959597],"dir":"ltr"},{"str":"Ages","boundary":[0.33999660130718967,0.5839532809343435,0.37953317614379095,0.5977273970959597],"dir":"ltr"},{"str":"ended,","boundary":[0.3856116339869282,0.5839532809343435,0.43942629558823537,0.5977273970959597],"dir":"ltr"},{"str":"the","boundary":[0.44589676470588246,0.5839532809343435,0.4725099776143792,0.5977273970959597],"dir":"ltr"},{"str":"human","boundary":[0.4785884313725491,0.5839532809343435,0.5373228831699347,0.5977273970959597],"dir":"ltr"},{"str":"intellect","boundary":[0.5430090196078433,0.5839532809343435,0.6101035496732028,0.5977273970959597],"dir":"ltr"},{"str":"was","boundary":[0.6163779738562093,0.5839532809343435,0.6480892174836602,0.5977273970959597],"dir":"ltr"},{"str":"liberated,","boundary":[0.6541676633986929,0.5839532809343435,0.7328130052287584,0.5977273970959597],"dir":"ltr"},{"str":"science","boundary":[0.7390874346405231,0.5839532809343435,0.7971980000000002,0.5977273970959597],"dir":"ltr"},{"str":"and","boundary":[0.8034724019607844,0.5839532809343435,0.8345954225490197,0.5977273970959597],"dir":"ltr"},{"str":"tech-","boundary":[0.8406737091503269,0.5839532809343435,0.8807807196078432,0.5977273970959597],"dir":"ltr"},{"str":"nology","boundary":[0.11764315359477134,0.6010744930555556,0.17106565800653606,0.6148486092171718],"dir":"ltr"},{"str":"triumphed,","boundary":[0.17655573529411775,0.6010744930555556,0.2687305001633988,0.6148486092171718],"dir":"ltr"},{"str":"the","boundary":[0.27441668300653604,0.6010744930555556,0.3010298959150328,0.6148486092171718],"dir":"ltr"},{"str":"Industrial","boundary":[0.30671602941176485,0.6010744930555556,0.39026333611111125,0.6148486092171718],"dir":"ltr"},{"str":"Revolution","boundary":[0.3955573692810459,0.6010744930555556,0.48459487663398704,0.6148486092171718],"dir":"ltr"},{"str":"happened.","boundary":[0.49008498366013087,0.6010744930555556,0.5750226658496734,0.6148486092171718],"dir":"ltr"},{"str":"Many","boundary":[0.5830617810457518,0.6010744930555556,0.6304414996732027,0.6148486092171718],"dir":"ltr"},{"str":"historians","boundary":[0.6357356372549021,0.6010744930555556,0.7188907867647061,0.6148486092171718],"dir":"ltr"},{"str":"say","boundary":[0.724184820261438,0.6010744930555556,0.7462883196078433,0.6148486092171718],"dir":"ltr"},{"str":"we","boundary":[0.7572685620915034,0.6010744930555556,0.7799780284313728,0.6148486092171718],"dir":"ltr"},{"str":"owe","boundary":[0.7854682352941178,0.6010744930555556,0.8169834130718956,0.6148486092171718],"dir":"ltr"},{"str":"all","boundary":[0.8226695424836603,0.6010744930555556,0.8439886333333335,0.6148486092171718],"dir":"ltr"},{"str":"this","boundary":[0.8492827777777778,0.6010744930555556,0.8809762088235294,0.6148486092171718],"dir":"ltr"},{"str":"to","boundary":[0.11764388888888899,0.6181957051767677,0.13329452581699358,0.631969821338384],"dir":"ltr"},{"str":"typography","boundary":[0.13780434640522887,0.6181957051767677,0.2313516614379086,0.631969821338384],"dir":"ltr"},{"str":"Imagine","boundary":[0.2401572549019609,0.6181957051767677,0.30826782859477136,0.631969821338384],"dir":"ltr"},{"str":"a","boundary":[0.3123853594771243,0.6181957051767677,0.3180538594771243,0.631969821338384],"dir":"ltr"},{"str":"world","boundary":[0.3266812254901962,0.6181957051767677,0.37306272581699357,0.631969821338384],"dir":"ltr"},{"str":"in","boundary":[0.3775724019607844,0.6181957051767677,0.3942034318627452,0.631969821338384],"dir":"ltr"},{"str":"which","boundary":[0.39832109477124195,0.6181957051767677,0.44313387745098043,0.631969821338384],"dir":"ltr"},{"str":"only","boundary":[0.4517612418300654,0.6181957051767677,0.48678800898692814,0.631969821338384],"dir":"ltr"},{"str":"an","boundary":[0.4911016013071896,0.6181957051767677,0.5120463602941178,0.631969821338384],"dir":"ltr"},{"str":"elite","boundary":[0.5161640196078432,0.6181957051767677,0.5519572758169935,0.631969821338384],"dir":"ltr"},{"str":"could","boundary":[0.5564669607843137,0.6181957051767677,0.5999072821895425,0.631969821338384],"dir":"ltr"},{"str":"read","boundary":[0.6044169607843136,0.6181957051767677,0.6412084352941175,0.631969821338384],"dir":"ltr"},{"str":"these","boundary":[0.6457181045751633,0.6181957051767677,0.6893545045751633,0.631969821338384],"dir":"ltr"},{"str":"lines!","boundary":[0.6938641830065359,0.6181957051767677,0.7384631506535947,0.631969821338384],"dir":"ltr"},{"str":"But","boundary":[0.7443453921568627,0.6181957051767677,0.7750762555555555,0.631969821338384],"dir":"ltr"},{"str":"others","boundary":[0.7793899999999999,0.6181957051767677,0.8308517184640521,0.631969821338384],"dir":"ltr"},{"str":"insist","boundary":[0.8355574836601306,0.6181957051767677,0.8811368442810457,0.631969821338384],"dir":"ltr"},{"str":"that","boundary":[0.11764408496732015,0.6353169172979799,0.1522786949346404,0.6490910334595961],"dir":"ltr"},{"str":"the","boundary":[0.1571805228758169,0.6353169172979799,0.18379373578431363,0.6490910334595961],"dir":"ltr"},{"str":"key","boundary":[0.1888917973856208,0.6353169172979799,0.21785795343137246,0.6490910334595961],"dir":"ltr"},{"str":"development","boundary":[0.22275977124182997,0.6353169172979799,0.3272696622549019,0.6490910334595961],"dir":"ltr"},{"str":"was","boundary":[0.3325636928104574,0.6353169172979799,0.36427493643790837,0.6490910334595961],"dir":"ltr"},{"str":"not","boundary":[0.369176748366013,0.6353169172979799,0.3957899612745097,0.6490910334595961],"dir":"ltr"},{"str":"typography","boundary":[0.40069178104575154,0.6353169172979799,0.49423909607843125,0.6490910334595961],"dir":"ltr"},{"str":"but","boundary":[0.5020642973856209,0.6353169172979799,0.529853981862745,0.6490910334595961],"dir":"ltr"},{"str":"algorithms","boundary":[0.5345597222222221,0.6353169172979799,0.6235972295751633,0.6490910334595961],"dir":"ltr"},{"str":".","boundary":[0.622616748366013,0.6353169172979799,0.6275008879084967,0.6490910334595961],"dir":"ltr"},{"str":"Today","boundary":[0.14529158496732017,0.6528926748737375,0.18912418562091493,0.6666667910353535],"dir":"ltr"},{"str":"we","boundary":[0.20010442810457507,0.6528926748737375,0.22281389444444435,0.6666667910353535],"dir":"ltr"},{"str":"are","boundary":[0.22850001633986916,0.6528926748737375,0.25511322924836594,0.6666667910353535],"dir":"ltr"},{"str":"so","boundary":[0.26060328431372537,0.6528926748737375,0.27762647140522867,0.6666667910353535],"dir":"ltr"},{"str":"used","boundary":[0.28331259803921555,0.6528926748737375,0.32147662271241817,0.6666667910353535],"dir":"ltr"},{"str":"to","boundary":[0.32716276143790834,0.6528926748737375,0.34281339836601293,0.6666667910353535],"dir":"ltr"},{"str":"writing","boundary":[0.34849968954248356,0.6528926748737375,0.40896319803921555,0.6666667910353535],"dir":"ltr"},{"str":"numbers","boundary":[0.4142572058823528,0.6528926748737375,0.4868775872549018,0.6666667910353535],"dir":"ltr"},{"str":"in","boundary":[0.4923676633986927,0.6528926748737375,0.5089986933006534,0.6666667910353535],"dir":"ltr"},{"str":"decimal,","boundary":[0.5142928267973855,0.6528926748737375,0.5831698895424836,0.6666667910353535],"dir":"ltr"},{"str":"that","boundary":[0.5888560620915032,0.6528926748737375,0.6234906720588234,0.6666667910353535],"dir":"ltr"},{"str":"it","boundary":[0.6289807352941176,0.6528926748737375,0.6358078209150326,0.6666667910353535],"dir":"ltr"},{"str":"is","boundary":[0.647180408496732,0.6528926748737375,0.655576123856209,0.6666667910353535],"dir":"ltr"},{"str":"easy","boundary":[0.6665565522875816,0.6528926748737375,0.7031519482026144,0.6666667910353535],"dir":"ltr"},{"str":"to","boundary":[0.7086420098039216,0.6528926748737375,0.7242926467320261,0.6666667910353535],"dir":"ltr"},{"str":"forget","boundary":[0.7299789379084967,0.6528926748737375,0.7777151630718954,0.6666667910353535],"dir":"ltr"},{"str":"that","boundary":[0.7835974019607843,0.6528926748737375,0.8182320119281045,0.6666667910353535],"dir":"ltr"},{"str":"Guten-","boundary":[0.8237220751633987,0.6528926748737375,0.8810661514705882,0.6666667910353535],"dir":"ltr"},{"str":"berg","boundary":[0.11764364379084966,0.6700138869949497,0.15384688251633985,0.6837880031565657],"dir":"ltr"},{"str":"would","boundary":[0.16031733660130718,0.6700138869949497,0.20983609444444443,0.6837880031565657],"dir":"ltr"},{"str":"write","boundary":[0.21611047385620913,0.6700138869949497,0.2591586380718954,0.6837880031565657],"dir":"ltr"},{"str":"the","boundary":[0.26582517973856207,0.6700138869949497,0.2924383926470588,0.6837880031565657],"dir":"ltr"},{"str":"number","boundary":[0.298908839869281,0.6700138869949497,0.3633117455882352,0.6837880031565657],"dir":"ltr"},{"str":"1448","boundary":[0.36958612745098035,0.6700138869949497,0.4095148594771241,0.6837880031565657],"dir":"ltr"},{"str":"as","boundary":[0.4155931535947712,0.6700138869949497,0.433792812254902,0.6837880031565657],"dir":"ltr"},{"str":"MCDXLVIII.","boundary":[0.44006717320261435,0.6700138869949497,0.5461635370915032,0.6837880031565657],"dir":"ltr"},{"str":"How","boundary":[0.5522418464052287,0.6700138869949497,0.589835460620915,0.6837880031565657],"dir":"ltr"},{"str":"do","boundary":[0.5963058986928104,0.6700138869949497,0.6152898717320261,0.6837880031565657],"dir":"ltr"},{"str":"you","boundary":[0.6217603104575162,0.6700138869949497,0.6511186236928104,0.6837880031565657],"dir":"ltr"},{"str":"add","boundary":[0.6575890686274508,0.6700138869949497,0.6879277748366012,0.6837880031565657],"dir":"ltr"},{"str":"two","boundary":[0.6943982189542482,0.6700138869949497,0.7239526107843136,0.6837880031565657],"dir":"ltr"},{"str":"Roman","boundary":[0.7304232189542482,0.6700138869949497,0.7889615921568626,0.6837880031565657],"dir":"ltr"},{"str":"numerals?","boundary":[0.7952359640522875,0.6700138869949497,0.8813501178104574,0.6837880031565657],"dir":"ltr"},{"str":"What","boundary":[0.11764282679738544,0.6869835839646465,0.16286568088235276,0.7007577001262627],"dir":"ltr"},{"str":"is","boundary":[0.16953220588235277,0.6869835839646465,0.18341813545751615,0.7007577001262627],"dir":"ltr"},{"str":"MCDXLVIII","boundary":[0.1900846568627449,0.6869835839646465,0.29129688120915015,0.7007577001262627],"dir":"ltr"},{"str":"+","boundary":[0.2975714215686272,0.6926998421717172,0.311475176470588,0.7064739583333334],"dir":"ltr"},{"str":"DCCCXII?","boundary":[0.3181418464052285,0.6869835839646465,0.40564637565359457,0.7007577001262627],"dir":"ltr"},{"str":"(And","boundary":[0.4121168464052285,0.6869835839646465,0.45204557843137233,0.7007577001262627],"dir":"ltr"},{"str":"just","boundary":[0.4585160294117645,0.6869835839646465,0.4898173032679736,0.7007577001262627],"dir":"ltr"},{"str":"try","boundary":[0.4964838398692809,0.6869835839646465,0.5207441096405228,0.7007577001262627],"dir":"ltr"},{"str":"to","boundary":[0.5276067156862743,0.6869835839646465,0.5432573526143789,0.7007577001262627],"dir":"ltr"},{"str":"think","boundary":[0.5501199509803919,0.6869835839646465,0.5951289011437907,0.7007577001262627],"dir":"ltr"},{"str":"about","boundary":[0.6015993627450978,0.6869835839646465,0.6481769416666665,0.7007577001262627],"dir":"ltr"},{"str":"multiplying","boundary":[0.6548434803921567,0.6869835839646465,0.7515102276143789,0.7007577001262627],"dir":"ltr"},{"str":"them.)","boundary":[0.7575885784313724,0.6869835839646465,0.8108150042483658,0.7007577001262627],"dir":"ltr"},{"str":"Even","boundary":[0.8223835130718952,0.6869835839646465,0.8646651882352939,0.7007577001262627],"dir":"ltr"},{"str":"a","boundary":[0.8711356372549017,0.6869835839646465,0.8811178202614377,0.7007577001262627],"dir":"ltr"},{"str":"clever","boundary":[0.11764217320261418,0.7041047960858587,0.1659666263071893,0.7178789122474749],"dir":"ltr"},{"str":"man","boundary":[0.17106454248365993,0.7041047960858587,0.20787384232026124,0.7178789122474749],"dir":"ltr"},{"str":"like","boundary":[0.21238366013071874,0.7041047960858587,0.24309669820261418,0.7178789122474749],"dir":"ltr"},{"str":"Gutenberg","boundary":[0.24780245098039194,0.7041047960858587,0.33548523349673176,0.7178789122474749],"dir":"ltr"},{"str":"probably","boundary":[0.3401910130718952,0.7041047960858587,0.4122053333333331,0.7178789122474749],"dir":"ltr"},{"str":"only","boundary":[0.41691111111111084,0.7041047960858587,0.4519378782679736,0.7178789122474749],"dir":"ltr"},{"str":"knew","boundary":[0.4566436274509802,0.7041047960858587,0.5008860885620913,0.7178789122474749],"dir":"ltr"},{"str":"how","boundary":[0.5055918300653592,0.7041047960858587,0.5392638723856207,0.7178789122474749],"dir":"ltr"},{"str":"to","boundary":[0.5439696078431371,0.7041047960858587,0.5596202447712417,0.7178789122474749],"dir":"ltr"},{"str":"add","boundary":[0.5645220588235292,0.7041047960858587,0.5948607650326796,0.7178789122474749],"dir":"ltr"},{"str":"and","boundary":[0.5995665032679737,0.7041047960858587,0.630689523856209,0.7178789122474749],"dir":"ltr"},{"str":"subtract","boundary":[0.6353952614379083,0.7041047960858587,0.7038801669934639,0.7178789122474749],"dir":"ltr"},{"str":"small","boundary":[0.7087820261437906,0.7041047960858587,0.7541831334967318,0.7178789122474749],"dir":"ltr"},{"str":"numbers","boundary":[0.7586929738562089,0.7041047960858587,0.8313133552287579,0.7178789122474749],"dir":"ltr"},{"str":"using","boundary":[0.835823039215686,0.7041047960858587,0.8812241465686272,0.7178789122474749],"dir":"ltr"},{"str":"his","boundary":[0.11764166666666644,0.7212260082070708,0.142490172222222,0.7350001243686869],"dir":"ltr"},{"str":"\u0002ngers;","boundary":[0.14739199346405207,0.7212260082070708,0.20863981633986906,0.7350001243686869],"dir":"ltr"},{"str":"for","boundary":[0.21354166666666644,0.7212260082070708,0.2360372290849671,0.7350001243686869],"dir":"ltr"},{"str":"anything","boundary":[0.24113529411764684,0.7212260082070708,0.31569863611111093,0.7350001243686869],"dir":"ltr"},{"str":"more","boundary":[0.3202083333333331,0.7212260082070708,0.3615096155228756,0.7350001243686869],"dir":"ltr"},{"str":"complicated","boundary":[0.3668035947712416,0.7212260082070708,0.46445073496732003,0.7350001243686869],"dir":"ltr"},{"str":"he","boundary":[0.4695486928104573,0.7212260082070708,0.48931698022875797,0.7350001243686869],"dir":"ltr"},{"str":"had","boundary":[0.49421879084967296,0.7212260082070708,0.5253418114379083,0.7350001243686869],"dir":"ltr"},{"str":"to","boundary":[0.5302436274509801,0.7212260082070708,0.5458942643790847,0.7350001243686869],"dir":"ltr"},{"str":"consult","boundary":[0.5509923202614376,0.7212260082070708,0.6102793571895422,0.7350001243686869],"dir":"ltr"},{"str":"an","boundary":[0.6151812091503265,0.7212260082070708,0.6361259681372545,0.7350001243686869],"dir":"ltr"},{"str":"abacus","boundary":[0.6410277777777774,0.7212260082070708,0.6979796968954245,0.7350001243686869],"dir":"ltr"},{"str":"specialist.","boundary":[0.702489379084967,0.7212260082070708,0.7844502316993461,0.7350001243686869],"dir":"ltr"},{"str":"The","boundary":[0.14528839869281016,0.7388017657828283,0.17699965506535917,0.7525758819444445],"dir":"ltr"},{"str":"decimal","boundary":[0.18327401960784281,0.7388017657828283,0.2472669428104572,0.7525758819444445],"dir":"ltr"},{"str":"system,","boundary":[0.2533452614379082,0.7388017657828283,0.31576955588235267,0.7525758819444445],"dir":"ltr"},{"str":"invented","boundary":[0.3224361111111108,0.7388017657828283,0.3942543527777775,0.7525758819444445],"dir":"ltr"},{"str":"in","boundary":[0.40052875816993433,0.7388017657828283,0.41715978807189513,0.7525758819444445],"dir":"ltr"},{"str":"India","boundary":[0.42323823529411736,0.7388017657828283,0.4672667924836598,0.7525758819444445],"dir":"ltr"},{"str":"around","boundary":[0.4733450980392153,0.7388017657828283,0.5320617245098036,0.7525758819444445],"dir":"ltr"},{"str":"AD","boundary":[0.5381400326797382,0.7388017657828283,0.5649671495098036,0.7525758819444445],"dir":"ltr"},{"str":"600,","boundary":[0.5710455882352937,0.7388017657828283,0.6058762767973852,0.7525758819444445],"dir":"ltr"},{"str":"was","boundary":[0.6123467320261434,0.7388017657828283,0.6440579756535945,0.7525758819444445],"dir":"ltr"},{"str":"a","boundary":[0.650136421568627,0.7388017657828283,0.6538441372549015,0.7525758819444445],"dir":"ltr"},{"str":"revolution","boundary":[0.6663930718954245,0.7388017657828283,0.7503325357843134,0.7525758819444445],"dir":"ltr"},{"str":"in","boundary":[0.7566069607843133,0.7388017657828283,0.7732379906862741,0.7525758819444445],"dir":"ltr"},{"str":"quantitative","boundary":[0.7793164379084963,0.7388017657828283,0.8814555604575159,0.7525758819444445],"dir":"ltr"},{"str":"reasoning:","boundary":[0.1176416013071891,0.7559229779040405,0.2033457725490192,0.7696970940656567],"dir":"ltr"},{"str":"using","boundary":[0.20942411764705843,0.7559229779040405,0.2548252249999996,0.7696970940656567],"dir":"ltr"},{"str":"only","boundary":[0.25972705882352903,0.7559229779040405,0.2947538259803918,0.7696970940656567],"dir":"ltr"},{"str":"10","boundary":[0.2996556535947708,0.7559229779040405,0.3196200196078427,0.7696970940656567],"dir":"ltr"},{"str":"symbols","boundary":[0.3243257516339865,0.7559229779040405,0.3906716179738558,0.7696970940656567],"dir":"ltr"},{"str":"even","boundary":[0.4000653921568623,0.7559229779040405,0.4382294168300649,0.7696970940656567],"dir":"ltr"},{"str":"very","boundary":[0.44332732026143745,0.7559229779040405,0.47913840179738515,0.7696970940656567],"dir":"ltr"},{"str":"large","boundary":[0.4842364705882349,0.7559229779040405,0.5261081632352937,0.7696970940656567],"dir":"ltr"},{"str":"numbers","boundary":[0.5310099999999996,0.7559229779040405,0.6036303813725487,0.7696970940656567],"dir":"ltr"},{"str":"could","boundary":[0.6085322222222218,0.7559229779040405,0.6519725436274506,0.7696970940656567],"dir":"ltr"},{"str":"be","boundary":[0.6570704575163395,0.7559229779040405,0.6758583519607839,0.7696970940656567],"dir":"ltr"},{"str":"written","boundary":[0.6807601633986925,0.7559229779040405,0.7416158290849669,0.7696970940656567],"dir":"ltr"},{"str":"down","boundary":[0.7467137581699343,0.7559229779040405,0.790564062091503,0.7696970940656567],"dir":"ltr"},{"str":"compactly","boundary":[0.7956619607843134,0.7559229779040405,0.878246699836601,0.7696970940656567],"dir":"ltr"},{"str":",","boundary":[0.8760897385620912,0.7559229779040405,0.8809738781045748,0.7696970940656567],"dir":"ltr"},{"str":"and","boundary":[0.1176403921568624,0.7728926748737374,0.1487634127450977,0.7866667910353535],"dir":"ltr"},{"str":"arithmetic","boundary":[0.1540575490196075,0.7728926748737374,0.24034995604575132,0.7866667910353535],"dir":"ltr"},{"str":"could","boundary":[0.2456439869281042,0.7728926748737374,0.289084308333333,0.7866667910353535],"dir":"ltr"},{"str":"be","boundary":[0.294574379084967,0.7728926748737374,0.31336227352941143,0.7866667910353535],"dir":"ltr"},{"str":"done","boundary":[0.3186564052287578,0.7728926748737374,0.3574086656862742,0.7866667910353535],"dir":"ltr"},{"str":"ef\u0002ciently","boundary":[0.36289872549019575,0.7728926748737374,0.443897010457516,0.7866667910353535],"dir":"ltr"},{"str":"on","boundary":[0.4491910457516336,0.7728926748737374,0.4689593331699343,0.7866667910353535],"dir":"ltr"},{"str":"them","boundary":[0.4744495424836597,0.7728926748737374,0.5169272962418296,0.7866667910353535],"dir":"ltr"},{"str":"by","boundary":[0.5222214379084963,0.7728926748737374,0.5417936467320257,0.7866667910353535],"dir":"ltr"},{"str":"following","boundary":[0.5470877777777774,0.7728926748737374,0.6220254516339866,0.7866667910353535],"dir":"ltr"},{"str":"elementary","boundary":[0.6271233986928101,0.7728926748737374,0.7202785565359474,0.7866667910353535],"dir":"ltr"},{"str":"steps","boundary":[0.7257686601307186,0.7728926748737374,0.76803250996732,0.7866667910353535],"dir":"ltr"},{"str":"Nonetheless","boundary":[0.7801714215686272,0.7728926748737374,0.8807597406862743,0.7866667910353535],"dir":"ltr"},{"str":"these","boundary":[0.11764037581699316,0.7900138869949496,0.16127677581699315,0.8037880031565657],"dir":"ltr"},{"str":"ideas","boundary":[0.16637468954248336,0.7900138869949496,0.20922677516339838,0.8037880031565657],"dir":"ltr"},{"str":"took","boundary":[0.21393253267973825,0.7900138869949496,0.24895929983660103,0.8037880031565657],"dir":"ltr"},{"str":"a","boundary":[0.25405720588235264,0.7900138869949496,0.25913748692810423,0.8037880031565657],"dir":"ltr"},{"str":"long","boundary":[0.2689412908496729,0.7900138869949496,0.30396805800653565,0.8037880031565657],"dir":"ltr"},{"str":"time","boundary":[0.3086738071895422,0.7900138869949496,0.3458574388888886,0.8037880031565657],"dir":"ltr"},{"str":"to","boundary":[0.3507592647058821,0.7900138869949496,0.3664099016339866,0.8037880031565657],"dir":"ltr"},{"str":"spread,","boundary":[0.3715079575163396,0.7900138869949496,0.43157930882352913,0.8037880031565657],"dir":"ltr"},{"str":"hindered","boundary":[0.43667723856209123,0.7900138869949496,0.5100641089869279,0.8037880031565657],"dir":"ltr"},{"str":"by","boundary":[0.5149659640522872,0.7900138869949496,0.5345381728758166,0.8037880031565657],"dir":"ltr"},{"str":"traditional","boundary":[0.5392440686274507,0.7900138869949496,0.6276755148692807,0.8037880031565657],"dir":"ltr"},{"str":"barriers","boundary":[0.6323813235294115,0.7900138869949496,0.6985132859477121,0.8037880031565657],"dir":"ltr"},{"str":"of","boundary":[0.7034151470588232,0.7900138869949496,0.712987497712418,0.8037880031565657],"dir":"ltr"},{"str":",","boundary":[0.7983349183006533,0.7900138869949496,0.7987093738562088,0.8037880031565657],"dir":"ltr"},{"str":"language","boundary":[0.7231832843137252,0.7900138869949496,0.7987270192810454,0.8037880031565657],"dir":"ltr"},{"str":"distance","boundary":[0.807728741830065,0.7900138869949496,0.8762136473856206,0.8037880031565657],"dir":"ltr"},{"str":",","boundary":[0.8758215522875813,0.7900138869949496,0.880705691830065,0.8037880031565657],"dir":"ltr"},{"str":"and","boundary":[0.11764017973856172,0.8071350991161617,0.14876320032679702,0.8209092152777778],"dir":"ltr"},{"str":"ignorance","boundary":[0.15582204248365975,0.8071350991161617,0.2362499169934637,0.8209092152777778],"dir":"ltr"},{"str":"The","boundary":[0.2534869117647055,0.8071350991161617,0.2851981681372545,0.8209092152777778],"dir":"ltr"},{"str":"most","boundary":[0.29225684640522837,0.8071350991161617,0.3319894998366009,0.8209092152777778],"dir":"ltr"},{"str":"in\u0003uential","boundary":[0.339244264705882,0.8071350991161617,0.425732750326797,0.8209092152777778],"dir":"ltr"},{"str":"medium","boundary":[0.43239933006535913,0.8071350991161617,0.49974341470588207,0.8209092152777778],"dir":"ltr"},{"str":"of","boundary":[0.5068021078431368,0.8071350991161617,0.5214723517973853,0.8209092152777778],"dir":"ltr"},{"str":"transmission","boundary":[0.5287272712418297,0.8071350991161617,0.6359644372549016,0.8209092152777778],"dir":"ltr"},{"str":"turned","boundary":[0.6430231862745095,0.8071350991161617,0.6986025552287578,0.8209092152777778],"dir":"ltr"},{"str":"out","boundary":[0.7058573366013068,0.8071350991161617,0.7324705495098036,0.8209092152777778],"dir":"ltr"},{"str":"to","boundary":[0.739725310457516,0.8071350991161617,0.7553759473856205,0.8209092152777778],"dir":"ltr"},{"str":"be","boundary":[0.7626308660130715,0.8071350991161617,0.7814187604575159,0.8209092152777778],"dir":"ltr"},{"str":"a","boundary":[0.7884775980392152,0.8071350991161617,0.7914009509803916,0.8209092152777778],"dir":"ltr"},{"str":"textbook,","boundary":[0.8055186111111107,0.8071350991161617,0.8806523635620911,0.8209092152777778],"dir":"ltr"},{"str":"written","boundary":[0.11763952614379036,0.8242563112373739,0.17849519183006488,0.83803042739899],"dir":"ltr"},{"str":"in","boundary":[0.18496566993464003,0.8242563112373739,0.2015966998366008,0.83803042739899],"dir":"ltr"},{"str":"Arabic","boundary":[0.20767514705882303,0.8242563112373739,0.2618819658496727,0.83803042739899],"dir":"ltr"},{"str":"in","boundary":[0.26796027777777726,0.8242563112373739,0.28459130767973806,0.83803042739899],"dir":"ltr"},{"str":"the","boundary":[0.2908658333333328,0.8242563112373739,0.3174790462418296,0.83803042739899],"dir":"ltr"},{"str":"ninth","boundary":[0.3239494934640518,0.8242563112373739,0.36935060081699295,0.83803042739899],"dir":"ltr"},{"str":"century","boundary":[0.3752328267973851,0.8242563112373739,0.4380492784313721,0.83803042739899],"dir":"ltr"},{"str":"by","boundary":[0.44451975490196033,0.8242563112373739,0.4640919637254897,0.83803042739899],"dir":"ltr"},{"str":"a","boundary":[0.47036648692810407,0.8242563112373739,0.47407420261437855,0.83803042739899],"dir":"ltr"},{"str":"man","boundary":[0.48662313725490147,0.8242563112373739,0.5234324370915028,0.83803042739899],"dir":"ltr"},{"str":"who","boundary":[0.5295108823529406,0.8242563112373739,0.5631829246732022,0.83803042739899],"dir":"ltr"},{"str":"lived","boundary":[0.5694572875816989,0.8242563112373739,0.6093681942810453,0.83803042739899],"dir":"ltr"},{"str":"in","boundary":[0.6156425816993459,0.8242563112373739,0.6322736116013067,0.83803042739899],"dir":"ltr"},{"str":"Baghdad.","boundary":[0.6383520588235289,0.8242563112373739,0.7170330513071891,0.83803042739899],"dir":"ltr"},{"str":"Al","boundary":[0.72703294117647,0.8242563112373739,0.7456247570261433,0.83803042739899],"dir":"ltr"},{"str":"Khwarizmi","boundary":[0.7518992810457511,0.8242563112373739,0.8438958052287577,0.83803042739899],"dir":"ltr"},{"str":"laid","boundary":[0.8497780392156857,0.8242563112373739,0.8812753916666661,0.83803042739899],"dir":"ltr"},{"str":"out","boundary":[0.11763915032679682,0.841377523358586,0.14425236323529356,0.855151639520202],"dir":"ltr"},{"str":"the","boundary":[0.14856594771241774,0.841377523358586,0.1751791606209145,0.855151639520202],"dir":"ltr"},{"str":"basic","boundary":[0.1796888235294112,0.841377523358586,0.2213644375816988,0.855151639520202],"dir":"ltr"},{"str":"methods","boundary":[0.22548196078431315,0.841377523358586,0.29516116323529357,0.855151639520202],"dir":"ltr"},{"str":"for","boundary":[0.299670849673202,0.841377523358586,0.32216641209150265,0.855151639520202],"dir":"ltr"},{"str":"adding","boundary":[0.3266760784313719,0.841377523358586,0.38323584035947655,0.855151639520202],"dir":"ltr"},{"str":",","boundary":[0.38284356209150266,0.841377523358586,0.38341399803921505,0.855151639520202],"dir":"ltr"},{"str":"multiplying","boundary":[0.3920414052287576,0.841377523358586,0.4887081524509798,0.855151639520202],"dir":"ltr"},{"str":",","boundary":[0.4883159150326792,0.841377523358586,0.48927854052287517,0.855151639520202],"dir":"ltr"},{"str":"and","boundary":[0.4971215686274503,0.841377523358586,0.5282445892156856,0.855151639520202],"dir":"ltr"},{"str":"dividing","boundary":[0.5325583333333327,0.841377523358586,0.600062845915032,0.855151639520202],"dir":"ltr"},{"str":"numbersóeven","boundary":[0.6039843137254896,0.841377523358586,0.7325940465686268,0.855151639520202],"dir":"ltr"},{"str":"extracting","boundary":[0.7369076797385614,0.841377523358586,0.8208471436274504,0.855151639520202],"dir":"ltr"},{"str":"square","boundary":[0.8251607843137249,0.841377523358586,0.8809362318627444,0.855151639520202],"dir":"ltr"},{"str":"roots","boundary":[0.11763954248365951,0.8584987354797982,0.15813868496731964,0.8722728516414142],"dir":"ltr"},{"str":"and","boundary":[0.1644130718954242,0.8584987354797982,0.19553609248365952,0.8722728516414142],"dir":"ltr"},{"str":"calculating","boundary":[0.20141830065359415,0.8584987354797982,0.29239876862745035,0.8722728516414142],"dir":"ltr"},{"str":"digits","boundary":[0.2980849673202608,0.8584987354797982,0.34425256372548957,0.8722728516414142],"dir":"ltr"},{"str":"of","boundary":[0.350134803921568,0.8584987354797982,0.36480504787581636,0.8722728516414142],"dir":"ltr"},{"str":"\u0019","boundary":[0.371079575163398,0.8642149936868688,0.3812578367647052,0.8779891098484849],"dir":"ltr"},{"str":"These","boundary":[0.3959458169934634,0.8584987354797982,0.44468026045751563,0.8722728516414142],"dir":"ltr"},{"str":"procedures","boundary":[0.4507585620915025,0.8584987354797982,0.5401882266339861,0.8722728516414142],"dir":"ltr"},{"str":"were","boundary":[0.5466587254901953,0.8584987354797982,0.5859992217320255,0.8722728516414142],"dir":"ltr"},{"str":"precise","boundary":[0.5922735947712411,0.8584987354797982,0.6495998457516332,0.8722728516414142],"dir":"ltr"},{"str":"unambiguous","boundary":[0.6607583496732018,0.8584987354797982,0.7727192272875809,0.8722728516414142],"dir":"ltr"},{"str":"mechanical,","boundary":[0.7828973039215678,0.8584987354797982,0.8811326975490187,0.8722728516414142],"dir":"ltr"},{"str":"11","boundary":[0.4899925653594762,0.8930441900252527,0.509956931372548,0.9068183061868688],"dir":"ltr"}],"boundary":[0.11764,0.20785,0.88146,0.90682],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":11,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/c5635d4188c8af9bb88a9afec10e4a15.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/85cfef0e88a22d2d20af91645929f90b.jpg"},"info":{"width":612,"height":792,"margin":[0.11764,0.08979,0.11767,0.12773]},"elements":[{"words":[{"str":"12","boundary":[0.11764705882352941,0.09001376073232323,0.1376114248366013,0.10378787689393938],"dir":"ltr"},{"str":"Algorithms","boundary":[0.7899640522875817,0.08979153426128839,0.8823348957516342,0.10356565042290454],"dir":"ltr"},{"str":"ef\u0002cient,","boundary":[0.11764705882352941,0.12880163952020204,0.18827100359477122,0.1425757556818182],"dir":"ltr"},{"str":"correctóin","boundary":[0.19434934640522875,0.12880163952020204,0.2845633253267974,0.1425757556818182],"dir":"ltr"},{"str":"short,","boundary":[0.29044558823529415,0.12880163952020204,0.33798573480392163,0.1425757556818182],"dir":"ltr"},{"str":"they","boundary":[0.34406405228758175,0.12880163952020204,0.38026729101307194,0.1425757556818182],"dir":"ltr"},{"str":"were","boundary":[0.38595343137254906,0.12880163952020204,0.4252939276143791,0.1425757556818182],"dir":"ltr"},{"str":"algorithms","boundary":[0.43117614379084973,0.12880163952020204,0.5202136511437909,0.1425757556818182],"dir":"ltr"},{"str":"a","boundary":[0.5311761111111112,0.12880163952020204,0.5354720784313727,0.1425757556818182],"dir":"ltr"},{"str":"term","boundary":[0.5468445098039216,0.12880163952020204,0.5861850060457517,0.1425757556818182],"dir":"ltr"},{"str":"coined","boundary":[0.5920672222222223,0.12880163952020204,0.6443132550653595,0.1425757556818182],"dir":"ltr"},{"str":"to","boundary":[0.649999411764706,0.12880163952020204,0.6656500486928106,0.1425757556818182],"dir":"ltr"},{"str":"honor","boundary":[0.6715322549019609,0.12880163952020204,0.7188941482026144,0.1425757556818182],"dir":"ltr"},{"str":"the","boundary":[0.7245802941176471,0.12880163952020204,0.7511935070261438,0.1425757556818182],"dir":"ltr"},{"str":"wise","boundary":[0.7568796405228758,0.12880163952020204,0.7934750364379085,0.1425757556818182],"dir":"ltr"},{"str":"man","boundary":[0.7991613398692811,0.12880163952020204,0.8359706397058824,0.1425757556818182],"dir":"ltr"},{"str":"after","boundary":[0.8414606862745098,0.12880163952020204,0.8807833571895425,0.1425757556818182],"dir":"ltr"},{"str":"the","boundary":[0.11764696078431369,0.1459228516414141,0.14426017369281044,0.15969696780303025],"dir":"ltr"},{"str":"decimal","boundary":[0.1493582352941176,0.1459228516414141,0.21335115849673197,0.15969696780303025],"dir":"ltr"},{"str":"system","boundary":[0.21825300653594767,0.1459228516414141,0.2757931614379085,0.15969696780303025],"dir":"ltr"},{"str":"was","boundary":[0.2806949999999999,0.1459228516414141,0.31240624362745095,0.15969696780303025],"dir":"ltr"},{"str":"\u0002nally","boundary":[0.3173080555555555,0.1459228516414141,0.3701423241830065,0.15969696780303025],"dir":"ltr"},{"str":"adopted","boundary":[0.3746520098039215,0.1459228516414141,0.43962532598039206,0.15969696780303025],"dir":"ltr"},{"str":"in","boundary":[0.44491933006535944,0.1459228516414141,0.4615503599673202,0.15969696780303025],"dir":"ltr"},{"str":"Europe","boundary":[0.4664521732026143,0.1459228516414141,0.5259531140522875,0.15969696780303025],"dir":"ltr"},{"str":"many","boundary":[0.5355429901960784,0.1459228516414141,0.5819423158496732,0.15969696780303025],"dir":"ltr"},{"str":"centuries","boundary":[0.5866480555555554,0.1459228516414141,0.6625661223856208,0.15969696780303025],"dir":"ltr"},{"str":"later","boundary":[0.6676640686274509,0.1459228516414141,0.7067906609477123,0.15969696780303025],"dir":"ltr"},{"str":".","boundary":[0.7050258333333332,0.1459228516414141,0.7099099728758169,0.15969696780303025],"dir":"ltr"},{"str":"Since","boundary":[0.14529380718954246,0.16304406376262615,0.18971452156862745,0.1768181799242423],"dir":"ltr"},{"str":"then,","boundary":[0.19618498366013068,0.16304406376262615,0.23864491209150324,0.1768181799242423],"dir":"ltr"},{"str":"this","boundary":[0.245311454248366,0.16304406376262615,0.27700488529411765,0.1768181799242423],"dir":"ltr"},{"str":"decimal","boundary":[0.2832794281045751,0.16304406376262615,0.34727235130718953,0.1768181799242423],"dir":"ltr"},{"str":"positional","boundary":[0.3535467483660131,0.16304406376262615,0.43434895473856205,0.1768181799242423],"dir":"ltr"},{"str":"system","boundary":[0.4406233823529412,0.16304406376262615,0.498163537254902,0.1768181799242423],"dir":"ltr"},{"str":"and","boundary":[0.5046340032679739,0.16304406376262615,0.5357570238562093,0.1768181799242423],"dir":"ltr"},{"str":"its","boundary":[0.5420315522875817,0.16304406376262615,0.5627624073529413,0.1768181799242423],"dir":"ltr"},{"str":"numerical","boundary":[0.5690367810457516,0.16304406376262615,0.6526019130718955,0.1768181799242423],"dir":"ltr"},{"str":"algorithms","boundary":[0.6586802450980392,0.16304406376262615,0.7481099096405229,0.1768181799242423],"dir":"ltr"},{"str":"have","boundary":[0.7543843300653595,0.16304406376262615,0.7935287601307189,0.1768181799242423],"dir":"ltr"},{"str":"played","boundary":[0.7998031209150327,0.16304406376262615,0.8540099629084967,0.1768181799242423],"dir":"ltr"},{"str":"an","boundary":[0.8602843300653595,0.16304406376262615,0.8812290890522876,0.1768181799242423],"dir":"ltr"},{"str":"enormous","boundary":[0.11764707516339865,0.1801652758838382,0.19789669640522872,0.19393939204545435],"dir":"ltr"},{"str":"role","boundary":[0.20515148692810453,0.1801652758838382,0.23625668218954243,0.19393939204545435],"dir":"ltr"},{"str":"in","boundary":[0.24370753267973852,0.1801652758838382,0.26033856258169935,0.19393939204545435],"dir":"ltr"},{"str":"Western","boundary":[0.26739740196078426,0.1801652758838382,0.3353118982026143,0.19393939204545435],"dir":"ltr"},{"str":"civilization.","boundary":[0.3425666830065359,0.1801652758838382,0.4384134651960784,0.19393939204545435],"dir":"ltr"},{"str":"They","boundary":[0.4509624346405229,0.1801652758838382,0.49226371683006537,0.19393939204545435],"dir":"ltr"},{"str":"enabled","boundary":[0.4993224019607843,0.1801652758838382,0.5637074823529412,0.19393939204545435],"dir":"ltr"},{"str":"science","boundary":[0.5707661928104575,0.1801652758838382,0.6288767581699346,0.19393939204545435],"dir":"ltr"},{"str":"and","boundary":[0.6361315522875817,0.1801652758838382,0.6672545728758169,0.19393939204545435],"dir":"ltr"},{"str":"technology;","boundary":[0.6743134150326797,0.1801652758838382,0.7668625369281045,0.19393939204545435],"dir":"ltr"},{"str":"they","boundary":[0.7752938071895424,0.1801652758838382,0.8114970459150326,0.19393939204545435],"dir":"ltr"},{"str":"acceler","boundary":[0.8187518137254901,0.1801652758838382,0.8754898289215686,0.19393939204545435],"dir":"ltr"},{"str":"-","boundary":[0.8749016503267973,0.1801652758838382,0.8807661828431371,0.19393939204545435],"dir":"ltr"},{"str":"ated","boundary":[0.11764674836601302,0.19728648800505025,0.15345782990196075,0.21106060416666642],"dir":"ltr"},{"str":"industry","boundary":[0.160124362745098,0.19728648800505025,0.23037397565359474,0.21106060416666642],"dir":"ltr"},{"str":"and","boundary":[0.2368444607843137,0.19728648800505025,0.267967481372549,0.21106060416666642],"dir":"ltr"},{"str":"commerce","boundary":[0.27424200980392155,0.19728648800505025,0.3558641812091503,0.21106060416666642],"dir":"ltr"},{"str":"And","boundary":[0.37192468954248364,0.19728648800505025,0.4059888890522876,0.21106060416666642],"dir":"ltr"},{"str":"when,","boundary":[0.4122634150326797,0.19728648800505025,0.46178217287581697,0.21106060416666642],"dir":"ltr"},{"str":"much","boundary":[0.46864478758169936,0.19728648800505025,0.5075931421568628,0.21106060416666642],"dir":"ltr"},{"str":"later","boundary":[0.5205343300653595,0.19728648800505025,0.5596609223856209,0.21106060416666642],"dir":"ltr"},{"str":"the","boundary":[0.5698391993464053,0.19728648800505025,0.596452412254902,0.21106060416666642],"dir":"ltr"},{"str":"computer","boundary":[0.6031189379084968,0.19728648800505025,0.680231301633987,0.21106060416666642],"dir":"ltr"},{"str":"was","boundary":[0.6870939379084968,0.19728648800505025,0.7188051815359479,0.21106060416666642],"dir":"ltr"},{"str":"\u0002nally","boundary":[0.7252756209150327,0.19728648800505025,0.7781098895424837,0.21106060416666642],"dir":"ltr"},{"str":"designed,","boundary":[0.7841882026143792,0.19728648800505025,0.8614788196078432,0.21106060416666642],"dir":"ltr"},{"str":"it","boundary":[0.8685375490196079,0.19728648800505025,0.8810509284313727,0.21106060416666642],"dir":"ltr"},{"str":"explicitly","boundary":[0.11764702614379084,0.2144077001262623,0.19315511045751635,0.22818181628787848],"dir":"ltr"},{"str":"embodied","boundary":[0.19962562091503266,0.2144077001262623,0.27791445620915034,0.22818181628787848],"dir":"ltr"},{"str":"the","boundary":[0.28458101307189543,0.2144077001262623,0.31119422598039215,0.22818181628787848],"dir":"ltr"},{"str":"positional","boundary":[0.3178607516339869,0.2144077001262623,0.3986629580065359,0.22818181628787848],"dir":"ltr"},{"str":"system","boundary":[0.40513346405228756,0.2144077001262623,0.46267361895424836,0.22818181628787848],"dir":"ltr"},{"str":"in","boundary":[0.4693401633986928,0.2144077001262623,0.4859711933006535,0.22818181628787848],"dir":"ltr"},{"str":"its","boundary":[0.4924417973856209,0.2144077001262623,0.5131726524509803,0.22818181628787848],"dir":"ltr"},{"str":"bits","boundary":[0.5196431045751634,0.2144077001262623,0.5503561426470588,0.22818181628787848],"dir":"ltr"},{"str":"and","boundary":[0.5568266013071895,0.2144077001262623,0.5879496218954248,0.22818181628787848],"dir":"ltr"},{"str":"words","boundary":[0.5944202287581699,0.2144077001262623,0.6433507508169933,0.22818181628787848],"dir":"ltr"},{"str":"and","boundary":[0.6500172875816993,0.2144077001262623,0.6811403081699345,0.22818181628787848],"dir":"ltr"},{"str":"arithmetic","boundary":[0.6876107516339869,0.2144077001262623,0.7739031586601307,0.22818181628787848],"dir":"ltr"},{"str":"unit.","boundary":[0.7803736601307188,0.2144077001262623,0.8196963310457516,0.22818181628787848],"dir":"ltr"},{"str":"Scien-","boundary":[0.8304805228758169,0.2144077001262623,0.8807657697712418,0.22818181628787848],"dir":"ltr"},{"str":"tists","boundary":[0.11764718954248352,0.23152891224747438,0.15344044575163385,0.24530302840909052],"dir":"ltr"},{"str":"everywhere","boundary":[0.15834228758169921,0.23152891224747438,0.25326215277777764,0.24530302840909052],"dir":"ltr"},{"str":"then","boundary":[0.2585561764705881,0.23152891224747438,0.29613196535947695,0.24530302840909052],"dir":"ltr"},{"str":"got","boundary":[0.3008377124183005,0.23152891224747438,0.3260783751633985,0.24530302840909052],"dir":"ltr"},{"str":"busy","boundary":[0.33117643790849655,0.23152891224747438,0.3699286983660129,0.24530302840909052],"dir":"ltr"},{"str":"developing","boundary":[0.3746344444444442,0.23152891224747438,0.4628876374183004,0.24530302840909052],"dir":"ltr"},{"str":"more","boundary":[0.46778950980392137,0.23152891224747438,0.5090907919934639,0.24530302840909052],"dir":"ltr"},{"str":"and","boundary":[0.5141886928104573,0.23152891224747438,0.5453117133986926,0.24530302840909052],"dir":"ltr"},{"str":"more","boundary":[0.550017450980392,0.23152891224747438,0.5913187331699344,0.24530302840909052],"dir":"ltr"},{"str":"complex","boundary":[0.5964166339869279,0.23152891224747438,0.6631546575163397,0.24530302840909052],"dir":"ltr"},{"str":"algorithms","boundary":[0.6680565032679736,0.23152891224747438,0.7574861678104573,0.24530302840909052],"dir":"ltr"},{"str":"for","boundary":[0.7621919607843135,0.23152891224747438,0.7846875232026141,0.24530302840909052],"dir":"ltr"},{"str":"all","boundary":[0.7897855882352939,0.23152891224747438,0.8111046790849671,0.24530302840909052],"dir":"ltr"},{"str":"kinds","boundary":[0.8158104248366012,0.23152891224747438,0.8614076107843135,0.24530302840909052],"dir":"ltr"},{"str":"of","boundary":[0.8661133660130717,0.23152891224747438,0.8807836099673202,0.24530302840909052],"dir":"ltr"},{"str":"problems","boundary":[0.11764767973856191,0.24865012436868641,0.19299533611111094,0.26242424053030255],"dir":"ltr"},{"str":"and","boundary":[0.198093267973856,0.24865012436868641,0.2292162885620913,0.26242424053030255],"dir":"ltr"},{"str":"inventing","boundary":[0.23392202614379065,0.24865012436868641,0.3129773504901959,0.26242424053030255],"dir":"ltr"},{"str":"novel","boundary":[0.31768313725490177,0.24865012436868641,0.361515615849673,0.26242424053030255],"dir":"ltr"},{"str":"applicationsóultimately","boundary":[0.36641745098039197,0.24865012436868641,0.5701252856209149,0.26242424053030255],"dir":"ltr"},{"str":"changing","boundary":[0.5746347712418298,0.24865012436868641,0.6499824197712416,0.26242424053030255],"dir":"ltr"},{"str":"the","boundary":[0.6546881862745095,0.24865012436868641,0.6813013991830063,0.26242424053030255],"dir":"ltr"},{"str":"world.","boundary":[0.6862032189542481,0.24865012436868641,0.7374688588235292,0.26242424053030255],"dir":"ltr"},{"str":"0.2","boundary":[0.1176476633986925,0.282385564393939,0.1511690130718951,0.3004994532828279],"dir":"ltr"},{"str":"Enter","boundary":[0.17450240196078398,0.282385564393939,0.2440533421568624,0.3004994532828279],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.2507202124183003,0.282385564393939,0.37006738856209115,0.3004994532828279],"dir":"ltr"},{"str":"Al","boundary":[0.11764782679738527,0.3225895183080804,0.13623964264705846,0.3363636344696966],"dir":"ltr"},{"str":"Khwarizmi's","boundary":[0.14055338235294082,0.3225895183080804,0.23996518006535916,0.3363636344696966],"dir":"ltr"},{"str":"work","boundary":[0.24820039215686243,0.3225895183080804,0.28930559575163367,0.3363636344696966],"dir":"ltr"},{"str":"could","boundary":[0.2938152614379082,0.3225895183080804,0.33725558284313695,0.3363636344696966],"dir":"ltr"},{"str":"not","boundary":[0.3417652614379082,0.3225895183080804,0.3683784743464049,0.3363636344696966],"dir":"ltr"},{"str":"have","boundary":[0.37308421568627426,0.3225895183080804,0.4122286457516337,0.3363636344696966],"dir":"ltr"},{"str":"gained","boundary":[0.4165423856209147,0.3225895183080804,0.47172959738562065,0.3363636344696966],"dir":"ltr"},{"str":"a","boundary":[0.47604320261437877,0.3225895183080804,0.4815156241830063,0.3363636344696966],"dir":"ltr"},{"str":"foothold","boundary":[0.4905351470588233,0.3225895183080804,0.5564710308823527,0.3363636344696966],"dir":"ltr"},{"str":"in","boundary":[0.56117681372549,0.3225895183080804,0.5778078436274507,0.3363636344696966],"dir":"ltr"},{"str":"the","boundary":[0.58212158496732,0.3225895183080804,0.6087347978758167,0.3363636344696966],"dir":"ltr"},{"str":"West","boundary":[0.613440539215686,0.3225895183080804,0.6537614295751631,0.3363636344696966],"dir":"ltr"},{"str":"were","boundary":[0.6582710947712416,0.3225895183080804,0.6976115910130717,0.3363636344696966],"dir":"ltr"},{"str":"it","boundary":[0.7023173366013069,0.3225895183080804,0.7103208928104573,0.3363636344696966],"dir":"ltr"},{"str":"not","boundary":[0.7193405392156861,0.3225895183080804,0.7459537521241828,0.3363636344696966],"dir":"ltr"},{"str":"for","boundary":[0.750659493464052,0.3225895183080804,0.7731550558823527,0.3363636344696966],"dir":"ltr"},{"str":"the","boundary":[0.7778609640522873,0.3225895183080804,0.804474176960784,0.3363636344696966],"dir":"ltr"},{"str":"efforts","boundary":[0.8089840032679736,0.3225895183080804,0.8612122107843135,0.3363636344696966],"dir":"ltr"},{"str":"of","boundary":[0.8661140686274507,0.3225895183080804,0.8807843125816991,0.3363636344696966],"dir":"ltr"},{"str":"one","boundary":[0.1176483823529409,0.3397107304292926,0.14622238120915004,0.3534848465909088],"dir":"ltr"},{"str":"man:","boundary":[0.15112419934640495,0.3397107304292926,0.19281763872548993,0.3534848465909088],"dir":"ltr"},{"str":"the","boundary":[0.1986998529411762,0.3397107304292926,0.22531306584967292,0.3534848465909088],"dir":"ltr"},{"str":"15th","boundary":[0.2300188071895422,0.3397107304292926,0.26779067467320233,0.3534848465909088],"dir":"ltr"},{"str":"century","boundary":[0.2724964215686272,0.3397107304292926,0.3353128732026141,0.3534848465909088],"dir":"ltr"},{"str":"Italian","boundary":[0.34021472222222193,0.3397107304292926,0.3965605802287579,0.3534848465909088],"dir":"ltr"},{"str":"mathematician","boundary":[0.40087419934640495,0.3397107304292926,0.5261327707516338,0.3534848465909088],"dir":"ltr"},{"str":"Leonardo","boundary":[0.5306424999999998,0.3397107304292926,0.6079509423202611,0.3534848465909088],"dir":"ltr"},{"str":"Fibonacci,","boundary":[0.6128527941176468,0.3397107304292926,0.6962040109477122,0.3534848465909088],"dir":"ltr"},{"str":"who","boundary":[0.7007137254901958,0.3397107304292926,0.7343857678104573,0.3534848465909088],"dir":"ltr"},{"str":"saw","boundary":[0.7390916666666665,0.3397107304292926,0.766293130718954,0.3534848465909088],"dir":"ltr"},{"str":"the","boundary":[0.7757049019607841,0.3397107304292926,0.8023181148692808,0.3534848465909088],"dir":"ltr"},{"str":"potential","boundary":[0.8072199346405226,0.3397107304292926,0.8809811369281042,0.3534848465909088],"dir":"ltr"},{"str":"of","boundary":[0.11764803921568603,0.3568319425505047,0.127220226470588,0.37060605871212093],"dir":"ltr"},{"str":"the","boundary":[0.1374163398692808,0.3568319425505047,0.16402955277777753,0.37060605871212093],"dir":"ltr"},{"str":"positional","boundary":[0.16912761437908475,0.3568319425505047,0.24992982075163378,0.37060605871212093],"dir":"ltr"},{"str":"system","boundary":[0.2546356209150325,0.3568319425505047,0.3121757758169933,0.37060605871212093],"dir":"ltr"},{"str":"and","boundary":[0.3172736928104573,0.3568319425505047,0.3483967133986926,0.37060605871212093],"dir":"ltr"},{"str":"worked","boundary":[0.3532985294117645,0.3568319425505047,0.4133877060457514,0.37060605871212093],"dir":"ltr"},{"str":"hard","boundary":[0.4184856209150325,0.3568319425505047,0.4574339599673201,0.37060605871212093],"dir":"ltr"},{"str":"to","boundary":[0.4623357843137253,0.3568319425505047,0.4779864212418299,0.37060605871212093],"dir":"ltr"},{"str":"develop","boundary":[0.4830844771241828,0.3568319425505047,0.5451166143790848,0.37060605871212093],"dir":"ltr"},{"str":"it","boundary":[0.5504106209150325,0.3568319425505047,0.5580220202614377,0.37060605871212093],"dir":"ltr"},{"str":"further","boundary":[0.5678259803921567,0.3568319425505047,0.6269169387254899,0.37060605871212093],"dir":"ltr"},{"str":"and","boundary":[0.6320148692810456,0.3568319425505047,0.6631378898692808,0.37060605871212093],"dir":"ltr"},{"str":"propagandize","boundary":[0.6680397058823527,0.3568319425505047,0.7788062866013069,0.37060605871212093],"dir":"ltr"},{"str":"it.","boundary":[0.7837081699346403,0.3568319425505047,0.8011056888888887,0.37060605871212093],"dir":"ltr"},{"str":"But","boundary":[0.14529477124182982,0.37395315467171686,0.17602563464052265,0.387727270833333],"dir":"ltr"},{"str":"today","boundary":[0.18092745098039192,0.37395315467171686,0.2210345287581697,0.387727270833333],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.2312304901960782,0.37395315467171686,0.3096975674836599,0.387727270833333],"dir":"ltr"},{"str":"is","boundary":[0.3144033496732023,0.37395315467171686,0.32338746372548993,0.387727270833333],"dir":"ltr"},{"str":"most","boundary":[0.33319109477124154,0.37395315467171686,0.3729237482026141,0.387727270833333],"dir":"ltr"},{"str":"widely","boundary":[0.3780218137254899,0.37395315467171686,0.4318364753267971,0.387727270833333],"dir":"ltr"},{"str":"known","boundary":[0.4365422385620912,0.37395315467171686,0.49174727565359444,0.387727270833333],"dir":"ltr"},{"str":"for","boundary":[0.4966491013071892,0.37395315467171686,0.5191446637254898,0.387727270833333],"dir":"ltr"},{"str":"his","boundary":[0.5242427287581696,0.37395315467171686,0.5490912343137251,0.387727270833333],"dir":"ltr"},{"str":"famous","boundary":[0.5539930555555551,0.37395315467171686,0.6136900749999996,0.387727270833333],"dir":"ltr"},{"str":"sequence","boundary":[0.6185919117647054,0.37395315467171686,0.6929591751633982,0.387727270833333],"dir":"ltr"},{"str":"of","boundary":[0.6980571078431368,0.37395315467171686,0.7076292950980387,0.387727270833333],"dir":"ltr"},{"str":"numbers","boundary":[0.7178254084967316,0.37395315467171686,0.7904457898692807,0.387727270833333],"dir":"ltr"},{"str":"0","boundary":[0.38803946078431334,0.4107300189393936,0.3968451722222218,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.3968451633986924,0.4107300189393936,0.4017293029411761,0.4245041351010098],"dir":"ltr"},{"str":"1","boundary":[0.40467042483660093,0.4107300189393936,0.4134761362745094,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.41347612745098006,0.4107300189393936,0.4183602669934637,0.4245041351010098],"dir":"ltr"},{"str":"1","boundary":[0.4213013888888885,0.4107300189393936,0.430107100326797,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.43010709150326765,0.4107300189393936,0.4349912310457513,0.4245041351010098],"dir":"ltr"},{"str":"2","boundary":[0.43793235294117616,0.4107300189393936,0.4467380643790846,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.44673805555555524,0.4107300189393936,0.4516221950980389,0.4245041351010098],"dir":"ltr"},{"str":"3","boundary":[0.45456331699346375,0.4107300189393936,0.46336902843137223,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.4633690196078429,0.4107300189393936,0.4682531591503265,0.4245041351010098],"dir":"ltr"},{"str":"5","boundary":[0.47119428104575134,0.4107300189393936,0.4799999924836598,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.47999998366013047,0.4107300189393936,0.48488412320261415,0.4245041351010098],"dir":"ltr"},{"str":"8","boundary":[0.487825245098039,0.4107300189393936,0.4966309565359474,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.49663094771241806,0.4107300189393936,0.5015150872549018,0.4245041351010098],"dir":"ltr"},{"str":"13","boundary":[0.5044562091503266,0.4107300189393936,0.5222636852941174,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.522263676470588,0.4107300189393936,0.5271478160130717,0.4245041351010098],"dir":"ltr"},{"str":"21","boundary":[0.5302850490196076,0.4107300189393936,0.5478964718954247,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.5480925653594769,0.4107300189393936,0.5529767049019605,0.4245041351010098],"dir":"ltr"},{"str":"34","boundary":[0.5559178267973854,0.4107300189393936,0.5735292496732024,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.5737253431372547,0.4107300189393936,0.5756683607843135,0.4245041351010098],"dir":"ltr"},{"str":":","boundary":[0.5815506045751632,0.4107300189393936,0.5832975111111108,0.4245041351010098],"dir":"ltr"},{"str":":","boundary":[0.5895719771241827,0.4107300189393936,0.5915149947712416,0.4245041351010098],"dir":"ltr"},{"str":":","boundary":[0.5973972385620911,0.4107300189393936,0.5981637529411762,0.4245041351010098],"dir":"ltr"},{"str":";","boundary":[0.6063990032679736,0.4107300189393936,0.6112831428104573,0.4245041351010098],"dir":"ltr"},{"str":"each","boundary":[0.11764736928104552,0.4362258819444441,0.15051734150326773,0.4499999981060603],"dir":"ltr"},{"str":"the","boundary":[0.15953686274509782,0.4362258819444441,0.18615007565359457,0.4499999981060603],"dir":"ltr"},{"str":"sum","boundary":[0.19065973856209129,0.4362258819444441,0.2257043310457514,0.4499999981060603],"dir":"ltr"},{"str":"of","boundary":[0.23001807189542461,0.4362258819444441,0.2401784944444442,0.4499999981060603],"dir":"ltr"},{"str":"its","boundary":[0.24919813725490175,0.4362258819444441,0.2699289923202612,0.4499999981060603],"dir":"ltr"},{"str":"two","boundary":[0.2742425816993462,0.4362258819444441,0.3037969735294116,0.4499999981060603],"dir":"ltr"},{"str":"immediate","boundary":[0.30830663398692787,0.4362258819444441,0.3959894165032678,0.4499999981060603],"dir":"ltr"},{"str":"predecessors","boundary":[0.4004991176470586,0.4362258819444441,0.5042068689542482,0.4499999981060603],"dir":"ltr"},{"str":"More","boundary":[0.5153654084967317,0.4362258819444441,0.5576470836601305,0.4499999981060603],"dir":"ltr"},{"str":",","boundary":[0.6292690032679736,0.4362258819444441,0.6296433771241827,0.4499999981060603],"dir":"ltr"},{"str":"formally","boundary":[0.5621567483660128,0.4362258819444441,0.6314259683006535,0.4499999981060603],"dir":"ltr"},{"str":"the","boundary":[0.6386629084967318,0.4362258819444441,0.6652761214052285,0.4499999981060603],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.6697857843137253,0.4362258819444441,0.7482528942810456,0.4499999981060603],"dir":"ltr"},{"str":"numbers","boundary":[0.7523704411764703,0.4362258819444441,0.8249908225490193,0.4499999981060603],"dir":"ltr"},{"str":"F","boundary":[0.8293044281045749,0.4419421401515148,0.8406591612745095,0.45571625631313095],"dir":"ltr"},{"str":"are","boundary":[0.8556863725490192,0.4362258819444441,0.882299585457516,0.4499999981060603],"dir":"ltr"},{"str":"n","boundary":[0.8419608823529409,0.44684646148989865,0.8503867992973854,0.4569097316919188],"dir":"ltr"},{"str":"generated","boundary":[0.11764715686274475,0.4533470940656562,0.19944758153594738,0.46712121022727243],"dir":"ltr"},{"str":"by","boundary":[0.20454552287581668,0.4533470940656562,0.22411773169934607,0.46712121022727243],"dir":"ltr"},{"str":"the","boundary":[0.22901954248365983,0.4533470940656562,0.2556327553921566,0.46712121022727243],"dir":"ltr"},{"str":"simple","boundary":[0.26073081699346373,0.4533470940656562,0.31513371437908466,0.46712121022727243],"dir":"ltr"},{"str":"rule","boundary":[0.32003555555555524,0.4533470940656562,0.3532976153594768,0.46712121022727243],"dir":"ltr"},{"str":"8","boundary":[0.4129412745098036,0.4779338757575754,0.4288058153594768,0.49170799191919157],"dir":"ltr"},{"str":"if","boundary":[0.5515687745098037,0.4833471066919189,0.5631017609477121,0.49712122285353505],"dir":"ltr"},{"str":"n","boundary":[0.5681998202614377,0.48906336489898955,0.5742604784313723,0.5028374810606058],"dir":"ltr"},{"str":">","boundary":[0.5836721568627448,0.48906336489898955,0.5975759117647056,0.5028374810606058],"dir":"ltr"},{"str":"1","boundary":[0.6024778758169932,0.48906336489898955,0.6112835872549016,0.5028374810606058],"dir":"ltr"},{"str":"<","boundary":[0.4129412745098036,0.49035813080808044,0.4288058153594768,0.5041322469696966],"dir":"ltr"},{"str":"Fn","boundary":[0.4368628431372546,0.48906336489898955,0.45666129276143763,0.5040309816919188],"dir":"ltr"},{"str":"\u0000","boundary":[0.4566612581699343,0.49396771148989865,0.4674443481699343,0.5040309816919188],"dir":"ltr"},{"str":"1","boundary":[0.4674443300653591,0.49396771148989865,0.47429445728758135,0.5040309816919188],"dir":"ltr"},{"str":"+","boundary":[0.4792157843137252,0.48906336489898955,0.49311953921568596,0.5028374810606058],"dir":"ltr"},{"str":"Fn","boundary":[0.4970411111111109,0.48906336489898955,0.5168574692320259,0.5040309816919188],"dir":"ltr"},{"str":"\u0000","boundary":[0.5168574346405226,0.49396771148989865,0.5276405246405226,0.5040309816919188],"dir":"ltr"},{"str":"2","boundary":[0.5276405065359475,0.49396771148989865,0.5344906337581696,0.5040309816919188],"dir":"ltr"},{"str":"Fn","boundary":[0.368431470588235,0.506184564393939,0.38822995289215656,0.5211521811868683],"dir":"ltr"},{"str":"=","boundary":[0.39411774509803893,0.506184564393939,0.4080214999999997,0.5199586805555552],"dir":"ltr"},{"str":"1","boundary":[0.4817649673202611,0.5061845770202017,0.49057067875816956,0.5199586931818179],"dir":"ltr"},{"str":"if","boundary":[0.5515510784313722,0.500468318813131,0.5630840648692808,0.5142424349747472],"dir":"ltr"},{"str":"n","boundary":[0.5681821241830062,0.5061845770202017,0.5789486215686271,0.5199586931818179],"dir":"ltr"},{"str":"=","boundary":[0.5836544607843134,0.5061845770202017,0.5926562516339865,0.5199586931818179],"dir":"ltr"},{"str":"1","boundary":[0.6024601797385617,0.5061845770202017,0.6112658911764701,0.5199586931818179],"dir":"ltr"},{"str":":","boundary":[0.4129412745098036,0.5152066156565653,0.4288058153594768,0.5289807318181815],"dir":"ltr"},{"str":".","boundary":[0.6163640196078427,0.5175895309343431,0.6212481591503264,0.5313636470959593],"dir":"ltr"},{"str":"0","boundary":[0.48176508169934606,0.5233057891414138,0.49057079313725455,0.53707990530303],"dir":"ltr"},{"str":"if","boundary":[0.5515511928104572,0.5175895309343431,0.5630841792483656,0.5313636470959593],"dir":"ltr"},{"str":"n","boundary":[0.5681822385620912,0.5233057891414138,0.5789487359477121,0.53707990530303],"dir":"ltr"},{"str":"=","boundary":[0.5836545751633984,0.5233057891414138,0.5926563660130715,0.53707990530303],"dir":"ltr"},{"str":"0","boundary":[0.6024602941176467,0.5233057891414138,0.6112660055555551,0.53707990530303],"dir":"ltr"},{"str":"No","boundary":[0.1176483333333329,0.5480440763888886,0.1409460354575159,0.5618181925505048],"dir":"ltr"},{"str":"other","boundary":[0.1487891830065355,0.5480440763888886,0.19203342581699304,0.5618181925505048],"dir":"ltr"},{"str":"sequence","boundary":[0.20007251633986886,0.5480440763888886,0.2744397797385617,0.5618181925505048],"dir":"ltr"},{"str":"of","boundary":[0.2822828104575159,0.5480440763888886,0.2969530544117643,0.5618181925505048],"dir":"ltr"},{"str":"numbers","boundary":[0.30479604575163355,0.5480440763888886,0.37741642712418255,0.5618181925505048],"dir":"ltr"},{"str":"has","boundary":[0.3850633660130715,0.5480440763888886,0.4142256006535944,0.5618181925505048],"dir":"ltr"},{"str":"been","boundary":[0.4218725163398689,0.5480440763888886,0.460428698202614,0.5618181925505048],"dir":"ltr"},{"str":"studied","boundary":[0.4682716993464048,0.5480440763888886,0.5291273650326793,0.5618181925505048],"dir":"ltr"},{"str":"as","boundary":[0.5369703921568623,0.5480440763888886,0.555170050816993,0.5618181925505048],"dir":"ltr"},{"str":"extensively","boundary":[0.5628169607843133,0.5480440763888886,0.6553660575163395,0.5618181925505048],"dir":"ltr"},{"str":"or","boundary":[0.6665245915032675,0.5480440763888886,0.6831556214052282,0.5618181925505048],"dir":"ltr"},{"str":"applied","boundary":[0.6909987745098035,0.5480440763888886,0.7516583616013068,0.5618181925505048],"dir":"ltr"},{"str":"to","boundary":[0.7595013888888885,0.5480440763888886,0.775152025816993,0.5618181925505048],"dir":"ltr"},{"str":"more","boundary":[0.7829951797385617,0.5480440763888886,0.8242964619281041,0.5618181925505048],"dir":"ltr"},{"str":"\u0002elds:","boundary":[0.8323355392156858,0.5480440763888886,0.8810521573529407,0.5618181925505048],"dir":"ltr"},{"str":"biology","boundary":[0.11764763071895383,0.5651652885101007,0.17575819607843096,0.5789394046717169],"dir":"ltr"},{"str":"demography","boundary":[0.18632844771241786,0.5651652885101007,0.2881110637254898,0.5789394046717169],"dir":"ltr"},{"str":"art,","boundary":[0.29868132352941135,0.5651652885101007,0.3282178900326793,0.5789394046717169],"dir":"ltr"},{"str":"architecture","boundary":[0.33625697712418257,0.5651652885101007,0.43623925849673156,0.5789394046717169],"dir":"ltr"},{"str":"music","boundary":[0.44916248366013023,0.5651652885101007,0.4977008485294112,0.5789394046717169],"dir":"ltr"},{"str":"to","boundary":[0.510232058823529,0.5651652885101007,0.5258826957516336,0.5789394046717169],"dir":"ltr"},{"str":"name","boundary":[0.5333336928104571,0.5651652885101007,0.5789487040849669,0.5789394046717169],"dir":"ltr"},{"str":"just","boundary":[0.5862034640522871,0.5651652885101007,0.6175047379084961,0.5789394046717169],"dir":"ltr"},{"str":"a","boundary":[0.624759509803921,0.5651652885101007,0.627486784313725,0.5789394046717169],"dir":"ltr"},{"str":"few","boundary":[0.641996601307189,0.5651652885101007,0.6705706001633982,0.5789394046717169],"dir":"ltr"},{"str":"And,","boundary":[0.6868271568627446,0.5651652885101007,0.7257754959150322,0.5789394046717169],"dir":"ltr"},{"str":"together","boundary":[0.7336184967320256,0.5651652885101007,0.8021034022875813,0.5789394046717169],"dir":"ltr"},{"str":"with","boundary":[0.8097503594771237,0.5651652885101007,0.8471300697712414,0.5789394046717169],"dir":"ltr"},{"str":"the","boundary":[0.8543849999999995,0.5651652885101007,0.8809982129084963,0.5789394046717169],"dir":"ltr"},{"str":"powers","boundary":[0.11764807189542442,0.5822865006313128,0.17538430539215646,0.596060616792929],"dir":"ltr"},{"str":"of","boundary":[0.18067830065359436,0.5822865006313128,0.1902504879084963,0.596060616792929],"dir":"ltr"},{"str":"2,","boundary":[0.20044660130718914,0.5822865006313128,0.21041110915032638,0.596060616792929],"dir":"ltr"},{"str":"it","boundary":[0.2202147385620911,0.5822865006313128,0.22782613790849632,0.596060616792929],"dir":"ltr"},{"str":"is","boundary":[0.23763009803921528,0.5822865006313128,0.24661421209150286,0.596060616792929],"dir":"ltr"},{"str":"computer","boundary":[0.25641784313725446,0.5822865006313128,0.33353020686274465,0.596060616792929],"dir":"ltr"},{"str":"science's","boundary":[0.3388242156862741,0.5822865006313128,0.4035657846405225,0.596060616792929],"dir":"ltr"},{"str":"favorite","boundary":[0.41336955882352905,0.5822865006313128,0.4765603099673199,0.596060616792929],"dir":"ltr"},{"str":"sequence","boundary":[0.4818543137254898,0.5822865006313128,0.5562215771241826,0.596060616792929],"dir":"ltr"},{"str":".","boundary":[0.5558293137254898,0.5822865006313128,0.5607134532679734,0.596060616792929],"dir":"ltr"},{"str":"In","boundary":[0.14529499999999956,0.5994077127525249,0.16349465866013027,0.6131818289141412],"dir":"ltr"},{"str":"fact,","boundary":[0.16878862745097997,0.5994077127525249,0.2041897264705878,0.6131818289141412],"dir":"ltr"},{"str":"the","boundary":[0.2096798039215682,0.5994077127525249,0.23629301683006496,0.6131818289141412],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.24158699346405185,0.5994077127525249,0.32005407075163356,0.6131818289141412],"dir":"ltr"},{"str":"numbers","boundary":[0.3251520098039211,0.5994077127525249,0.3977723911764701,0.6131818289141412],"dir":"ltr"},{"str":"grow","boundary":[0.4030663888888884,0.5994077127525249,0.44319119950980346,0.6131818289141412],"dir":"ltr"},{"str":"almost","boundary":[0.44848517973856156,0.5994077127525249,0.5032802343137249,0.6131818289141412],"dir":"ltr"},{"str":"as","boundary":[0.5087703104575158,0.5994077127525249,0.5269699691176465,0.6131818289141412],"dir":"ltr"},{"str":"fast","boundary":[0.5322639379084962,0.5994077127525249,0.5631730545751629,0.6131818289141412],"dir":"ltr"},{"str":"as","boundary":[0.5684670424836596,0.5994077127525249,0.5866667011437903,0.6131818289141412],"dir":"ltr"},{"str":"the","boundary":[0.59196066993464,0.5994077127525249,0.6185738828431367,0.6131818289141412],"dir":"ltr"},{"str":"powers","boundary":[0.6238678594771236,0.5994077127525249,0.6816040929738557,0.6131818289141412],"dir":"ltr"},{"str":"of","boundary":[0.6872902450980387,0.5994077127525249,0.701960489052287,0.6131818289141412],"dir":"ltr"},{"str":"2:","boundary":[0.7072546241830061,0.5994077127525249,0.7221209467320258,0.6131818289141412],"dir":"ltr"},{"str":"for","boundary":[0.7289835457516335,0.5994077127525249,0.7514791081699341,0.6131818289141412],"dir":"ltr"},{"str":"example","boundary":[0.7569691666666662,0.5994077127525249,0.8258640547385616,0.6131818289141412],"dir":"ltr"},{"str":",","boundary":[0.8254717810457513,0.5994077127525249,0.8303559205882348,0.6131818289141412],"dir":"ltr"},{"str":"F","boundary":[0.835846078431372,0.6051239709595956,0.8472008116013068,0.6188980871212119],"dir":"ltr"},{"str":"is","boundary":[0.8684312908496727,0.5994077127525249,0.882317220424836,0.6131818289141412],"dir":"ltr"},{"str":"30","boundary":[0.8484312908496727,0.6100283175505048,0.8621315452941171,0.6200915877525249],"dir":"ltr"},{"str":"over","boundary":[0.11764697712418247,0.6165289248737371,0.15267374428104524,0.6303030410353533],"dir":"ltr"},{"str":"a","boundary":[0.15777165032679683,0.6165289248737371,0.16285193137254847,0.6303030410353533],"dir":"ltr"},{"str":"million,","boundary":[0.1726557352941171,0.6165289248737371,0.23584651879084914,0.6303030410353533],"dir":"ltr"},{"str":"and","boundary":[0.24055230392156807,0.6165289248737371,0.27167532450980336,0.6303030410353533],"dir":"ltr"},{"str":"F","boundary":[0.27657714052287524,0.6222451830808078,0.2879318736928099,0.636019299242424],"dir":"ltr"},{"str":"is","boundary":[0.31470560457516283,0.6165289248737371,0.32368971862745044,0.6303030410353533],"dir":"ltr"},{"str":"already","boundary":[0.33349334967320204,0.6165289248737371,0.395525486928104,0.6303030410353533],"dir":"ltr"},{"str":"21","boundary":[0.40042733660130664,0.6222451830808078,0.41803875947712366,0.636019299242424],"dir":"ltr"},{"str":"digits","boundary":[0.4231368137254896,0.6165289248737371,0.4693044101307184,0.6303030410353533],"dir":"ltr"},{"str":"long!","boundary":[0.47420625816993406,0.6165289248737371,0.5145093220588229,0.6303030410353533],"dir":"ltr"},{"str":"In","boundary":[0.5205876307189536,0.6165289248737371,0.5387872893790845,0.6303030410353533],"dir":"ltr"},{"str":"general,","boundary":[0.543689101307189,0.6165289248737371,0.610213220915032,0.6303030410353533],"dir":"ltr"},{"str":"F","boundary":[0.6151150816993458,0.6222451830808078,0.6264698148692804,0.636019299242424],"dir":"ltr"},{"str":"\u0019","boundary":[0.6413720915032675,0.6219421525252522,0.6552758464052282,0.6357162686868684],"dir":"ltr"},{"str":"20","boundary":[0.6601778104575158,0.6200283301767674,0.6758693429084961,0.636019299242424],"dir":"ltr"},{"str":":","boundary":[0.6758693137254895,0.6200283301767674,0.6797892534477118,0.6300916003787875],"dir":"ltr"},{"str":"694n","boundary":[0.679789281045751,0.6200283301767674,0.708765524787581,0.6300916003787875],"dir":"ltr"},{"str":"(see","boundary":[0.7147055228758163,0.6165289248737371,0.746398953921568,0.6303030410353533],"dir":"ltr"},{"str":"Exercise","boundary":[0.75169294117647,0.6165289248737371,0.821354318300653,0.6303030410353533],"dir":"ltr"},{"str":"0.3).","boundary":[0.8264522549019602,0.6165289248737371,0.8620494325163393,0.6303030410353533],"dir":"ltr"},{"str":"100","boundary":[0.28823501633986875,0.6271495296717169,0.3087853980065354,0.637212799873737],"dir":"ltr"},{"str":"n","boundary":[0.6270583496732021,0.6271495296717169,0.6354842666176465,0.637212799873737],"dir":"ltr"},{"str":"But","boundary":[0.145293758169934,0.6336501369949491,0.1760246215686268,0.6474242531565653],"dir":"ltr"},{"str":"what","boundary":[0.18327937908496666,0.6336501369949491,0.22497281846405162,0.6474242531565653],"dir":"ltr"},{"str":"is","boundary":[0.23222758169934574,0.6336501369949491,0.24611351127450914,0.6474242531565653],"dir":"ltr"},{"str":"the","boundary":[0.25336843137254833,0.6336501369949491,0.2799816442810451,0.6474242531565653],"dir":"ltr"},{"str":"precise","boundary":[0.2874324836601301,0.6336501369949491,0.34475873464052226,0.6474242531565653],"dir":"ltr"},{"str":"value","boundary":[0.35240568627450913,0.6336501369949491,0.39741463643790786,0.6474242531565653],"dir":"ltr"},{"str":"of","boundary":[0.4044733333333327,0.6336501369949491,0.41914357728758106,0.6474242531565653],"dir":"ltr"},{"str":"F","boundary":[0.4267906535947706,0.6393663952020198,0.4381453867647052,0.6531405113636359],"dir":"ltr"},{"str":"or","boundary":[0.47311888888888826,0.6336501369949491,0.489749918790849,0.6474242531565653],"dir":"ltr"},{"str":"of","boundary":[0.4972009150326791,0.6336501369949491,0.5118711589869275,0.6474242531565653],"dir":"ltr"},{"str":"F","boundary":[0.5193221568627445,0.6393663952020198,0.5306768900326791,0.6531405113636359],"dir":"ltr"},{"str":"?","boundary":[0.5525486274509798,0.6336501369949491,0.5603739459150321,0.6474242531565653],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.5737072875816986,0.6336501369949491,0.6521743648692805,0.6474242531565653],"dir":"ltr"},{"str":"himself","boundary":[0.6592330882352935,0.6336501369949491,0.7202848325163392,0.6474242531565653],"dir":"ltr"},{"str":"would","boundary":[0.7275396241830059,0.6336501369949491,0.7770583820261432,0.6474242531565653],"dir":"ltr"},{"str":"surely","boundary":[0.7843133169934634,0.6336501369949491,0.8353828782679732,0.6474242531565653],"dir":"ltr"},{"str":"have","boundary":[0.8428337418300647,0.6336501369949491,0.8819781718954243,0.6474242531565653],"dir":"ltr"},{"str":"100","boundary":[0.43862692810457454,0.644270741792929,0.45917730977124116,0.6543340119949492],"dir":"ltr"},{"str":"200","boundary":[0.5307839215686269,0.644270741792929,0.5513343032352934,0.6543340119949492],"dir":"ltr"},{"str":"wanted","boundary":[0.11764616013071834,0.6507713491161613,0.17793140261437848,0.6645454652777775],"dir":"ltr"},{"str":"to","boundary":[0.1818528431372543,0.6507713491161613,0.19358205816993404,0.6645454652777775],"dir":"ltr"},{"str":"know","boundary":[0.20142490196078372,0.6507713491161613,0.24566736307189482,0.6645454652777775],"dir":"ltr"},{"str":"such","boundary":[0.24958879084967261,0.6507713491161613,0.2836352499999994,0.6645454652777775],"dir":"ltr"},{"str":"things","boundary":[0.2910861111111105,0.6507713491161613,0.34333214395424777,0.6645454652777775],"dir":"ltr"},{"str":"To","boundary":[0.3535102450980386,0.6507713491161613,0.36955310588235235,0.6645454652777775],"dir":"ltr"},{"str":",","boundary":[0.4349363562091497,0.6507713491161613,0.4357028705882347,0.6645454652777775],"dir":"ltr"},{"str":"answer","boundary":[0.37700400326797323,0.6507713491161613,0.43670102271241773,0.6645454652777775],"dir":"ltr"},{"str":"we","boundary":[0.44393812091503204,0.6507713491161613,0.46664758725490135,0.6645454652777775],"dir":"ltr"},{"str":"need","boundary":[0.4705690032679732,0.6507713491161613,0.5093212637254895,0.6645454652777775],"dir":"ltr"},{"str":"an","boundary":[0.5132426960784308,0.6507713491161613,0.5341874550653588,0.6645454652777775],"dir":"ltr"},{"str":"algorithm","boundary":[0.5379127941176464,0.6507713491161613,0.6191249830065353,0.6645454652777775],"dir":"ltr"},{"str":"for","boundary":[0.6228503758169929,0.6507713491161613,0.6453459382352935,0.6645454652777775],"dir":"ltr"},{"str":"computing","boundary":[0.6494636111111105,0.6507713491161613,0.7361660006535942,0.6645454652777775],"dir":"ltr"},{"str":"the","boundary":[0.7398913888888883,0.6507713491161613,0.766504601797385,0.6645454652777775],"dir":"ltr"},{"str":"nth","boundary":[0.7704261928104569,0.6507713491161613,0.7990001321895418,0.6702617234848481],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.8027254738562085,0.6507713491161613,0.8811925838235288,0.6645454652777775],"dir":"ltr"},{"str":"number","boundary":[0.11764558823529346,0.6678925612373735,0.18204849395424771,0.6816666773989897],"dir":"ltr"},{"str":".","boundary":[0.18028366013071828,0.6678925612373735,0.18516779967320196,0.6816666773989897],"dir":"ltr"},{"str":"An","boundary":[0.11764558823529346,0.7053856736111108,0.14329623349673137,0.719159789772727],"dir":"ltr"},{"str":"exponential","boundary":[0.14839428104575098,0.7053856736111108,0.2583943727124177,0.719159789772727],"dir":"ltr"},{"str":"algorithm","boundary":[0.26329624183006467,0.7053856736111108,0.35529275343137184,0.719159789772727],"dir":"ltr"},{"str":"One","boundary":[0.11764575163398626,0.7328925612373736,0.1513177939542477,0.7466666773989896],"dir":"ltr"},{"str":"idea","boundary":[0.15680784313725424,0.7328925612373736,0.1914424531045745,0.7466666773989896],"dir":"ltr"},{"str":"is","boundary":[0.19712859477124117,0.7328925612373736,0.20552431013071829,0.7466666773989896],"dir":"ltr"},{"str":"to","boundary":[0.21650473856209085,0.7328925612373736,0.2321553754901954,0.7466666773989896],"dir":"ltr"},{"str":"slavishly","boundary":[0.23803758169934575,0.7328925612373736,0.3114066516339863,0.7466666773989896],"dir":"ltr"},{"str":"implement","boundary":[0.3167006535947706,0.7328925612373736,0.4053638290849667,0.7466666773989896],"dir":"ltr"},{"str":"the","boundary":[0.4108539215686268,0.7328925612373736,0.4374671344771236,0.7466666773989896],"dir":"ltr"},{"str":"recursive","boundary":[0.4431532679738556,0.7328925612373736,0.5186791776143784,0.7466666773989896],"dir":"ltr"},{"str":"de\u0002nition","boundary":[0.5245614379084961,0.7328925612373736,0.6034206836601301,0.7466666773989896],"dir":"ltr"},{"str":"of","boundary":[0.6089107843137249,0.7328925612373736,0.6235810282679732,0.7466666773989896],"dir":"ltr"},{"str":"F","boundary":[0.6294632352941171,0.7386088194444442,0.6408179684640517,0.7523829356060604],"dir":"ltr"},{"str":"Here","boundary":[0.6640982516339864,0.7328925612373736,0.7044191408496727,0.7466666773989896],"dir":"ltr"},{"str":"is","boundary":[0.7103013562091498,0.7328925612373736,0.7186970715686268,0.7466666773989896],"dir":"ltr"},{"str":"the","boundary":[0.7296774999999994,0.7328925612373736,0.7562907129084963,0.7466666773989896],"dir":"ltr"},{"str":"resulting","boundary":[0.7619768464052282,0.7328925612373736,0.836522363071895,0.7466666773989896],"dir":"ltr"},{"str":"algo-","boundary":[0.8420124673202609,0.7328925612373736,0.8819233740196074,0.7466666773989896],"dir":"ltr"},{"str":"n","boundary":[0.6417631372549013,0.7435131660353532,0.6501890541993458,0.7535764362373734],"dir":"ltr"},{"str":"rithm,","boundary":[0.11764482026143742,0.7500137733585857,0.16969477450980344,0.7637878895202017],"dir":"ltr"},{"str":"in","boundary":[0.17459661764705836,0.7500137733585857,0.19122764754901914,0.7637878895202017],"dir":"ltr"},{"str":"the","boundary":[0.19612946078431326,0.7500137733585857,0.22274267369280998,0.7637878895202017],"dir":"ltr"},{"str":"ìpseudocodeî","boundary":[0.2276444934640518,0.7500137733585857,0.33409734509803873,0.7637878895202017],"dir":"ltr"},{"str":"notation","boundary":[0.3397835457516335,0.7500137733585857,0.4086606084967315,0.7637878895202017],"dir":"ltr"},{"str":"used","boundary":[0.4135624673202609,0.7500137733585857,0.45172649199346354,0.7637878895202017],"dir":"ltr"},{"str":"throughout","boundary":[0.45662831699346357,0.7500137733585857,0.5491952390522872,0.7637878895202017],"dir":"ltr"},{"str":"this","boundary":[0.5542931862745093,0.7500137733585857,0.5859866173202609,0.7637878895202017],"dir":"ltr"},{"str":"book:","boundary":[0.5908884477124178,0.7500137733585857,0.6339366119281041,0.7637878895202017],"dir":"ltr"},{"str":"function","boundary":[0.16215478758169885,0.7876584090909087,0.2477163562091498,0.8014325252525248],"dir":"ltr"},{"str":"fib1","boundary":[0.2582866503267969,0.7876584090909087,0.3010674346405223,0.8014325252525248],"dir":"ltr"},{"str":"(","boundary":[0.30096241830065357,0.7876583964646464,0.31165761437908496,0.8014325126262625],"dir":"ltr"},{"str":"n","boundary":[0.3117289052287582,0.7842148674242424,0.32249540261437903,0.7979889835858585],"dir":"ltr"},{"str":")","boundary":[0.32249539215686274,0.7876583964646464,0.33319058823529407,0.8014325126262625],"dir":"ltr"},{"str":"if","boundary":[0.16215683006535947,0.8047796085858586,0.1835472222222222,0.8185537247474747],"dir":"ltr"},{"str":"n","boundary":[0.19427807189542484,0.8013360795454546,0.20504456928104575,0.8151101957070707],"dir":"ltr"},{"str":"=","boundary":[0.20994647058823526,0.8013360795454546,0.21894826143790846,0.8151101957070707],"dir":"ltr"},{"str":"0","boundary":[0.2287521895424836,0.8013360795454546,0.23755790098039212,0.8151101957070707],"dir":"ltr"},{"str":"return","boundary":[0.2696969444444444,0.8047796085858586,0.3338681209150327,0.8185537247474747],"dir":"ltr"},{"str":"0","boundary":[0.3444918790849673,0.8013360795454546,0.3532975905228758,0.8151101957070707],"dir":"ltr"},{"str":"if","boundary":[0.16215691176470587,0.8219008207070706,0.1835473039215686,0.8356749368686868],"dir":"ltr"},{"str":"n","boundary":[0.1942781535947712,0.8184572916666666,0.20504465098039212,0.8322314078282828],"dir":"ltr"},{"str":"=","boundary":[0.20994655228758166,0.8184572916666666,0.21894834313725486,0.8322314078282828],"dir":"ltr"},{"str":"1","boundary":[0.22875227124183,0.8184572916666666,0.23755798267973852,0.8322314078282828],"dir":"ltr"},{"str":"return","boundary":[0.2696970261437908,0.8219008207070706,0.33386820261437905,0.8356749368686868],"dir":"ltr"},{"str":"1","boundary":[0.3444919607843137,0.8184572916666666,0.3532976722222222,0.8322314078282828],"dir":"ltr"},{"str":"return","boundary":[0.16215699346405224,0.8390220328282828,0.2263281699346405,0.852796148989899],"dir":"ltr"},{"str":"fib1(n","boundary":[0.2369519281045751,0.8355785037878788,0.3015507784313725,0.852796148989899],"dir":"ltr"},{"str":"\u0000","boundary":[0.30508014705882347,0.8352754732323232,0.31898390196078424,0.8490495893939394],"dir":"ltr"},{"str":"1","boundary":[0.3227093954248365,0.8355785037878788,0.33151510686274505,0.849352619949495],"dir":"ltr"},{"str":"+","boundary":[0.35306591503267964,0.8390220328282828,0.3531015686274509,0.852796148989899],"dir":"ltr"},{"str":"fib1(n","boundary":[0.37442065359477117,0.8355785037878788,0.4390195039215686,0.852796148989899],"dir":"ltr"},{"str":"\u0000","boundary":[0.4425488725490196,0.8352754732323232,0.45645262745098036,0.8490495893939394],"dir":"ltr"},{"str":"2","boundary":[0.4603741993464052,0.8355785037878788,0.4691799107843137,0.849352619949495],"dir":"ltr"},{"str":")","boundary":[0.46917990196078435,0.8390220328282828,0.4798750980392157,0.852796148989899],"dir":"ltr"},{"str":"Whenever","boundary":[0.14529428104575168,0.8584986092171717,0.22848508120915037,0.8722727253787879],"dir":"ltr"},{"str":"we","boundary":[0.23358300653594774,0.8584986092171717,0.256292472875817,0.8722727253787879],"dir":"ltr"},{"str":"have","boundary":[0.26139052287581704,0.8584986092171717,0.30053495294117655,0.8722727253787879],"dir":"ltr"},{"str":"an","boundary":[0.3052408496732027,0.8584986092171717,0.32618560866013085,0.8722727253787879],"dir":"ltr"},{"str":"algorithm,","boundary":[0.3310874183006537,0.8584986092171717,0.41718374673202624,0.8722727253787879],"dir":"ltr"},{"str":"there","boundary":[0.4218895424836602,0.8584986092171717,0.4651337852941177,0.8722727253787879],"dir":"ltr"},{"str":"are","boundary":[0.47042777777777783,0.8584986092171717,0.49704099068627455,0.8722727253787879],"dir":"ltr"},{"str":"three","boundary":[0.5021390522875818,0.8584986092171717,0.5453832950980393,0.8722727253787879],"dir":"ltr"},{"str":"questions","boundary":[0.5504812091503268,0.8584986092171717,0.6289482977124183,0.8722727253787879],"dir":"ltr"},{"str":"we","boundary":[0.6338501633986928,0.8584986092171717,0.6565596297385622,0.8722727253787879],"dir":"ltr"},{"str":"always","boundary":[0.6614614379084968,0.8584986092171717,0.7182171583333333,0.8722727253787879],"dir":"ltr"},{"str":"ask","boundary":[0.7231189705882353,0.8584986092171717,0.7518890480392157,0.8722727253787879],"dir":"ltr"},{"str":"about","boundary":[0.7565949509803922,0.8584986092171717,0.8031725299019608,0.8722727253787879],"dir":"ltr"},{"str":"it:","boundary":[0.808074362745098,0.8584986092171717,0.8254718816993464,0.8722727253787879],"dir":"ltr"}],"boundary":[0.11764,0.08979,0.88233,0.87227],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":12,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/24a2d225b589acd78b109011b48c660e.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/ff92c23b2f82ad54d8da84545b14052f.jpg"},"info":{"width":612,"height":792,"margin":[0.11764,0.08979,0.11512,0.12773]},"elements":[{"words":[{"str":"S","boundary":[0.11764705882352941,0.08979153426128839,0.1293939594771242,0.10356565042290454],"dir":"ltr"},{"str":"Dasgupta,","boundary":[0.13800351307189543,0.08979153426128839,0.2225490380718954,0.10356565042290454],"dir":"ltr"},{"str":"C.H.","boundary":[0.22745089869281046,0.08979153426128839,0.26443845637254904,0.10356565042290454],"dir":"ltr"},{"str":"Papadimitriou,","boundary":[0.2693402777777778,0.08979153426128839,0.3932084790849673,0.10356565042290454],"dir":"ltr"},{"str":"and","boundary":[0.39771821895424836,0.08979153426128839,0.42884123954248365,0.10356565042290454],"dir":"ltr"},{"str":"U.V","boundary":[0.43374305555555553,0.08979153426128839,0.4664347251633986,0.10356565042290454],"dir":"ltr"},{"str":"Vazirani","boundary":[0.47190697712418295,0.08979153426128839,0.5419605168300654,0.10356565042290454],"dir":"ltr"},{"str":"13","boundary":[0.8617647058823529,0.09001376073232323,0.8817290718954248,0.10378787689393938],"dir":"ltr"},{"str":"1.","boundary":[0.13843137254901955,0.12880163952020204,0.15329769509803917,0.1425757556818182],"dir":"ltr"},{"str":"Is","boundary":[0.1621210784313725,0.12880163952020204,0.17757563676470584,0.1425757556818182],"dir":"ltr"},{"str":"it","boundary":[0.18267369281045745,0.12880163952020204,0.19028509215686268,0.1425757556818182],"dir":"ltr"},{"str":"correct?","boundary":[0.20008905228758164,0.12880163952020204,0.2636719929738562,0.1425757556818182],"dir":"ltr"},{"str":"2.","boundary":[0.13843137254901955,0.15864999810606065,0.15329769509803917,0.17242411426767681],"dir":"ltr"},{"str":"How","boundary":[0.1621210784313725,0.15864999810606065,0.19971469264705877,0.17242411426767681],"dir":"ltr"},{"str":"much","boundary":[0.2046165032679738,0.15864999810606065,0.24513355065359474,0.17242411426767681],"dir":"ltr"},{"str":"time","boundary":[0.2549373529411764,0.15864999810606065,0.29212098464052283,0.17242411426767681],"dir":"ltr"},{"str":"does","boundary":[0.2972188888888888,0.15864999810606065,0.3332260490196078,0.17242411426767681],"dir":"ltr"},{"str":"it","boundary":[0.3383239542483659,0.15864999810606065,0.3457392751633986,0.17242411426767681],"dir":"ltr"},{"str":"take","boundary":[0.35593539215686265,0.15864999810606065,0.39213863088235285,0.17242411426767681],"dir":"ltr"},{"str":"as","boundary":[0.4017286601307189,0.15864999810606065,0.4199283187908496,0.17242411426767681],"dir":"ltr"},{"str":"a","boundary":[0.42483013071895415,0.15864999810606065,0.42991041176470574,0.17242411426767681],"dir":"ltr"},{"str":"function","boundary":[0.4397142156862744,0.15864999810606065,0.5076108854575162,0.17242411426767681],"dir":"ltr"},{"str":"of","boundary":[0.5125127450980391,0.15864999810606065,0.5271829890522874,0.17242411426767681],"dir":"ltr"},{"str":"n","boundary":[0.5322810457516339,0.16436625631313137,0.5430475431372549,0.1781403724747475],"dir":"ltr"},{"str":"?","boundary":[0.5430475326797385,0.15864999810606065,0.5508728511437908,0.17242411426767681],"dir":"ltr"},{"str":"3.","boundary":[0.13843151960784308,0.1884984829545455,0.15329784215686268,0.20227259911616163],"dir":"ltr"},{"str":"And","boundary":[0.16212122549019603,0.1884984829545455,0.19618542499999997,0.20227259911616163],"dir":"ltr"},{"str":"can","boundary":[0.20108723856209146,0.1884984829545455,0.22985731601307186,0.20227259911616163],"dir":"ltr"},{"str":"we","boundary":[0.23475913398692805,0.1884984829545455,0.2574686003267973,0.20227259911616163],"dir":"ltr"},{"str":"do","boundary":[0.26237040849673193,0.1884984829545455,0.2813543815359476,0.20227259911616163],"dir":"ltr"},{"str":"better?","boundary":[0.28645243464052283,0.1884984829545455,0.3433865284313725,0.20227259911616163],"dir":"ltr"},{"str":"The","boundary":[0.14529410130718948,0.21849848295454546,0.1770053576797385,0.23227259911616163],"dir":"ltr"},{"str":"\u0002rst","boundary":[0.18249540849673196,0.21849848295454546,0.21634570408496723,0.23227259911616163],"dir":"ltr"},{"str":"question","boundary":[0.22203184640522872,0.21849848295454546,0.29228145931372546,0.23227259911616163],"dir":"ltr"},{"str":"is","boundary":[0.2977715522875816,0.21849848295454546,0.30616726764705876,0.23227259911616163],"dir":"ltr"},{"str":"moot","boundary":[0.31714769607843135,0.21849848295454546,0.3574685852941176,0.23227259911616163],"dir":"ltr"},{"str":"here","boundary":[0.3633508006535947,0.21849848295454546,0.3997501179738562,0.23227259911616163],"dir":"ltr"},{"str":"as","boundary":[0.4101244281045751,0.21849848295454546,0.42832408676470585,0.23227259911616163],"dir":"ltr"},{"str":"this","boundary":[0.43381413398692803,0.21849848295454546,0.46550756503267965,0.23227259911616163],"dir":"ltr"},{"str":"algorithm","boundary":[0.47119370915032677,0.21849848295454546,0.5524058980392157,0.23227259911616163],"dir":"ltr"},{"str":"is","boundary":[0.5576999183006536,0.21849848295454546,0.5660956336601307,0.23227259911616163],"dir":"ltr"},{"str":"precisely","boundary":[0.5770760620915033,0.21849848295454546,0.6496607928104575,0.23227259911616163],"dir":"ltr"},{"str":"Fibonacci's","boundary":[0.6555430555555555,0.21849848295454546,0.7404449513071896,0.23227259911616163],"dir":"ltr"},{"str":"de\u0002nition","boundary":[0.7506411111111111,0.21849848295454546,0.829500356862745,0.23227259911616163],"dir":"ltr"},{"str":"of","boundary":[0.8349904575163398,0.21849848295454546,0.8496607014705883,0.23227259911616163],"dir":"ltr"},{"str":"F","boundary":[0.8553469934640523,0.2242147411616162,0.8667017266339869,0.23798885732323233],"dir":"ltr"},{"str":".","boundary":[0.8774509803921569,0.21849848295454546,0.8823351199346405,0.23227259911616163],"dir":"ltr"},{"str":"n","boundary":[0.8680391993464053,0.22911912563131312,0.8764651162908498,0.23918239583333334],"dir":"ltr"},{"str":"But","boundary":[0.11764705882352941,0.23561969507575753,0.14837792222222224,0.24939381123737367],"dir":"ltr"},{"str":"the","boundary":[0.15543660130718956,0.23561969507575753,0.18204981421568625,0.24939381123737367],"dir":"ltr"},{"str":"second","boundary":[0.18950065359477125,0.23561969507575753,0.24429570816993465,0.24939381123737367],"dir":"ltr"},{"str":"demands","boundary":[0.25174656862745093,0.23561969507575753,0.3259355787581699,0.24939381123737367],"dir":"ltr"},{"str":"an","boundary":[0.33299428104575163,0.23561969507575753,0.35393904003267973,0.24939381123737367],"dir":"ltr"},{"str":"answer","boundary":[0.36099787581699344,0.23561969507575753,0.4206948952614379,0.24939381123737367],"dir":"ltr"},{"str":"Let","boundary":[0.4367555555555556,0.23561969507575753,0.4643491614379086,0.24939381123737367],"dir":"ltr"},{"str":"T","boundary":[0.47160392156862757,0.24133595328282823,0.481978261764706,0.25511006944444437],"dir":"ltr"},{"str":"(","boundary":[0.48452722222222233,0.24133595328282823,0.4913721477124184,0.25511006944444437],"dir":"ltr"},{"str":"n","boundary":[0.491372140522876,0.24133595328282823,0.5021386379084969,0.25511006944444437],"dir":"ltr"},{"str":")","boundary":[0.5021386274509806,0.24133595328282823,0.5089835529411766,0.25511006944444437],"dir":"ltr"},{"str":"be","boundary":[0.5162384313725491,0.23561969507575753,0.5350263258169936,0.24939381123737367],"dir":"ltr"},{"str":"the","boundary":[0.5422812418300654,0.23561969507575753,0.5688944547385623,0.24939381123737367],"dir":"ltr"},{"str":"number","boundary":[0.5761492156862746,0.23561969507575753,0.6405521214052289,0.24939381123737367],"dir":"ltr"},{"str":"of","boundary":[0.6476108169934642,0.23561969507575753,0.6622810609477126,0.24939381123737367],"dir":"ltr"},{"str":"computer","boundary":[0.6697318954248367,0.23561969507575753,0.7452756303921569,0.24939381123737367],"dir":"ltr"},{"str":"steps","boundary":[0.752726503267974,0.23561969507575753,0.7926374099673203,0.24939381123737367],"dir":"ltr"},{"str":"needed","boundary":[0.8000882679738563,0.23561969507575753,0.8578245014705883,0.24939381123737367],"dir":"ltr"},{"str":"to","boundary":[0.8652753594771243,0.23561969507575753,0.8809259964052288,0.24939381123737367],"dir":"ltr"},{"str":"compute","boundary":[0.11764627450980404,0.25258939204545455,0.18693331977124195,0.2663635082070707],"dir":"ltr"},{"str":"(","boundary":[0.23627356209150338,0.25258939204545455,0.24213809460784325,0.2663635082070707],"dir":"ltr"},{"str":"n","boundary":[0.24213808823529423,0.2583056502525253,0.2529045856209151,0.27207976641414144],"dir":"ltr"},{"str":");","boundary":[0.2529045751633988,0.25258939204545455,0.2573787166666668,0.2663635082070707],"dir":"ltr"},{"str":"what","boundary":[0.2699277777777779,0.25258939204545455,0.31162121715686286,0.2663635082070707],"dir":"ltr"},{"str":"can","boundary":[0.31730735294117657,0.25258939204545455,0.34607743039215694,0.2663635082070707],"dir":"ltr"},{"str":"we","boundary":[0.3519596405228759,0.25258939204545455,0.3746691068627452,0.2663635082070707],"dir":"ltr"},{"str":"say","boundary":[0.38074754901960794,0.25258939204545455,0.40245890784313737,0.2663635082070707],"dir":"ltr"},{"str":"about","boundary":[0.41422343137254913,0.25258939204545455,0.4608010102941178,0.2663635082070707],"dir":"ltr"},{"str":"this","boundary":[0.4666832352941178,0.25258939204545455,0.49837666633986943,0.2663635082070707],"dir":"ltr"},{"str":"function?","boundary":[0.5044551307189544,0.25258939204545455,0.5801771189542486,0.2663635082070707],"dir":"ltr"},{"str":"For","boundary":[0.5893927124183008,0.25258939204545455,0.6169863403594773,0.2663635082070707],"dir":"ltr"},{"str":"starters","boundary":[0.6230647875816996,0.25258939204545455,0.6876281212418303,0.2663635082070707],"dir":"ltr"},{"str":"if","boundary":[0.6987867483660133,0.25258939204545455,0.7103197348039217,0.2663635082070707],"dir":"ltr"},{"str":"n","boundary":[0.7162021078431374,0.2583056502525253,0.7269686052287584,0.27207976641414144],"dir":"ltr"},{"str":"is","boundary":[0.7328509640522878,0.25258939204545455,0.7467368936274512,0.2663635082070707],"dir":"ltr"},{"str":"less","boundary":[0.7528153431372552,0.25258939204545455,0.7837244598039218,0.2663635082070707],"dir":"ltr"},{"str":"than","boundary":[0.7896068464052289,0.25258939204545455,0.8283591068627453,0.2663635082070707],"dir":"ltr"},{"str":"2","boundary":[0.834241323529412,0.2583056502525253,0.8430470349673205,0.27207976641414144],"dir":"ltr"},{"str":"the","boundary":[0.8544017483660132,0.25258939204545455,0.88101496127451,0.2663635082070707],"dir":"ltr"},{"str":"fib1","boundary":[0.1932077124183008,0.2617491792929293,0.2359884967320263,0.27552329545454546],"dir":"ltr"},{"str":"procedure","boundary":[0.11764684640522892,0.2697106041666666,0.19885903529411783,0.28348472032828276],"dir":"ltr"},{"str":"halts","boundary":[0.20434913398692828,0.2697106041666666,0.24602474803921587,0.28348472032828276],"dir":"ltr"},{"str":"almost","boundary":[0.2507305065359479,0.2697106041666666,0.306113796895425,0.28348472032828276],"dir":"ltr"},{"str":"immediately","boundary":[0.3110156372549021,0.2697106041666666,0.41395689950980413,0.28348472032828276],"dir":"ltr"},{"str":"after","boundary":[0.4215859967320263,0.2697106041666666,0.460908667647059,0.28348472032828276],"dir":"ltr"},{"str":"just","boundary":[0.46600658496732045,0.2697106041666666,0.49730785882352957,0.28348472032828276],"dir":"ltr"},{"str":"a","boundary":[0.5022096895424838,0.2697106041666666,0.5072899705882354,0.28348472032828276],"dir":"ltr"},{"str":"couple","boundary":[0.5170937745098041,0.2697106041666666,0.5693398073529413,0.28348472032828276],"dir":"ltr"},{"str":"of","boundary":[0.5744377287581701,0.2697106041666666,0.584009916013072,0.28348472032828276],"dir":"ltr"},{"str":"steps","boundary":[0.5942060294117649,0.2697106041666666,0.6364698792483662,0.28348472032828276],"dir":"ltr"},{"str":"Therefore","boundary":[0.647236388888889,0.2697106041666666,0.726879949019608,0.28348472032828276],"dir":"ltr"},{"str":",","boundary":[0.7264876960784314,0.2697106041666666,0.7313718356209151,0.28348472032828276],"dir":"ltr"},{"str":"T","boundary":[0.42195991830065377,0.30754807449494953,0.43233425849673224,0.32132219065656564],"dir":"ltr"},{"str":"(","boundary":[0.43488321895424853,0.30754807449494953,0.4417281444444446,0.32132219065656564],"dir":"ltr"},{"str":"n","boundary":[0.4417281372549022,0.30754807449494953,0.45249463464052314,0.32132219065656564],"dir":"ltr"},{"str":")","boundary":[0.45249462418300673,0.30754807449494953,0.4593395496732028,0.32132219065656564],"dir":"ltr"},{"str":"\u0014","boundary":[0.4642414542483662,0.30724504393939395,0.478145209150327,0.3210191601010101],"dir":"ltr"},{"str":"2","boundary":[0.48304717320261453,0.30754807449494953,0.491852884640523,0.32132219065656564],"dir":"ltr"},{"str":"for","boundary":[0.5018528921568629,0.3018318162878788,0.5243484545751635,0.315605932449495],"dir":"ltr"},{"str":"n","boundary":[0.5296425980392158,0.30754807449494953,0.5404090954248367,0.32132219065656564],"dir":"ltr"},{"str":"\u0014","boundary":[0.545114934640523,0.30724504393939395,0.5590186895424838,0.3210191601010101],"dir":"ltr"},{"str":"1","boundary":[0.5639206535947713,0.30754807449494953,0.5727263650326798,0.32132219065656564],"dir":"ltr"},{"str":".","boundary":[0.5727263562091505,0.3018318162878788,0.5776104957516341,0.315605932449495],"dir":"ltr"},{"str":"For","boundary":[0.11764629084967329,0.3338015132575759,0.14523991879084974,0.34757562941919207],"dir":"ltr"},{"str":"larger","boundary":[0.15073013071895433,0.3338015132575759,0.20042714183006546,0.34757562941919207],"dir":"ltr"},{"str":"values","boundary":[0.2059172222222223,0.3338015132575759,0.25914364803921575,0.34757562941919207],"dir":"ltr"},{"str":"of","boundary":[0.2642415686274511,0.3338015132575759,0.2789118125816994,0.34757562941919207],"dir":"ltr"},{"str":"n","boundary":[0.2844020261437909,0.33951777146464657,0.2951685235294118,0.35329188762626274],"dir":"ltr"},{"str":"there","boundary":[0.3055428104575164,0.3338015132575759,0.348787053267974,0.34757562941919207],"dir":"ltr"},{"str":"are","boundary":[0.3544732026143792,0.3338015132575759,0.3810864155228759,0.34757562941919207],"dir":"ltr"},{"str":"two","boundary":[0.3865764705882354,0.3338015132575759,0.4161308624183007,0.34757562941919207],"dir":"ltr"},{"str":"recursive","boundary":[0.4216209150326798,0.3338015132575759,0.49714682467320265,0.34757562941919207],"dir":"ltr"},{"str":"invocations","boundary":[0.5026369281045752,0.3338015132575759,0.5959703392156863,0.34757562941919207],"dir":"ltr"},{"str":"of","boundary":[0.6012643790849674,0.3338015132575759,0.6159346230392158,0.34757562941919207],"dir":"ltr"},{"str":"taking","boundary":[0.6746689215686275,0.3338015132575759,0.7282875045751634,0.34757562941919207],"dir":"ltr"},{"str":"time","boundary":[0.7333854248366013,0.3338015132575759,0.7705690565359478,0.34757562941919207],"dir":"ltr"},{"str":"T","boundary":[0.7760591176470589,0.33951777146464657,0.7864334578431373,0.35329188762626274],"dir":"ltr"},{"str":"(","boundary":[0.7889824509803922,0.33951777146464657,0.7958273764705883,0.35329188762626274],"dir":"ltr"},{"str":"n","boundary":[0.795827320261438,0.33951777146464657,0.806593817647059,0.35329188762626274],"dir":"ltr"},{"str":"\u0000","boundary":[0.8107114379084968,0.339214740909091,0.8246151928104576,0.3529888570707072],"dir":"ltr"},{"str":"1)","boundary":[0.828732843137255,0.33951777146464657,0.8443834800653596,0.35329188762626274],"dir":"ltr"},{"str":"and","boundary":[0.8500697712418301,0.3338015132575759,0.8811927918300654,0.34757562941919207],"dir":"ltr"},{"str":"fib1","boundary":[0.6214248366013072,0.34296130050505064,0.6642056209150328,0.3567354166666668],"dir":"ltr"},{"str":"T","boundary":[0.11764656862745101,0.35663898358585866,0.12802090882352946,0.3704130997474749],"dir":"ltr"},{"str":"(","boundary":[0.13056986928104578,0.35663898358585866,0.13741479477124185,0.3704130997474749],"dir":"ltr"},{"str":"n","boundary":[0.1374147875816994,0.35663898358585866,0.1481812849673203,0.3704130997474749],"dir":"ltr"},{"str":"\u0000","boundary":[0.14935772875816997,0.35633595303030313,0.16326148366013074,0.3701100691919193],"dir":"ltr"},{"str":"2)","boundary":[0.16443792483660133,0.35663898358585866,0.18008856176470592,0.3704130997474749],"dir":"ltr"},{"str":",","boundary":[0.18008852941176473,0.350922725378788,0.18046290326797387,0.3646968415404042],"dir":"ltr"},{"str":",","boundary":[0.2851508986928105,0.350922725378788,0.2853291941176471,0.3646968415404042],"dir":"ltr"},{"str":"respectively","boundary":[0.1894824346405229,0.350922725378788,0.2873078281045752,0.3646968415404042],"dir":"ltr"},{"str":"plus","boundary":[0.2947408823529412,0.350922725378788,0.329767649509804,0.3646968415404042],"dir":"ltr"},{"str":"three","boundary":[0.3336890849673203,0.350922725378788,0.3769333277777778,0.3646968415404042],"dir":"ltr"},{"str":"computer","boundary":[0.38144300653594776,0.350922725378788,0.458555370261438,0.3646968415404042],"dir":"ltr"},{"str":"steps","boundary":[0.46306506535947717,0.350922725378788,0.5053289151960785,0.3646968415404042],"dir":"ltr"},{"str":"(checks","boundary":[0.5096425163398693,0.350922725378788,0.5693217179738562,0.3646968415404042],"dir":"ltr"},{"str":"on","boundary":[0.5738315359477124,0.350922725378788,0.593599823366013,0.3646968415404042],"dir":"ltr"},{"str":"the","boundary":[0.5977174836601307,0.350922725378788,0.6243306965686274,0.3646968415404042],"dir":"ltr"},{"str":"value","boundary":[0.6284483660130719,0.350922725378788,0.6734573161764705,0.3646968415404042],"dir":"ltr"},{"str":"of","boundary":[0.6775748366013071,0.350922725378788,0.6922450805555556,0.3646968415404042],"dir":"ltr"},{"str":"n","boundary":[0.6965588235294118,0.35663898358585866,0.7073253209150326,0.3704130997474749],"dir":"ltr"},{"str":"and","boundary":[0.7112468300653595,0.350922725378788,0.7423698506535947,0.3646968415404042],"dir":"ltr"},{"str":"a","boundary":[0.7464875163398692,0.350922725378788,0.7525482385620914,0.3646968415404042],"dir":"ltr"},{"str":"\u0002nal","boundary":[0.760391160130719,0.350922725378788,0.7979669490196077,0.3646968415404042],"dir":"ltr"},{"str":"addition).","boundary":[0.8018883823529411,0.350922725378788,0.8809258813725489,0.3646968415404042],"dir":"ltr"},{"str":"Therefore","boundary":[0.11764655228758168,0.36804406376262633,0.19729011241830066,0.38181817992424255],"dir":"ltr"},{"str":",","boundary":[0.19689785947712415,0.36804406376262633,0.20178199901960783,0.38181817992424255],"dir":"ltr"},{"str":"T","boundary":[0.33196027777777776,0.3919421401515152,0.34233461797385617,0.40571625631313135],"dir":"ltr"},{"str":"(","boundary":[0.3448835784313725,0.3919421401515152,0.3517285039215686,0.40571625631313135],"dir":"ltr"},{"str":"n","boundary":[0.3517284967320261,0.3919421401515152,0.362494994117647,0.40571625631313135],"dir":"ltr"},{"str":")","boundary":[0.3624949836601307,0.3919421401515152,0.3642418934640523,0.40571625631313135],"dir":"ltr"},{"str":"=","boundary":[0.37443792483660127,0.3919421401515152,0.38834167973856204,0.40571625631313135],"dir":"ltr"},{"str":"T","boundary":[0.39304756535947705,0.3919421401515152,0.40342190555555546,0.40571625631313135],"dir":"ltr"},{"str":"(","boundary":[0.40597086601307186,0.3919421401515152,0.4128157915032679,0.40571625631313135],"dir":"ltr"},{"str":"n","boundary":[0.41281578431372545,0.3919421401515152,0.42358228169934636,0.40571625631313135],"dir":"ltr"},{"str":"\u0000","boundary":[0.4275037908496732,0.3916391095959596,0.441407545751634,0.4054132257575758],"dir":"ltr"},{"str":"1)","boundary":[0.44532911764705885,0.3919421401515152,0.4568620908496733,0.40571625631313135],"dir":"ltr"},{"str":"+","boundary":[0.46509741830065365,0.3919421401515152,0.4790011732026144,0.40571625631313135],"dir":"ltr"},{"str":"T","boundary":[0.48292274509803934,0.3919421401515152,0.49329708529411775,0.40571625631313135],"dir":"ltr"},{"str":"(","boundary":[0.4958460457516341,0.3919421401515152,0.5026909712418302,0.40571625631313135],"dir":"ltr"},{"str":"n","boundary":[0.5026909640522877,0.3919421401515152,0.5134574614379087,0.40571625631313135],"dir":"ltr"},{"str":"\u0000","boundary":[0.5173789705882355,0.3916391095959596,0.5312827254901962,0.4054132257575758],"dir":"ltr"},{"str":"2)","boundary":[0.5352042973856211,0.3919421401515152,0.5467372705882355,0.40571625631313135],"dir":"ltr"},{"str":"+","boundary":[0.554972598039216,0.3919421401515152,0.5649547810457519,0.40571625631313135],"dir":"ltr"},{"str":"3","boundary":[0.5727979248366014,0.3919421401515152,0.58160363627451,0.40571625631313135],"dir":"ltr"},{"str":"for","boundary":[0.59160364379085,0.3862258819444445,0.6140992062091506,0.3999999981060607],"dir":"ltr"},{"str":"n","boundary":[0.6191972712418302,0.3919421401515152,0.6250618673202617,0.40571625631313135],"dir":"ltr"},{"str":">","boundary":[0.6348656699346408,0.3919421401515152,0.6487694248366015,0.40571625631313135],"dir":"ltr"},{"str":"1","boundary":[0.6536713888888891,0.3919421401515152,0.6624771003267975,0.40571625631313135],"dir":"ltr"},{"str":".","boundary":[0.6624770915032682,0.3862258819444445,0.6673612310457518,0.3999999981060607],"dir":"ltr"},{"str":"Compare","boundary":[0.11764702614379112,0.412741033459596,0.19203211486928132,0.42651514962121223],"dir":"ltr"},{"str":"this","boundary":[0.19713003267973883,0.412741033459596,0.22882346372549045,0.42651514962121223],"dir":"ltr"},{"str":"to","boundary":[0.2337252941176473,0.412741033459596,0.24937593104575187,0.42651514962121223],"dir":"ltr"},{"str":"the","boundary":[0.2544739869281048,0.412741033459596,0.2810871998366015,0.42651514962121223],"dir":"ltr"},{"str":"recurrence","boundary":[0.28598901960784334,0.412741033459596,0.3734578982026146,0.42651514962121223],"dir":"ltr"},{"str":"relation","boundary":[0.3789480065359479,0.412741033459596,0.44351134019607863,0.42651514962121223],"dir":"ltr"},{"str":"for","boundary":[0.4484132026143793,0.412741033459596,0.4709087650326799,0.42651514962121223],"dir":"ltr"},{"str":"F","boundary":[0.4762029084967322,0.4184572916666667,0.4875576416666668,0.4322314078282829],"dir":"ltr"},{"str":"we","boundary":[0.5084134313725491,0.412741033459596,0.5311228977124185,0.42651514962121223],"dir":"ltr"},{"str":"immediately","boundary":[0.5362209477124183,0.412741033459596,0.6391622099673204,0.42651514962121223],"dir":"ltr"},{"str":"see","boundary":[0.6440640849673204,0.412741033459596,0.6698929834967321,0.42651514962121223],"dir":"ltr"},{"str":"that","boundary":[0.6749908823529412,0.412741033459596,0.7096254923202614,0.42651514962121223],"dir":"ltr"},{"str":"T","boundary":[0.714527320261438,0.4184572916666667,0.7249016604575164,0.4322314078282829],"dir":"ltr"},{"str":"(","boundary":[0.7274505718954248,0.4184572916666667,0.7342954973856208,0.4322314078282829],"dir":"ltr"},{"str":"n","boundary":[0.734295522875817,0.4184572916666667,0.745062020261438,0.4322314078282829],"dir":"ltr"},{"str":")","boundary":[0.7450620424836601,0.4184572916666667,0.7519069679738563,0.4322314078282829],"dir":"ltr"},{"str":"\u0015","boundary":[0.7568088725490196,0.41815426111111115,0.7707126274509803,0.4319283772727273],"dir":"ltr"},{"str":"F","boundary":[0.7756144281045753,0.4184572916666667,0.7869691612745098,0.4322314078282829],"dir":"ltr"},{"str":".","boundary":[0.7968625653594772,0.412741033459596,0.8017467049019609,0.42651514962121223],"dir":"ltr"},{"str":"n","boundary":[0.4882352124183008,0.42336161300505054,0.49666112936274526,0.43342488320707073],"dir":"ltr"},{"str":"n","boundary":[0.7874507843137255,0.42336161300505054,0.79587670125817,0.43342488320707073],"dir":"ltr"},{"str":"This","boundary":[0.14529393790849685,0.43031679103535364,0.18208541241830076,0.4440909071969698],"dir":"ltr"},{"str":"is","boundary":[0.18796763071895434,0.43031679103535364,0.1959713526143792,0.4440909071969698],"dir":"ltr"},{"str":"very","boundary":[0.20773576797385632,0.43031679103535364,0.24354684950980401,0.4440909071969698],"dir":"ltr"},{"str":"bad","boundary":[0.24982122549019617,0.43031679103535364,0.2799638531045753,0.4440909071969698],"dir":"ltr"},{"str":"news:","boundary":[0.2858460620915034,0.43031679103535364,0.3326197196078432,0.4440909071969698],"dir":"ltr"},{"str":"the","boundary":[0.34085488562091515,0.43031679103535364,0.36746809852941187,0.4440909071969698],"dir":"ltr"},{"str":"running","boundary":[0.3737424673202615,0.43031679103535364,0.4406765694444446,0.4440909071969698],"dir":"ltr"},{"str":"time","boundary":[0.44636272875817,0.43031679103535364,0.4835463604575164,0.4440909071969698],"dir":"ltr"},{"str":"of","boundary":[0.48962465686274514,0.43031679103535364,0.5042949008169936,0.4440909071969698],"dir":"ltr"},{"str":"the","boundary":[0.5103733496732027,0.43031679103535364,0.5369865625816994,0.4440909071969698],"dir":"ltr"},{"str":"algorithm","boundary":[0.5430650163398693,0.43031679103535364,0.6242772052287582,0.4440909071969698],"dir":"ltr"},{"str":"grows","boundary":[0.6303555392156863,0.43031679103535364,0.6786978254901962,0.4440909071969698],"dir":"ltr"},{"str":"as","boundary":[0.6847761274509805,0.43031679103535364,0.7029757861111112,0.4440909071969698],"dir":"ltr"},{"str":"fast","boundary":[0.7088579901960784,0.43031679103535364,0.7397671068627452,0.4440909071969698],"dir":"ltr"},{"str":"as","boundary":[0.7458454084967321,0.43031679103535364,0.7640450671568627,0.4440909071969698],"dir":"ltr"},{"str":"the","boundary":[0.7701235130718955,0.43031679103535364,0.7967367259803922,0.4440909071969698],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.8028150163398694,0.43031679103535364,0.8812820446078431,0.4440909071969698],"dir":"ltr"},{"str":"numbers!","boundary":[0.11764681372549025,0.44743800315656573,0.19554349183006542,0.46121211931818196],"dir":"ltr"},{"str":"T","boundary":[0.20789632352941181,0.4531542613636364,0.21827066372549023,0.4669283775252526],"dir":"ltr"},{"str":"(","boundary":[0.2208196241830066,0.4531542613636364,0.22766454967320265,0.4669283775252526],"dir":"ltr"},{"str":"n","boundary":[0.2276645424836602,0.4531542613636364,0.23843103986928108,0.4669283775252526],"dir":"ltr"},{"str":")","boundary":[0.23843102941176475,0.4531542613636364,0.24527595490196083,0.4669283775252526],"dir":"ltr"},{"str":"is","boundary":[0.25233475490196083,0.44743800315656573,0.26602460588235305,0.46121211931818196],"dir":"ltr"},{"str":"exponential","boundary":[0.2732795261437909,0.44743800315656573,0.3668090158496733,0.46121211931818196],"dir":"ltr"},{"str":"in","boundary":[0.37425991830065364,0.44743800315656573,0.39108702679738566,0.46121211931818196],"dir":"ltr"},{"str":"n","boundary":[0.39814586601307195,0.4531542613636364,0.4089123633986928,0.4669283775252526],"dir":"ltr"},{"str":"which","boundary":[0.4214435130718954,0.44743800315656573,0.463707227124183,0.46121211931818196],"dir":"ltr"},{"str":"implies","boundary":[0.47743272875816994,0.44743800315656573,0.5375040800653594,0.46121211931818196],"dir":"ltr"},{"str":"that","boundary":[0.5443667156862745,0.44743800315656573,0.5790013256535947,0.46121211931818196],"dir":"ltr"},{"str":"the","boundary":[0.5860601797385621,0.44743800315656573,0.6126733926470588,0.46121211931818196],"dir":"ltr"},{"str":"algorithm","boundary":[0.6199281535947712,0.44743800315656573,0.70114034248366,0.46121211931818196],"dir":"ltr"},{"str":"is","boundary":[0.7080029901960783,0.44743800315656573,0.7218889197712417,0.46121211931818196],"dir":"ltr"},{"str":"impractically","boundary":[0.7289477614379084,0.44743800315656573,0.8375396522875815,0.46121211931818196],"dir":"ltr"},{"str":"slow","boundary":[0.844402336601307,0.44743800315656573,0.8809977325163397,0.46121211931818196],"dir":"ltr"},{"str":"except","boundary":[0.11764743464052267,0.4645592152777779,0.1696973888888887,0.47833333143939405],"dir":"ltr"},{"str":"for","boundary":[0.17499138888888868,0.4645592152777779,0.19748695130718935,0.47833333143939405],"dir":"ltr"},{"str":"very","boundary":[0.20258501633986906,0.4645592152777779,0.23839609787581678,0.47833333143939405],"dir":"ltr"},{"str":"small","boundary":[0.24349416666666643,0.4645592152777779,0.28889527401960763,0.47833333143939405],"dir":"ltr"},{"str":"values","boundary":[0.29360102941176447,0.4645592152777779,0.34682745522875796,0.47833333143939405],"dir":"ltr"},{"str":"of","boundary":[0.3515332189542481,0.4645592152777779,0.3662034629084965,0.47833333143939405],"dir":"ltr"},{"str":"n","boundary":[0.3713015196078429,0.47027547348484855,0.38206801699346377,0.4840495896464647],"dir":"ltr"},{"str":".","boundary":[0.38206800653594747,0.4645592152777779,0.38695214607843115,0.47833333143939405],"dir":"ltr"},{"str":"Let's","boundary":[0.145295130718954,0.4819834577020203,0.1781472879084965,0.4957575738636365],"dir":"ltr"},{"str":"be","boundary":[0.19069622549019583,0.4819834577020203,0.20948411993464028,0.4957575738636365],"dir":"ltr"},{"str":"a","boundary":[0.2157586437908494,0.4819834577020203,0.21946635947712395,0.4957575738636365],"dir":"ltr"},{"str":"little","boundary":[0.23201529411764682,0.4819834577020203,0.27151621830065337,0.4957575738636365],"dir":"ltr"},{"str":"more","boundary":[0.2777906209150324,0.4819834577020203,0.3190919031045749,0.4957575738636365],"dir":"ltr"},{"str":"concrete","boundary":[0.32556235294117625,0.4819834577020203,0.39326294411764684,0.4957575738636365],"dir":"ltr"},{"str":"about","boundary":[0.40012558823529387,0.4819834577020203,0.4467031671568625,0.4957575738636365],"dir":"ltr"},{"str":"just","boundary":[0.4529775490196076,0.4819834577020203,0.4842788228758167,0.4957575738636365],"dir":"ltr"},{"str":"how","boundary":[0.49055320261437885,0.4819834577020203,0.5242252449346403,0.4957575738636365],"dir":"ltr"},{"str":"bad","boundary":[0.5303035294117645,0.4819834577020203,0.5604461570261435,0.4957575738636365],"dir":"ltr"},{"str":"exponential","boundary":[0.5667206862745096,0.4819834577020203,0.6629952763071894,0.4957575738636365],"dir":"ltr"},{"str":"time","boundary":[0.6692697058823527,0.4819834577020203,0.7064533375816991,0.4957575738636365],"dir":"ltr"},{"str":"is","boundary":[0.7127277124183005,0.4819834577020203,0.727005780718954,0.4957575738636365],"dir":"ltr"},{"str":"To","boundary":[0.7413017320261436,0.4819834577020203,0.7547954751633984,0.4957575738636365],"dir":"ltr"},{"str":"compute","boundary":[0.7673445098039213,0.4819834577020203,0.8366315550653592,0.4957575738636365],"dir":"ltr"},{"str":"F","boundary":[0.8431020261437906,0.48769971590909095,0.8544567593137253,0.5014738320707072],"dir":"ltr"},{"str":",","boundary":[0.8774519444444442,0.4819834577020203,0.8823360839869279,0.4957575738636365],"dir":"ltr"},{"str":"200","boundary":[0.8556872385620912,0.4926040625000001,0.8762376202287578,0.5026673327020202],"dir":"ltr"},{"str":"the","boundary":[0.11764802287581679,0.4991046698232324,0.14426123578431352,0.5128787859848486],"dir":"ltr"},{"str":"algorithm","boundary":[0.19752302287581677,0.4991046698232324,0.27873521176470567,0.5128787859848486],"dir":"ltr"},{"str":"executes","boundary":[0.283833153594771,0.4991046698232324,0.3536906093137253,0.5128787859848486],"dir":"ltr"},{"str":"T","boundary":[0.35937678104575144,0.5048209280303031,0.36975112124182985,0.5185950441919193],"dir":"ltr"},{"str":"(200)","boundary":[0.3723000816993462,0.5048209280303031,0.41240706699346386,0.5185950441919193],"dir":"ltr"},{"str":"\u0015","boundary":[0.4182892973856207,0.5045178974747475,0.4321930522875815,0.5182920136363638],"dir":"ltr"},{"str":"F","boundary":[0.43748717320261415,0.5048209280303031,0.4488419063725488,0.5185950441919193],"dir":"ltr"},{"str":"\u0015","boundary":[0.4766674999999998,0.5045178974747475,0.4905712549019606,0.5182920136363638],"dir":"ltr"},{"str":"2138","boundary":[0.49606145424836584,0.5026040498737374,0.5254532411437906,0.5185950441919193],"dir":"ltr"},{"str":"elementary","boundary":[0.5317656045751632,0.4991046698232324,0.6249207624183005,0.5128787859848486],"dir":"ltr"},{"str":"computer","boundary":[0.6302147875816991,0.4991046698232324,0.7073271513071894,0.5128787859848486],"dir":"ltr"},{"str":"steps","boundary":[0.7130133169934638,0.4991046698232324,0.7552771668300652,0.5128787859848486],"dir":"ltr"},{"str":"How","boundary":[0.7670240196078429,0.4991046698232324,0.8046176338235292,0.5128787859848486],"dir":"ltr"},{"str":"long","boundary":[0.8099116013071894,0.4991046698232324,0.8449383684640521,0.5128787859848486],"dir":"ltr"},{"str":"this","boundary":[0.8500362745098038,0.4991046698232324,0.8817297055555554,0.5128787859848486],"dir":"ltr"},{"str":"fib1","boundary":[0.14955521241830044,0.5082644570707071,0.19233599673202592,0.5220385732323234],"dir":"ltr"},{"str":"200","boundary":[0.44941259803921546,0.509725249368687,0.4699629797058822,0.5197885195707072],"dir":"ltr"},{"str":"actually","boundary":[0.11764738562091495,0.5162258819444445,0.18417150522875808,0.5299999981060607],"dir":"ltr"},{"str":"takes","boundary":[0.18985767973856202,0.5162258819444445,0.234278394117647,0.5299999981060607],"dir":"ltr"},{"str":"depends","boundary":[0.24055277777777767,0.5162258819444445,0.30787903709150316,0.5299999981060607],"dir":"ltr"},{"str":"of","boundary":[0.3188414542483659,0.5162258819444445,0.3335116982026143,0.5299999981060607],"dir":"ltr"},{"str":"course","boundary":[0.33978622549019594,0.5162258819444445,0.3922283369281045,0.5299999981060607],"dir":"ltr"},{"str":"on","boundary":[0.40338683006535936,0.5162258819444445,0.42315511748366,0.5299999981060607],"dir":"ltr"},{"str":"the","boundary":[0.4292335620915032,0.5162258819444445,0.4558467749999999,0.5299999981060607],"dir":"ltr"},{"str":"computer","boundary":[0.4619252287581698,0.5162258819444445,0.5390375924836601,0.5299999981060607],"dir":"ltr"},{"str":"used.","boundary":[0.5455080718954247,0.5162258819444445,0.588556236111111,0.5299999981060607],"dir":"ltr"},{"str":"At","boundary":[0.5979678758169934,0.5162258819444445,0.6177361632352941,0.5299999981060607],"dir":"ltr"},{"str":"this","boundary":[0.6238146078431371,0.5162258819444445,0.6555080388888888,0.5299999981060607],"dir":"ltr"},{"str":"time","boundary":[0.6615865032679737,0.5162258819444445,0.6987701349673202,0.5299999981060607],"dir":"ltr"},{"str":"the","boundary":[0.7097326143790849,0.5162258819444445,0.7363458272875816,0.5299999981060607],"dir":"ltr"},{"str":"fastest","boundary":[0.7424241176470587,0.5162258819444445,0.7972013468954248,0.5299999981060607],"dir":"ltr"},{"str":"computer","boundary":[0.8034757516339869,0.5162258819444445,0.880588115359477,0.5299999981060607],"dir":"ltr"},{"str":"in","boundary":[0.1176473202614379,0.5333470940656567,0.13427835016339867,0.5471212102272729],"dir":"ltr"},{"str":"the","boundary":[0.13976856209150326,0.5333470940656567,0.16638177499999998,0.5471212102272729],"dir":"ltr"},{"str":"world","boundary":[0.17206790849673204,0.5333470940656567,0.21844940882352942,0.5471212102272729],"dir":"ltr"},{"str":"is","boundary":[0.22413555555555556,0.5333470940656567,0.23233535588235293,0.5471212102272729],"dir":"ltr"},{"str":"the","boundary":[0.243707614379085,0.5333470940656567,0.2703208272875817,0.5471212102272729],"dir":"ltr"},{"str":"NEC","boundary":[0.27600696078431375,0.5333470940656567,0.3163456753267974,0.5471212102272729],"dir":"ltr"},{"str":"Earth","boundary":[0.3218357189542484,0.5333470940656567,0.3703740838235295,0.5471212102272729],"dir":"ltr"},{"str":"Simulator","boundary":[0.3758641503267974,0.5333470940656567,0.4586449679738563,0.5471212102272729],"dir":"ltr"},{"str":"which","boundary":[0.46745053921568624,0.5333470940656567,0.5110868022875816,0.5471212102272729],"dir":"ltr"},{"str":"clocks","boundary":[0.5220672058823529,0.5333470940656567,0.5705877637254901,0.5471212102272729],"dir":"ltr"},{"str":"40","boundary":[0.5764699673202613,0.5333470940656567,0.5964343333333332,0.5471212102272729],"dir":"ltr"},{"str":"trillion","boundary":[0.6019243790849672,0.5333470940656567,0.6590367261437907,0.5471212102272729],"dir":"ltr"},{"str":"steps","boundary":[0.6645268300653594,0.5333470940656567,0.7067906799019608,0.5471212102272729],"dir":"ltr"},{"str":"per","boundary":[0.7126729084967319,0.5333470940656567,0.7394821999999999,0.5471212102272729],"dir":"ltr"},{"str":"second.","boundary":[0.7453644117647058,0.5333470940656567,0.8050436058823529,0.5471212102272729],"dir":"ltr"},{"str":"Even","boundary":[0.8134748692810457,0.5333470940656567,0.8557565444444444,0.5471212102272729],"dir":"ltr"},{"str":"on","boundary":[0.8612466013071894,0.5333470940656567,0.88101488872549,0.5471212102272729],"dir":"ltr"},{"str":"this","boundary":[0.11764692810457503,0.5503167910353537,0.14934035915032667,0.5640909071969699],"dir":"ltr"},{"str":"machine","boundary":[0.15620297385620902,0.5503167910353537,0.2260782715686273,0.5640909071969699],"dir":"ltr"},{"str":",","boundary":[0.22568614379084956,0.5503167910353537,0.2305702833333332,0.5640909071969699],"dir":"ltr"},{"str":"(200)","boundary":[0.2808910130718953,0.5503167910353537,0.3225666271241829,0.5640909071969699],"dir":"ltr"},{"str":"would","boundary":[0.3290370915032678,0.5503167910353537,0.37855584934640507,0.5640909071969699],"dir":"ltr"},{"str":"take","boundary":[0.3852223856209149,0.5503167910353537,0.4214256243464051,0.5640909071969699],"dir":"ltr"},{"str":"at","boundary":[0.42848431372549006,0.5503167910353537,0.44531142222222214,0.5640909071969699],"dir":"ltr"},{"str":"least","boundary":[0.45217401960784304,0.5503167910353537,0.491692769117647,0.5640909071969699],"dir":"ltr"},{"str":"2","boundary":[0.4985553921568627,0.5560330492424244,0.5073611035947712,0.5698071654040405],"dir":"ltr"},{"str":"92","boundary":[0.5080387745098038,0.553816196338384,0.5217390289542483,0.5638794665404041],"dir":"ltr"},{"str":"seconds","boundary":[0.5296074019607843,0.5503167910353537,0.5926199321895425,0.5640909071969699],"dir":"ltr"},{"str":"This","boundary":[0.6092686764705881,0.5503167910353537,0.646060150980392,0.5640909071969699],"dir":"ltr"},{"str":"means","boundary":[0.6527266830065358,0.5503167910353537,0.7065591699346405,0.5640909071969699],"dir":"ltr"},{"str":"that,","boundary":[0.7134217810457515,0.5503167910353537,0.7529405305555554,0.5640909071969699],"dir":"ltr"},{"str":"if","boundary":[0.7601953104575162,0.5503167910353537,0.7646694532679738,0.5640909071969699],"dir":"ltr"},{"str":"we","boundary":[0.7787871405228757,0.5503167910353537,0.801496606862745,0.5640909071969699],"dir":"ltr"},{"str":"start","boundary":[0.8083591993464051,0.5503167910353537,0.8480740274509803,0.5640909071969699],"dir":"ltr"},{"str":"the","boundary":[0.8551327287581697,0.5503167910353537,0.8817459416666665,0.5640909071969699],"dir":"ltr"},{"str":"fib1","boundary":[0.23782516339869267,0.5594765782828284,0.28060594771241815,0.5732506944444445],"dir":"ltr"},{"str":"computation","boundary":[0.1176458006535946,0.5674380031565658,0.22039098431372534,0.581212119318182],"dir":"ltr"},{"str":"today","boundary":[0.22548893790849656,0.5674380031565658,0.27285090130718936,0.581212119318182],"dir":"ltr"},{"str":"it","boundary":[0.2783231372549018,0.5674380031565658,0.285934536601307,0.581212119318182],"dir":"ltr"},{"str":"would","boundary":[0.29573849673202596,0.5674380031565658,0.3452572545751632,0.581212119318182],"dir":"ltr"},{"str":"still","boundary":[0.35015908496732007,0.5674380031565658,0.38222684787581684,0.581212119318182],"dir":"ltr"},{"str":"be","boundary":[0.3871286928104573,0.5674380031565658,0.40591658725490176,0.581212119318182],"dir":"ltr"},{"str":"going","boundary":[0.4108183986928102,0.5674380031565658,0.4554351916666664,0.581212119318182],"dir":"ltr"},{"str":"long","boundary":[0.46033702614379063,0.5674380031565658,0.49536379330065333,0.581212119318182],"dir":"ltr"},{"str":"after","boundary":[0.5000695424836599,0.5674380031565658,0.5393922133986926,0.581212119318182],"dir":"ltr"},{"str":"the","boundary":[0.5446862091503266,0.5674380031565658,0.5712994220588233,0.581212119318182],"dir":"ltr"},{"str":"sun","boundary":[0.5762012418300652,0.5674380031565658,0.6063438694444442,0.581212119318182],"dir":"ltr"},{"str":"turns","boundary":[0.6112456862745096,0.5674380031565658,0.656058557843137,0.581212119318182],"dir":"ltr"},{"str":"into","boundary":[0.6609603921568626,0.5674380031565658,0.6932420589869279,0.581212119318182],"dir":"ltr"},{"str":"a","boundary":[0.6981438888888888,0.5674380031565658,0.7032241372549017,0.581212119318182],"dir":"ltr"},{"str":"red","boundary":[0.7130280065359476,0.5674380031565658,0.7398372980392155,0.581212119318182],"dir":"ltr"},{"str":"giant","boundary":[0.7449351960784313,0.5674380031565658,0.7879833602941175,0.581212119318182],"dir":"ltr"},{"str":"star","boundary":[0.7926891176470586,0.5674380031565658,0.8255590202614378,0.581212119318182],"dir":"ltr"},{"str":".","boundary":[0.8237943464052286,0.5674380031565658,0.8286784859477123,0.581212119318182],"dir":"ltr"},{"str":"But","boundary":[0.14529271241830052,0.5850137607323234,0.17602357581699332,0.5987878768939395],"dir":"ltr"},{"str":"technology","boundary":[0.1813175490196077,0.5850137607323234,0.26898253137254885,0.5987878768939395],"dir":"ltr"},{"str":"is","boundary":[0.2744726143790848,0.5850137607323234,0.2830644081699345,0.5987878768939395],"dir":"ltr"},{"str":"rapidly","boundary":[0.29365267973856196,0.5850137607323234,0.3527436380718953,0.5987878768939395],"dir":"ltr"},{"str":"improvingócomputer","boundary":[0.3580376470588234,0.5850137607323234,0.5371287053921568,0.5987878768939395],"dir":"ltr"},{"str":"speeds","boundary":[0.5424232679738561,0.5850137607323234,0.596826165359477,0.5987878768939395],"dir":"ltr"},{"str":"have","boundary":[0.6025123202614378,0.5850137607323234,0.6416567503267973,0.5987878768939395],"dir":"ltr"},{"str":"been","boundary":[0.646950882352941,0.5850137607323234,0.6855070642156861,0.5987878768939395],"dir":"ltr"},{"str":"doubling","boundary":[0.6908010457516338,0.5850137607323234,0.7626192874183004,0.5987878768939395],"dir":"ltr"},{"str":"roughly","boundary":[0.7677173856209148,0.5850137607323234,0.8311220730392155,0.5987878768939395],"dir":"ltr"},{"str":"every","boundary":[0.8362199999999999,0.5850137607323234,0.880836792973856,0.5987878768939395],"dir":"ltr"},{"str":"18","boundary":[0.1176464705882351,0.6021349728535355,0.13761083660130702,0.6159090890151516],"dir":"ltr"},{"str":"months","boundary":[0.1442773529411763,0.6021349728535355,0.20593515833333317,0.6159090890151516],"dir":"ltr"},{"str":"a","boundary":[0.21787812091503247,0.6021349728535355,0.22099755228758147,0.6159090890151516],"dir":"ltr"},{"str":"phenomenon","boundary":[0.23472305555555537,0.6021349728535355,0.3398390076797384,0.6159090890151516],"dir":"ltr"},{"str":"sometimes","boundary":[0.3467016503267972,0.6021349728535355,0.4337961970588234,0.6159090890151516],"dir":"ltr"},{"str":"called","boundary":[0.4408549183006534,0.6021349728535355,0.4889833006535945,0.6159090890151516],"dir":"ltr"},{"str":"Moore's","boundary":[0.4958459313725488,0.6021349728535355,0.5498389212418298,0.6159090890151516],"dir":"ltr"},{"str":"law","boundary":[0.564348676470588,0.6021349728535355,0.5942952254901959,0.6159090890151516],"dir":"ltr"},{"str":"With","boundary":[0.6113362581699343,0.6021349728535355,0.6518532266339867,0.6159090890151516],"dir":"ltr"},{"str":"this","boundary":[0.6587158333333331,0.6021349728535355,0.6904092643790847,0.6159090890151516],"dir":"ltr"},{"str":"extraordinary","boundary":[0.697271879084967,0.6021349728535355,0.8111578919934638,0.6159090890151516],"dir":"ltr"},{"str":"growth,","boundary":[0.8180204084967317,0.6021349728535355,0.8808368601307186,0.6159090890151516],"dir":"ltr"},{"str":"perhaps","boundary":[0.11764622549019577,0.6192561849747477,0.18379601323529382,0.6330303011363638],"dir":"ltr"},{"str":"will","boundary":[0.2394107679738559,0.6192561849747477,0.2703198846405226,0.6330303011363638],"dir":"ltr"},{"str":"run","boundary":[0.27659426470588205,0.6192561849747477,0.3063447351307187,0.6330303011363638],"dir":"ltr"},{"str":"a","boundary":[0.3126191013071893,0.6192561849747477,0.31632681699346377,0.6330303011363638],"dir":"ltr"},{"str":"lot","boundary":[0.32887575163398663,0.6192561849747477,0.35019484248365984,0.6330303011363638],"dir":"ltr"},{"str":"faster","boundary":[0.35686137254901934,0.6192561849747477,0.4044015191176468,0.6330303011363638],"dir":"ltr"},{"str":"on","boundary":[0.41106807189542455,0.6192561849747477,0.43083635931372516,0.6330303011363638],"dir":"ltr"},{"str":"next","boundary":[0.43730696078431347,0.6192561849747477,0.4735101995098036,0.6330303011363638],"dir":"ltr"},{"str":"year's","boundary":[0.47998065359477105,0.6192561849747477,0.5214422879084966,0.6330303011363638],"dir":"ltr"},{"str":"machines","boundary":[0.533991225490196,0.6192561849747477,0.612083998856209,0.6330303011363638],"dir":"ltr"},{"str":"Let's","boundary":[0.6269681372549017,0.6192561849747477,0.6596242650326796,0.6330303011363638],"dir":"ltr"},{"str":"seeóthe","boundary":[0.6725652614379083,0.6192561849747477,0.7428326996732024,0.6330303011363638],"dir":"ltr"},{"str":"running","boundary":[0.7494992483660129,0.6192561849747477,0.8164333504901959,0.6330303011363638],"dir":"ltr"},{"str":"time","boundary":[0.8225116666666665,0.6192561849747477,0.8596952983660129,0.6330303011363638],"dir":"ltr"},{"str":"of","boundary":[0.8661657516339867,0.6192561849747477,0.8808359955882352,0.6330303011363638],"dir":"ltr"},{"str":"fib1","boundary":[0.19026648692810427,0.6284159722222223,0.23304727124182975,0.6421900883838385],"dir":"ltr"},{"str":"(","boundary":[0.1607119934640521,0.6362258819444446,0.16657652598039197,0.6499999981060608],"dir":"ltr"},{"str":")","boundary":[0.1773430065359475,0.6362258819444446,0.17752130359477106,0.6499999981060608],"dir":"ltr"},{"str":"is","boundary":[0.1888937745098037,0.6362258819444446,0.19709357483660112,0.6499999981060608],"dir":"ltr"},{"str":"proportional","boundary":[0.20846583333333313,0.6362258819444446,0.31001672009803904,0.6499999981060608],"dir":"ltr"},{"str":"to","boundary":[0.31629116013071873,0.6362258819444446,0.33194179705882326,0.6499999981060608],"dir":"ltr"},{"str":"0","boundary":[0.347253905228758,0.6397252872474749,0.35410403245098016,0.6497885574494952],"dir":"ltr"},{"str":":","boundary":[0.35410400326797364,0.6397252872474749,0.35802394299019585,0.6497885574494952],"dir":"ltr"},{"str":"694n","boundary":[0.3580239379084965,0.6397252872474749,0.38700018165032657,0.6497885574494952],"dir":"ltr"},{"str":"\u0019","boundary":[0.39470485294117624,0.6416391095959598,0.408608607843137,0.655413225757576],"dir":"ltr"},{"str":"(1","boundary":[0.41507919934640497,0.6419421401515153,0.4307298362745096,0.6557162563131315],"dir":"ltr"},{"str":":","boundary":[0.4307298039215684,0.6419421401515153,0.4356139434640521,0.6557162563131315],"dir":"ltr"},{"str":"6)n","boundary":[0.43561393790849645,0.6397252872474749,0.45979745289215657,0.6557162563131315],"dir":"ltr"},{"str":"so","boundary":[0.47213800653594734,0.6362258819444446,0.4891611936274506,0.6499999981060608],"dir":"ltr"},{"str":"it","boundary":[0.4950433986928101,0.6362258819444446,0.50147832745098,0.6499999981060608],"dir":"ltr"},{"str":"takes","boundary":[0.5136352287581696,0.6362258819444446,0.5580559431372545,0.6499999981060608],"dir":"ltr"},{"str":"1","boundary":[0.5639381699346402,0.6419421401515153,0.5727438813725486,0.6557162563131315],"dir":"ltr"},{"str":":","boundary":[0.5727438725490193,0.6419421401515153,0.5776280120915029,0.6557162563131315],"dir":"ltr"},{"str":"6","boundary":[0.5776280065359473,0.6419421401515153,0.5864337179738558,0.6557162563131315],"dir":"ltr"},{"str":"times","boundary":[0.5927082026143787,0.6362258819444446,0.6381093099673198,0.6499999981060608],"dir":"ltr"},{"str":"longer","boundary":[0.6439915359477121,0.6362258819444446,0.6956493330065356,0.6499999981060608],"dir":"ltr"},{"str":"to","boundary":[0.7017276470588232,0.6362258819444446,0.7173782839869277,0.6499999981060608],"dir":"ltr"},{"str":"compute","boundary":[0.7234565686274506,0.6362258819444446,0.7927436138888885,0.6499999981060608],"dir":"ltr"},{"str":"F","boundary":[0.7988219281045748,0.6419421401515153,0.8101766612745094,0.6557162563131315],"dir":"ltr"},{"str":"than","boundary":[0.8437242320261434,0.6362258819444446,0.8824764924836599,0.6499999981060608],"dir":"ltr"},{"str":"fib1","boundary":[0.11764614379084948,0.6453856691919194,0.16042692810457496,0.6591597853535356],"dir":"ltr"},{"str":"n","boundary":[0.16657651960784295,0.6419421401515153,0.17734301699346386,0.6557162563131315],"dir":"ltr"},{"str":"2","boundary":[0.338020245098039,0.6419421401515153,0.3468259565359475,0.6557162563131315],"dir":"ltr"},{"str":"n+1","boundary":[0.810782990196078,0.6468464867424243,0.8368420897712414,0.6569097569444444],"dir":"ltr"},{"str":"And","boundary":[0.1537063398692807,0.6533470940656567,0.18777053937908464,0.6671212102272728],"dir":"ltr"},{"str":"under","boundary":[0.19404506535947677,0.6533470940656567,0.24277950882352906,0.6671212102272728],"dir":"ltr"},{"str":"Moore's","boundary":[0.24905388888888855,0.6533470940656567,0.30500769640522846,0.6671212102272728],"dir":"ltr"},{"str":"law","boundary":[0.3183409150326794,0.6533470940656567,0.34985608823529374,0.6671212102272728],"dir":"ltr"},{"str":"computers","boundary":[0.3568970261437905,0.6533470940656567,0.4422268655228755,0.6671212102272728],"dir":"ltr"},{"str":"get","boundary":[0.44889343137254867,0.6533470940656567,0.4741340941176467,0.6671212102272728],"dir":"ltr"},{"str":"roughly","boundary":[0.4806047058823526,0.6533470940656567,0.5440093933006532,0.6671212102272728],"dir":"ltr"},{"str":"1","boundary":[0.5502837908496728,0.6590633522727274,0.5590895022875813,0.6728374684343434],"dir":"ltr"},{"str":":","boundary":[0.5590894934640519,0.6590633522727274,0.5639736330065356,0.6728374684343434],"dir":"ltr"},{"str":"6","boundary":[0.56397362745098,0.6590633522727274,0.5727793388888884,0.6728374684343434],"dir":"ltr"},{"str":"times","boundary":[0.5794459640522872,0.6533470940656567,0.6248470714052283,0.6671212102272728],"dir":"ltr"},{"str":"faster","boundary":[0.6311214542483656,0.6533470940656567,0.6786616008169931,0.6671212102272728],"dir":"ltr"},{"str":"each","boundary":[0.685328153594771,0.6533470940656567,0.716237129084967,0.6671212102272728],"dir":"ltr"},{"str":"year","boundary":[0.7291783169934637,0.6533470940656567,0.7653815557189539,0.6671212102272728],"dir":"ltr"},{"str":"So","boundary":[0.7788931372549015,0.6533470940656567,0.7988575032679734,0.6671212102272728],"dir":"ltr"},{"str":"if","boundary":[0.8053279411764701,0.6533470940656567,0.8103903192810453,0.6671212102272728],"dir":"ltr"},{"str":"we","boundary":[0.8233315359477119,0.6533470940656567,0.8460410022875812,0.6671212102272728],"dir":"ltr"},{"str":"can","boundary":[0.8525116013071891,0.6533470940656567,0.8812816787581695,0.6671212102272728],"dir":"ltr"},{"str":"Fn","boundary":[0.11764580065359442,0.6590633522727274,0.13744425027777743,0.6740309690656566],"dir":"ltr"},{"str":"And","boundary":[0.848411895424836,0.6704683061868687,0.88247609493464,0.6842424223484849],"dir":"ltr"},{"str":"with","boundary":[0.3235279084967316,0.6704683061868687,0.3609076187908492,0.6842424223484849],"dir":"ltr"},{"str":"this","boundary":[0.36522120915032635,0.6704683061868687,0.39691464019607803,0.6842424223484849],"dir":"ltr"},{"str":"year's","boundary":[0.40122839869281,0.6704683061868687,0.44465081732026096,0.6842424223484849],"dir":"ltr"},{"str":"tec","boundary":[0.45327818627450933,0.6704683061868687,0.47675414166666624,0.6842424223484849],"dir":"ltr"},{"str":",","boundary":[0.538786192810457,0.6704683061868687,0.5389644882352936,0.6842424223484849],"dir":"ltr"},{"str":"hnology","boundary":[0.47655808823529366,0.6704683061868687,0.5409431686274505,0.6842424223484849],"dir":"ltr"},{"str":"then","boundary":[0.5483761764705878,0.6704683061868687,0.5859519653594767,0.6842424223484849],"dir":"ltr"},{"str":"next","boundary":[0.5904616339869276,0.6704683061868687,0.6266648727124179,0.6842424223484849],"dir":"ltr"},{"str":"year","boundary":[0.6311745424836597,0.6704683061868687,0.6673777812091499,0.6842424223484849],"dir":"ltr"},{"str":"we","boundary":[0.6718876143790845,0.6704683061868687,0.6945970807189539,0.6842424223484849],"dir":"ltr"},{"str":"will","boundary":[0.6991067320261434,0.6704683061868687,0.73001584869281,0.6842424223484849],"dir":"ltr"},{"str":"manage","boundary":[0.7341335294117642,0.6704683061868687,0.7993207495098035,0.6842424223484849],"dir":"ltr"},{"str":"F","boundary":[0.8034382679738556,0.6761845643939394,0.8147930011437903,0.6899586805555555],"dir":"ltr"},{"str":"101","boundary":[0.8156846405228753,0.6810888857323234,0.836235022189542,0.6911521559343435],"dir":"ltr"},{"str":"reasonably","boundary":[0.11764558823529365,0.6704683061868687,0.2074674099673198,0.6842424223484849],"dir":"ltr"},{"str":"compute","boundary":[0.21178104575163353,0.6704683061868687,0.2810680910130715,0.6842424223484849],"dir":"ltr"},{"str":"F100","boundary":[0.2857738562091499,0.6761845643939394,0.31799985879084924,0.6911521559343435],"dir":"ltr"},{"str":"the","boundary":[0.11764555555555499,0.6875895183080809,0.14425876846405172,0.7013636344696971],"dir":"ltr"},{"str":"year","boundary":[0.14935683006535888,0.6875895183080809,0.1855600687908491,0.7013636344696971],"dir":"ltr"},{"str":"after","boundary":[0.19065797385620856,0.6875895183080809,0.22998064477124122,0.7013636344696971],"dir":"ltr"},{"str":",","boundary":[0.22821598039215626,0.6875895183080809,0.23310011993463994,0.7013636344696971],"dir":"ltr"},{"str":"F","boundary":[0.23819813725490138,0.6933057765151516,0.24955287042483604,0.7070798926767677],"dir":"ltr"},{"str":"And","boundary":[0.2827257679738556,0.6875895183080809,0.31678996748365956,0.7013636344696971],"dir":"ltr"},{"str":"so","boundary":[0.321691781045751,0.6875895183080809,0.3387149681372543,0.7013636344696971],"dir":"ltr"},{"str":"on:","boundary":[0.3438130228758164,0.6875895183080809,0.3684654498366007,0.7013636344696971],"dir":"ltr"},{"str":"just","boundary":[0.3747398202614373,0.6875895183080809,0.40604109411764644,0.7013636344696971],"dir":"ltr"},{"str":"one","boundary":[0.41094292483660066,0.6875895183080809,0.4395169236928098,0.7013636344696971],"dir":"ltr"},{"str":"more","boundary":[0.4446149836601301,0.6875895183080809,0.48591626584967257,0.7013636344696971],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.4912102450980386,0.6875895183080809,0.5696773223856204,0.7013636344696971],"dir":"ltr"},{"str":"number","boundary":[0.5743831045751628,0.6875895183080809,0.6387860102941171,0.7013636344696971],"dir":"ltr"},{"str":"every","boundary":[0.6436878431372542,0.6875895183080809,0.6883046361111105,0.7013636344696971],"dir":"ltr"},{"str":"year!","boundary":[0.6934025490196072,0.6875895183080809,0.7348820844771237,0.7013636344696971],"dir":"ltr"},{"str":"Such","boundary":[0.7411564705882346,0.6875895183080809,0.7767715735294111,0.7013636344696971],"dir":"ltr"},{"str":"is","boundary":[0.7869674999999993,0.6875895183080809,0.7959516140522869,0.7013636344696971],"dir":"ltr"},{"str":"the","boundary":[0.8057552450980385,0.6875895183080809,0.8323684580065353,0.7013636344696971],"dir":"ltr"},{"str":"curse","boundary":[0.8374665196078425,0.6875895183080809,0.8811029196078426,0.7013636344696971],"dir":"ltr"},{"str":"102","boundary":[0.2498024346405223,0.6982101231060606,0.270352816307189,0.7082733933080808],"dir":"ltr"},{"str":"of","boundary":[0.1176446241830059,0.7047107304292931,0.12721681143790786,0.7184848465909093],"dir":"ltr"},{"str":"exponential","boundary":[0.13741292483660067,0.7047107304292931,0.23368751486928044,0.7184848465909093],"dir":"ltr"},{"str":"time","boundary":[0.23858939542483598,0.7047107304292931,0.2757730271241824,0.7184848465909093],"dir":"ltr"},{"str":".","boundary":[0.27538089869280985,0.7047107304292931,0.28026503823529353,0.7184848465909093],"dir":"ltr"},{"str":"In","boundary":[0.14529184640522813,0.7221349728535356,0.16349150506535884,0.7359090890151516],"dir":"ltr"},{"str":"short,","boundary":[0.17035410130718892,0.7221349728535356,0.21789424787581638,0.7359090890151516],"dir":"ltr"},{"str":"our","boundary":[0.22534511437908433,0.7221349728535356,0.25293872026143727,0.7359090890151516],"dir":"ltr"},{"str":"naive","boundary":[0.2599975653594765,0.7221349728535356,0.3050065155228752,0.7359090890151516],"dir":"ltr"},{"str":"recursive","boundary":[0.31167305555555497,0.7221349728535356,0.3871989651960778,0.7359090890151516],"dir":"ltr"},{"str":"algorithm","boundary":[0.39425769607843075,0.7221349728535356,0.4754698849673197,0.7359090890151516],"dir":"ltr"},{"str":"is","boundary":[0.48233253267973797,0.7221349728535356,0.49621846225490135,0.7359090890151516],"dir":"ltr"},{"str":"correct","boundary":[0.5028849836601301,0.7221349728535356,0.5586426058823524,0.7359090890151516],"dir":"ltr"},{"str":"but","boundary":[0.5660934803921563,0.7221349728535356,0.5938831648692805,0.7359090890151516],"dir":"ltr"},{"str":"hopelessly","boundary":[0.6007457679738556,0.7221349728535356,0.6856656248366008,0.7359090890151516],"dir":"ltr"},{"str":"inef\u0002cient.","boundary":[0.6925282843137249,0.7221349728535356,0.7797832589869276,0.7359090890151516],"dir":"ltr"},{"str":"Can","boundary":[0.7917439705882348,0.7221349728535356,0.8258081700980388,0.7359090890151516],"dir":"ltr"},{"str":"we","boundary":[0.8326709313725486,0.7221349728535356,0.8544000047385615,0.7359090890151516],"dir":"ltr"},{"str":"do","boundary":[0.8612625980392151,0.7221349728535356,0.8810308854575157,0.7359090890151516],"dir":"ltr"},{"str":"better?","boundary":[0.11764495098039163,0.7392561849747475,0.17144178725490145,0.7530303011363637],"dir":"ltr"},{"str":"A","boundary":[0.11764495098039163,0.7787189943181819,0.12605850588235243,0.7924931104797981],"dir":"ltr"},{"str":"polynomial","boundary":[0.13625459150326744,0.7787189943181819,0.24058622924836548,0.7924931104797981],"dir":"ltr"},{"str":"algorithm","boundary":[0.24509593137254848,0.7787189943181819,0.33709244297385565,0.7924931104797981],"dir":"ltr"},{"str":"Let's","boundary":[0.11764495098039163,0.8068319425505053,0.15128143823529358,0.8206060587121213],"dir":"ltr"},{"str":"try","boundary":[0.16226171568627398,0.8068319425505053,0.1865219854575158,0.8206060587121213],"dir":"ltr"},{"str":"to","boundary":[0.19220812091503214,0.8068319425505053,0.20785875784313673,0.8206060587121213],"dir":"ltr"},{"str":"understand","boundary":[0.21374096405228707,0.8068319425505053,0.3086608292483655,0.8206060587121213],"dir":"ltr"},{"str":"why","boundary":[0.3141509313725485,0.8068319425505053,0.3486072880718949,0.8206060587121213],"dir":"ltr"},{"str":"is","boundary":[0.40226122549019555,0.8068319425505053,0.41065694084967264,0.8206060587121213],"dir":"ltr"},{"str":"so","boundary":[0.4216373692810452,0.8068319425505053,0.43866055637254847,0.8206060587121213],"dir":"ltr"},{"str":"slow","boundary":[0.4443466830065354,0.8068319425505053,0.48094207892156804,0.8206060587121213],"dir":"ltr"},{"str":"Figure","boundary":[0.491708578431372,0.8068319425505053,0.5463075431372543,0.8206060587121213],"dir":"ltr"},{"str":"0.1","boundary":[0.5517976143790845,0.8068319425505053,0.57664611993464,0.8206060587121213],"dir":"ltr"},{"str":"shows","boundary":[0.5819400980392152,0.8068319425505053,0.6320470916666662,0.8206060587121213],"dir":"ltr"},{"str":"the","boundary":[0.6377332352941172,0.8068319425505053,0.6643464482026139,0.8206060587121213],"dir":"ltr"},{"str":"cascade","boundary":[0.6700325816993459,0.8068319425505053,0.7328490333333328,0.8206060587121213],"dir":"ltr"},{"str":"of","boundary":[0.7385351960784309,0.8068319425505053,0.7532054400326793,0.8206060587121213],"dir":"ltr"},{"str":"recursive","boundary":[0.7588917320261434,0.8068319425505053,0.8344176416666662,0.8206060587121213],"dir":"ltr"},{"str":"invo-","boundary":[0.8401038235294113,0.8068319425505053,0.8809951232026139,0.8206060587121213],"dir":"ltr"},{"str":"fib1","boundary":[0.3539012581699341,0.81599172979798,0.3966820424836596,0.829765845959596],"dir":"ltr"},{"str":"cations","boundary":[0.1176446732026139,0.8239531546717173,0.1759513171568623,0.8377272708333334],"dir":"ltr"},{"str":"triggered","boundary":[0.18085316993464004,0.8239531546717173,0.25598692238562043,0.8377272708333334],"dir":"ltr"},{"str":"by","boundary":[0.2612809477124178,0.8239531546717173,0.28085315653594717,0.8377272708333334],"dir":"ltr"},{"str":"a","boundary":[0.28575496732026096,0.8239531546717173,0.29103132679738514,0.8377272708333334],"dir":"ltr"},{"str":"single","boundary":[0.30044297385620866,0.8239531546717173,0.3493556705882348,0.8377272708333334],"dir":"ltr"},{"str":"call","boundary":[0.3542575163398688,0.8239531546717173,0.38340192565359427,0.8377272708333334],"dir":"ltr"},{"str":"to","boundary":[0.3881076797385616,0.8239531546717173,0.4037583166666661,0.8377272708333334],"dir":"ltr"},{"str":"(","boundary":[0.4519222222222216,0.8239531546717173,0.45778675473856156,0.8377272708333334],"dir":"ltr"},{"str":"n","boundary":[0.45778674836601246,0.829669412878788,0.46855324575163343,0.8434435290404041],"dir":"ltr"},{"str":").","boundary":[0.4685532352941171,0.8239531546717173,0.473419697058823,0.8377272708333334],"dir":"ltr"},{"str":"Notice","boundary":[0.48518411764705827,0.8239531546717173,0.5376262290849668,0.8377272708333334],"dir":"ltr"},{"str":"that","boundary":[0.5429202287581694,0.8239531546717173,0.5775548387254896,0.8377272708333334],"dir":"ltr"},{"str":"many","boundary":[0.5824566666666661,0.8239531546717173,0.6288559923202609,0.8377272708333334],"dir":"ltr"},{"str":"computations","boundary":[0.6335617320261432,0.8239531546717173,0.7445243913398687,0.8377272708333334],"dir":"ltr"},{"str":"are","boundary":[0.7496223529411759,0.8239531546717173,0.7762355658496726,0.8377272708333334],"dir":"ltr"},{"str":"repeated!","boundary":[0.7811373856209144,0.8239531546717173,0.8578397668300648,0.8377272708333334],"dir":"ltr"},{"str":"fib1","boundary":[0.4088563725490191,0.8331129419191919,0.4516371568627446,0.8468870580808081],"dir":"ltr"},{"str":"A","boundary":[0.14529098039215627,0.8413773970959598,0.1544888480392151,0.855151513257576],"dir":"ltr"},{"str":"more","boundary":[0.1619398366013066,0.8413773970959598,0.20324111879084905,0.855151513257576],"dir":"ltr"},{"str":"sensible","boundary":[0.20716254901960723,0.8413773970959598,0.2734905900326791,0.855151513257576],"dir":"ltr"},{"str":"scheme","boundary":[0.2772159803921563,0.8413773970959598,0.3375012031045746,0.855151513257576],"dir":"ltr"},{"str":"would","boundary":[0.3414226307189537,0.8413773970959598,0.39094138856209093,0.855151513257576],"dir":"ltr"},{"str":"store","boundary":[0.3946667483660125,0.8413773970959598,0.43516589084967267,0.855151513257576],"dir":"ltr"},{"str":"the","boundary":[0.4392834150326792,0.8413773970959598,0.4658966279411759,0.855151513257576],"dir":"ltr"},{"str":"intermediate","boundary":[0.46981805555555506,0.8413773970959598,0.5760748285947708,0.855151513257576],"dir":"ltr"},{"str":"resultsóthe","boundary":[0.5799963235294112,0.8413773970959598,0.6809767998366008,0.855151513257576],"dir":"ltr"},{"str":"values","boundary":[0.684898284313725,0.8413773970959598,0.7381247101307185,0.855151513257576],"dir":"ltr"},{"str":"F","boundary":[0.7416540032679733,0.8470936553030305,0.7530087364379079,0.8608677714646467],"dir":"ltr"},{"str":";","boundary":[0.7619574836601302,0.8470936553030305,0.7639005013071889,0.8608677714646467],"dir":"ltr"},{"str":"F","boundary":[0.7697827450980387,0.8470936553030305,0.7811374782679732,0.8608677714646467],"dir":"ltr"},{"str":";","boundary":[0.7892123529411759,0.8470936553030305,0.7911553705882347,0.8608677714646467],"dir":"ltr"},{"str":":","boundary":[0.7970376143790844,0.8470936553030305,0.7989806320261432,0.8608677714646467],"dir":"ltr"},{"str":":","boundary":[0.8048628758169929,0.8470936553030305,0.8068058934640517,0.8608677714646467],"dir":"ltr"},{"str":":","boundary":[0.8126881372549014,0.8470936553030305,0.8144350437908491,0.8608677714646467],"dir":"ltr"},{"str":";","boundary":[0.820709509803921,0.8470936553030305,0.8226525274509797,0.8608677714646467],"dir":"ltr"},{"str":"F","boundary":[0.8285347712418294,0.8470936553030305,0.8398895044117641,0.8608677714646467],"dir":"ltr"},{"str":"ó","boundary":[0.8670554575163393,0.8413773970959598,0.8848807843137249,0.855151513257576],"dir":"ltr"},{"str":"0","boundary":[0.7541143464052281,0.8519980018939395,0.7609644736274503,0.8620612720959596],"dir":"ltr"},{"str":"1","boundary":[0.7811731862745093,0.8519980018939395,0.7880233134967315,0.8620612720959596],"dir":"ltr"},{"str":"n","boundary":[0.8399966993464048,0.8519980018939395,0.8484226162908491,0.8620612720959596],"dir":"ltr"},{"str":"\u0000","boundary":[0.8484225816993459,0.8519980018939395,0.859205671699346,0.8620612720959596],"dir":"ltr"},{"str":"1","boundary":[0.8592056209150322,0.8519980018939395,0.8660557481372544,0.8620612720959596],"dir":"ltr"},{"str":"as","boundary":[0.11764369281045692,0.8584986092171719,0.13584335147058763,0.872272725378788],"dir":"ltr"},{"str":"soon","boundary":[0.1407451633986922,0.8584986092171719,0.1775366379084961,0.872272725378788],"dir":"ltr"},{"str":"as","boundary":[0.1826347058823523,0.8584986092171719,0.20083436454248305,0.872272725378788],"dir":"ltr"},{"str":"they","boundary":[0.20573617647058762,0.8584986092171719,0.24193941519607778,0.872272725378788],"dir":"ltr"},{"str":"become","boundary":[0.24684124183006473,0.8584986092171719,0.30693041846405167,0.872272725378788],"dir":"ltr"},{"str":"known.","boundary":[0.3120283333333327,0.8584986092171719,0.3721175099673196,0.872272725378788],"dir":"ltr"}],"boundary":[0.11764,0.08979,0.88488,0.87227],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":13,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/92618a10c9c4a390552ac379eaab9383.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/1262603bd4f8e51e4648dc01657d305e.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11767,0.12732]},"elements":[{"words":[{"str":"14","boundary":[0.11764705882352941,0.09001376073232323,0.1376114248366013,0.10378787689393938],"dir":"ltr"},{"str":"Figure","boundary":[0.11764705882352941,0.12796141856060608,0.1793048522875817,0.14173553472222222],"dir":"ltr"},{"str":"0.1","boundary":[0.18440276143790849,0.12796141856060608,0.20964342418300655,0.14173553472222222],"dir":"ltr"},{"str":"The","boundary":[0.21474148692810455,0.1286501243686869,0.24645274330065356,0.14242424053030306],"dir":"ltr"},{"str":"proliferation","boundary":[0.25135455882352936,0.1286501243686869,0.3542601704248366,0.14242424053030306],"dir":"ltr"},{"str":"of","boundary":[0.35935815359477125,0.1286501243686869,0.3689303408496732,0.14242424053030306],"dir":"ltr"},{"str":"recursive","boundary":[0.379126454248366,0.1286501243686869,0.4546523638888889,0.14242424053030306],"dir":"ltr"},{"str":"calls","boundary":[0.45975031045751635,0.1286501243686869,0.49711219542483664,0.14242424053030306],"dir":"ltr"},{"str":"in","boundary":[0.5020140359477124,0.1286501243686869,0.5186450658496732,0.14242424053030306],"dir":"ltr"},{"str":".","boundary":[0.5664168137254901,0.1286501243686869,0.5713009532679738,0.14242424053030306],"dir":"ltr"},{"str":"fib1","boundary":[0.5233509640522876,0.13780991161616166,0.5661317483660131,0.1515840277777778],"dir":"ltr"},{"str":"Fn","boundary":[0.47518573529411795,0.16263035353535366,0.49568659328431397,0.17852454229797993],"dir":"ltr"}],"boundary":[0.11765,0.09001,0.5713,0.17852],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.29372364379084975,0.2916379797979799,0.3142244691013073,0.30753210542929305],"dir":"ltr"},{"str":"\u0000","boundary":[0.31422444444444453,0.2976034816919193,0.32486325679738576,0.30753210542929305],"dir":"ltr"},{"str":"2","boundary":[0.32486323529411776,0.2976034816919193,0.3316217078758171,0.30753210542929305],"dir":"ltr"}],"boundary":[0.29372,0.29164,0.33162,0.30753],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.26470544117647077,0.36443845959595966,0.28520629916666684,0.3803327114898991],"dir":"ltr"},{"str":"\u0000","boundary":[0.28520627450980407,0.37040408775252537,0.2958450868627453,0.3803327114898991],"dir":"ltr"},{"str":"3","boundary":[0.2958450653594773,0.37040408775252537,0.3026035379411766,0.3803327114898991],"dir":"ltr"}],"boundary":[0.26471,0.36444,0.3026,0.38033],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.3509874673202614,0.22705875000000011,0.3714883253104575,0.24295287563131326],"dir":"ltr"},{"str":"\u0000","boundary":[0.3714883006535947,0.23302425189393952,0.38212711300653596,0.24295287563131326],"dir":"ltr"},{"str":"1","boundary":[0.38212709150326796,0.23302425189393952,0.3888855640849673,0.24295287563131326],"dir":"ltr"}],"boundary":[0.35099,0.22706,0.38889,0.24295],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.39741666666666664,0.29268383838383843,0.4179174919771242,0.3085780271464647],"dir":"ltr"},{"str":"\u0000","boundary":[0.4179174673202614,0.29864940340909096,0.4285562796732026,0.3085780271464647],"dir":"ltr"},{"str":"3","boundary":[0.42855625816993465,0.29864940340909096,0.435314730751634,0.3085780271464647],"dir":"ltr"}],"boundary":[0.39742,0.29268,0.43531,0.30858],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.3227419607843139,0.36443845959595966,0.34324278609477143,0.3803327114898991],"dir":"ltr"},{"str":"\u0000","boundary":[0.34324276143790866,0.37040408775252537,0.3538815737908499,0.3803327114898991],"dir":"ltr"},{"str":"4","boundary":[0.3538815522875819,0.37040408775252537,0.3606400248692812,0.3803327114898991],"dir":"ltr"},{"str":"Fn","boundary":[0.3736216993464052,0.3644386489898991,0.39412252465686276,0.38033290088383853],"dir":"ltr"},{"str":"\u0000","boundary":[0.3941225,0.3704042771464648,0.4047613123529412,0.38033290088383853],"dir":"ltr"},{"str":"4","boundary":[0.4047612908496732,0.3704042771464648,0.41151976343137253,0.38033290088383853],"dir":"ltr"},{"str":"Fn","boundary":[0.4243070915032682,0.36443845959595966,0.44480791681372567,0.3803327114898991],"dir":"ltr"},{"str":"\u0000","boundary":[0.444807892156863,0.37040408775252537,0.4554467045098041,0.3803327114898991],"dir":"ltr"},{"str":"5","boundary":[0.4554466830065362,0.37040408775252537,0.46220515558823555,0.3803327114898991],"dir":"ltr"}],"boundary":[0.32274,0.36444,0.46221,0.38033],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.5258697712418302,0.2916379797979799,0.5463705965522877,0.30753210542929305],"dir":"ltr"},{"str":"\u0000","boundary":[0.546370571895425,0.2976034816919193,0.5570093842483661,0.30753210542929305],"dir":"ltr"},{"str":"3","boundary":[0.5570093627450982,0.2976034816919193,0.5637678353267975,0.30753210542929305],"dir":"ltr"}],"boundary":[0.52587,0.29164,0.56377,0.30753],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.5839067156862745,0.22989948232323246,0.6044075736764706,0.24579367108585873],"dir":"ltr"},{"str":"\u0000","boundary":[0.6044075490196079,0.23586504734848499,0.615046361372549,0.24579367108585873],"dir":"ltr"},{"str":"2","boundary":[0.615046339869281,0.23586504734848499,0.6218048124509804,0.24579367108585873],"dir":"ltr"}],"boundary":[0.58391,0.2299,0.6218,0.24579],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.6274340849673203,0.2916380303030304,0.6479349429575163,0.3075321559343436],"dir":"ltr"},{"str":"\u0000","boundary":[0.6479349183006536,0.29760353219696983,0.6585737306535948,0.3075321559343436],"dir":"ltr"},{"str":"4","boundary":[0.6585737091503269,0.29760353219696983,0.6653321817320262,0.3075321559343436],"dir":"ltr"}],"boundary":[0.62743,0.29164,0.66533,0.30753],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Fn","boundary":[0.4968520261437909,0.3644385101010102,0.5173528514542485,0.38033276199494964],"dir":"ltr"},{"str":"\u0000","boundary":[0.5173528267973857,0.3704041382575759,0.5279916391503269,0.38033276199494964],"dir":"ltr"},{"str":"4","boundary":[0.5279916176470589,0.3704041382575759,0.5347500902287583,0.38033276199494964],"dir":"ltr"},{"str":"Fn","boundary":[0.5477307026143792,0.3644385101010102,0.5682315606045752,0.38033276199494964],"dir":"ltr"},{"str":"\u0000","boundary":[0.5682315359477125,0.3704041382575759,0.5788703483006536,0.38033276199494964],"dir":"ltr"},{"str":"5","boundary":[0.5788703267973857,0.3704041382575759,0.5856287993790851,0.38033276199494964],"dir":"ltr"},{"str":"Fn","boundary":[0.6057671732026145,0.36443845959595966,0.626267998513072,0.3803327114898991],"dir":"ltr"},{"str":"\u0000","boundary":[0.6262679738562094,0.37040408775252537,0.6369067862091505,0.3803327114898991],"dir":"ltr"},{"str":"5","boundary":[0.6369067647058826,0.37040408775252537,0.643665237287582,0.3803327114898991],"dir":"ltr"},{"str":"Fn","boundary":[0.656452320261438,0.3644385101010102,0.676953178251634,0.38033276199494964],"dir":"ltr"},{"str":"\u0000","boundary":[0.6769531862745098,0.3704041382575759,0.687591998627451,0.38033276199494964],"dir":"ltr"},{"str":"6","boundary":[0.6875919771241831,0.3704041382575759,0.6943504497058824,0.38033276199494964],"dir":"ltr"},{"str":"\u0006","boundary":[0.4808823529411765,0.38863636363636367,0.5289705882352942,0.3887626262626263],"dir":"ltr"},{"str":"\u0007","boundary":[0.4808823529411765,0.38863636363636367,0.5289705882352942,0.3887626262626263],"dir":"ltr"},{"str":"\u0000","boundary":[0.4808823529411765,0.3958333333333333,0.5289705882352942,0.395959595959596],"dir":"ltr"},{"str":"\u0001","boundary":[0.4808823529411765,0.3958333333333333,0.5289705882352942,0.395959595959596],"dir":"ltr"},{"str":"\u0003","boundary":[0.4808823529411765,0.3958333333333333,0.5289705882352942,0.395959595959596],"dir":"ltr"},{"str":"\u0002","boundary":[0.4808823529411765,0.3958333333333333,0.5289705882352942,0.395959595959596],"dir":"ltr"},{"str":"\u0005","boundary":[0.4808823529411765,0.4093434343434344,0.5289705882352942,0.40946969696969704],"dir":"ltr"},{"str":"\u0004","boundary":[0.4808823529411765,0.4093434343434344,0.5289705882352942,0.40946969696969704],"dir":"ltr"}],"boundary":[0.48088,0.36444,0.69435,0.40947],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Algorithms","boundary":[0.7899640522875817,0.08979153426128839,0.8823348957516342,0.10356565042290454],"dir":"ltr"}],"boundary":[0.78996,0.08979,0.88233,0.10357],"dir":"ltr","type":"paragraph"},{"words":[{"str":"function","boundary":[0.16215669934640523,0.471143244949495,0.2477182679738562,0.48491736111111117],"dir":"ltr"},{"str":"fib2","boundary":[0.2582885620915033,0.471143244949495,0.3010693464052288,0.48491736111111117],"dir":"ltr"},{"str":"(","boundary":[0.30096241830065357,0.471143244949495,0.31165761437908496,0.48491736111111117],"dir":"ltr"},{"str":"n","boundary":[0.3117289052287582,0.46769971590909093,0.32249540261437903,0.4814738320707071],"dir":"ltr"},{"str":")","boundary":[0.32249539215686274,0.471143244949495,0.33319058823529407,0.48491736111111117],"dir":"ltr"},{"str":"if","boundary":[0.16215683006535947,0.48826445707070715,0.1835472222222222,0.5020385732323233],"dir":"ltr"},{"str":"n","boundary":[0.19427807189542484,0.4848209280303031,0.20504456928104575,0.49859504419191925],"dir":"ltr"},{"str":"=","boundary":[0.20994651960784314,0.4848209280303031,0.21894831045751634,0.49859504419191925],"dir":"ltr"},{"str":"0","boundary":[0.22875223856209148,0.4848209280303031,0.23755795,0.49859504419191925],"dir":"ltr"},{"str":"return","boundary":[0.24834227124183006,0.48826445707070715,0.3125134477124183,0.5020385732323233],"dir":"ltr"},{"str":"0","boundary":[0.32313720588235295,0.4848209280303031,0.33194291732026143,0.49859504419191925],"dir":"ltr"},{"str":"create","boundary":[0.162156977124183,0.5053856691919193,0.22632815359477126,0.5191597853535355],"dir":"ltr"},{"str":"an","boundary":[0.23695191176470587,0.5053856691919193,0.247611454248366,0.5191597853535355],"dir":"ltr"},{"str":"array","boundary":[0.26907315359477124,0.5053856691919193,0.3225491339869281,0.5191597853535355],"dir":"ltr"},{"str":"f[0","boundary":[0.33310158496732023,0.5019421401515152,0.36344030294117646,0.5191597853535355],"dir":"ltr"},{"str":":","boundary":[0.3663814705882352,0.5019421401515152,0.3683244392156862,0.5157162563131313],"dir":"ltr"},{"str":":","boundary":[0.37420678104575156,0.5019421401515152,0.3761497496732025,0.5157162563131313],"dir":"ltr"},{"str":":","boundary":[0.38203209150326795,0.5019421401515152,0.3837789980392156,0.5157162563131313],"dir":"ltr"},{"str":"n","boundary":[0.3900534640522875,0.5019421401515152,0.40081996143790843,0.5157162563131313],"dir":"ltr"},{"str":"]","boundary":[0.400819950980392,0.5053856691919193,0.4115151470588234,0.5191597853535355],"dir":"ltr"},{"str":"f[0","boundary":[0.16215655228758158,0.5190633522727273,0.19249527026143778,0.5362809974747476],"dir":"ltr"},{"str":"]","boundary":[0.19249526143790838,0.5225068813131314,0.20319045751633974,0.5362809974747476],"dir":"ltr"},{"str":"=","boundary":[0.21384999999999987,0.5190633522727273,0.22285179084967308,0.5328374684343435],"dir":"ltr"},{"str":"0","boundary":[0.23265571895424822,0.5190633522727273,0.24146143039215673,0.5328374684343435],"dir":"ltr"},{"str":",","boundary":[0.24146142156862732,0.5225068813131314,0.24149707516339855,0.5362809974747476],"dir":"ltr"},{"str":"f[1","boundary":[0.26281616013071885,0.5190633522727273,0.293154878104575,0.5362809974747476],"dir":"ltr"},{"str":"]","boundary":[0.2931548692810456,0.5225068813131314,0.303850065359477,0.5362809974747476],"dir":"ltr"},{"str":"=","boundary":[0.31450960784313714,0.5190633522727273,0.3235113986928103,0.5328374684343435],"dir":"ltr"},{"str":"1","boundary":[0.33331532679738546,0.5190633522727273,0.342121038235294,0.5328374684343435],"dir":"ltr"},{"str":"for","boundary":[0.16215683006535933,0.5396280934343435,0.19424241830065347,0.5534022095959596],"dir":"ltr"},{"str":"i","boundary":[0.2048483333333332,0.5361845643939395,0.21090894444444433,0.5499586805555556],"dir":"ltr"},{"str":"=","boundary":[0.21600696078431358,0.5361845643939395,0.2250087516339868,0.5499586805555556],"dir":"ltr"},{"str":"2","boundary":[0.23481267973856193,0.5361845643939395,0.24361839117647044,0.5499586805555556],"dir":"ltr"},{"str":":","boundary":[0.24655955882352923,0.5361845643939395,0.2485025274509802,0.5499586805555556],"dir":"ltr"},{"str":":","boundary":[0.25438486928104553,0.5361845643939395,0.2563278379084965,0.5499586805555556],"dir":"ltr"},{"str":":","boundary":[0.2622101797385619,0.5361845643939395,0.2637610078431371,0.5499586805555556],"dir":"ltr"},{"str":"n","boundary":[0.2704276307189541,0.5361845643939395,0.28119412810457495,0.5499586805555556],"dir":"ltr"},{"str":":","boundary":[0.2811941176470586,0.5396280934343435,0.29188931372548993,0.5534022095959596],"dir":"ltr"},{"str":"f[i","boundary":[0.19431372549019585,0.5533057765151516,0.22190734313725463,0.5705234217171719],"dir":"ltr"},{"str":"]","boundary":[0.22190732026143767,0.5567493055555556,0.22213905228758143,0.5705234217171719],"dir":"ltr"},{"str":"f[i","boundary":[0.26461679738562066,0.5533057765151516,0.29221041503267947,0.5705234217171719],"dir":"ltr"},{"str":"\u0000","boundary":[0.29593584967320236,0.553002745959596,0.30983960457516313,0.5667768621212121],"dir":"ltr"},{"str":"1","boundary":[0.31376117647058793,0.5533057765151516,0.32256688790849647,0.5670798926767677],"dir":"ltr"},{"str":"+","boundary":[0.3441176960784311,0.5567493055555556,0.3441533496732023,0.5705234217171719],"dir":"ltr"},{"str":"f[i","boundary":[0.3654724346405226,0.5533057765151516,0.3930660522875814,0.5705234217171719],"dir":"ltr"},{"str":"\u0000","boundary":[0.3967914869281043,0.553002745959596,0.41069524183006506,0.5667768621212121],"dir":"ltr"},{"str":"2","boundary":[0.4146168137254899,0.5533057765151516,0.4234225251633984,0.5670798926767677],"dir":"ltr"},{"str":"]","boundary":[0.42342251633986894,0.5567493055555556,0.4341177124183003,0.5705234217171719],"dir":"ltr"},{"str":"return","boundary":[0.162157810457516,0.5737190025252525,0.22632898692810424,0.5874931186868688],"dir":"ltr"},{"str":"f[n","boundary":[0.23695274509803887,0.5702754734848485,0.2692522490196075,0.5874931186868688],"dir":"ltr"},{"str":"]","boundary":[0.26925223856209113,0.5737190025252525,0.2799474346405225,0.5874931186868688],"dir":"ltr"},{"str":"As","boundary":[0.11764799019607808,0.5978925486111112,0.13878882777777743,0.6116666647727274],"dir":"ltr"},{"str":"with","boundary":[0.14584766339869246,0.5978925486111112,0.1832273736928101,0.6116666647727274],"dir":"ltr"},{"str":"the","boundary":[0.24509893790849638,0.5978925486111112,0.2717121508169931,0.6116666647727274],"dir":"ltr"},{"str":"correctness","boundary":[0.27896691176470556,0.5978925486111112,0.37092777271241795,0.6116666647727274],"dir":"ltr"},{"str":"of","boundary":[0.37837867647058787,0.5978925486111112,0.39304892042483625,0.6116666647727274],"dir":"ltr"},{"str":"this","boundary":[0.4003038398692807,0.5978925486111112,0.43199727091503237,0.6116666647727274],"dir":"ltr"},{"str":"algorithm","boundary":[0.4388600490196075,0.5978925486111112,0.5200722379084964,0.6116666647727274],"dir":"ltr"},{"str":"is","boundary":[0.5269348856209146,0.5978925486111112,0.540820815196078,0.6116666647727274],"dir":"ltr"},{"str":"self-evident","boundary":[0.5478796568627448,0.5978925486111112,0.6431560285947708,0.6116666647727274],"dir":"ltr"},{"str":"because","boundary":[0.6504108660130715,0.5978925486111112,0.7149920249999996,0.6116666647727274],"dir":"ltr"},{"str":"it","boundary":[0.7218546568627446,0.5978925486111112,0.7273091934640519,0.6116666647727274],"dir":"ltr"},{"str":"directly","boundary":[0.741426879084967,0.5978925486111112,0.803833348202614,0.6116666647727274],"dir":"ltr"},{"str":"uses","boundary":[0.8110881535947708,0.5978925486111112,0.847291392320261,0.6116666647727274],"dir":"ltr"},{"str":"the","boundary":[0.854350081699346,0.5978925486111112,0.8809632946078428,0.6116666647727274],"dir":"ltr"},{"str":"fib1","boundary":[0.19009014705882316,0.6070523358585859,0.23287093137254863,0.620826452020202],"dir":"ltr"},{"str":"de\u0002nition","boundary":[0.11764746732026106,0.6150137607323233,0.19650671307189504,0.6287878768939394],"dir":"ltr"},{"str":"of","boundary":[0.20140857843137216,0.6150137607323233,0.2160788223856205,0.6287878768939394],"dir":"ltr"},{"str":"F","boundary":[0.22137295751633948,0.620730018939394,0.23272769068627414,0.6345041351010101],"dir":"ltr"},{"str":"How","boundary":[0.2535119771241826,0.6150137607323233,0.2911055913398689,0.6287878768939394],"dir":"ltr"},{"str":"long","boundary":[0.2962036437908493,0.6150137607323233,0.33123041094771205,0.6287878768939394],"dir":"ltr"},{"str":"does","boundary":[0.3361324019607839,0.6150137607323233,0.37213956209150284,0.6287878768939394],"dir":"ltr"},{"str":"it","boundary":[0.37743354575163357,0.6150137607323233,0.38504494509803877,0.6287878768939394],"dir":"ltr"},{"str":"take?","boundary":[0.3948489052287577,0.6150137607323233,0.43887746241830017,0.6287878768939394],"dir":"ltr"},{"str":"The","boundary":[0.4455440032679734,0.6150137607323233,0.47725525964052246,0.6287878768939394],"dir":"ltr"},{"str":"inner","boundary":[0.4821572385620911,0.6150137607323233,0.5263818743464048,0.6287878768939394],"dir":"ltr"},{"str":"loop","boundary":[0.5312838725490192,0.6150137607323233,0.5647420109477119,0.6287878768939394],"dir":"ltr"},{"str":"consists","boundary":[0.5700361601307186,0.6150137607323233,0.6347955723856205,0.6287878768939394],"dir":"ltr"},{"str":"of","boundary":[0.639893513071895,0.6150137607323233,0.649465700326797,0.6287878768939394],"dir":"ltr"},{"str":"a","boundary":[0.6596618137254898,0.6150137607323233,0.6645460326797382,0.6287878768939394],"dir":"ltr"},{"str":"single","boundary":[0.6747419607843134,0.6150137607323233,0.7236546575163394,0.6287878768939394],"dir":"ltr"},{"str":"computer","boundary":[0.7285566666666663,0.6150137607323233,0.8056690303921565,0.6287878768939394],"dir":"ltr"},{"str":"step","boundary":[0.8109630392156859,0.6150137607323233,0.8450094133986924,0.6287878768939394],"dir":"ltr"},{"str":"and","boundary":[0.850303562091503,0.6150137607323233,0.8814265826797383,0.6287878768939394],"dir":"ltr"},{"str":"n","boundary":[0.23294158496731987,0.625634365530303,0.24136750191176434,0.6356976357323233],"dir":"ltr"},{"str":"is","boundary":[0.11764833333333309,0.6321349728535354,0.12643620555555532,0.6459090890151516],"dir":"ltr"},{"str":"executed","boundary":[0.13663232026143768,0.6321349728535354,0.20845056192810435,0.6459090890151516],"dir":"ltr"},{"str":"n","boundary":[0.21394065359477102,0.637851231060606,0.2247071509803919,0.6516253472222222],"dir":"ltr"},{"str":"\u0000","boundary":[0.22882477124182984,0.6375482005050506,0.24272852614379062,0.6513223166666667],"dir":"ltr"},{"str":"1","boundary":[0.246846176470588,0.637851231060606,0.2556518879084965,0.6516253472222222],"dir":"ltr"},{"str":"times","boundary":[0.2609459803921566,0.6321349728535354,0.3063470877450978,0.6459090890151516],"dir":"ltr"},{"str":"Therefore","boundary":[0.3177018464052285,0.6321349728535354,0.39734540653594747,0.6459090890151516],"dir":"ltr"},{"str":"the","boundary":[0.40283550653594746,0.6321349728535354,0.4294487194444441,0.6459090890151516],"dir":"ltr"},{"str":"number","boundary":[0.43474269607843113,0.6321349728535354,0.49914560179738543,0.6459090890151516],"dir":"ltr"},{"str":"of","boundary":[0.5042435130718952,0.6321349728535354,0.5189137570261435,0.6459090890151516],"dir":"ltr"},{"str":"computer","boundary":[0.5242078921568626,0.6321349728535354,0.6013202558823528,0.6459090890151516],"dir":"ltr"},{"str":"steps","boundary":[0.6068103431372547,0.6321349728535354,0.649074192973856,0.6459090890151516],"dir":"ltr"},{"str":"used","boundary":[0.6545642647058821,0.6321349728535354,0.6927282893790848,0.6459090890151516],"dir":"ltr"},{"str":"by","boundary":[0.6980224346405227,0.6321349728535354,0.7175946434640521,0.6459090890151516],"dir":"ltr"},{"str":"is","boundary":[0.7704642647058821,0.6321349728535354,0.7843501942810455,0.6459090890151516],"dir":"ltr"},{"str":"linear","boundary":[0.7894482516339867,0.6321349728535354,0.8379687911764703,0.6459090890151516],"dir":"ltr"},{"str":"in","boundary":[0.8434588725490194,0.6321349728535354,0.8602859810457514,0.6459090890151516],"dir":"ltr"},{"str":"n","boundary":[0.8653840359477121,0.637851231060606,0.876150533333333,0.6516253472222222],"dir":"ltr"},{"str":".","boundary":[0.8761505555555553,0.6321349728535354,0.8810346950980389,0.6459090890151516],"dir":"ltr"},{"str":"fib2","boundary":[0.7224964542483658,0.6412947601010102,0.7652772385620913,0.6550688762626263],"dir":"ltr"},{"str":"From","boundary":[0.1176489215686272,0.6492561849747476,0.1618913714052285,0.6630303011363637],"dir":"ltr"},{"str":"exponential","boundary":[0.16640102941176443,0.6492561849747476,0.2626756194444442,0.6630303011363637],"dir":"ltr"},{"str":"we","boundary":[0.2669892647058821,0.6492561849747476,0.2896987310457514,0.6630303011363637],"dir":"ltr"},{"str":"are","boundary":[0.29420854575163374,0.6492561849747476,0.32082175866013046,0.6630303011363637],"dir":"ltr"},{"str":"down","boundary":[0.3253314215686272,0.6492561849747476,0.36918172549019584,0.6630303011363637],"dir":"ltr"},{"str":"to","boundary":[0.3734953104575161,0.6492561849747476,0.38914594738562064,0.6630303011363637],"dir":"ltr"},{"str":"polynomial","boundary":[0.393655767973856,0.6492561849747476,0.4846540852941174,0.6630303011363637],"dir":"ltr"},{"str":"a","boundary":[0.4946361274509801,0.6492561849747476,0.5003046274509801,0.6630303011363637],"dir":"ltr"},{"str":"huge","boundary":[0.508931993464052,0.6492561849747476,0.5492528826797384,0.6630303011363637],"dir":"ltr"},{"str":"breakthrough","boundary":[0.5535666339869278,0.6492561849747476,0.666686157843137,0.6630303011363637],"dir":"ltr"},{"str":"in","boundary":[0.6709998039215683,0.6492561849747476,0.6876308338235291,0.6630303011363637],"dir":"ltr"},{"str":"running","boundary":[0.6917483333333331,0.6492561849747476,0.7586824354575161,0.6630303011363637],"dir":"ltr"},{"str":"time","boundary":[0.7627999673202612,0.6492561849747476,0.7999835990196076,0.6630303011363637],"dir":"ltr"},{"str":"It","boundary":[0.8105540196078428,0.6492561849747476,0.8201263692810454,0.6630303011363637],"dir":"ltr"},{"str":"is","boundary":[0.8291456862745096,0.6492561849747476,0.8387178722222219,0.6630303011363637],"dir":"ltr"},{"str":"now","boundary":[0.8473453594771239,0.6492561849747476,0.8810174017973853,0.6630303011363637],"dir":"ltr"},{"str":"perfectly","boundary":[0.11764928104575131,0.6662258819444445,0.18905754019607815,0.6799999981060606],"dir":"ltr"},{"str":"reasonable","boundary":[0.19435156862745068,0.6662258819444445,0.28338907598039187,0.6799999981060606],"dir":"ltr"},{"str":"to","boundary":[0.288290947712418,0.6662258819444445,0.30394158464052257,0.6799999981060606],"dir":"ltr"},{"str":"compute","boundary":[0.30903964052287547,0.6662258819444445,0.37832668578431344,0.6799999981060606],"dir":"ltr"},{"str":"F","boundary":[0.38362068627450946,0.6719421401515152,0.39497541944444414,0.6857162563131313],"dir":"ltr"},{"str":"or","boundary":[0.42196297385620885,0.6662258819444445,0.4385940037581696,0.6799999981060606],"dir":"ltr"},{"str":"even","boundary":[0.44369205882352913,0.6662258819444445,0.48185608349673176,0.6799999981060606],"dir":"ltr"},{"str":"F","boundary":[0.48695398692810427,0.6719421401515152,0.49830872009803884,0.6857162563131313],"dir":"ltr"},{"str":".","boundary":[0.5447080555555552,0.6662258819444445,0.5495921950980389,0.6799999981060606],"dir":"ltr"},{"str":"1","boundary":[0.549610016339869,0.6655490048611111,0.5568638582843133,0.6756122750631313],"dir":"ltr"},{"str":"200","boundary":[0.3954923856209147,0.6768464867424241,0.4160427672875814,0.6869097569444443],"dir":"ltr"},{"str":"200","boundary":[0.4984335457516336,0.6768464867424241,0.5189839274183002,0.6869097569444443],"dir":"ltr"},{"str":";","boundary":[0.5189838725490192,0.6768464867424241,0.5229038122712415,0.6869097569444443],"dir":"ltr"},{"str":"000","boundary":[0.5229038071895421,0.6768464867424241,0.5434541888562089,0.6869097569444443],"dir":"ltr"},{"str":"As","boundary":[0.14529629084967285,0.6836501117424243,0.1664371284313722,0.6974242279040404],"dir":"ltr"},{"str":"we","boundary":[0.1721234150326794,0.6836501117424243,0.19483288137254867,0.6974242279040404],"dir":"ltr"},{"str":"will","boundary":[0.20071524509803887,0.6836501117424243,0.23162436176470552,0.6974242279040404],"dir":"ltr"},{"str":"see","boundary":[0.2371144281045748,0.6836501117424243,0.2629433266339866,0.6974242279040404],"dir":"ltr"},{"str":"repeatedly","boundary":[0.2690217810457513,0.6836501117424243,0.35570634526143763,0.6974242279040404],"dir":"ltr"},{"str":"throughout","boundary":[0.36178468954248333,0.6836501117424243,0.4543516116013069,0.6974242279040404],"dir":"ltr"},{"str":"this","boundary":[0.46023387254901926,0.6836501117424243,0.4919273035947709,0.6974242279040404],"dir":"ltr"},{"str":"book,","boundary":[0.497613447712418,0.6836501117424243,0.5406616119281042,0.6974242279040404],"dir":"ltr"},{"str":"the","boundary":[0.5467400816993461,0.6836501117424243,0.5733532946078428,0.6974242279040404],"dir":"ltr"},{"str":"right","boundary":[0.5792356699346402,0.6836501117424243,0.6201269696078427,0.6974242279040404],"dir":"ltr"},{"str":"algorithm","boundary":[0.6258131209150324,0.6836501117424243,0.7070253098039212,0.6974242279040404],"dir":"ltr"},{"str":"makes","boundary":[0.7127114869281043,0.6836501117424243,0.7661518166666664,0.6974242279040404],"dir":"ltr"},{"str":"all","boundary":[0.7720341993464049,0.6836501117424243,0.7933532901960781,0.6974242279040404],"dir":"ltr"},{"str":"the","boundary":[0.7988433496732023,0.6836501117424243,0.825456562581699,0.6974242279040404],"dir":"ltr"},{"str":"differ","boundary":[0.8313389379084963,0.6836501117424243,0.8755457483660126,0.6974242279040404],"dir":"ltr"},{"str":"-","boundary":[0.8749575653594767,0.6836501117424243,0.8808220978758166,0.6974242279040404],"dir":"ltr"},{"str":"ence","boundary":[0.11764874183006492,0.7007713238636365,0.15404805915032635,0.7145454400252526],"dir":"ltr"},{"str":".","boundary":[0.15365593137254857,0.7007713238636365,0.15854007091503225,0.7145454400252526],"dir":"ltr"},{"str":"More","boundary":[0.11764874183006492,0.7391735271464646,0.1654206176470584,0.7529476433080807],"dir":"ltr"},{"str":"careful","boundary":[0.170518513071895,0.7391735271464646,0.23608006503267928,0.7529476433080807],"dir":"ltr"},{"str":"analysis","boundary":[0.24117799019607797,0.7391735271464646,0.31672172516339825,0.7529476433080807],"dir":"ltr"},{"str":"In","boundary":[0.11764857843137211,0.7669834450757576,0.13584823709150282,0.7807575612373737],"dir":"ltr"},{"str":"our","boundary":[0.1411423692810453,0.7669834450757576,0.16873597516339822,0.7807575612373737],"dir":"ltr"},{"str":"discussion","boundary":[0.17422602941176424,0.7669834450757576,0.25894980767973813,0.7807575612373737],"dir":"ltr"},{"str":"so","boundary":[0.26443991830065317,0.7669834450757576,0.2814631053921564,0.7807575612373737],"dir":"ltr"},{"str":"far","boundary":[0.2869531535947708,0.7669834450757576,0.3106251875816989,0.7807575612373737],"dir":"ltr"},{"str":"we","boundary":[0.31923480392156817,0.7669834450757576,0.3419442702614374,0.7807575612373737],"dir":"ltr"},{"str":"have","boundary":[0.3474344771241825,0.7669834450757576,0.386578907189542,0.7807575612373737],"dir":"ltr"},{"str":"been","boundary":[0.39187303921568584,0.7669834450757576,0.43042922107843096,0.7807575612373737],"dir":"ltr"},{"str":"counting","boundary":[0.4359192810457512,0.7669834450757576,0.5075414441176466,0.7807575612373737],"dir":"ltr"},{"str":"the","boundary":[0.5128354575163394,0.7669834450757576,0.5394486704248361,0.7807575612373737],"dir":"ltr"},{"str":"number","boundary":[0.5449387254901956,0.7669834450757576,0.6093416312091499,0.7807575612373737],"dir":"ltr"},{"str":"of","boundary":[0.6146356209150322,0.7669834450757576,0.6293058648692805,0.7807575612373737],"dir":"ltr"},{"str":"basic","boundary":[0.6347960784313721,0.7669834450757576,0.6764716924836597,0.7807575612373737],"dir":"ltr"},{"str":"computer","boundary":[0.6821578431372545,0.7669834450757576,0.7577015781045747,0.7807575612373737],"dir":"ltr"},{"str":"steps","boundary":[0.7631916666666663,0.7669834450757576,0.8031025733660127,0.7807575612373737],"dir":"ltr"},{"str":"executed","boundary":[0.8087887254901956,0.7669834450757576,0.8806069671568623,0.7807575612373737],"dir":"ltr"},{"str":"by","boundary":[0.11764820261437861,0.7841046571969698,0.13722041143790803,0.7978787733585859],"dir":"ltr"},{"str":"each","boundary":[0.1442792483660126,0.7841046571969698,0.17420799509803878,0.7978787733585859],"dir":"ltr"},{"str":"algorithm","boundary":[0.18910996732026097,0.7841046571969698,0.27032215620914984,0.7978787733585859],"dir":"ltr"},{"str":"and","boundary":[0.27738088235294067,0.7841046571969698,0.30850390294117597,0.7978787733585859],"dir":"ltr"},{"str":"thinking","boundary":[0.31575882352941126,0.7841046571969698,0.3869888294117642,0.7978787733585859],"dir":"ltr"},{"str":"of","boundary":[0.3938514705882348,0.7841046571969698,0.40852171454248315,0.7978787733585859],"dir":"ltr"},{"str":"these","boundary":[0.41597271241830014,0.7841046571969698,0.4596091124183001,0.7978787733585859],"dir":"ltr"},{"str":"basic","boundary":[0.46705996732026095,0.7841046571969698,0.5087355813725485,0.7978787733585859],"dir":"ltr"},{"str":"steps","boundary":[0.5157942810457511,0.7841046571969698,0.5580581308823525,0.7978787733585859],"dir":"ltr"},{"str":"as","boundary":[0.5655089869281041,0.7841046571969698,0.5837086455882349,0.7978787733585859],"dir":"ltr"},{"str":"taking","boundary":[0.5909635620915028,0.7841046571969698,0.6445821450980387,0.7978787733585859],"dir":"ltr"},{"str":"a","boundary":[0.6516408496732021,0.7841046571969698,0.6545642026143785,0.7978787733585859],"dir":"ltr"},{"str":"constant","boundary":[0.6686818627450976,0.7841046571969698,0.7391275542483655,0.7978787733585859],"dir":"ltr"},{"str":"amount","boundary":[0.7465784313725485,0.7841046571969698,0.8100009441176466,0.7978787733585859],"dir":"ltr"},{"str":"of","boundary":[0.8170598039215682,0.7841046571969698,0.8317300478758165,0.7978787733585859],"dir":"ltr"},{"str":"time","boundary":[0.8391808823529406,0.7841046571969698,0.8763645140522871,0.7978787733585859],"dir":"ltr"},{"str":".","boundary":[0.8759723856209145,0.7841046571969698,0.8808565251633982,0.7978787733585859],"dir":"ltr"},{"str":"This","boundary":[0.11764885620914978,0.8012258693181818,0.1544403307189537,0.814999985479798],"dir":"ltr"},{"str":"is","boundary":[0.16091078431372494,0.8012258693181818,0.17479671388888834,0.814999985479798],"dir":"ltr"},{"str":"a","boundary":[0.1814632352941171,0.8012258693181818,0.18477874509803865,0.814999985479798],"dir":"ltr"},{"str":"very","boundary":[0.1981120915032674,0.8012258693181818,0.23392317303921512,0.814999985479798],"dir":"ltr"},{"str":"useful","boundary":[0.24078594771241774,0.8012258693181818,0.2912672732026138,0.814999985479798],"dir":"ltr"},{"str":"simpli\u0002cation.","boundary":[0.2979338235294112,0.8012258693181818,0.4151353472222217,0.814999985479798],"dir":"ltr"},{"str":"After","boundary":[0.42631176470588183,0.8012258693181818,0.46857561454248314,0.814999985479798],"dir":"ltr"},{"str":"all,","boundary":[0.4756343137254897,0.8012258693181818,0.5018375441176466,0.814999985479798],"dir":"ltr"},{"str":"a","boundary":[0.5087003267973851,0.8012258693181818,0.5120158366013067,0.814999985479798],"dir":"ltr"},{"str":"processor's","boundary":[0.5253491830065354,0.8012258693181818,0.6061335297385617,0.814999985479798],"dir":"ltr"},{"str":"instruction","boundary":[0.6206432516339865,0.8012258693181818,0.7112315624183002,0.814999985479798],"dir":"ltr"},{"str":"set","boundary":[0.7178981535947707,0.8012258693181818,0.7417662661764701,0.814999985479798],"dir":"ltr"},{"str":"has","boundary":[0.7486290359477119,0.8012258693181818,0.7777912705882348,0.814999985479798],"dir":"ltr"},{"str":"a","boundary":[0.7844577941176465,0.8012258693181818,0.7877733039215681,0.814999985479798],"dir":"ltr"},{"str":"variety","boundary":[0.8011066503267968,0.8012258693181818,0.8594132942810453,0.814999985479798],"dir":"ltr"},{"str":"of","boundary":[0.8660798529411758,0.8012258693181818,0.8807500968954243,0.814999985479798],"dir":"ltr"},{"str":"basic","boundary":[0.11764848039215615,0.8183470814393939,0.15932409444444373,0.83212119760101],"dir":"ltr"},{"str":"primitivesóbranching","boundary":[0.16461808823529342,0.8183470814393939,0.3503401186274503,0.83212119760101],"dir":"ltr"},{"str":"storing","boundary":[0.35993014705882287,0.8183470814393939,0.4178446338235287,0.83212119760101],"dir":"ltr"},{"str":"to","boundary":[0.42313864379084903,0.8183470814393939,0.4387892807189536,0.83212119760101],"dir":"ltr"},{"str":"memory","boundary":[0.4442794934640516,0.8183470814393939,0.5110353423202608,0.83212119760101],"dir":"ltr"},{"str":"comparing","boundary":[0.5194487254901954,0.8183470814393939,0.606151115032679,0.83212119760101],"dir":"ltr"},{"str":"numbers","boundary":[0.6114451307189536,0.8183470814393939,0.6840655120915026,0.83212119760101],"dir":"ltr"},{"str":"simple","boundary":[0.6938515849673196,0.8183470814393939,0.7482544823529405,0.83212119760101],"dir":"ltr"},{"str":"arithmetic","boundary":[0.7535484803921562,0.8183470814393939,0.8398408874183,0.83212119760101],"dir":"ltr"},{"str":"and","boundary":[0.850019052287581,0.8183470814393939,0.8811420728758164,0.83212119760101],"dir":"ltr"},{"str":"1","boundary":[0.13784297385620914,0.8471163122474747,0.14333218947712417,0.8546637617424242],"dir":"ltr"},{"str":"To","boundary":[0.14392140522875815,0.8475684056818182,0.1548967094771242,0.858889592550505],"dir":"ltr"},{"str":"better","boundary":[0.165484885620915,0.8475684056818182,0.20605335983660128,0.858889592550505],"dir":"ltr"},{"str":"appreciate","boundary":[0.211543545751634,0.8475684056818182,0.2826738968954249,0.858889592550505],"dir":"ltr"},{"str":"the","boundary":[0.2877718137254902,0.8475684056818182,0.30971893339869283,0.858889592550505],"dir":"ltr"},{"str":"importance","boundary":[0.3150129901960785,0.8475684056818182,0.3914323334640524,0.858889592550505],"dir":"ltr"},{"str":"of","boundary":[0.39672638888888895,0.8475684056818182,0.40887202454248367,0.858889592550505],"dir":"ltr"},{"str":"this","boundary":[0.4143621732026144,0.8475684056818182,0.440616671503268,0.858889592550505],"dir":"ltr"},{"str":"dichotomy","boundary":[0.445518545751634,0.8475684056818182,0.514885085261438,0.858889592550505],"dir":"ltr"},{"str":"between","boundary":[0.5203752450980392,0.8475684056818182,0.5764297710457517,0.858889592550505],"dir":"ltr"},{"str":"exponential","boundary":[0.5819198529411764,0.8475684056818182,0.6612840366993464,0.858889592550505],"dir":"ltr"},{"str":"and","boundary":[0.6663819444444445,0.8475684056818182,0.6920504048366014,0.858889592550505],"dir":"ltr"},{"str":"polynomial","boundary":[0.6971484477124184,0.8475684056818182,0.7722052528431372,0.858889592550505],"dir":"ltr"},{"str":"algorithms","boundary":[0.7773031862745099,0.8475684056818182,0.8509828023202615,0.858889592550505],"dir":"ltr"},{"str":"the","boundary":[0.8600016666666667,0.8475684056818182,0.8819487863398692,0.858889592550505],"dir":"ltr"},{"str":"reader","boundary":[0.1176470915032679,0.8613562844696969,0.16173179316993455,0.8726774713383838],"dir":"ltr"},{"str":"may","boundary":[0.16584937908496722,0.8613562844696969,0.19054453692810447,0.8726774713383838],"dir":"ltr"},{"str":"want","boundary":[0.1987797549019607,0.8613562844696969,0.2328815109477123,0.8726774713383838],"dir":"ltr"},{"str":"to","boundary":[0.2368031045751633,0.8613562844696969,0.24973989140522868,0.8726774713383838],"dir":"ltr"},{"str":"peek","boundary":[0.25385751633986914,0.8613562844696969,0.28540100676470576,0.8726774713383838],"dir":"ltr"},{"str":"ahead","boundary":[0.2897147058823528,0.8613562844696969,0.33086921800653585,0.8726774713383838],"dir":"ltr"},{"str":"to","boundary":[0.3347906862745097,0.8613562844696969,0.3477274731045751,0.8726774713383838],"dir":"ltr"},{"str":"the","boundary":[0.3518450980392156,0.8613562844696969,0.37240037767973844,0.8726774713383838],"dir":"ltr"},{"str":"story","boundary":[0.376517973856209,0.8613562844696969,0.4090284268300652,0.8726774713383838],"dir":"ltr"},{"str":"of","boundary":[0.413342156862745,0.8613562844696969,0.42137019287581684,0.8726774713383838],"dir":"ltr"},{"str":"Sissa","boundary":[0.42960539215686266,0.8613562844696969,0.4656467235294117,0.8726774713383838],"dir":"ltr"},{"str":"and","boundary":[0.4697643790849672,0.8613562844696969,0.4962093397058822,0.8726774713383838],"dir":"ltr"},{"str":"Moore","boundary":[0.500130882352941,0.8613562844696969,0.5414758567973854,0.8726774713383838],"dir":"ltr"},{"str":",","boundary":[0.5408875816993463,0.8613562844696969,0.5450044980065358,0.8726774713383838],"dir":"ltr"},{"str":"in","boundary":[0.5491221078431372,0.8613562844696969,0.5628353949019607,0.8726774713383838],"dir":"ltr"},{"str":"Chapter","boundary":[0.5667569117647058,0.8613562844696969,0.6224012111764705,0.8726774713383838],"dir":"ltr"},{"str":"8.","boundary":[0.6265188398692809,0.8613562844696969,0.6388695887908497,0.8726774713383838],"dir":"ltr"}],"boundary":[0.11765,0.4677,0.88195,0.87268],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":14,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/56d6f7dc53bd04d6793a4cdb69630f7f.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/3ef42ac325517483230140e7c19e30cb.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.1177,0.12201]},"elements":[{"words":[{"str":"S","boundary":[0.11764705882352941,0.08979153426128839,0.1293939594771242,0.10356565042290454],"dir":"ltr"},{"str":"Dasgupta,","boundary":[0.13800351307189543,0.08979153426128839,0.2225490380718954,0.10356565042290454],"dir":"ltr"},{"str":"C.H.","boundary":[0.22745089869281046,0.08979153426128839,0.26443845637254904,0.10356565042290454],"dir":"ltr"},{"str":"Papadimitriou,","boundary":[0.2693402777777778,0.08979153426128839,0.3932084790849673,0.10356565042290454],"dir":"ltr"},{"str":"and","boundary":[0.39771821895424836,0.08979153426128839,0.42884123954248365,0.10356565042290454],"dir":"ltr"},{"str":"U.V","boundary":[0.43374305555555553,0.08979153426128839,0.4664347251633986,0.10356565042290454],"dir":"ltr"},{"str":"Vazirani","boundary":[0.47190697712418295,0.08979153426128839,0.5419605168300654,0.10356565042290454],"dir":"ltr"},{"str":"15","boundary":[0.8617647058823529,0.09001376073232323,0.8817290718954248,0.10378787689393938],"dir":"ltr"},{"str":"so","boundary":[0.11764705882352941,0.12880163952020204,0.13467024591503268,0.1425757556818182],"dir":"ltr"},{"str":"onóand","boundary":[0.1415328431372549,0.12880163952020204,0.2102494779411765,0.1425757556818182],"dir":"ltr"},{"str":"rather","boundary":[0.21671993464052286,0.12880163952020204,0.26896596748366014,0.1425757556818182],"dir":"ltr"},{"str":"than","boundary":[0.27563251633986924,0.12880163952020204,0.31438477679738563,0.1425757556818182],"dir":"ltr"},{"str":"distinguishing","boundary":[0.3208552287581699,0.12880163952020204,0.4400175383986928,0.1425757556818182],"dir":"ltr"},{"str":"between","boundary":[0.4462919934640523,0.12880163952020204,0.5144025671568627,0.1425757556818182],"dir":"ltr"},{"str":"these","boundary":[0.5210691176470588,0.12880163952020204,0.5647055176470588,0.1425757556818182],"dir":"ltr"},{"str":"elementary","boundary":[0.571568137254902,0.12880163952020204,0.6647232950980393,0.1425757556818182],"dir":"ltr"},{"str":"operations","boundary":[0.6715859477124182,0.12880163952020204,0.7576822761437908,0.1425757556818182],"dir":"ltr"},{"str":"it","boundary":[0.7694290032679738,0.12880163952020204,0.7752758601307189,0.1425757556818182],"dir":"ltr"},{"str":"is","boundary":[0.788608905228758,0.12880163952020204,0.8024948348039215,0.1425757556818182],"dir":"ltr"},{"str":"far","boundary":[0.809161519607843,0.12880163952020204,0.8328335535947711,0.1425757556818182],"dir":"ltr"},{"str":"more","boundary":[0.8395000816993462,0.12880163952020204,0.8808013638888886,0.1425757556818182],"dir":"ltr"},{"str":"convenient","boundary":[0.11764714052287562,0.1459228516414141,0.20688072647058806,0.15969696780303025],"dir":"ltr"},{"str":"to","boundary":[0.2117825980392155,0.1459228516414141,0.22743323496732007,0.15969696780303025],"dir":"ltr"},{"str":"lump","boundary":[0.23272736928104557,0.1459228516414141,0.27540120163398674,0.15969696780303025],"dir":"ltr"},{"str":"them","boundary":[0.28010694444444423,0.1459228516414141,0.3225846982026142,0.15969696780303025],"dir":"ltr"},{"str":"together","boundary":[0.3274865196078429,0.1459228516414141,0.39597142516339845,0.15969696780303025],"dir":"ltr"},{"str":"into","boundary":[0.4014615196078429,0.1459228516414141,0.43374318643790827,0.15969696780303025],"dir":"ltr"},{"str":"one","boundary":[0.438645016339869,0.1459228516414141,0.46721901519607817,0.15969696780303025],"dir":"ltr"},{"str":"category","boundary":[0.4723170751633985,0.1459228516414141,0.5415862950980389,0.15969696780303025],"dir":"ltr"},{"str":".","boundary":[0.5394293300653592,0.1459228516414141,0.5443134696078429,0.15969696780303025],"dir":"ltr"},{"str":"But","boundary":[0.14529370915032655,0.16304406376262615,0.17602457254901938,0.1768181799242423],"dir":"ltr"},{"str":"looking","boundary":[0.18151462418300632,0.16304406376262615,0.24158597549019584,0.1768181799242423],"dir":"ltr"},{"str":"back","boundary":[0.2468799836601305,0.16304406376262615,0.279553909477124,0.1768181799242423],"dir":"ltr"},{"str":"at","boundary":[0.2905341503267972,0.16304406376262615,0.3073612588235292,0.1768181799242423],"dir":"ltr"},{"str":"our","boundary":[0.3128514705882351,0.16304406376262615,0.340445076470588,0.1768181799242423],"dir":"ltr"},{"str":"treatment","boundary":[0.345935130718954,0.16304406376262615,0.4287159483660129,0.1768181799242423],"dir":"ltr"},{"str":"of","boundary":[0.4344021241830063,0.16304406376262615,0.44907236813725465,0.1768181799242423],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.45475866013071864,0.16304406376262615,0.5332257374183004,0.1768181799242423],"dir":"ltr"},{"str":"algorithms","boundary":[0.5385197549019606,0.16304406376262615,0.6279494194444442,0.1768181799242423],"dir":"ltr"},{"str":"we","boundary":[0.6379314705882351,0.16304406376262615,0.6606409369281043,0.1768181799242423],"dir":"ltr"},{"str":"have","boundary":[0.6661311437908494,0.16304406376262615,0.7052755738562089,0.1768181799242423],"dir":"ltr"},{"str":"been","boundary":[0.7107657843137252,0.16304406376262615,0.7493219661764703,0.1768181799242423],"dir":"ltr"},{"str":"too","boundary":[0.7548120261437905,0.16304406376262615,0.7792683745098036,0.1768181799242423],"dir":"ltr"},{"str":"liberal","boundary":[0.784954673202614,0.16304406376262615,0.8385554308823525,0.1768181799242423],"dir":"ltr"},{"str":"with","boundary":[0.8438494444444441,0.16304406376262615,0.8812291547385618,0.1768181799242423],"dir":"ltr"},{"str":"what","boundary":[0.11764683006535921,0.1801652758838382,0.15934026944444418,0.19393939204545435],"dir":"ltr"},{"str":"we","boundary":[0.16483032679738535,0.1801652758838382,0.18753979313725463,0.19393939204545435],"dir":"ltr"},{"str":"consider","boundary":[0.1932259150326795,0.1801652758838382,0.2615147419934638,0.19393939204545435],"dir":"ltr"},{"str":"a","boundary":[0.26739699346405205,0.1801652758838382,0.27188902287581673,0.19393939204545435],"dir":"ltr"},{"str":"basic","boundary":[0.2828693300653592,0.1801652758838382,0.3245449441176468,0.19393939204545435],"dir":"ltr"},{"str":"step","boundary":[0.3302310947712415,0.1801652758838382,0.3642774689542481,0.19393939204545435],"dir":"ltr"},{"str":"It","boundary":[0.37720081699346375,0.1801652758838382,0.39128282516339835,0.19393939204545435],"dir":"ltr"},{"str":"is","boundary":[0.39716503267973824,0.1801652758838382,0.4055607480392153,0.19393939204545435],"dir":"ltr"},{"str":"reasonable","boundary":[0.4165411764705879,0.1801652758838382,0.5055786838235291,0.19393939204545435],"dir":"ltr"},{"str":"to","boundary":[0.5112648692810454,0.1801652758838382,0.5269155062091501,0.19393939204545435],"dir":"ltr"},{"str":"treat","boundary":[0.5326017973856206,0.1801652758838382,0.5729048612745095,0.19393939204545435],"dir":"ltr"},{"str":"addition","boundary":[0.5787870915032677,0.1801652758838382,0.647075918464052,0.19393939204545435],"dir":"ltr"},{"str":"as","boundary":[0.6527620915032677,0.1801652758838382,0.6709617501633983,0.19393939204545435],"dir":"ltr"},{"str":"a","boundary":[0.6764517973856207,0.1801652758838382,0.680747764705882,0.19393939204545435],"dir":"ltr"},{"str":"single","boundary":[0.6921201960784311,0.1801652758838382,0.7410328928104573,0.19393939204545435],"dir":"ltr"},{"str":"computer","boundary":[0.7465229738562088,0.1801652758838382,0.823635337581699,0.19393939204545435],"dir":"ltr"},{"str":"step","boundary":[0.8295175816993461,0.1801652758838382,0.8635639558823527,0.19393939204545435],"dir":"ltr"},{"str":"if","boundary":[0.869446176470588,0.1801652758838382,0.8809791629084964,0.19393939204545435],"dir":"ltr"},{"str":"small","boundary":[0.11764715686274485,0.19728648800505025,0.16304826421568602,0.21106060416666642],"dir":"ltr"},{"str":"numbers","boundary":[0.16834225490196053,0.19728648800505025,0.2409626362745096,0.21106060416666642],"dir":"ltr"},{"str":"are","boundary":[0.2464527124183004,0.19728648800505025,0.27306592532679713,0.21106060416666642],"dir":"ltr"},{"str":"being","boundary":[0.27875205882352916,0.19728648800505025,0.3237610089869279,0.21106060416666642],"dir":"ltr"},{"str":"added,","boundary":[0.32905499999999976,0.19728648800505025,0.3832618187908495,0.21106060416666642],"dir":"ltr"},{"str":"32-bit","boundary":[0.38914405228758153,0.19728648800505025,0.43746851323529395,0.21106060416666642],"dir":"ltr"},{"str":"numbers","boundary":[0.4427625163398691,0.19728648800505025,0.5153828977124182,0.21106060416666642],"dir":"ltr"},{"str":"say","boundary":[0.520872973856209,0.19728648800505025,0.5506234993464051,0.21106060416666642],"dir":"ltr"},{"str":"But","boundary":[0.5590369117647057,0.19728648800505025,0.5897677751633986,0.21106060416666642],"dir":"ltr"},{"str":"the","boundary":[0.5952578267973855,0.19728648800505025,0.6218710397058822,0.21106060416666642],"dir":"ltr"},{"str":"nth","boundary":[0.6275571732026143,0.19728648800505025,0.656131161601307,0.2167768623737371],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.6616213725490194,0.19728648800505025,0.7400884498366012,0.21106060416666642],"dir":"ltr"},{"str":"number","boundary":[0.7453824673202613,0.19728648800505025,0.8097853730392156,0.21106060416666642],"dir":"ltr"},{"str":"is","boundary":[0.8150793627450978,0.19728648800505025,0.8232791630718953,0.21106060416666642],"dir":"ltr"},{"str":"about","boundary":[0.8346514215686273,0.19728648800505025,0.8812290004901959,0.21106060416666642],"dir":"ltr"},{"str":"0","boundary":[0.11764651960784292,0.219972443181818,0.12645223104575143,0.23374655934343416],"dir":"ltr"},{"str":":","boundary":[0.126452222222222,0.219972443181818,0.13133636176470567,0.23374655934343416],"dir":"ltr"},{"str":"694n","boundary":[0.1313363562091501,0.219972443181818,0.16852001045751613,0.23374655934343416],"dir":"ltr"},{"str":"bits","boundary":[0.17479452614379062,0.2142561849747473,0.20550756421568606,0.22803030113636347],"dir":"ltr"},{"str":"long","boundary":[0.21119370915032656,0.2142561849747473,0.24622047630718932,0.22803030113636347],"dir":"ltr"},{"str":"and","boundary":[0.25679089869281024,0.2142561849747473,0.28791391928104554,0.22803030113636347],"dir":"ltr"},{"str":"this","boundary":[0.2936000490196076,0.2142561849747473,0.32529348006535924,0.22803030113636347],"dir":"ltr"},{"str":"can","boundary":[0.33097962418300636,0.2142561849747473,0.35974970163398673,0.22803030113636347],"dir":"ltr"},{"str":"far","boundary":[0.36563191176470566,0.2142561849747473,0.3893039457516338,0.22803030113636347],"dir":"ltr"},{"str":"exceed","boundary":[0.3951861601307188,0.2142561849747473,0.4491969003267972,0.22803030113636347],"dir":"ltr"},{"str":"32","boundary":[0.45547129084967297,0.219972443181818,0.47308271372549,0.23374655934343416],"dir":"ltr"},{"str":"as","boundary":[0.4789649183006534,0.2142561849747473,0.4971645769607841,0.22803030113636347],"dir":"ltr"},{"str":"n","boundary":[0.5030467810457514,0.219972443181818,0.5138132784313724,0.23374655934343416],"dir":"ltr"},{"str":"grows","boundary":[0.5194995588235292,0.2142561849747473,0.567841845098039,0.22803030113636347],"dir":"ltr"},{"str":"Arithmetic","boundary":[0.581353447712418,0.2142561849747473,0.6705870336601305,0.22803030113636347],"dir":"ltr"},{"str":"operations","boundary":[0.6764692973856207,0.2142561849747473,0.7625656258169933,0.22803030113636347],"dir":"ltr"},{"str":"on","boundary":[0.768643970588235,0.2142561849747473,0.7884122580065357,0.22803030113636347],"dir":"ltr"},{"str":"arbitrarily","boundary":[0.7942944607843134,0.2142561849747473,0.8811572782679736,0.22803030113636347],"dir":"ltr"},{"str":"large","boundary":[0.11764576797385594,0.23137739709595936,0.15951746062091476,0.2451515132575755],"dir":"ltr"},{"str":"numbers","boundary":[0.1642232189542481,0.23137739709595936,0.23684360032679713,0.2451515132575755],"dir":"ltr"},{"str":"cannot","boundary":[0.24154936274509778,0.23137739709595936,0.2969326531045749,0.2451515132575755],"dir":"ltr"},{"str":"possibly","boundary":[0.30163841503267946,0.23137739709595936,0.3679664560457514,0.2451515132575755],"dir":"ltr"},{"str":"be","boundary":[0.37267223856209125,0.23137739709595936,0.39146013300653565,0.2451515132575755],"dir":"ltr"},{"str":"performed","boundary":[0.39616586601307163,0.23137739709595936,0.4803192338235292,0.2451515132575755],"dir":"ltr"},{"str":"in","boundary":[0.48561325163398666,0.23137739709595936,0.5022442815359475,0.2451515132575755],"dir":"ltr"},{"str":"a","boundary":[0.5069501797385618,0.23137739709595936,0.512226539215686,0.2451515132575755],"dir":"ltr"},{"str":",","boundary":[0.5701587745098036,0.23137739709595936,0.5703370699346402,0.2451515132575755],"dir":"ltr"},{"str":"single","boundary":[0.5216381862745095,0.23137739709595936,0.5705508830065357,0.2451515132575755],"dir":"ltr"},{"str":"constant-time","boundary":[0.5797487581699343,0.23137739709595936,0.6932426138888885,0.2451515132575755],"dir":"ltr"},{"str":"step","boundary":[0.6981445098039213,0.23137739709595936,0.7321908839869278,0.2451515132575755],"dir":"ltr"},{"str":"We","boundary":[0.7431533660130716,0.23137739709595936,0.7635099522875813,0.2451515132575755],"dir":"ltr"},{"str":"need","boundary":[0.7733137581699343,0.23137739709595936,0.8120660186274506,0.2451515132575755],"dir":"ltr"},{"str":"to","boundary":[0.8169680065359474,0.23137739709595936,0.8326186434640519,0.2451515132575755],"dir":"ltr"},{"str":"audit","boundary":[0.8375204575163394,0.23137739709595936,0.8811568575163394,0.2451515132575755],"dir":"ltr"},{"str":"our","boundary":[0.11764627450980349,0.2484986092171714,0.14523988039215643,0.26227272537878754],"dir":"ltr"},{"str":"earlier","boundary":[0.15033794117647015,0.2484986092171714,0.2049190918300649,0.26227272537878754],"dir":"ltr"},{"str":"running","boundary":[0.20982094771241785,0.2484986092171714,0.2767550498366009,0.26227272537878754],"dir":"ltr"},{"str":"time","boundary":[0.28146081699346365,0.2484986092171714,0.31864444869281,0.26227272537878754],"dir":"ltr"},{"str":"estimates","boundary":[0.3235462745098035,0.2484986092171714,0.40279767745098,0.26227272537878754],"dir":"ltr"},{"str":"and","boundary":[0.4078956209150323,0.2484986092171714,0.4390186415032676,0.26227272537878754],"dir":"ltr"},{"str":"make","boundary":[0.44392045751633946,0.2484986092171714,0.4891433116013068,0.26227272537878754],"dir":"ltr"},{"str":"them","boundary":[0.49404513071895384,0.2484986092171714,0.5365228844771238,0.26227272537878754],"dir":"ltr"},{"str":"more","boundary":[0.5414247058823526,0.2484986092171714,0.582725988071895,0.26227272537878754],"dir":"ltr"},{"str":"honest.","boundary":[0.5880199673202611,0.2484986092171714,0.6475030828431368,0.26227272537878754],"dir":"ltr"},{"str":"We","boundary":[0.14529284313725452,0.26561982133838347,0.16604156993464014,0.27939393749999963],"dir":"ltr"},{"str":"will","boundary":[0.17506109477124146,0.26561982133838347,0.2059702114379081,0.27939393749999963],"dir":"ltr"},{"str":"see","boundary":[0.21008789215686238,0.26561982133838347,0.23591679068627416,0.27939393749999963],"dir":"ltr"},{"str":"in","boundary":[0.24042645424836562,0.26561982133838347,0.2570574841503264,0.27939393749999963],"dir":"ltr"},{"str":"Chapter","boundary":[0.26137122549019565,0.26561982133838347,0.3288935633986924,0.27939393749999963],"dir":"ltr"},{"str":"1","boundary":[0.33320717320261395,0.26561982133838347,0.33887567320261397,0.27939393749999963],"dir":"ltr"},{"str":"that","boundary":[0.3475030392156858,0.26561982133838347,0.38213764918300613,0.27939393749999963],"dir":"ltr"},{"str":"the","boundary":[0.3864514052287577,0.26561982133838347,0.4130646181372545,0.27939393749999963],"dir":"ltr"},{"str":"addition","boundary":[0.41757428104575117,0.26561982133838347,0.4858631080065355,0.27939393749999963],"dir":"ltr"},{"str":"of","boundary":[0.4901767320261433,0.26561982133838347,0.5003371545751629,0.27939393749999963],"dir":"ltr"},{"str":"two","boundary":[0.5093567973856205,0.26561982133838347,0.5389111892156858,0.27939393749999963],"dir":"ltr"},{"str":"n-bit","boundary":[0.5434208496732021,0.26561982133838347,0.5825474315359471,0.2851101957070703],"dir":"ltr"},{"str":"numbers","boundary":[0.5866649509803917,0.26561982133838347,0.6592853323529407,0.27939393749999963],"dir":"ltr"},{"str":"takes","boundary":[0.6635989379084962,0.26561982133838347,0.7080196522875812,0.27939393749999963],"dir":"ltr"},{"str":"time","boundary":[0.7125294934640518,0.26561982133838347,0.7497131251633982,0.27939393749999963],"dir":"ltr"},{"str":"roughly","boundary":[0.7542227941176466,0.26561982133838347,0.8176274815359472,0.27939393749999963],"dir":"ltr"},{"str":"propor","boundary":[0.8217450163398687,0.26561982133838347,0.8753635993464048,0.27939393749999963],"dir":"ltr"},{"str":"-","boundary":[0.8747752450980388,0.26561982133838347,0.8806397776143786,0.27939393749999963],"dir":"ltr"},{"str":"tional","boundary":[0.11764616013071853,0.2827410334595955,0.16557846388888847,0.29651514962121167],"dir":"ltr"},{"str":"to","boundary":[0.1704803104575159,0.2827410334595955,0.18613094738562047,0.29651514962121167],"dir":"ltr"},{"str":"n","boundary":[0.19142508169934597,0.2884572916666662,0.2021915790849669,0.3022314078282824],"dir":"ltr"},{"str":"this","boundary":[0.21236980392156818,0.2827410334595955,0.24406323496731983,0.29651514962121167],"dir":"ltr"},{"str":"is","boundary":[0.24896506535947668,0.2827410334595955,0.2577529375816989,0.29651514962121167],"dir":"ltr"},{"str":"not","boundary":[0.26794905228758126,0.2827410334595955,0.294562265196078,0.29651514962121167],"dir":"ltr"},{"str":"too","boundary":[0.29985624183006493,0.2827410334595955,0.32431259019607794,0.29651514962121167],"dir":"ltr"},{"str":"hard","boundary":[0.3296067320261433,0.2827410334595955,0.36855507107843094,0.29651514962121167],"dir":"ltr"},{"str":"to","boundary":[0.3736529738562087,0.2827410334595955,0.38930361078431325,0.29651514962121167],"dir":"ltr"},{"str":"understand","boundary":[0.39459774509803874,0.2827410334595955,0.4895176102941172,0.29651514962121167],"dir":"ltr"},{"str":"if","boundary":[0.4946155555555551,0.2827410334595955,0.5010504826797381,0.29651514962121167],"dir":"ltr"},{"str":"you","boundary":[0.5112466013071891,0.2827410334595955,0.5406049145424832,0.29651514962121167],"dir":"ltr"},{"str":"think","boundary":[0.5457029738562087,0.2827410334595955,0.5907119240196074,0.29651514962121167],"dir":"ltr"},{"str":"back","boundary":[0.5956137581699341,0.2827410334595955,0.6286798245098034,0.29651514962121167],"dir":"ltr"},{"str":"to","boundary":[0.6388757843137249,0.2827410334595955,0.6545264212418296,0.29651514962121167],"dir":"ltr"},{"str":"the","boundary":[0.659820555555555,0.2827410334595955,0.6864337684640518,0.29651514962121167],"dir":"ltr"},{"str":"grade-school","boundary":[0.691531830065359,0.2827410334595955,0.7938669299019603,0.29651514962121167],"dir":"ltr"},{"str":"procedure","boundary":[0.7993571568627446,0.2827410334595955,0.8805693457516335,0.29651514962121167],"dir":"ltr"},{"str":"for","boundary":[0.11764637254901911,0.29986237184343395,0.14014193496731978,0.3136364880050501],"dir":"ltr"},{"str":"addition,","boundary":[0.1468084640522871,0.29986237184343395,0.21998143055555505,0.3136364880050501],"dir":"ltr"},{"str":"which","boundary":[0.22684408496731978,0.29986237184343395,0.269696034313725,0.3136364880050501],"dir":"ltr"},{"str":"works","boundary":[0.2822450653594767,0.29986237184343395,0.33156774460784266,0.3136364880050501],"dir":"ltr"},{"str":"on","boundary":[0.33823428104575115,0.29986237184343395,0.3580025684640518,0.3136364880050501],"dir":"ltr"},{"str":"one","boundary":[0.3644731699346401,0.29986237184343395,0.3930471687908492,0.3136364880050501],"dir":"ltr"},{"str":"digit","boundary":[0.39971369281045704,0.29986237184343395,0.437663813562091,0.3136364880050501],"dir":"ltr"},{"str":"at","boundary":[0.4441342810457512,0.29986237184343395,0.4609613895424832,0.3136364880050501],"dir":"ltr"},{"str":"a","boundary":[0.4674319934640518,0.29986237184343395,0.47113970915032627,0.3136364880050501],"dir":"ltr"},{"str":"time","boundary":[0.4836886437908492,0.29986237184343395,0.5208722754901955,0.3136364880050501],"dir":"ltr"},{"str":"Thus","boundary":[0.5363446568627446,0.29986237184343395,0.578430253431372,0.3136364880050501],"dir":"ltr"},{"str":"which","boundary":[0.6391251633986922,0.29986237184343395,0.6817811977124176,0.3136364880050501],"dir":"ltr"},{"str":"performs","boundary":[0.6947220588235288,0.29986237184343395,0.7681089292483654,0.3136364880050501],"dir":"ltr"},{"str":"about","boundary":[0.7749715686274503,0.29986237184343395,0.821549147549019,0.3136364880050501],"dir":"ltr"},{"str":"F","boundary":[0.8278236928104569,0.3055786300505046,0.8391784259803915,0.3193527462121208],"dir":"ltr"},{"str":"ad-","boundary":[0.8562734967320255,0.29986237184343395,0.8822984738562084,0.3136364880050501],"dir":"ltr"},{"str":"fib1","boundary":[0.584704624183006,0.3090221590909087,0.6274854084967315,0.3227962752525248],"dir":"ltr"},{"str":"n","boundary":[0.8403911928104568,0.3104829513888885,0.8488171097549013,0.3205462215909087],"dir":"ltr"},{"str":"ditions","boundary":[0.11764604575163329,0.316983583964646,0.17399190375816923,0.33075770012626216],"dir":"ltr"},{"str":"actually","boundary":[0.186719052287581,0.316983583964646,0.25324317189542417,0.33075770012626216],"dir":"ltr"},{"str":"uses","boundary":[0.260694052287581,0.316983583964646,0.2968972910130712,0.33075770012626216],"dir":"ltr"},{"str":"a","boundary":[0.3045442156862738,0.316983583964646,0.3070754117647052,0.33075770012626216],"dir":"ltr"},{"str":"number","boundary":[0.3219773856209144,0.316983583964646,0.3863802913398687,0.33075770012626216],"dir":"ltr"},{"str":"of","boundary":[0.39402722222222153,0.316983583964646,0.4086974661764699,0.33075770012626216],"dir":"ltr"},{"str":"basic","boundary":[0.41634454248365943,0.316983583964646,0.4580201565359471,0.33075770012626216],"dir":"ltr"},{"str":"steps","boundary":[0.46586316993463983,0.316983583964646,0.5057740766339862,0.33075770012626216],"dir":"ltr"},{"str":"roughly","boundary":[0.5136170915032673,0.316983583964646,0.5770217789215679,0.33075770012626216],"dir":"ltr"},{"str":"proportional","boundary":[0.5844726470588228,0.316983583964646,0.6860235338235288,0.33075770012626216],"dir":"ltr"},{"str":"to","boundary":[0.6940626797385614,0.316983583964646,0.709713316666666,0.33075770012626216],"dir":"ltr"},{"str":"Likewise","boundary":[0.7690006535947705,0.316983583964646,0.8425836026143785,0.33075770012626216],"dir":"ltr"},{"str":"the","boundary":[0.8555068954248358,0.316983583964646,0.8821201083333325,0.33075770012626216],"dir":"ltr"},{"str":"nF","boundary":[0.717360392156862,0.3226998421717167,0.7394816227124176,0.3364739583333329],"dir":"ltr"},{"str":"n","boundary":[0.7405871895424829,0.3276041635101006,0.7490131064869274,0.3376674337121207],"dir":"ltr"},{"str":"number","boundary":[0.11764578431372462,0.3341047960858581,0.18204869003267887,0.34787891224747425],"dir":"ltr"},{"str":"of","boundary":[0.18793091503267886,0.3341047960858581,0.20260115898692724,0.34787891224747425],"dir":"ltr"},{"str":"steps","boundary":[0.20887568627450895,0.3341047960858581,0.2511395361111103,0.34787891224747425],"dir":"ltr"},{"str":"taken","boundary":[0.2574139215686266,0.3341047960858581,0.30457973627450896,0.34787891224747425],"dir":"ltr"},{"str":"by","boundary":[0.3106580392156854,0.3341047960858581,0.3302302480392148,0.34787891224747425],"dir":"ltr"},{"str":"is","boundary":[0.38486457516339784,0.3341047960858581,0.3987505047385612,0.34787891224747425],"dir":"ltr"},{"str":"proportional","boundary":[0.4048289542483651,0.3341047960858581,0.5063798410130711,0.34787891224747425],"dir":"ltr"},{"str":"to","boundary":[0.5126542810457508,0.3341047960858581,0.5283049179738554,0.34787891224747425],"dir":"ltr"},{"str":"n","boundary":[0.5345794444444436,0.33982105429292875,0.5453459418300646,0.3535951704545449],"dir":"ltr"},{"str":"2","boundary":[0.5460770751633979,0.3376041761363631,0.55292720238562,0.34766744633838326],"dir":"ltr"},{"str":"still","boundary":[0.5648827614379076,0.3341047960858581,0.5969505243464043,0.34787891224747425],"dir":"ltr"},{"str":"polynomial","boundary":[0.6028327614379075,0.3341047960858581,0.6940271333333324,0.34787891224747425],"dir":"ltr"},{"str":"in","boundary":[0.6999093954248358,0.3341047960858581,0.7165404253267965,0.34787891224747425],"dir":"ltr"},{"str":"n","boundary":[0.7224227941176462,0.33982105429292875,0.7331892915032672,0.3535951704545449],"dir":"ltr"},{"str":"and","boundary":[0.739267728758169,0.3341047960858581,0.7703907493464044,0.34787891224747425],"dir":"ltr"},{"str":"therefore","boundary":[0.7762729575163391,0.3341047960858581,0.8508184741830057,0.34787891224747425],"dir":"ltr"},{"str":"ex-","boundary":[0.8572889705882345,0.3341047960858581,0.8815492403594763,0.34787891224747425],"dir":"ltr"},{"str":"fib2","boundary":[0.33611245098039133,0.3432645833333328,0.3788932352941168,0.357038699494949],"dir":"ltr"},{"str":"ponentially","boundary":[0.11764517973856135,0.3512260082070702,0.21078251225490127,0.3650001243686864],"dir":"ltr"},{"str":"superior","boundary":[0.21588047385620843,0.3512260082070702,0.28416930081699276,0.3650001243686864],"dir":"ltr"},{"str":"to","boundary":[0.2896593954248359,0.3512260082070702,0.30531003235294046,0.3650001243686864],"dir":"ltr"},{"str":"This","boundary":[0.36541684640522804,0.3512260082070702,0.402208320915032,0.3650001243686864],"dir":"ltr"},{"str":"correction","boundary":[0.4073063888888882,0.3512260082070702,0.4885007524509797,0.3650001243686864],"dir":"ltr"},{"str":"to","boundary":[0.4941869444444438,0.3512260082070702,0.5098375813725484,0.3650001243686864],"dir":"ltr"},{"str":"the","boundary":[0.5153277941176464,0.3512260082070702,0.5419410070261431,0.3650001243686864],"dir":"ltr"},{"str":"running","boundary":[0.54723498366013,0.3512260082070702,0.6141690857843131,0.3650001243686864],"dir":"ltr"},{"str":"time","boundary":[0.6190709313725483,0.3512260082070702,0.6562545630718947,0.3650001243686864],"dir":"ltr"},{"str":"analysis","boundary":[0.6615485457516334,0.3512260082070702,0.7298373727124177,0.3650001243686864],"dir":"ltr"},{"str":"does","boundary":[0.7347392320261431,0.3512260082070702,0.7707463921568621,0.3650001243686864],"dir":"ltr"},{"str":"not","boundary":[0.7762366176470582,0.3512260082070702,0.8028498305555549,0.3650001243686864],"dir":"ltr"},{"str":"diminish","boundary":[0.8081438071895418,0.3512260082070702,0.8813345990196072,0.3650001243686864],"dir":"ltr"},{"str":"fib1","boundary":[0.31060416666666596,0.3603857954545449,0.3533849509803914,0.37415991161616113],"dir":"ltr"},{"str":"our","boundary":[0.11764544117646994,0.3683472203282823,0.14523904705882287,0.3821213364898985],"dir":"ltr"},{"str":"breakthrough.","boundary":[0.1503371078431366,0.3683472203282823,0.2683407712418294,0.3821213364898985],"dir":"ltr"},{"str":"But","boundary":[0.14529256535947646,0.38546855871212066,0.17543519297385557,0.3992426748737369],"dir":"ltr"},{"str":"can","boundary":[0.1803370098039209,0.38546855871212066,0.20930316584967254,0.3992426748737369],"dir":"ltr"},{"str":"we","boundary":[0.21420498366013005,0.38546855871212066,0.23593405702614312,0.3992426748737369],"dir":"ltr"},{"str":"do","boundary":[0.24083586601307125,0.38546855871212066,0.2606041534313719,0.3992426748737369],"dir":"ltr"},{"str":"even","boundary":[0.26570220588235227,0.38546855871212066,0.30151328741829997,0.3992426748737369],"dir":"ltr"},{"str":"better","boundary":[0.3064151143790843,0.38546855871212066,0.35238663218954186,0.3992426748737369],"dir":"ltr"},{"str":"than","boundary":[0.35748455882352875,0.38546855871212066,0.3958446620915026,0.3992426748737369],"dir":"ltr"},{"str":"?","boundary":[0.4438123366013066,0.38546855871212066,0.45163765506535886,0.3992426748737369],"dir":"ltr"},{"str":"Indeed","boundary":[0.4575199509803916,0.38546855871212066,0.5136875557189537,0.3992426748737369],"dir":"ltr"},{"str":"we","boundary":[0.5187854738562087,0.38546855871212066,0.5414949401960779,0.3992426748737369],"dir":"ltr"},{"str":"can:","boundary":[0.5463967483660125,0.38546855871212066,0.5800509653594766,0.3992426748737369],"dir":"ltr"},{"str":"see","boundary":[0.5861294281045746,0.38546855871212066,0.6119583266339864,0.3992426748737369],"dir":"ltr"},{"str":"Exercise","boundary":[0.6170562254901956,0.38546855871212066,0.6867176026143786,0.3992426748737369],"dir":"ltr"},{"str":"0.4.","boundary":[0.6918155392156857,0.38546855871212066,0.7215481843137249,0.3992426748737369],"dir":"ltr"},{"str":"fib2","boundary":[0.40074648692810394,0.3946283459595954,0.44352727124182945,0.4084024621212116],"dir":"ltr"},{"str":"0.3","boundary":[0.11764560457516289,0.41920387247474694,0.1511669542483655,0.4373177613636358],"dir":"ltr"},{"str":"Big-O","boundary":[0.17450034313725438,0.41920387247474694,0.24091026601307136,0.44574071969696916],"dir":"ltr"},{"str":"notation","boundary":[0.24836129084967268,0.41920387247474694,0.3519727352941171,0.4373177613636358],"dir":"ltr"},{"str":"We've","boundary":[0.11764576797385569,0.4594078263888884,0.16500766241830014,0.4731819425505046],"dir":"ltr"},{"str":"just","boundary":[0.1704977287581694,0.4594078263888884,0.20179900261437858,0.4731819425505046],"dir":"ltr"},{"str":"seen","boundary":[0.207485147058823,0.4594078263888884,0.24427662156862692,0.4731819425505046],"dir":"ltr"},{"str":"how","boundary":[0.24996276143790797,0.4594078263888884,0.2836348037581694,0.4731819425505046],"dir":"ltr"},{"str":"sloppiness","boundary":[0.2891248529411759,0.4594078263888884,0.374044709803921,0.4731819425505046],"dir":"ltr"},{"str":"in","boundary":[0.3797308986928099,0.4594078263888884,0.3963619285947707,0.4731819425505046],"dir":"ltr"},{"str":"the","boundary":[0.4018521405228752,0.4594078263888884,0.42846535343137193,0.4731819425505046],"dir":"ltr"},{"str":"analysis","boundary":[0.4339554084967315,0.4594078263888884,0.5022442354575158,0.4731819425505046],"dir":"ltr"},{"str":"of","boundary":[0.5075382516339864,0.4594078263888884,0.5222084955882347,0.4731819425505046],"dir":"ltr"},{"str":"running","boundary":[0.5278947875816987,0.4594078263888884,0.5948288897058818,0.4731819425505046],"dir":"ltr"},{"str":"times","boundary":[0.6001228921568621,0.4594078263888884,0.6455239995098033,0.4731819425505046],"dir":"ltr"},{"str":"can","boundary":[0.6510140686274504,0.4594078263888884,0.6797841460784307,0.4731819425505046],"dir":"ltr"},{"str":"lead","boundary":[0.6852741993464045,0.4594078263888884,0.7199088093137248,0.4731819425505046],"dir":"ltr"},{"str":"to","boundary":[0.7255951143790843,0.4594078263888884,0.741245751307189,0.4731819425505046],"dir":"ltr"},{"str":"an","boundary":[0.7469320424836595,0.4594078263888884,0.7678768014705876,0.4731819425505046],"dir":"ltr"},{"str":"unacceptable","boundary":[0.7731709313725483,0.4594078263888884,0.880996333169934,0.4731819425505046],"dir":"ltr"},{"str":"level","boundary":[0.11764642156862683,0.47652903851010053,0.15618477810457454,0.4903031546717167],"dir":"ltr"},{"str":"of","boundary":[0.1618709313725484,0.47652903851010053,0.17654117532679675,0.4903031546717167],"dir":"ltr"},{"str":"inaccuracy","boundary":[0.18261962418300592,0.47652903851010053,0.2710688957516334,0.4903031546717167],"dir":"ltr"},{"str":"in","boundary":[0.2765590032679732,0.47652903851010053,0.29319003316993403,0.4903031546717167],"dir":"ltr"},{"str":"the","boundary":[0.2988763235294111,0.47652903851010053,0.3254895364379079,0.4903031546717167],"dir":"ltr"},{"str":"result.","boundary":[0.3311756699346399,0.47652903851010053,0.38438427042483597,0.4903031546717167],"dir":"ltr"},{"str":"But","boundary":[0.39320769607843076,0.47652903851010053,0.4239385594771236,0.4903031546717167],"dir":"ltr"},{"str":"the","boundary":[0.42962468954248306,0.47652903851010053,0.4562379024509798,0.4903031546717167],"dir":"ltr"},{"str":"opposite","boundary":[0.46212011437908435,0.47652903851010053,0.5296246269607837,0.4903031546717167],"dir":"ltr"},{"str":"danger","boundary":[0.5357029575163392,0.47652903851010053,0.5930470338235287,0.4903031546717167],"dir":"ltr"},{"str":"is","boundary":[0.5987331862745091,0.47652903851010053,0.6069329866013066,0.4903031546717167],"dir":"ltr"},{"str":"also","boundary":[0.6183052450980385,0.47652903851010053,0.6509790691176464,0.4903031546717167],"dir":"ltr"},{"str":"present:","boundary":[0.6566652124183,0.47652903851010053,0.7231893320261431,0.4903031546717167],"dir":"ltr"},{"str":"it","boundary":[0.7314245261437902,0.47652903851010053,0.738251775163398,0.4903031546717167],"dir":"ltr"},{"str":"is","boundary":[0.7496240359477118,0.47652903851010053,0.7578236728758163,0.4903031546717167],"dir":"ltr"},{"str":"possible","boundary":[0.769196258169934,0.47652903851010053,0.834739984803921,0.4903031546717167],"dir":"ltr"},{"str":"to","boundary":[0.8406222385620908,0.47652903851010053,0.8562728754901954,0.4903031546717167],"dir":"ltr"},{"str":"be","boundary":[0.8621552450980384,0.47652903851010053,0.8809431395424829,0.4903031546717167],"dir":"ltr"},{"str":"too","boundary":[0.11764544117646984,0.4936502506313126,0.14151355375816918,0.5074243667929288],"dir":"ltr"},{"str":"precise","boundary":[0.14661145424836527,0.4936502506313126,0.20393770522875743,0.5074243667929288],"dir":"ltr"},{"str":"An","boundary":[0.21509620915032607,0.4936502506313126,0.23898214705882276,0.5074243667929288],"dir":"ltr"},{"str":"insightful","boundary":[0.24368787581699272,0.4936502506313126,0.32409792499999923,0.5074243667929288],"dir":"ltr"},{"str":"analysis","boundary":[0.3286076470588228,0.4936502506313126,0.3968964740196071,0.5074243667929288],"dir":"ltr"},{"str":"is","boundary":[0.40160225490196,0.4936502506313126,0.4105863689542476,0.5074243667929288],"dir":"ltr"},{"str":"based","boundary":[0.42038999999999926,0.4936502506313126,0.46755581470588164,0.5074243667929288],"dir":"ltr"},{"str":"on","boundary":[0.4724576470588228,0.4936502506313126,0.49222593447712354,0.5074243667929288],"dir":"ltr"},{"str":"the","boundary":[0.4971277450980385,0.4936502506313126,0.5237409580065352,0.5074243667929288],"dir":"ltr"},{"str":"right","boundary":[0.5288390196078424,0.4936502506313126,0.5697303192810451,0.5074243667929288],"dir":"ltr"},{"str":"simpli\u0002cations","boundary":[0.5746321568627444,0.4936502506313126,0.695167016666666,0.5074243667929288],"dir":"ltr"},{"str":".","boundary":[0.6947746405228751,0.4936502506313126,0.6996587800653588,0.5074243667929288],"dir":"ltr"},{"str":"Expressing","boundary":[0.14529261437908425,0.5106199476010096,0.23727130065359403,0.5243940637626258],"dir":"ltr"},{"str":"running","boundary":[0.24158493464052216,0.5106199476010096,0.30851903676470516,0.5243940637626258],"dir":"ltr"},{"str":"time","boundary":[0.3124404901960777,0.5106199476010096,0.3496241218954241,0.5243940637626258],"dir":"ltr"},{"str":"in","boundary":[0.35413379084967245,0.5106199476010096,0.37076482075163325,0.5243940637626258],"dir":"ltr"},{"str":"terms","boundary":[0.37488248366013,0.5106199476010096,0.4224404555555549,0.5243940637626258],"dir":"ltr"},{"str":"of","boundary":[0.4269501307189536,0.5106199476010096,0.4416203746732019,0.5243940637626258],"dir":"ltr"},{"str":"basic","boundary":[0.44613019607843074,0.5106199476010096,0.4878058101307183,0.5243940637626258],"dir":"ltr"},{"str":"computer","boundary":[0.4923154901960778,0.5106199476010096,0.567859225163398,0.5243940637626258],"dir":"ltr"},{"str":"steps","boundary":[0.5723689215686268,0.5106199476010096,0.6122798282679732,0.5243940637626258],"dir":"ltr"},{"str":"is","boundary":[0.6169855882352935,0.5106199476010096,0.626557774183006,0.5243940637626258],"dir":"ltr"},{"str":"already","boundary":[0.6351852614379079,0.5106199476010096,0.6972173986928099,0.5243940637626258],"dir":"ltr"},{"str":"a","boundary":[0.7013349346405223,0.5106199476010096,0.7070033529411759,0.5243940637626258],"dir":"ltr"},{"str":"simpli\u0002cation.","boundary":[0.7156308823529406,0.5106199476010096,0.832832406045751,0.5243940637626258],"dir":"ltr"},{"str":"After","boundary":[0.8385184640522871,0.5106199476010096,0.8807823138888884,0.5243940637626258],"dir":"ltr"},{"str":"all,","boundary":[0.11764591503267928,0.5277411597222217,0.14384914542483615,0.541515275883838],"dir":"ltr"},{"str":"the","boundary":[0.14835882352941132,0.5277411597222217,0.17497203643790804,0.541515275883838],"dir":"ltr"},{"str":"time","boundary":[0.1794816993464048,0.5277411597222217,0.21666533104575117,0.541515275883838],"dir":"ltr"},{"str":"taken","boundary":[0.2213710784313721,0.5277411597222217,0.2685368931372545,0.541515275883838],"dir":"ltr"},{"str":"by","boundary":[0.272850490196078,0.5277411597222217,0.2924226990196074,0.541515275883838],"dir":"ltr"},{"str":"one","boundary":[0.2969325163398689,0.5277411597222217,0.325506515196078,0.541515275883838],"dir":"ltr"},{"str":"such","boundary":[0.3302122549019604,0.5277411597222217,0.36347438398692766,0.541515275883838],"dir":"ltr"},{"str":"step","boundary":[0.3724939052287577,0.5277411597222217,0.4065402794117643,0.541515275883838],"dir":"ltr"},{"str":"depends","boundary":[0.41124602941176425,0.5277411597222217,0.4785722887254897,0.541515275883838],"dir":"ltr"},{"str":"crucially","boundary":[0.4832780555555551,0.5277411597222217,0.5542941575163394,0.541515275883838],"dir":"ltr"},{"str":"on","boundary":[0.5586077941176465,0.5277411597222217,0.5783760815359472,0.541515275883838],"dir":"ltr"},{"str":"the","boundary":[0.5828858986928099,0.5277411597222217,0.6094991116013067,0.541515275883838],"dir":"ltr"},{"str":"particular","boundary":[0.6142048529411759,0.5277411597222217,0.6969678452614374,0.541515275883838],"dir":"ltr"},{"str":"processor","boundary":[0.7012814869281041,0.5277411597222217,0.7777877895424832,0.541515275883838],"dir":"ltr"},{"str":"and","boundary":[0.7828857352941171,0.5277411597222217,0.8140087558823524,0.541515275883838],"dir":"ltr"},{"str":"even","boundary":[0.8185184150326793,0.5277411597222217,0.8566824397058818,0.541515275883838],"dir":"ltr"},{"str":"on","boundary":[0.8611921078431367,0.5277411597222217,0.8809603952614373,0.541515275883838],"dir":"ltr"},{"str":"details","boundary":[0.11764635620914977,0.5448623718434339,0.1730118212418295,0.5586364880050501],"dir":"ltr"},{"str":"such","boundary":[0.17810975490196024,0.5448623718434339,0.21078363235294062,0.5586364880050501],"dir":"ltr"},{"str":"as","boundary":[0.22097965686274457,0.5448623718434339,0.23917931552287527,0.5586364880050501],"dir":"ltr"},{"str":"caching","boundary":[0.24427736928104518,0.5448623718434339,0.3068977656862739,0.5586364880050501],"dir":"ltr"},{"str":"strategy","boundary":[0.31199566993463995,0.5448623718434339,0.37969626111111054,0.5586364880050501],"dir":"ltr"},{"str":"(as","boundary":[0.3849902777777772,0.5448623718434339,0.4090544689542478,0.5586364880050501],"dir":"ltr"},{"str":"a","boundary":[0.41415253267973795,0.5448623718434339,0.4190367026143785,0.5586364880050501],"dir":"ltr"},{"str":"result","boundary":[0.42923272875816937,0.5448623718434339,0.4775571897058818,0.5586364880050501],"dir":"ltr"},{"str":"of","boundary":[0.48285119281045696,0.5448623718434339,0.49752143676470534,0.5586364880050501],"dir":"ltr"},{"str":"which","boundary":[0.5028155718954244,0.5448623718434339,0.5470401356209145,0.5586364880050501],"dir":"ltr"},{"str":"the","boundary":[0.5568439379084962,0.5448623718434339,0.583457150816993,0.5586364880050501],"dir":"ltr"},{"str":"running","boundary":[0.5887511274509799,0.5448623718434339,0.655685229575163,0.5586364880050501],"dir":"ltr"},{"str":"time","boundary":[0.6603909967320256,0.5448623718434339,0.697574628431372,0.5586364880050501],"dir":"ltr"},{"str":"can","boundary":[0.7028686111111105,0.5448623718434339,0.731638688562091,0.5586364880050501],"dir":"ltr"},{"str":"differ","boundary":[0.7365405065359472,0.5448623718434339,0.7807473169934636,0.5586364880050501],"dir":"ltr"},{"str":"subtly","boundary":[0.7862375653594765,0.5448623718434339,0.8375032052287577,0.5586364880050501],"dir":"ltr"},{"str":"from","boundary":[0.8424050490196072,0.5448623718434339,0.880765152287581,0.5586364880050501],"dir":"ltr"},{"str":"one","boundary":[0.11764687908496665,0.561983583964646,0.1462208779411758,0.5757577001262622],"dir":"ltr"},{"str":"execution","boundary":[0.15131893790849607,0.561983583964646,0.22958994787581635,0.5757577001262622],"dir":"ltr"},{"str":"to","boundary":[0.2346878921568621,0.561983583964646,0.2503385290849666,0.5757577001262622],"dir":"ltr"},{"str":"the","boundary":[0.2554365849673196,0.561983583964646,0.2820497978758163,0.5757577001262622],"dir":"ltr"},{"str":"next).","boundary":[0.28714785947712346,0.561983583964646,0.3340997702614372,0.5757577001262622],"dir":"ltr"},{"str":"Accounting","boundary":[0.3405702450980385,0.561983583964646,0.43294108856209085,0.5757577001262622],"dir":"ltr"},{"str":"for","boundary":[0.43764687908496663,0.561983583964646,0.4601424415032673,0.5757577001262622],"dir":"ltr"},{"str":"these","boundary":[0.46543658496731954,0.561983583964646,0.5090729849673196,0.5757577001262622],"dir":"ltr"},{"str":"architecture-speci\u0002c","boundary":[0.5141708986928097,0.561983583964646,0.6795008281045744,0.5757577001262622],"dir":"ltr"},{"str":"minutiae","boundary":[0.6849908333333325,0.561983583964646,0.7597502539215678,0.5757577001262622],"dir":"ltr"},{"str":"is","boundary":[0.7644560294117639,0.561983583964646,0.7734401434640514,0.5757577001262622],"dir":"ltr"},{"str":"a","boundary":[0.7832437745098032,0.561983583964646,0.7883240228758163,0.5757577001262622],"dir":"ltr"},{"str":"nightmar","boundary":[0.798127892156862,0.561983583964646,0.8758284916666659,0.5757577001262622],"dir":"ltr"},{"str":"-","boundary":[0.8752401470588228,0.561983583964646,0.8811046795751626,0.5757577001262622],"dir":"ltr"},{"str":"ishly","boundary":[0.11764700980392086,0.5791047960858581,0.1577539950980385,0.5928789122474742],"dir":"ltr"},{"str":"complex","boundary":[0.16206759803921497,0.5791047960858581,0.22880562156862674,0.5928789122474742],"dir":"ltr"},{"str":"task","boundary":[0.23351138888888817,0.5791047960858581,0.26912639183006465,0.5928789122474742],"dir":"ltr"},{"str":"and","boundary":[0.27363606209150254,0.5791047960858581,0.30475908267973784,0.5928789122474742],"dir":"ltr"},{"str":"yields","boundary":[0.30926890522875744,0.5791047960858581,0.35739728758169864,0.5928789122474742],"dir":"ltr"},{"str":"a","boundary":[0.3619069771241823,0.5791047960858581,0.3673793986928097,0.5928789122474742],"dir":"ltr"},{"str":"result","boundary":[0.3763989215686267,0.5791047960858581,0.4247233825163391,0.5928789122474742],"dir":"ltr"},{"str":"that","boundary":[0.4294291503267967,0.5791047960858581,0.46406376029411694,0.5928789122474742],"dir":"ltr"},{"str":"does","boundary":[0.4685734313725483,0.5791047960858581,0.5045805915032673,0.5928789122474742],"dir":"ltr"},{"str":"not","boundary":[0.5092863398692803,0.5791047960858581,0.535899552777777,0.5928789122474742],"dir":"ltr"},{"str":"generalize","boundary":[0.5406052941176464,0.5791047960858581,0.6253290723856202,0.5928789122474742],"dir":"ltr"},{"str":"from","boundary":[0.6298387908496724,0.5791047960858581,0.6681988941176463,0.5928789122474742],"dir":"ltr"},{"str":"one","boundary":[0.672904640522875,0.5791047960858581,0.7014786393790842,0.5928789122474742],"dir":"ltr"},{"str":"computer","boundary":[0.7061843790849666,0.5791047960858581,0.7832967428104568,0.5928789122474742],"dir":"ltr"},{"str":"to","boundary":[0.7881985947712411,0.5791047960858581,0.8038492316993457,0.5928789122474742],"dir":"ltr"},{"str":"the","boundary":[0.8085549673202607,0.5791047960858581,0.8351681802287575,0.5928789122474742],"dir":"ltr"},{"str":"next.","boundary":[0.8398740849673194,0.5791047960858581,0.8809614632352932,0.5928789122474742],"dir":"ltr"},{"str":"It","boundary":[0.11764696078431296,0.5962260082070703,0.12682715359477048,0.6100001243686864],"dir":"ltr"},{"str":"therefore","boundary":[0.13663078431372472,0.5962260082070703,0.21117630098039136,0.6100001243686864],"dir":"ltr"},{"str":"makes","boundary":[0.21647032679738482,0.5962260082070703,0.2699106565359469,0.6100001243686864],"dir":"ltr"},{"str":"more","boundary":[0.27461640522875735,0.5962260082070703,0.31591768741829984,0.6100001243686864],"dir":"ltr"},{"str":"sense","boundary":[0.32081950980392077,0.5962260082070703,0.36582845996731944,0.6100001243686864],"dir":"ltr"},{"str":"to","boundary":[0.37073029411764624,0.5962260082070703,0.3863809310457508,0.6100001243686864],"dir":"ltr"},{"str":"seek","boundary":[0.3914789869281038,0.5962260082070703,0.4278783042483652,0.6100001243686864],"dir":"ltr"},{"str":"an","boundary":[0.43278013071895344,0.5962260082070703,0.45372488970588154,0.6100001243686864],"dir":"ltr"},{"str":"uncluttered,","boundary":[0.45823454248365936,0.5962260082070703,0.5586089776143783,0.6100001243686864],"dir":"ltr"},{"str":"machine-independent","boundary":[0.5637069281045743,0.5962260082070703,0.7417997848039207,0.6100001243686864],"dir":"ltr"},{"str":"characterization","boundary":[0.7467015359477116,0.5962260082070703,0.8809263205882345,0.6100001243686864],"dir":"ltr"},{"str":"of","boundary":[0.11764620915032606,0.6133472203282824,0.12721839640522803,0.6271213364898985],"dir":"ltr"},{"str":"an","boundary":[0.13741450980392084,0.6133472203282824,0.15835926879084894,0.6271213364898985],"dir":"ltr"},{"str":"algorithm's","boundary":[0.16326107843137183,0.6133472203282824,0.25130034346405156,0.6271213364898985],"dir":"ltr"},{"str":"ef\u0002ciency","boundary":[0.26071199346405155,0.6133472203282824,0.3370222174836594,0.6271213364898985],"dir":"ltr"},{"str":"To","boundary":[0.34621995098039143,0.6133472203282824,0.3610863575163391,0.6271213364898985],"dir":"ltr"},{"str":"this","boundary":[0.3708901633986921,0.6133472203282824,0.4025835944444437,0.6271213364898985],"dir":"ltr"},{"str":"end,","boundary":[0.407681666666666,0.6133472203282824,0.4425123552287575,0.6271213364898985],"dir":"ltr"},{"str":"we","boundary":[0.44761042483660063,0.6133472203282824,0.47031989117646994,0.6271213364898985],"dir":"ltr"},{"str":"will","boundary":[0.47541794117646985,0.6133472203282824,0.5063270578431365,0.6271213364898985],"dir":"ltr"},{"str":"always","boundary":[0.5110328104575156,0.6133472203282824,0.5677886616013064,0.6271213364898985],"dir":"ltr"},{"str":"express","boundary":[0.5724943954248358,0.6133472203282824,0.6341343754901952,0.6271213364898985],"dir":"ltr"},{"str":"running","boundary":[0.6394283823529403,0.6133472203282824,0.7063624844771235,0.6271213364898985],"dir":"ltr"},{"str":"time","boundary":[0.7110682516339861,0.6133472203282824,0.7482518833333325,0.6271213364898985],"dir":"ltr"},{"str":"by","boundary":[0.7533497875816986,0.6133472203282824,0.772921996405228,0.6271213364898985],"dir":"ltr"},{"str":"counting","boundary":[0.7778239705882345,0.6133472203282824,0.8494461336601299,0.6271213364898985],"dir":"ltr"},{"str":"the","boundary":[0.8543479901960777,0.6133472203282824,0.8809612031045744,0.6271213364898985],"dir":"ltr"},{"str":"number","boundary":[0.11764700980392076,0.6304684324494945,0.18204991552287503,0.6442425486111106],"dir":"ltr"},{"str":"of","boundary":[0.18695174836601228,0.6304684324494945,0.19652393562091425,0.6442425486111106],"dir":"ltr"},{"str":"basic","boundary":[0.20672004901960706,0.6304684324494945,0.24839566307189462,0.6442425486111106],"dir":"ltr"},{"str":"computer","boundary":[0.25310142156862664,0.6304684324494945,0.3302137852941168,0.6442425486111106],"dir":"ltr"},{"str":"steps","boundary":[0.33550779411764625,0.6304684324494945,0.37777164395424756,0.6442425486111106],"dir":"ltr"},{"str":"as","boundary":[0.3873616830065352,0.6304684324494945,0.40556134166666585,0.6442425486111106],"dir":"ltr"},{"str":"a","boundary":[0.4104631535947705,0.6304684324494945,0.41554343464052207,0.6442425486111106],"dir":"ltr"},{"str":"function","boundary":[0.4253472385620907,0.6304684324494945,0.49324390833333254,0.6442425486111106],"dir":"ltr"},{"str":"of","boundary":[0.49814576797385546,0.6304684324494945,0.5077179552287574,0.6442425486111106],"dir":"ltr"},{"str":"the","boundary":[0.5179140686274503,0.6304684324494945,0.544527281535947,0.6442425486111106],"dir":"ltr"},{"str":"size","boundary":[0.5496253431372542,0.6304684324494945,0.5809266169934634,0.6442425486111106],"dir":"ltr"},{"str":"of","boundary":[0.5858284477124176,0.6304684324494945,0.5954006349673195,0.6442425486111106],"dir":"ltr"},{"str":"the","boundary":[0.6055967483660124,0.6304684324494945,0.6322099612745091,0.6442425486111106],"dir":"ltr"},{"str":"input.","boundary":[0.637111781045751,0.6304684324494945,0.6866127135620909,0.6442425486111106],"dir":"ltr"},{"str":"And","boundary":[0.14529478758169861,0.6475896445707067,0.17935898709150255,0.6613637607323228],"dir":"ltr"},{"str":"this","boundary":[0.18406472222222148,0.6475896445707067,0.2157581532679731,0.6613637607323228],"dir":"ltr"},{"str":"simpli\u0002cation","boundary":[0.22026782679738488,0.6475896445707067,0.3325852109477117,0.6613637607323228],"dir":"ltr"},{"str":"leads","boundary":[0.33709495098039144,0.6475896445707067,0.3799470366013064,0.6613637607323228],"dir":"ltr"},{"str":"to","boundary":[0.3846527941176463,0.6475896445707067,0.4003034310457509,0.6613637607323228],"dir":"ltr"},{"str":"another","boundary":[0.4050093300653587,0.6475896445707067,0.4691983318627444,0.6613637607323228],"dir":"ltr"},{"str":"Instead","boundary":[0.4785921405228751,0.6475896445707067,0.5408203563725483,0.6613637607323228],"dir":"ltr"},{"str":"of","boundary":[0.5455261274509796,0.6475896445707067,0.555294556535947,0.6613637607323228],"dir":"ltr"},{"str":"reporting","boundary":[0.565098186274509,0.6475896445707067,0.6416044888888881,0.6613637607323228],"dir":"ltr"},{"str":"that","boundary":[0.6465063562091495,0.6475896445707067,0.6811409661764698,0.6613637607323228],"dir":"ltr"},{"str":"an","boundary":[0.6858467156862738,0.6475896445707067,0.7067914746732018,0.6613637607323228],"dir":"ltr"},{"str":"algorithm","boundary":[0.7113012908496724,0.6475896445707067,0.7925134797385613,0.6613637607323228],"dir":"ltr"},{"str":"takes","boundary":[0.797023186274509,0.6475896445707067,0.8414439006535939,0.6613637607323228],"dir":"ltr"},{"str":"say","boundary":[0.8508378267973847,0.6475896445707067,0.8805884339869272,0.6613637607323228],"dir":"ltr"},{"str":",","boundary":[0.8762744607843129,0.6475896445707067,0.8811586003267965,0.6613637607323228],"dir":"ltr"},{"str":"5n3","boundary":[0.11764700980392076,0.6682102367424236,0.14410494748365932,0.6842012310606055],"dir":"ltr"},{"str":"+","boundary":[0.14803913398692728,0.6704271148989894,0.15900170915032596,0.6842012310606055],"dir":"ltr"},{"str":"4n","boundary":[0.16488406862745017,0.6704271148989894,0.18445626862745015,0.6842012310606055],"dir":"ltr"},{"str":"+","boundary":[0.1875934967320253,0.6704271148989894,0.198556071895424,0.6842012310606055],"dir":"ltr"},{"str":"3","boundary":[0.2044384313725482,0.6704271148989894,0.2132441428104567,0.6842012310606055],"dir":"ltr"},{"str":"steps","boundary":[0.21794998366012988,0.6647108566919188,0.26021383349673116,0.6784849728535348],"dir":"ltr"},{"str":"on","boundary":[0.2651156699346397,0.6647108566919188,0.2848839573529403,0.6784849728535348],"dir":"ltr"},{"str":"an","boundary":[0.2895896895424828,0.6647108566919188,0.310534448529411,0.6784849728535348],"dir":"ltr"},{"str":"input","boundary":[0.31504410130718874,0.6647108566919188,0.359660894281045,0.6784849728535348],"dir":"ltr"},{"str":"of","boundary":[0.36436665032679655,0.6647108566919188,0.3743309944444436,0.6784849728535348],"dir":"ltr"},{"str":"size","boundary":[0.3837427941176462,0.6647108566919188,0.4150440679738554,0.6784849728535348],"dir":"ltr"},{"str":"n","boundary":[0.4197498202614371,0.6704271148989894,0.430516317647058,0.6842012310606055],"dir":"ltr"},{"str":",","boundary":[0.43051630718954165,0.6647108566919188,0.4306946026143782,0.6784849728535348],"dir":"ltr"},{"str":"it","boundary":[0.4401062908496724,0.6647108566919188,0.4479137686274502,0.6784849728535348],"dir":"ltr"},{"str":"is","boundary":[0.45732557189542394,0.6647108566919188,0.4667016794117639,0.6784849728535348],"dir":"ltr"},{"str":"much","boundary":[0.475721323529411,0.6647108566919188,0.5164344493464045,0.6784849728535348],"dir":"ltr"},{"str":"simpler","boundary":[0.5258460947712411,0.6647108566919188,0.5880743106209143,0.6784849728535348],"dir":"ltr"},{"str":"to","boundary":[0.5927800816993457,0.6647108566919188,0.6084307186274502,0.6784849728535348],"dir":"ltr"},{"str":"leave","boundary":[0.6133325326797379,0.6647108566919188,0.6559885640522869,0.6784849728535348],"dir":"ltr"},{"str":"out","boundary":[0.6606944607843129,0.6647108566919188,0.6873076736928098,0.6784849728535348],"dir":"ltr"},{"str":"lower-order","boundary":[0.692013415032679,0.6647108566919188,0.7857388571895417,0.6784849728535348],"dir":"ltr"},{"str":"terms","boundary":[0.790836781045751,0.6647108566919188,0.8383947529411758,0.6784849728535348],"dir":"ltr"},{"str":"such","boundary":[0.8432965849673196,0.6647108566919188,0.8810684746732019,0.6784849728535348],"dir":"ltr"},{"str":"as","boundary":[0.11764674836601237,0.6818320688131307,0.1358464070261431,0.6956061849747469],"dir":"ltr"},{"str":"4n","boundary":[0.14192485294117577,0.6875483270202014,0.16149705294117575,0.7013224431818176],"dir":"ltr"},{"str":"and","boundary":[0.16757549019607773,0.6818320688131307,0.19869851078431303,0.6956061849747469],"dir":"ltr"},{"str":"3","boundary":[0.20458071895424765,0.6875483270202014,0.21338643039215616,0.7013224431818176],"dir":"ltr"},{"str":"(which","boundary":[0.21946483660130647,0.6818320688131307,0.2683775702614372,0.6956061849747469],"dir":"ltr"},{"str":"become","boundary":[0.28053444444444375,0.6818320688131307,0.3406236210784307,0.6956061849747469],"dir":"ltr"},{"str":"insigni\u0002cant","boundary":[0.34689800653594705,0.6818320688131307,0.4502136006535941,0.6956061849747469],"dir":"ltr"},{"str":"as","boundary":[0.4557037254901954,0.6818320688131307,0.4739033841503262,0.6956061849747469],"dir":"ltr"},{"str":"n","boundary":[0.4799818300653588,0.6875483270202014,0.49074832745097974,0.7013224431818176],"dir":"ltr"},{"str":"grows),","boundary":[0.49682676470588166,0.6818320688131307,0.5559177230392149,0.6956061849747469],"dir":"ltr"},{"str":"and","boundary":[0.5623882026143784,0.6818320688131307,0.5935112232026137,0.6956061849747469],"dir":"ltr"},{"str":"even","boundary":[0.5993934313725484,0.6818320688131307,0.637557456045751,0.6956061849747469],"dir":"ltr"},{"str":"the","boundary":[0.6438318300653588,0.6818320688131307,0.6704450429738555,0.6956061849747469],"dir":"ltr"},{"str":"detail","boundary":[0.6765233333333327,0.6818320688131307,0.7236713227124177,0.6956061849747469],"dir":"ltr"},{"str":"of","boundary":[0.729749803921568,0.6818320688131307,0.7444200478758163,0.6956061849747469],"dir":"ltr"},{"str":"the","boundary":[0.750694575163398,0.6818320688131307,0.7773077880718947,0.6956061849747469],"dir":"ltr"},{"str":"coef\u0002cient","boundary":[0.7833862418300647,0.6818320688131307,0.8657570769607835,0.6956061849747469],"dir":"ltr"},{"str":"5","boundary":[0.8722275816993457,0.6875483270202014,0.8810332931372541,0.7013224431818176],"dir":"ltr"},{"str":"in","boundary":[0.1176475163398685,0.698953280934343,0.13427854624182928,0.7127273970959591],"dir":"ltr"},{"str":"the","boundary":[0.1395726797385613,0.698953280934343,0.16618589264705802,0.7127273970959591],"dir":"ltr"},{"str":"leading","boundary":[0.1716759477124175,0.698953280934343,0.23253161339869202,0.7127273970959591],"dir":"ltr"},{"str":"term","boundary":[0.2378256209150319,0.698953280934343,0.277166117156862,0.7127273970959591],"dir":"ltr"},{"str":"(computers","boundary":[0.28285225490196,0.698953280934343,0.3740466267973848,0.7127273970959591],"dir":"ltr"},{"str":"will","boundary":[0.3799288888888881,0.698953280934343,0.4108380055555548,0.7127273970959591],"dir":"ltr"},{"str":"be","boundary":[0.41613199346405155,0.698953280934343,0.43491988790849595,0.7127273970959591],"dir":"ltr"},{"str":"\u0002ve","boundary":[0.4402140196078424,0.698953280934343,0.4695723328431365,0.7127273970959591],"dir":"ltr"},{"str":"times","boundary":[0.4750623856209143,0.698953280934343,0.5204634929738554,0.7127273970959591],"dir":"ltr"},{"str":"faster","boundary":[0.526149640522875,0.698953280934343,0.5736897870915025,0.7127273970959591],"dir":"ltr"},{"str":"in","boundary":[0.5793759477124175,0.698953280934343,0.5960069776143783,0.7127273970959591],"dir":"ltr"},{"str":"a","boundary":[0.6013011111111104,0.698953280934343,0.6059892189542476,0.7127273970959591],"dir":"ltr"},{"str":"few","boundary":[0.616577369281045,0.698953280934343,0.6451513681372542,0.7127273970959591],"dir":"ltr"},{"str":"years","boundary":[0.6508374999999993,0.698953280934343,0.6952582143790842,0.7127273970959591],"dir":"ltr"},{"str":"anyway),","boundary":[0.7007482843137247,0.698953280934343,0.7749195148692801,0.7127273970959591],"dir":"ltr"},{"str":"and","boundary":[0.7802134967320253,0.698953280934343,0.8113365173202606,0.7127273970959591],"dir":"ltr"},{"str":"just","boundary":[0.816826732026143,0.698953280934343,0.848128005882352,0.7127273970959591],"dir":"ltr"},{"str":"say","boundary":[0.8534219934640516,0.698953280934343,0.8810156140522868,0.7127273970959591],"dir":"ltr"},{"str":"that","boundary":[0.11764781045751556,0.7159229779040399,0.1522824204248358,0.729697094065656],"dir":"ltr"},{"str":"the","boundary":[0.1571842483660123,0.7159229779040399,0.18379746127450905,0.729697094065656],"dir":"ltr"},{"str":"algorithm","boundary":[0.1888955228758162,0.7159229779040399,0.2701077117647051,0.729697094065656],"dir":"ltr"},{"str":"takes","boundary":[0.2748134967320254,0.7159229779040399,0.3192342111111104,0.729697094065656],"dir":"ltr"},{"str":"time","boundary":[0.3243321241830058,0.7159229779040399,0.3615157558823522,0.729697094065656],"dir":"ltr"},{"str":"O","boundary":[0.36641758169934563,0.7216392361111106,0.37992917941176396,0.7354133522727266],"dir":"ltr"},{"str":"(","boundary":[0.38051733660130643,0.7216392361111106,0.3873622620915025,0.7354133522727266],"dir":"ltr"},{"str":"n3","boundary":[0.38736225490196,0.7194223832070702,0.40547823179738485,0.7354133522727266],"dir":"ltr"},{"str":")","boundary":[0.4064712418300646,0.7216392361111106,0.41331616732026066,0.7354133522727266],"dir":"ltr"},{"str":"(pronounced","boundary":[0.4182180718954241,0.7159229779040399,0.5193946267973849,0.729697094065656],"dir":"ltr"},{"str":"ìbig","boundary":[0.5246886601307182,0.7159229779040399,0.5567742483660124,0.729697094065656],"dir":"ltr"},{"str":"oh","boundary":[0.5614799999999993,0.7159229779040399,0.5812482874182999,0.729697094065656],"dir":"ltr"},{"str":"of","boundary":[0.5863463398692804,0.7159229779040399,0.6010165838235287,0.729697094065656],"dir":"ltr"},{"str":"n3","boundary":[0.6061146405228751,0.7194223832070702,0.6241057154575157,0.7354133522727266],"dir":"ltr"},{"str":"î).","boundary":[0.6249026470588229,0.7159229779040399,0.6424962446078425,0.729697094065656],"dir":"ltr"},{"str":"It","boundary":[0.14529480392156804,0.733044190025252,0.15937681209150267,0.7468183061868682],"dir":"ltr"},{"str":"is","boundary":[0.1654552614379079,0.733044190025252,0.1736550617647053,0.7468183061868682],"dir":"ltr"},{"str":"time","boundary":[0.1850273202614373,0.733044190025252,0.22221095196078372,0.7468183061868682],"dir":"ltr"},{"str":"to","boundary":[0.22828924836601247,0.733044190025252,0.24393988529411703,0.7468183061868682],"dir":"ltr"},{"str":"de\u0002ne","boundary":[0.25001833333333273,0.733044190025252,0.29973316977124126,0.7468183061868682],"dir":"ltr"},{"str":"this","boundary":[0.3056153921568621,0.733044190025252,0.3373088232026138,0.7468183061868682],"dir":"ltr"},{"str":"notation","boundary":[0.3431910457516334,0.733044190025252,0.4120681084967314,0.7468183061868682],"dir":"ltr"},{"str":"precisely","boundary":[0.41795035947712356,0.733044190025252,0.4905350901960778,0.7468183061868682],"dir":"ltr"},{"str":"In","boundary":[0.5022818627450973,0.733044190025252,0.5204815214052281,0.7468183061868682],"dir":"ltr"},{"str":"what","boundary":[0.5263637254901954,0.733044190025252,0.5680571648692804,0.7468183061868682],"dir":"ltr"},{"str":"follows","boundary":[0.5737433006535941,0.733044190025252,0.6306773944444438,0.7468183061868682],"dir":"ltr"},{"str":"think","boundary":[0.6414437581699339,0.733044190025252,0.6864527083333326,0.7468183061868682],"dir":"ltr"},{"str":"of","boundary":[0.6921388562091496,0.733044190025252,0.7068091001633979,0.7468183061868682],"dir":"ltr"},{"str":"f","boundary":[0.7128873856209142,0.7387604482323228,0.7216930970588228,0.7525345643939388],"dir":"ltr"},{"str":"(","boundary":[0.7236538235294111,0.7387604482323228,0.7304987490196071,0.7525345643939388],"dir":"ltr"},{"str":"n","boundary":[0.7304986928104568,0.7387604482323228,0.7412651901960777,0.7525345643939388],"dir":"ltr"},{"str":")","boundary":[0.7412652124182999,0.7387604482323228,0.748110137908496,0.7525345643939388],"dir":"ltr"},{"str":"and","boundary":[0.7539924346405221,0.733044190025252,0.7851154552287575,0.7468183061868682],"dir":"ltr"},{"str":"g","boundary":[0.7908015849673196,0.7387604482323228,0.7992151392156855,0.7525345643939388],"dir":"ltr"},{"str":"(","boundary":[0.7998032679738555,0.7387604482323228,0.8066481934640515,0.7525345643939388],"dir":"ltr"},{"str":"n","boundary":[0.8066482189542477,0.7387604482323228,0.8174147163398686,0.7525345643939388],"dir":"ltr"},{"str":")","boundary":[0.8174147385620908,0.7387604482323228,0.8242596640522869,0.7525345643939388],"dir":"ltr"},{"str":"as","boundary":[0.8303380718954242,0.733044190025252,0.8485377305555548,0.7468183061868682],"dir":"ltr"},{"str":"the","boundary":[0.8544199346405222,0.733044190025252,0.8810331475490191,0.7468183061868682],"dir":"ltr"},{"str":"running","boundary":[0.11764705882352886,0.7501654021464642,0.18458116094771188,0.7639395183080804],"dir":"ltr"},{"str":"times","boundary":[0.18909084967320205,0.7501654021464642,0.23449195702614326,0.7639395183080804],"dir":"ltr"},{"str":"of","boundary":[0.23958986928104523,0.7501654021464642,0.2491620565359472,0.7639395183080804],"dir":"ltr"},{"str":"two","boundary":[0.25935816993464,0.7501654021464642,0.2889125617647053,0.7639395183080804],"dir":"ltr"},{"str":"algorithms","boundary":[0.29401062091503216,0.7501654021464642,0.38344028545751585,0.7639395183080804],"dir":"ltr"},{"str":"on","boundary":[0.38814607843137205,0.7501654021464642,0.40791436584967267,0.7639395183080804],"dir":"ltr"},{"str":"inputs","boundary":[0.4130124183006531,0.7501654021464642,0.46584668692810405,0.7639395183080804],"dir":"ltr"},{"str":"of","boundary":[0.47055245098039167,0.7501654021464642,0.4801246382352936,0.7639395183080804],"dir":"ltr"},{"str":"size","boundary":[0.4903207516339865,0.7501654021464642,0.5216220254901955,0.7639395183080804],"dir":"ltr"},{"str":"n","boundary":[0.5265238562091499,0.7558816603535349,0.5372903535947708,0.769655776515151],"dir":"ltr"},{"str":".","boundary":[0.5372903431372544,0.7501654021464642,0.5421744826797381,0.7639395183080804],"dir":"ltr"},{"str":"Let","boundary":[0.16215635620914987,0.7786502506313127,0.1897499620915028,0.7924243667929288],"dir":"ltr"},{"str":"f","boundary":[0.19739687908496684,0.7843665088383833,0.20620259052287535,0.7981406249999995],"dir":"ltr"},{"str":"(","boundary":[0.20816331699346358,0.7843665088383833,0.21500824248365966,0.7981406249999995],"dir":"ltr"},{"str":"n","boundary":[0.21500823529411717,0.7843665088383833,0.22577473267973808,0.7981406249999995],"dir":"ltr"},{"str":")","boundary":[0.22577472222222175,0.7843665088383833,0.2326196477124178,0.7981406249999995],"dir":"ltr"},{"str":"and","boundary":[0.24026666666666618,0.7786502506313127,0.2713896872549015,0.7924243667929288],"dir":"ltr"},{"str":"g","boundary":[0.2788406862745093,0.7843665088383833,0.28725424052287535,0.7981406249999995],"dir":"ltr"},{"str":"(","boundary":[0.2878424183006531,0.7843665088383833,0.2946873437908492,0.7981406249999995],"dir":"ltr"},{"str":"n","boundary":[0.2946873366013067,0.7843665088383833,0.3054538339869276,0.7981406249999995],"dir":"ltr"},{"str":")","boundary":[0.3054538235294113,0.7843665088383833,0.31229874901960736,0.7981406249999995],"dir":"ltr"},{"str":"be","boundary":[0.320141830065359,0.7786502506313127,0.3389297245098034,0.7924243667929288],"dir":"ltr"},{"str":"functions","boundary":[0.3463807189542479,0.7786502506313127,0.42249486437908446,0.7924243667929288],"dir":"ltr"},{"str":"from","boundary":[0.430141830065359,0.7786502506313127,0.46850193333333284,0.7924243667929288],"dir":"ltr"},{"str":"positive","boundary":[0.4763449346405224,0.7786502506313127,0.5401239539215682,0.7924243667929288],"dir":"ltr"},{"str":"integers","boundary":[0.5477709150326793,0.7786502506313127,0.6144911132352937,0.7924243667929288],"dir":"ltr"},{"str":"to","boundary":[0.6221380718954244,0.7786502506313127,0.6377887088235289,0.7924243667929288],"dir":"ltr"},{"str":"positive","boundary":[0.6456316993464047,0.7786502506313127,0.7094107186274505,0.7924243667929288],"dir":"ltr"},{"str":"reals","boundary":[0.7170576797385616,0.7786502506313127,0.7575568222222218,0.7924243667929288],"dir":"ltr"},{"str":"eW","boundary":[0.7761665032679733,0.7786502506313127,0.7945800647058818,0.7924243667929288],"dir":"ltr"},{"str":"say","boundary":[0.8090720588235288,0.7786502506313127,0.8366656794117643,0.7924243667929288],"dir":"ltr"},{"str":"f","boundary":[0.1621573529411759,0.8014877209595954,0.1709630643790844,0.8152618371212115],"dir":"ltr"},{"str":"=","boundary":[0.17821794117647002,0.8014877209595954,0.1921216960784308,0.8152618371212115],"dir":"ltr"},{"str":"O","boundary":[0.19741581699346347,0.8014877209595954,0.21092741470588178,0.8152618371212115],"dir":"ltr"},{"str":"(","boundary":[0.21151557189542428,0.8014877209595954,0.21836049738562033,0.8152618371212115],"dir":"ltr"},{"str":"g","boundary":[0.21836049019607787,0.8014877209595954,0.22677404444444388,0.8152618371212115],"dir":"ltr"},{"str":")","boundary":[0.22736222222222166,0.8014877209595954,0.2342071477124177,0.8152618371212115],"dir":"ltr"},{"str":"(which","boundary":[0.23969730392156807,0.7957714627525247,0.2895904624183001,0.8095455789141408],"dir":"ltr"},{"str":"means","boundary":[0.29978648692810406,0.7957714627525247,0.3536189738562086,0.8095455789141408],"dir":"ltr"},{"str":"that","boundary":[0.3587168790849668,0.7957714627525247,0.39335148905228706,0.8095455789141408],"dir":"ltr"},{"str":"ìf","boundary":[0.3984495588235289,0.7957714627525247,0.41410018856209097,0.8152618371212115],"dir":"ltr"},{"str":"grows","boundary":[0.4213550653594766,0.7957714627525247,0.4696973516339864,0.8095455789141408],"dir":"ltr"},{"str":"no","boundary":[0.4749913398692805,0.7957714627525247,0.4947596272875812,0.8095455789141408],"dir":"ltr"},{"str":"faster","boundary":[0.4998576797385616,0.7957714627525247,0.547397826307189,0.8095455789141408],"dir":"ltr"},{"str":"than","boundary":[0.5528879084967315,0.7957714627525247,0.5916401689542479,0.8095455789141408],"dir":"ltr"},{"str":"g","boundary":[0.5967382352941172,0.8014877209595954,0.6051517895424832,0.8152618371212115],"dir":"ltr"},{"str":"î)","boundary":[0.6057399673202609,0.7957714627525247,0.6129592101307184,0.8095455789141408],"dir":"ltr"},{"str":"if","boundary":[0.6239396405228753,0.7957714627525247,0.6354726269607838,0.8095455789141408],"dir":"ltr"},{"str":"there","boundary":[0.6405706862745093,0.7957714627525247,0.6812659073529406,0.8095455789141408],"dir":"ltr"},{"str":"is","boundary":[0.6865600653594766,0.7957714627525247,0.6949557803921563,0.8095455789141408],"dir":"ltr"},{"str":"a","boundary":[0.7055440522875811,0.7957714627525247,0.7104282879084961,0.8095455789141408],"dir":"ltr"},{"str":"constant","boundary":[0.7210163398692805,0.7957714627525247,0.7900894812091498,0.8095455789141408],"dir":"ltr"},{"str":"c","boundary":[0.7953834967320256,0.8014877209595954,0.7975225320261432,0.8152618371212115],"dir":"ltr"},{"str":">","boundary":[0.80850294117647,0.8014877209595954,0.8224066960784309,0.8152618371212115],"dir":"ltr"},{"str":"0","boundary":[0.8277006535947707,0.8014877209595954,0.8365063650326792,0.8152618371212115],"dir":"ltr"},{"str":"such","boundary":[0.16215816993464002,0.812892674873737,0.19424381209150277,0.826666791035353],"dir":"ltr"},{"str":"that","boundary":[0.2044398366013067,0.812892674873737,0.23809405359477076,0.826666791035353],"dir":"ltr"},{"str":"f","boundary":[0.24299588235294073,0.8186089330808076,0.2518015937908492,0.8323830492424237],"dir":"ltr"},{"str":"(","boundary":[0.2537623202614374,0.8186089330808076,0.26060724575163347,0.8323830492424237],"dir":"ltr"},{"str":"n","boundary":[0.260607238562091,0.8186089330808076,0.2713737359477119,0.8323830492424237],"dir":"ltr"},{"str":")","boundary":[0.2713737254901956,0.8186089330808076,0.27821865098039167,0.8323830492424237],"dir":"ltr"},{"str":"\u0014","boundary":[0.2831205555555551,0.8183059025252521,0.29702431045751587,0.8320800186868682],"dir":"ltr"},{"str":"c","boundary":[0.3019262745098034,0.8186089330808076,0.3095555143790845,0.8323830492424237],"dir":"ltr"},{"str":"\u0001","boundary":[0.3134769934640518,0.8183059025252521,0.31836113300653546,0.8320800186868682],"dir":"ltr"},{"str":"g","boundary":[0.32228264705882304,0.8186089330808076,0.3306962013071891,0.8323830492424237],"dir":"ltr"},{"str":"(","boundary":[0.33128437908496683,0.8186089330808076,0.3381293045751629,0.8323830492424237],"dir":"ltr"},{"str":"n","boundary":[0.3381292973856204,0.8186089330808076,0.34889579477124133,0.8323830492424237],"dir":"ltr"},{"str":").","boundary":[0.348895784313725,0.812892674873737,0.36062484215686225,0.8323830492424237],"dir":"ltr"},{"str":"Saying","boundary":[0.11764919934640475,0.8413775233585855,0.17440505212418253,0.8551516395202016],"dir":"ltr"},{"str":"f","boundary":[0.18185589869280996,0.8470937815656562,0.19066161013071847,0.8608678977272722],"dir":"ltr"},{"str":"=","boundary":[0.20183808823529364,0.8470937815656562,0.21574184313725445,0.8608678977272722],"dir":"ltr"},{"str":"O","boundary":[0.22495753267973806,0.8470937815656562,0.23846913039215636,0.8608678977272722],"dir":"ltr"},{"str":"(","boundary":[0.23905728758169886,0.8470937815656562,0.24590221307189492,0.8608678977272722],"dir":"ltr"},{"str":"g","boundary":[0.24590220588235245,0.8470937815656562,0.2543157601307185,0.8608678977272722],"dir":"ltr"},{"str":")","boundary":[0.25490393790849625,0.8470937815656562,0.2617488633986923,0.8608678977272722],"dir":"ltr"},{"str":"is","boundary":[0.26959194444444395,0.8413775233585855,0.28347787401960733,0.8551516395202016],"dir":"ltr"},{"str":"a","boundary":[0.29112478758169885,0.8413775233585855,0.29365598366013024,0.8551516395202016],"dir":"ltr"},{"str":"very","boundary":[0.3085579575163394,0.8413775233585855,0.3443690390522871,0.8551516395202016],"dir":"ltr"},{"str":"loose","boundary":[0.35221204248365967,0.8413775233585855,0.39251510637254855,0.8551516395202016],"dir":"ltr"},{"str":"analog","boundary":[0.4003581209150322,0.8413775233585855,0.45534925408496674,0.8551516395202016],"dir":"ltr"},{"str":"of","boundary":[0.4626040359477119,0.8413775233585855,0.47727427990196025,0.8551516395202016],"dir":"ltr"},{"str":"ìf","boundary":[0.48492135620914983,0.8413775233585855,0.5005719859477119,0.8608678977272722],"dir":"ltr"},{"str":"\u0014","boundary":[0.5119445424836597,0.8467907510101005,0.5258482973856204,0.8605648671717167],"dir":"ltr"},{"str":"g","boundary":[0.5352600653594767,0.8470937815656562,0.5436736196078427,0.8608678977272722],"dir":"ltr"},{"str":".","boundary":[0.5442617973856204,0.8413775233585855,0.549734161437908,0.8551516395202016],"dir":"ltr"},{"str":"î","boundary":[0.5485577124183001,0.8413775233585855,0.5554026379084962,0.8551516395202016],"dir":"ltr"},{"str":"It","boundary":[0.5697163725490191,0.8413775233585855,0.5837983807189537,0.8551516395202016],"dir":"ltr"},{"str":"differs","boundary":[0.5914452941176465,0.8413775233585855,0.6438695802287576,0.8551516395202016],"dir":"ltr"},{"str":"from","boundary":[0.6517126143790845,0.8413775233585855,0.6900727176470582,0.8551516395202016],"dir":"ltr"},{"str":"the","boundary":[0.6979157189542478,0.8413775233585855,0.7245289318627445,0.8551516395202016],"dir":"ltr"},{"str":"usual","boundary":[0.732175849673202,0.8413775233585855,0.7779691142156857,0.8551516395202016],"dir":"ltr"},{"str":"notion","boundary":[0.7852238888888883,0.8413775233585855,0.8372738431372543,0.8551516395202016],"dir":"ltr"},{"str":"of","boundary":[0.8449207843137249,0.8413775233585855,0.8595910282679733,0.8551516395202016],"dir":"ltr"},{"str":"\u0014","boundary":[0.8672381045751627,0.8467907510101005,0.8811418594771234,0.8605648671717167],"dir":"ltr"},{"str":"because","boundary":[0.11764986928104507,0.8584987354797975,0.1822310282679732,0.8722728516414137],"dir":"ltr"},{"str":"of","boundary":[0.18870150326797316,0.8584987354797975,0.2033717472222215,0.8722728516414137],"dir":"ltr"},{"str":"the","boundary":[0.21003843137254832,0.8584987354797975,0.23665164428104507,0.8722728516414137],"dir":"ltr"},{"str":"constant","boundary":[0.2433181699346398,0.8584987354797975,0.3137638614379078,0.8722728516414137],"dir":"ltr"},{"str":"c","boundary":[0.3204304248366006,0.8642149936868682,0.32805966470588166,0.8779891098484843],"dir":"ltr"},{"str":"so","boundary":[0.3400025653594764,0.8584987354797975,0.3570257524509797,0.8722728516414137],"dir":"ltr"},{"str":"that","boundary":[0.36369227124182935,0.8584987354797975,0.3983268812091496,0.8722728516414137],"dir":"ltr"},{"str":"for","boundary":[0.40479733660130646,0.8584987354797975,0.4272928990196071,0.8722728516414137],"dir":"ltr"},{"str":"instance","boundary":[0.43395942810457444,0.8584987354797975,0.503228648039215,0.8722728516414137],"dir":"ltr"},{"str":"10n","boundary":[0.5096991339869273,0.8642149936868682,0.5380770692810452,0.8779891098484843],"dir":"ltr"},{"str":"=","boundary":[0.5457241339869274,0.8642149936868682,0.5596278888888881,0.8779891098484843],"dir":"ltr"},{"str":"O","boundary":[0.5672749509803915,0.8642149936868682,0.5807865486928098,0.8779891098484843],"dir":"ltr"},{"str":"(","boundary":[0.5813747058823523,0.8642149936868682,0.5882196313725483,0.8779891098484843],"dir":"ltr"},{"str":"n","boundary":[0.5882196241830059,0.8642149936868682,0.5989861215686269,0.8779891098484843],"dir":"ltr"},{"str":")","boundary":[0.5989861111111104,0.8642149936868682,0.6058310366013065,0.8779891098484843],"dir":"ltr"},{"str":"This","boundary":[0.6216955392156857,0.8584987354797975,0.6584870137254896,0.8722728516414137],"dir":"ltr"},{"str":"constant","boundary":[0.6647613888888882,0.8584987354797975,0.7352070803921563,0.8722728516414137],"dir":"ltr"},{"str":"also","boundary":[0.7418736437908491,0.8584987354797975,0.7745474678104569,0.8722728516414137],"dir":"ltr"},{"str":"allows","boundary":[0.7810179248366007,0.8584987354797975,0.8332639576797379,0.8722728516414137],"dir":"ltr"},{"str":"us","boundary":[0.8395383496732021,0.8584987354797975,0.858718401307189,0.8722728516414137],"dir":"ltr"},{"str":"to","boundary":[0.8651888398692804,0.8584987354797975,0.880839476797385,0.8722728516414137],"dir":"ltr"}],"boundary":[0.11765,0.08979,0.8823,0.87799],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":15,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/dee28c253ed606f714a80f30665193fa.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/8d6b05a989d5e9c9eeaf282fd256f52d.jpg"},"info":{"width":612,"height":792,"margin":[0.11764,0.08979,0.11756,0.12716]},"elements":[{"words":[{"str":"16","boundary":[0.11764705882352941,0.09001376073232323,0.1376114248366013,0.10378787689393938],"dir":"ltr"},{"str":"Figure","boundary":[0.11764705882352941,0.12796141856060608,0.1793048522875817,0.14173553472222222],"dir":"ltr"},{"str":"0.2","boundary":[0.18440276143790849,0.12796141856060608,0.20964342418300655,0.14173553472222222],"dir":"ltr"},{"str":"Which","boundary":[0.21474148692810455,0.1286501243686869,0.2624956258169935,0.14242424053030306],"dir":"ltr"},{"str":"running","boundary":[0.27229942810457514,0.1286501243686869,0.33923353022875813,0.14242424053030306],"dir":"ltr"},{"str":"time","boundary":[0.34374321895424836,0.1286501243686869,0.3809268506535948,0.14242424053030306],"dir":"ltr"},{"str":"is","boundary":[0.38602475490196075,0.1286501243686869,0.39500886895424836,0.14242424053030306],"dir":"ltr"},{"str":"better?","boundary":[0.40481249999999996,0.1286501243686869,0.4617465937908496,0.14242424053030306],"dir":"ltr"},{"str":"100","boundary":[0.30909150326797385,0.16726390782828288,0.3224899313071895,0.17347094065656568],"dir":"ltr"},{"str":"90","boundary":[0.3135767973856209,0.1890921906565657,0.322509082745098,0.19529922348484852],"dir":"ltr"},{"str":"80","boundary":[0.3135767973856209,0.2109204734848484,0.322509082745098,0.2171275063131312],"dir":"ltr"},{"str":"70","boundary":[0.3135767973856209,0.2327992613636364,0.322509082745098,0.2390062941919192],"dir":"ltr"},{"str":"60","boundary":[0.3135767973856209,0.25467931186868686,0.322509082745098,0.26088634469696964],"dir":"ltr"},{"str":"50","boundary":[0.3135767973856209,0.27650759469696967,0.322509082745098,0.2827146275252525],"dir":"ltr"},{"str":"40","boundary":[0.3135767973856209,0.2983876452020201,0.322509082745098,0.30459467803030293],"dir":"ltr"},{"str":"30","boundary":[0.3135767973856209,0.32021592803030297,0.322509082745098,0.3264229608585858],"dir":"ltr"},{"str":"2n+20","boundary":[0.4011991830065359,0.3168016792929292,0.4398762736928104,0.32797433080808075],"dir":"ltr"},{"str":"20","boundary":[0.3135767973856209,0.34209471590909096,0.322509082745098,0.3483017487373738],"dir":"ltr"},{"str":"10","boundary":[0.3135767973856209,0.3639229987373737,0.322509082745098,0.3701300315656566],"dir":"ltr"},{"str":"0","boundary":[0.3180604575163399,0.38580304924242426,0.32252660019607843,0.3920100820707071],"dir":"ltr"},{"str":"1","boundary":[0.3226127450980392,0.3910277967171717,0.32707888777777777,0.3972348295454545],"dir":"ltr"},{"str":"2","boundary":[0.3624411764705882,0.3910277967171717,0.3669073191503268,0.3972348295454545],"dir":"ltr"},{"str":"3","boundary":[0.4023366013071895,0.3910277967171717,0.4068027439869281,0.3972348295454545],"dir":"ltr"},{"str":"4","boundary":[0.44223202614379087,0.3910277967171717,0.4466981688235295,0.3972348295454545],"dir":"ltr"}],"boundary":[0.11765,0.09001,0.46175,0.39723],"dir":"ltr","type":"paragraph"},{"words":[{"str":"5","boundary":[0.4820604575163399,0.3910277967171717,0.48652660019607846,0.3972348295454545],"dir":"ltr"}],"boundary":[0.48206,0.39103,0.48653,0.39723],"dir":"ltr","type":"paragraph"},{"words":[{"str":"n","boundary":[0.5005359477124183,0.3988379166666666,0.5077653104575163,0.41001056818181814],"dir":"ltr"}],"boundary":[0.50054,0.39884,0.50777,0.41001],"dir":"ltr","type":"paragraph"},{"words":[{"str":"6","boundary":[0.5219558823529412,0.3910277967171717,0.5264220250326798,0.3972348295454545],"dir":"ltr"}],"boundary":[0.52196,0.39103,0.52642,0.39723],"dir":"ltr","type":"paragraph"},{"words":[{"str":"n2","boundary":[0.5568313725490195,0.26264539772727274,0.5696835702614378,0.27816296717171707],"dir":"ltr"}],"boundary":[0.55683,0.26265,0.56968,0.27816],"dir":"ltr","type":"paragraph"},{"words":[{"str":"7","boundary":[0.5618513071895425,0.3910277967171717,0.5663174498692811,0.3972348295454545],"dir":"ltr"}],"boundary":[0.56185,0.39103,0.56632,0.39723],"dir":"ltr","type":"paragraph"},{"words":[{"str":"8","boundary":[0.6016797385620916,0.3910277967171717,0.6061458812418301,0.3972348295454545],"dir":"ltr"}],"boundary":[0.60168,0.39103,0.60615,0.39723],"dir":"ltr","type":"paragraph"},{"words":[{"str":"9","boundary":[0.6415751633986928,0.3910277967171717,0.6460413060784314,0.3972348295454545],"dir":"ltr"}],"boundary":[0.64158,0.39103,0.64604,0.39723],"dir":"ltr","type":"paragraph"},{"words":[{"str":"10","boundary":[0.6792614379084968,0.3910277967171717,0.6881937232679739,0.3972348295454545],"dir":"ltr"}],"boundary":[0.67926,0.39103,0.68819,0.39723],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Algorithms","boundary":[0.7899640522875817,0.08979153426128839,0.8823348957516342,0.10356565042290454],"dir":"ltr"}],"boundary":[0.78996,0.08979,0.88233,0.10357],"dir":"ltr","type":"paragraph"},{"words":[{"str":"disregard","boundary":[0.11764705882352941,0.44561982133838385,0.1959180687908497,0.45939393750000007],"dir":"ltr"},{"str":"what","boundary":[0.2008199346405229,0.44561982133838385,0.24251337401960785,0.45939393750000007],"dir":"ltr"},{"str":"happens","boundary":[0.24702303921568627,0.44561982133838385,0.31631008447712416,0.45939393750000007],"dir":"ltr"},{"str":"for","boundary":[0.3210158496732026,0.44561982133838385,0.34351141209150327,0.45939393750000007],"dir":"ltr"},{"str":"small","boundary":[0.34841323529411766,0.44561982133838385,0.39381434264705883,0.45939393750000007],"dir":"ltr"},{"str":"values","boundary":[0.39832401960784314,0.44561982133838385,0.4515504454248366,0.45939393750000007],"dir":"ltr"},{"str":"of","boundary":[0.45625620915032683,0.44561982133838385,0.4709264531045752,0.45939393750000007],"dir":"ltr"},{"str":"n","boundary":[0.47563235294117656,0.4513360795454545,0.48639885032679747,0.46511019570707074],"dir":"ltr"},{"str":"For","boundary":[0.4973613888888889,0.44561982133838385,0.5249550168300654,0.45939393750000007],"dir":"ltr"},{"str":"example","boundary":[0.5298568300653594,0.44561982133838385,0.5987517181372549,0.45939393750000007],"dir":"ltr"},{"str":"suppose","boundary":[0.6081454901960784,0.44561982133838385,0.6735109635620915,0.45939393750000007],"dir":"ltr"},{"str":"we","boundary":[0.6784128104575163,0.44561982133838385,0.7011222767973857,0.45939393750000007],"dir":"ltr"},{"str":"are","boundary":[0.7058281699346406,0.44561982133838385,0.7324413828431373,0.45939393750000007],"dir":"ltr"},{"str":"choosing","boundary":[0.7373432026143791,0.44561982133838385,0.8079849648692811,0.45939393750000007],"dir":"ltr"},{"str":"between","boundary":[0.8126907352941177,0.44561982133838385,0.8808013089869282,0.45939393750000007],"dir":"ltr"},{"str":"two","boundary":[0.11764661764705882,0.4627411597222222,0.14720100947712417,0.4765152758838384],"dir":"ltr"},{"str":"algorithms","boundary":[0.1540636111111111,0.4627411597222222,0.24349327565359477,0.4765152758838384],"dir":"ltr"},{"str":"for","boundary":[0.2499637745098039,0.4627411597222222,0.27245933692810453,0.4765152758838384],"dir":"ltr"},{"str":"a","boundary":[0.2793219444444444,0.4627411597222222,0.2828335326797385,0.4765152758838384],"dir":"ltr"},{"str":"particular","boundary":[0.2957747222222222,0.4627411597222222,0.3785377145424836,0.4765152758838384],"dir":"ltr"},{"str":"computational","boundary":[0.38520429738562084,0.4627411597222222,0.5036001179738562,0.4765152758838384],"dir":"ltr"},{"str":"task.","boundary":[0.5100706372549019,0.4627411597222222,0.550569779738562,0.4765152758838384],"dir":"ltr"},{"str":"One","boundary":[0.5619422058823529,0.4627411597222222,0.5956142482026143,0.4765152758838384],"dir":"ltr"},{"str":"takes","boundary":[0.6020846895424836,0.4627411597222222,0.6465054039215685,0.4765152758838384],"dir":"ltr"},{"str":"f","boundary":[0.653368022875817,0.46845741792929285,0.6621737343137254,0.4822315340909091],"dir":"ltr"},{"str":"(","boundary":[0.6707836928104575,0.46845741792929285,0.6776286183006536,0.4822315340909091],"dir":"ltr"},{"str":"n","boundary":[0.6776286437908496,0.46845741792929285,0.6883951411764706,0.4822315340909091],"dir":"ltr"},{"str":"=","boundary":[0.7030830882352942,0.46845741792929285,0.7169868431372549,0.4822315340909091],"dir":"ltr"},{"str":"n2","boundary":[0.7246339052287581,0.4662404766414141,0.7423397514052288,0.4822315340909091],"dir":"ltr"},{"str":"steps","boundary":[0.749803366013072,0.4627411597222222,0.7920672158496733,0.4765152758838384],"dir":"ltr"},{"str":"while","boundary":[0.8040100163398695,0.4627411597222222,0.849018966503268,0.4765152758838384],"dir":"ltr"},{"str":"the","boundary":[0.8554894281045753,0.4627411597222222,0.8821026410130721,0.4765152758838384],"dir":"ltr"},{"str":"1","boundary":[0.663136633986928,0.4733617392676767,0.6699867612091502,0.4834250094696969],"dir":"ltr"},{"str":"other","boundary":[0.11764629084967337,0.47986237184343433,0.1608905336601309,0.4936364880050505],"dir":"ltr"},{"str":"takes","boundary":[0.16775315359477141,0.47986237184343433,0.2121738679738564,0.4936364880050505],"dir":"ltr"},{"str":"f","boundary":[0.2188404084967322,0.485578630050505,0.2276461199346407,0.49935274621212117],"dir":"ltr"},{"str":"(","boundary":[0.2354893137254904,0.485578630050505,0.24233423921568645,0.49935274621212117],"dir":"ltr"},{"str":"n","boundary":[0.24233423202614396,0.485578630050505,0.25310072941176487,0.49935274621212117],"dir":"ltr"},{"str":"=","boundary":[0.267592663398693,0.485578630050505,0.27384935620915046,0.49935274621212117],"dir":"ltr"},{"str":"2n","boundary":[0.28914348039215704,0.485578630050505,0.308715680392157,0.49935274621212117],"dir":"ltr"},{"str":"+","boundary":[0.3138136928104577,0.485578630050505,0.3228154836601309,0.49935274621212117],"dir":"ltr"},{"str":"20","boundary":[0.33261941176470605,0.485578630050505,0.35023083464052307,0.49935274621212117],"dir":"ltr"},{"str":"steps","boundary":[0.35689751633986944,0.47986237184343433,0.39916136617647074,0.4936364880050505],"dir":"ltr"},{"str":"(Figure","boundary":[0.40602398692810476,0.47986237184343433,0.4664875104575165,0.4936364880050505],"dir":"ltr"},{"str":"0.2).","boundary":[0.47295797385620936,0.47986237184343433,0.5085551514705885,0.4936364880050505],"dir":"ltr"},{"str":"Which","boundary":[0.5195354248366015,0.47986237184343433,0.5655247924836604,0.4936364880050505],"dir":"ltr"},{"str":"is","boundary":[0.5788581372549022,0.47986237184343433,0.5927440668300656,0.4936364880050505],"dir":"ltr"},{"str":"better?","boundary":[0.5992146732026146,0.47986237184343433,0.6561487669934642,0.4936364880050505],"dir":"ltr"},{"str":"Well,","boundary":[0.667521209150327,0.47986237184343433,0.7090007457516342,0.4936364880050505],"dir":"ltr"},{"str":"this","boundary":[0.7158633660130721,0.47986237184343433,0.7475567970588237,0.4936364880050505],"dir":"ltr"},{"str":"depends","boundary":[0.754027254901961,0.47986237184343433,0.8213535142156865,0.4936364880050505],"dir":"ltr"},{"str":"on","boundary":[0.8282161437908498,0.47986237184343433,0.8479844312091505,0.4936364880050505],"dir":"ltr"},{"str":"the","boundary":[0.8546509477124185,0.47986237184343433,0.8812641606209152,0.4936364880050505],"dir":"ltr"},{"str":"2","boundary":[0.22784225490196097,0.4904829766414141,0.23469238212418317,0.5005462468434343],"dir":"ltr"},{"str":"value","boundary":[0.11764604575163413,0.4969835839646465,0.16265499591503282,0.5107577001262626],"dir":"ltr"},{"str":"of","boundary":[0.16834114379084983,0.4969835839646465,0.18301138774509818,0.5107577001262626],"dir":"ltr"},{"str":"For","boundary":[0.21376004901960802,0.4969835839646465,0.24135367696078447,0.5107577001262626],"dir":"ltr"},{"str":",","boundary":[0.2938492647058826,0.4969835839646465,0.29873340424836625,0.5107577001262626],"dir":"ltr"},{"str":"is","boundary":[0.3276461928104577,0.4969835839646465,0.3356499147058825,0.5107577001262626],"dir":"ltr"},{"str":"smaller;","boundary":[0.34741433006535966,0.4969835839646465,0.4143306068627453,0.5107577001262626],"dir":"ltr"},{"str":"thereafter","boundary":[0.42080109477124195,0.4969835839646465,0.5033680084967321,0.5107577001262626],"dir":"ltr"},{"str":",","boundary":[0.5016032189542485,0.4969835839646465,0.5064873584967322,0.5107577001262626],"dir":"ltr"},{"str":"is","boundary":[0.5358813562091505,0.4969835839646465,0.5438850781045753,0.5107577001262626],"dir":"ltr"},{"str":"the","boundary":[0.5556494934640525,0.4969835839646465,0.5822627063725492,0.5107577001262626],"dir":"ltr"},{"str":"clear","boundary":[0.5881449183006537,0.4969835839646465,0.6280558171568629,0.5107577001262626],"dir":"ltr"},{"str":"winner","boundary":[0.634134117647059,0.4969835839646465,0.6922625083333335,0.5107577001262626],"dir":"ltr"},{"str":"In","boundary":[0.7044015686274511,0.4969835839646465,0.7226012272875818,0.5107577001262626],"dir":"ltr"},{"str":"this","boundary":[0.728483431372549,0.4969835839646465,0.7601768624183006,0.5107577001262626],"dir":"ltr"},{"str":"case","boundary":[0.7658631699346405,0.4969835839646465,0.800693858496732,0.5107577001262626],"dir":"ltr"},{"str":",","boundary":[0.8003017320261437,0.4969835839646465,0.8051858715686274,0.5107577001262626],"dir":"ltr"},{"str":"scales","boundary":[0.8345087908496732,0.4969835839646465,0.8818528588235294,0.5107577001262626],"dir":"ltr"},{"str":"n","boundary":[0.18908983660130735,0.5026998421717171,0.19985633398692826,0.5164739583333333],"dir":"ltr"},{"str":"n","boundary":[0.24743212418300672,0.5026998421717171,0.2581986215686276,0.5164739583333333],"dir":"ltr"},{"str":"\u0014","boundary":[0.2646692156862747,0.5023968116161616,0.2785729705882355,0.5161709277777777],"dir":"ltr"},{"str":"5","boundary":[0.28504356209150344,0.5026998421717171,0.293849273529412,0.5164739583333333],"dir":"ltr"},{"str":"f1","boundary":[0.30500789215686297,0.5026998421717171,0.3209669409477126,0.5176674589646464],"dir":"ltr"},{"str":"f2","boundary":[0.5131539869281048,0.5026998421717171,0.5292021043464054,0.5176674589646464],"dir":"ltr"},{"str":"f2","boundary":[0.8116564215686274,0.5026998421717171,0.8278294572875816,0.5176674589646464],"dir":"ltr"},{"str":"much","boundary":[0.11764604575163394,0.5141047960858586,0.15816309313725488,0.5278789122474747],"dir":"ltr"},{"str":"better","boundary":[0.16796689542483656,0.5141047960858586,0.21707567075163395,0.5278789122474747],"dir":"ltr"},{"str":"as","boundary":[0.22236967320261433,0.5141047960858586,0.24056933186274504,0.5278789122474747],"dir":"ltr"},{"str":"n","boundary":[0.24547114379084964,0.5198210542929292,0.2562376411764705,0.5335951704545454],"dir":"ltr"},{"str":"grows","boundary":[0.2609434803921568,0.5141047960858586,0.30928576666666663,0.5278789122474747],"dir":"ltr"},{"str":"and","boundary":[0.3188758006535947,0.5141047960858586,0.34999882124183,0.5278789122474747],"dir":"ltr"},{"str":"therefore","boundary":[0.3549006372549019,0.5141047960858586,0.42944615392156854,0.5278789122474747],"dir":"ltr"},{"str":"it","boundary":[0.4349362581699346,0.5141047960858586,0.4425476575163398,0.5278789122474747],"dir":"ltr"},{"str":"is","boundary":[0.4523516176470588,0.5141047960858586,0.46133573169934633,0.5278789122474747],"dir":"ltr"},{"str":"superior","boundary":[0.47113936274509793,0.5141047960858586,0.5394281897058822,0.5278789122474747],"dir":"ltr"},{"str":".","boundary":[0.5376633823529411,0.5141047960858586,0.5425475218954248,0.5278789122474747],"dir":"ltr"},{"str":"This","boundary":[0.1452924673202614,0.5312260082070707,0.18208394183006532,0.545000124368687],"dir":"ltr"},{"str":"superiority","boundary":[0.18678968954248362,0.5312260082070707,0.2771819217320261,0.545000124368687],"dir":"ltr"},{"str":"is","boundary":[0.282279885620915,0.5312260082070707,0.2912639996732026,0.545000124368687],"dir":"ltr"},{"str":"captured","boundary":[0.3010676307189542,0.5312260082070707,0.3736701867647058,0.545000124368687],"dir":"ltr"},{"str":"by","boundary":[0.3789641993464052,0.5312260082070707,0.3985364081699346,0.545000124368687],"dir":"ltr"},{"str":"the","boundary":[0.40324230392156857,0.5312260082070707,0.4298555168300653,0.545000124368687],"dir":"ltr"},{"str":"big-O","boundary":[0.4349535784313725,0.5312260082070707,0.47957040490196073,0.5507163825757576],"dir":"ltr"},{"str":"notation:","boundary":[0.4848645261437908,0.5312260082070707,0.5586257284313726,0.545000124368687],"dir":"ltr"},{"str":"f","boundary":[0.5649001470588235,0.5369422664141413,0.573705858496732,0.5507163825757576],"dir":"ltr"},{"str":"=","boundary":[0.5870573039215686,0.5369422664141413,0.6009610588235293,0.5507163825757576],"dir":"ltr"},{"str":"O","boundary":[0.605863022875817,0.5369422664141413,0.6193746205882352,0.5507163825757576],"dir":"ltr"},{"str":"(","boundary":[0.6199627777777778,0.5369422664141413,0.6268077032679739,0.5507163825757576],"dir":"ltr"},{"str":"f1","boundary":[0.6268076960784313,0.5369422664141413,0.6425349311437909,0.5519098832070707],"dir":"ltr"},{"str":")","boundary":[0.6433318627450981,0.5369422664141413,0.6501767882352941,0.5507163825757576],"dir":"ltr"},{"str":"because","boundary":[0.6601589379084968,0.5312260082070707,0.724740096895425,0.545000124368687],"dir":"ltr"},{"str":"2","boundary":[0.5745082843137255,0.5418466130050505,0.5813584115359477,0.5519098832070707],"dir":"ltr"},{"str":"f2","boundary":[0.4052929248366014,0.5616392361111111,0.42096658147058835,0.5766068276515152],"dir":"ltr"},{"str":"(","boundary":[0.42176351307189547,0.5616392361111111,0.4286084385620915,0.5754133522727273],"dir":"ltr"},{"str":"n","boundary":[0.4286084313725491,0.5616392361111111,0.43937492875817,0.5754133522727273],"dir":"ltr"},{"str":")","boundary":[0.43937491830065367,0.5616392361111111,0.4462198437908497,0.5754133522727273],"dir":"ltr"},{"str":"2n","boundary":[0.48392153594771253,0.56163913510101,0.5034937359477126,0.5754132512626262],"dir":"ltr"},{"str":"+","boundary":[0.5074152450980394,0.56163913510101,0.5173974281045753,0.5754132512626262],"dir":"ltr"},{"str":"20","boundary":[0.5252405718954251,0.56163913510101,0.542851994771242,0.5754132512626262],"dir":"ltr"},{"str":"=","boundary":[0.4582352614379086,0.5710330618686869,0.4721390163398694,0.584807178030303],"dir":"ltr"},{"str":"2","boundary":[0.5150980392156863,0.5792707291666667,0.5219481664379085,0.5893339993686868],"dir":"ltr"},{"str":"\u0014","boundary":[0.5550980392156863,0.5707300186868687,0.5690017941176471,0.5845041348484848],"dir":"ltr"},{"str":"22","boundary":[0.5788057189542484,0.5710330492424243,0.5964171418300654,0.5848071654040404],"dir":"ltr"},{"str":"f1","boundary":[0.4052941176470588,0.5804269886363637,0.42096777428104576,0.5953946054292929],"dir":"ltr"},{"str":"(","boundary":[0.42176470588235293,0.5804269886363637,0.428609631372549,0.5942011047979798],"dir":"ltr"},{"str":"n","boundary":[0.4286096241830066,0.5804269886363637,0.43937612156862754,0.5942011047979798],"dir":"ltr"},{"str":")","boundary":[0.43937611111111113,0.5804269886363637,0.4462210366013072,0.5942011047979798],"dir":"ltr"},{"str":"n","boundary":[0.504313725490196,0.5804269886363637,0.515080222875817,0.5942011047979798],"dir":"ltr"},{"str":"since","boundary":[0.46427803921568633,0.6006198213383839,0.5057575746732026,0.6143939375],"dir":"ltr"},{"str":"the","boundary":[0.5124241176470589,0.6006198213383839,0.5390373305555556,0.6143939375],"dir":"ltr"},{"str":"ratio","boundary":[0.5457038562091504,0.6006198213383839,0.5848304485294118,0.6143939375],"dir":"ltr"},{"str":"f","boundary":[0.5914969934640524,0.6063360795454545,0.6003027049019608,0.6201101957070707],"dir":"ltr"},{"str":"(","boundary":[0.6082351470588236,0.6063360795454545,0.6150800725490196,0.6201101957070707],"dir":"ltr"},{"str":"n","boundary":[0.6150800653594772,0.6063360795454545,0.6258465627450982,0.6201101957070707],"dir":"ltr"},{"str":")","boundary":[0.6258465522875818,0.6063360795454545,0.6326914777777779,0.6201101957070707],"dir":"ltr"},{"str":"=f","boundary":[0.6326914705882355,0.6063360795454545,0.6503028934640525,0.6201101957070707],"dir":"ltr"},{"str":"(","boundary":[0.6582350980392159,0.6063360795454545,0.6650800235294119,0.6201101957070707],"dir":"ltr"},{"str":"n","boundary":[0.6650800163398695,0.6063360795454545,0.6758465137254904,0.6201101957070707],"dir":"ltr"},{"str":"=","boundary":[0.6905345424836603,0.6063360795454545,0.7044382973856211,0.6201101957070707],"dir":"ltr"},{"str":"n2","boundary":[0.7120853594771244,0.6041192266414142,0.7297911239542485,0.6201101957070707],"dir":"ltr"},{"str":"=","boundary":[0.7305881045751635,0.6063360795454545,0.739393816013072,0.6201101957070707],"dir":"ltr"},{"str":"(2n","boundary":[0.7393938398692812,0.6063360795454545,0.7658108601307192,0.6201101957070707],"dir":"ltr"},{"str":"+","boundary":[0.7711049836601309,0.6063360795454545,0.7799106960784316,0.6201101957070707],"dir":"ltr"},{"str":"20)","boundary":[0.7901067810457518,0.6063360795454545,0.8145631294117649,0.6201101957070707],"dir":"ltr"},{"str":"can","boundary":[0.8214257352941178,0.6006198213383839,0.8501958127450981,0.6143939375],"dir":"ltr"},{"str":"get","boundary":[0.8566664215686276,0.6006198213383839,0.8819070843137257,0.6143939375],"dir":"ltr"},{"str":"all","boundary":[0.14700539215686279,0.6006198213383839,0.168324483006536,0.6143939375],"dir":"ltr"},{"str":"=","boundary":[0.3862744444444444,0.6063360795454545,0.4001781993464052,0.6201101957070707],"dir":"ltr"},{"str":"O6","boundary":[0.3862744444444444,0.606033048989899,0.4249018888888889,0.6201101957070707],"dir":"ltr"},{"str":"(","boundary":[0.42192501633986923,0.6063360795454545,0.4287699418300653,0.6201101957070707],"dir":"ltr"},{"str":"f2","boundary":[0.4287699346405229,0.6063360795454545,0.4444971697058823,0.6213036963383838],"dir":"ltr"},{"str":")","boundary":[0.44529410130718955,0.6063360795454545,0.4521390267973856,0.6201101957070707],"dir":"ltr"},{"str":"1","boundary":[0.6005880882352942,0.6112404261363636,0.6074382154575164,0.6213036963383838],"dir":"ltr"},{"str":"2","boundary":[0.6503919607843138,0.6112404261363636,0.657242088006536,0.6213036963383838],"dir":"ltr"},{"str":"for","boundary":[0.11764722222222228,0.6006198213383839,0.14014278464052293,0.6143939375],"dir":"ltr"},{"str":"n","boundary":[0.17479509803921572,0.6063360795454545,0.18556159542483663,0.6201101957070707],"dir":"ltr"},{"str":"on","boundary":[0.1978966666666667,0.6006198213383839,0.21766495408496736,0.6143939375],"dir":"ltr"},{"str":"the","boundary":[0.2243314705882353,0.6006198213383839,0.25094468349673205,0.6143939375],"dir":"ltr"},{"str":"other","boundary":[0.2576112091503268,0.6006198213383839,0.30085545196078434,0.6143939375],"dir":"ltr"},{"str":"hand,","boundary":[0.3077180718954249,0.6006198213383839,0.35468780800653593,0.6143939375],"dir":"ltr"},{"str":"f1","boundary":[0.3615504248366013,0.6063360795454545,0.37763437558823526,0.6213036963383838],"dir":"ltr"},{"str":"arbitrarily","boundary":[0.11764681372549045,0.617741033459596,0.20450963120915058,0.6315151496212121],"dir":"ltr"},{"str":"large","boundary":[0.2092154411764708,0.617741033459596,0.25108713382352965,0.6315151496212121],"dir":"ltr"},{"str":"and","boundary":[0.26067700980392183,0.617741033459596,0.29180003039215713,0.6315151496212121],"dir":"ltr"},{"str":"so","boundary":[0.29650576797385647,0.617741033459596,0.3135289550653597,0.6315151496212121],"dir":"ltr"},{"str":"no","boundary":[0.3186270098039218,0.617741033459596,0.33839529722222245,0.6315151496212121],"dir":"ltr"},{"str":"constant","boundary":[0.3432971078431375,0.617741033459596,0.4137427993464054,0.6315151496212121],"dir":"ltr"},{"str":"c","boundary":[0.41884073529411786,0.6234572916666666,0.42646997516339885,0.6372314078282828],"dir":"ltr"},{"str":"will","boundary":[0.4315679575163401,0.617741033459596,0.4624770741830067,0.6315151496212121],"dir":"ltr"},{"str":"make","boundary":[0.46698674836601334,0.617741033459596,0.5122096024509807,0.6315151496212121],"dir":"ltr"},{"str":"the","boundary":[0.5171114215686278,0.617741033459596,0.5437246344771245,0.6315151496212121],"dir":"ltr"},{"str":"de\u0002nition","boundary":[0.5488226960784317,0.617741033459596,0.6276819418300656,0.6315151496212121],"dir":"ltr"},{"str":"work.","boundary":[0.6325838071895428,0.617741033459596,0.6785731503267978,0.6315151496212121],"dir":"ltr"},{"str":"Now","boundary":[0.14529295751634022,0.6348622455808081,0.18249441454248402,0.6486363617424242],"dir":"ltr"},{"str":"another","boundary":[0.1899452450980396,0.6348622455808081,0.2541342468954252,0.6486363617424242],"dir":"ltr"},{"str":"algorithm","boundary":[0.2613890359477128,0.6348622455808081,0.3426012248366017,0.6486363617424242],"dir":"ltr"},{"str":"comes","boundary":[0.3498560294117651,0.6348622455808081,0.3993747872549024,0.6486363617424242],"dir":"ltr"},{"str":"along","boundary":[0.40682563725490234,0.6348622455808081,0.451834587418301,0.6486363617424242],"dir":"ltr"},{"str":"one","boundary":[0.4639734640522879,0.6348622455808081,0.49254746290849705,0.6486363617424242],"dir":"ltr"},{"str":"that","boundary":[0.4999983006535951,0.6348622455808081,0.5346329106209153,0.6486363617424242],"dir":"ltr"},{"str":"uses","boundary":[0.5418878431372551,0.6348622455808081,0.5780910818627454,0.6486363617424242],"dir":"ltr"},{"str":"f","boundary":[0.5855419281045754,0.6405785037878787,0.5943476395424838,0.6543526199494949],"dir":"ltr"},{"str":"(","boundary":[0.6027436601307192,0.6405785037878787,0.6095885856209153,0.6543526199494949],"dir":"ltr"},{"str":"n","boundary":[0.6095885784313728,0.6405785037878787,0.6203550758169938,0.6543526199494949],"dir":"ltr"},{"str":"=","boundary":[0.6360234640522879,0.6405785037878787,0.6499272189542487,0.6543526199494949],"dir":"ltr"},{"str":"n","boundary":[0.6587507516339873,0.6405785037878787,0.6695172490196083,0.6543526199494949],"dir":"ltr"},{"str":"+","boundary":[0.6750074509803925,0.6405785037878787,0.6834211699346409,0.6543526199494949],"dir":"ltr"},{"str":"1","boundary":[0.6944012418300658,0.6405785037878787,0.7032069532679742,0.6543526199494949],"dir":"ltr"},{"str":"steps","boundary":[0.7106578921568631,0.6348622455808081,0.7529217419934645,0.6486363617424242],"dir":"ltr"},{"str":"Is","boundary":[0.7707469444444448,0.6348622455808081,0.7862015027777781,0.6486363617424242],"dir":"ltr"},{"str":"this","boundary":[0.7936525000000003,0.6348622455808081,0.8253459310457519,0.6486363617424242],"dir":"ltr"},{"str":"better","boundary":[0.8324046241830069,0.6348622455808081,0.8815133995098043,0.6486363617424242],"dir":"ltr"},{"str":"3","boundary":[0.5950966013071898,0.6454828251262626,0.601946728529412,0.6555460953282829],"dir":"ltr"},{"str":"than","boundary":[0.11764482026143827,0.6518319425505051,0.1563970807189546,0.6656060587121212],"dir":"ltr"},{"str":"Certainly","boundary":[0.1950779084967324,0.6518319425505051,0.2733489184640527,0.6656060587121212],"dir":"ltr"},{"str":"but","boundary":[0.2819583986928108,0.6518319425505051,0.309748083169935,0.6656060587121212],"dir":"ltr"},{"str":"only","boundary":[0.3154342156862749,0.6518319425505051,0.35046098284313765,0.6656060587121212],"dir":"ltr"},{"str":"by","boundary":[0.3561471241830069,0.6518319425505051,0.3757193330065363,0.6656060587121212],"dir":"ltr"},{"str":"a","boundary":[0.38140562091503305,0.6518319425505051,0.38550550980392195,0.6656060587121212],"dir":"ltr"},{"str":"constant","boundary":[0.39727009803921604,0.6518319425505051,0.46771578954248405,0.6656060587121212],"dir":"ltr"},{"str":"factor","boundary":[0.47340196078431407,0.6518319425505051,0.5205499501633991,0.6656060587121212],"dir":"ltr"},{"str":"The","boundary":[0.5326890196078434,0.6518319425505051,0.5644002759803926,0.6656060587121212],"dir":"ltr"},{"str":"discrepancy","boundary":[0.5702824836601311,0.6518319425505051,0.6673413880718958,0.6656060587121212],"dir":"ltr"},{"str":"between","boundary":[0.6732236601307193,0.6518319425505051,0.7413342338235298,0.6656060587121212],"dir":"ltr"},{"str":"and","boundary":[0.7705859967320264,0.6518319425505051,0.8017090173202618,0.6656060587121212],"dir":"ltr"},{"str":"is","boundary":[0.8296054738562094,0.6518319425505051,0.8376091957516342,0.6656060587121212],"dir":"ltr"},{"str":"tiny","boundary":[0.8493736111111114,0.6518319425505051,0.8824395923202618,0.6656060587121212],"dir":"ltr"},{"str":"f2","boundary":[0.16208321895424874,0.6575482007575758,0.17782819911764744,0.6725158175505049],"dir":"ltr"},{"str":"f","boundary":[0.7472164705882356,0.6575482007575758,0.7560221820261441,0.6713223169191919],"dir":"ltr"},{"str":"2","boundary":[0.7570565359477127,0.6624525473484848,0.7639066631699349,0.6725158175505049],"dir":"ltr"},{"str":"f3","boundary":[0.8073951470588239,0.6575482007575758,0.823122251405229,0.6725158175505049],"dir":"ltr"},{"str":"compared","boundary":[0.11764485294117684,0.6689531546717172,0.19711015980392196,0.6827272708333333],"dir":"ltr"},{"str":"to","boundary":[0.20299240196078466,0.6689531546717172,0.21864303888888922,0.6827272708333333],"dir":"ltr"},{"str":"the","boundary":[0.2245252450980396,0.6689531546717172,0.25113845800653634,0.6827272708333333],"dir":"ltr"},{"str":"huge","boundary":[0.25682459150326836,0.6689531546717172,0.29714548071895464,0.6827272708333333],"dir":"ltr"},{"str":"gap","boundary":[0.30263553921568664,0.6689531546717172,0.3323860096405233,0.6827272708333333],"dir":"ltr"},{"str":"between","boundary":[0.3378760620915036,0.6689531546717172,0.4059866357843141,0.6827272708333333],"dir":"ltr"},{"str":"f","boundary":[0.4116727941176474,0.6746694128787879,0.42047850555555594,0.688443529040404],"dir":"ltr"},{"str":"and","boundary":[0.43431125816993504,0.6689531546717172,0.46543427875817034,0.6827272708333333],"dir":"ltr"},{"str":"f","boundary":[0.47092449346405274,0.6746694128787879,0.47973020490196117,0.688443529040404],"dir":"ltr"},{"str":"In","boundary":[0.5005679901960789,0.6689531546717172,0.5187676488562097,0.6827272708333333],"dir":"ltr"},{"str":"order","boundary":[0.524257696078432,0.6689531546717172,0.5676980174836607,0.6827272708333333],"dir":"ltr"},{"str":"to","boundary":[0.5737763235294123,0.6689531546717172,0.589426960457517,0.6827272708333333],"dir":"ltr"},{"str":"stay","boundary":[0.5951132516339875,0.6689531546717172,0.6238656071895431,0.6827272708333333],"dir":"ltr"},{"str":"focused","boundary":[0.6352380065359482,0.6689531546717172,0.6958975936274515,0.6827272708333333],"dir":"ltr"},{"str":"on","boundary":[0.7017798366013076,0.6689531546717172,0.7215481240196083,0.6827272708333333],"dir":"ltr"},{"str":"the","boundary":[0.7272342483660136,0.6689531546717172,0.7538474612745103,0.6827272708333333],"dir":"ltr"},{"str":"big","boundary":[0.7595337581699351,0.6689531546717172,0.7847744209150331,0.6827272708333333],"dir":"ltr"},{"str":"picture","boundary":[0.7902644771241835,0.6689531546717172,0.8483750424836606,0.6827272708333333],"dir":"ltr"},{"str":"we","boundary":[0.8589453267973861,0.6689531546717172,0.8816547931372554,0.6827272708333333],"dir":"ltr"},{"str":"1","boundary":[0.42097790849673244,0.6795737342171716,0.4278280357189546,0.6896370044191918],"dir":"ltr"},{"str":"2","boundary":[0.4798015196078436,0.6795737342171716,0.4866516468300658,0.6896370044191918],"dir":"ltr"},{"str":"treat","boundary":[0.11764467320261492,0.6860743667929292,0.15794773709150384,0.6998484829545454],"dir":"ltr"},{"str":"functions","boundary":[0.16304565359477177,0.6860743667929292,0.23915979901960838,0.6998484829545454],"dir":"ltr"},{"str":"as","boundary":[0.2440616666666672,0.6860743667929292,0.2622613253267979,0.6998484829545454],"dir":"ltr"},{"str":"equivalent","boundary":[0.26716313725490254,0.6860743667929292,0.3544359372549025,0.6998484829545454],"dir":"ltr"},{"str":"if","boundary":[0.35914173202614436,0.6860743667929292,0.3657727375816999,0.6998484829545454],"dir":"ltr"},{"str":"they","boundary":[0.37557669934640575,0.6860743667929292,0.41177993807189595,0.6998484829545454],"dir":"ltr"},{"str":"differ","boundary":[0.41687784313725545,0.6860743667929292,0.4610846535947718,0.6998484829545454],"dir":"ltr"},{"str":"only","boundary":[0.46618258169934695,0.6860743667929292,0.5012093488562097,0.6998484829545454],"dir":"ltr"},{"str":"by","boundary":[0.5061111764705888,0.6860743667929292,0.5256833852941182,0.6998484829545454],"dir":"ltr"},{"str":"multiplicative","boundary":[0.5305851960784319,0.6860743667929292,0.6458259338235299,0.6998484829545454],"dir":"ltr"},{"str":"constants","boundary":[0.6505317647058829,0.6860743667929292,0.7291949318627458,0.6998484829545454],"dir":"ltr"},{"str":".","boundary":[0.7288026797385626,0.6860743667929292,0.7336868192810463,0.6998484829545454],"dir":"ltr"},{"str":"Returning","boundary":[0.14529124183006595,0.7031955789141414,0.22983676683006599,0.7169696950757576],"dir":"ltr"},{"str":"to","boundary":[0.23454254901960844,0.7031955789141414,0.250193185947713,0.7169696950757576],"dir":"ltr"},{"str":"the","boundary":[0.25529124183006596,0.7031955789141414,0.2819044547385627,0.7169696950757576],"dir":"ltr"},{"str":"de\u0002nition","boundary":[0.28700251633986984,0.7031955789141414,0.3658617620915039,0.7169696950757576],"dir":"ltr"},{"str":"of","boundary":[0.37076362745098096,0.7031955789141414,0.3803358147058829,0.7169696950757576],"dir":"ltr"},{"str":"big-O","boundary":[0.3905319281045757,0.7031955789141414,0.43514875457516394,0.7226859532828283],"dir":"ltr"},{"str":",","boundary":[0.43573691176470647,0.7031955789141414,0.435915207189543,0.7169696950757576],"dir":"ltr"},{"str":"we","boundary":[0.4453268954248372,0.7031955789141414,0.46803636176470653,0.7169696950757576],"dir":"ltr"},{"str":"see","boundary":[0.4731344117647065,0.7031955789141414,0.4989633102941183,0.7169696950757576],"dir":"ltr"},{"str":"that","boundary":[0.5040612091503274,0.7031955789141414,0.5386958191176475,0.7169696950757576],"dir":"ltr"},{"str":"f","boundary":[0.5435976470588241,0.7089118371212121,0.5524033584967325,0.7226859532828283],"dir":"ltr"},{"str":"=","boundary":[0.5656835457516345,0.7089118371212121,0.5795873006535953,0.7226859532828283],"dir":"ltr"},{"str":"O","boundary":[0.5844892647058829,0.7089118371212121,0.5980008624183012,0.7226859532828283],"dir":"ltr"},{"str":"(","boundary":[0.5985890196078437,0.7089118371212121,0.6054339450980397,0.7226859532828283],"dir":"ltr"},{"str":"f3","boundary":[0.6054339379084973,0.7089118371212121,0.6211611729738568,0.723879428661616],"dir":"ltr"},{"str":"):","boundary":[0.621958104575164,0.7031955789141414,0.6336871624183013,0.7226859532828283],"dir":"ltr"},{"str":"2","boundary":[0.5531345261437914,0.7138161584595959,0.5599846533660136,0.723879428661616],"dir":"ltr"},{"str":"f","boundary":[0.4029386437908503,0.7336088068181819,0.4117443552287588,0.747382922979798],"dir":"ltr"},{"str":"(","boundary":[0.41940923202614444,0.7336088068181819,0.4262541575163405,0.747382922979798],"dir":"ltr"},{"str":"n","boundary":[0.4262541503267981,0.7336088068181819,0.437020647712419,0.747382922979798],"dir":"ltr"},{"str":")","boundary":[0.43702063725490264,0.7336088068181819,0.4438655627450987,0.747382922979798],"dir":"ltr"},{"str":"2n","boundary":[0.4813725163398694,0.7336088068181819,0.5009447163398695,0.747382922979798],"dir":"ltr"},{"str":"+","boundary":[0.5050623366013073,0.7336088068181819,0.5150445196078434,0.747382922979798],"dir":"ltr"},{"str":"20","boundary":[0.522887663398693,0.7336088068181819,0.54049908627451,0.747382922979798],"dir":"ltr"},{"str":"2","boundary":[0.411762173202615,0.7385131534090909,0.4186123004248372,0.748576423611111],"dir":"ltr"},{"str":"=","boundary":[0.45568624183006545,0.743002758838384,0.4695899967320262,0.756776875],"dir":"ltr"},{"str":"\u0014","boundary":[0.5525491176470589,0.7426997282828283,0.5664528725490197,0.7564738444444444],"dir":"ltr"},{"str":"20","boundary":[0.576256797385621,0.743002758838384,0.5938682202614379,0.756776875],"dir":"ltr"},{"str":";","boundary":[0.5938682352941177,0.743002758838384,0.5987523748366014,0.756776875],"dir":"ltr"},{"str":"f3","boundary":[0.40294117647058825,0.7523966856060607,0.41861483310457515,0.7673643023989898],"dir":"ltr"},{"str":"(","boundary":[0.4194117647058824,0.7523966856060607,0.4262566901960784,0.7661708017676768],"dir":"ltr"},{"str":"n","boundary":[0.426256683006536,0.7523966856060607,0.43702318039215693,0.7661708017676768],"dir":"ltr"},{"str":")","boundary":[0.4370231699346406,0.7523966856060607,0.44386809542483663,0.7661708017676768],"dir":"ltr"},{"str":"n","boundary":[0.4903921568627451,0.7523966856060607,0.501158654248366,0.7661708017676768],"dir":"ltr"},{"str":"+","boundary":[0.5050801633986928,0.7523966856060607,0.5150623464052287,0.7661708017676768],"dir":"ltr"},{"str":"1","boundary":[0.5229054901960785,0.7523966856060607,0.5317112016339869,0.7661708017676768],"dir":"ltr"},{"str":"and","boundary":[0.11764764705882362,0.7715289248737374,0.14877066764705893,0.7853030410353535],"dir":"ltr"},{"str":"of","boundary":[0.1536724836601308,0.7715289248737374,0.16324467091503278,0.7853030410353535],"dir":"ltr"},{"str":"course","boundary":[0.1734407843137256,0.7715289248737374,0.2258828957516341,0.7853030410353535],"dir":"ltr"},{"str":"f3","boundary":[0.23098081699346415,0.777245183080808,0.24685061741830075,0.7922127998737374],"dir":"ltr"},{"str":"=","boundary":[0.25254950980392166,0.777245183080808,0.26645326470588243,0.7910192992424242],"dir":"ltr"},{"str":"O","boundary":[0.27135522875817003,0.777245183080808,0.2848668264705883,0.7910192992424242],"dir":"ltr"},{"str":"(","boundary":[0.28545498366013083,0.777245183080808,0.2922999091503269,0.7910192992424242],"dir":"ltr"},{"str":"f2","boundary":[0.2922999019607844,0.777245183080808,0.30802713702614387,0.7922127998737374],"dir":"ltr"},{"str":")","boundary":[0.3088240686274511,0.777245183080808,0.31566899411764715,0.7910192992424242],"dir":"ltr"},{"str":"this","boundary":[0.3256511437908498,0.7715289248737374,0.3573445748366014,0.7853030410353535],"dir":"ltr"},{"str":"time","boundary":[0.3622464052287583,0.7715289248737374,0.3994300369281047,0.7853030410353535],"dir":"ltr"},{"str":"with","boundary":[0.4045279411764707,0.7715289248737374,0.44190765147058836,0.7853030410353535],"dir":"ltr"},{"str":"c","boundary":[0.4466133986928106,0.777245183080808,0.45424263856209157,0.7910192992424242],"dir":"ltr"},{"str":"=","boundary":[0.4593406209150328,0.777245183080808,0.468342411764706,0.7910192992424242],"dir":"ltr"},{"str":"1","boundary":[0.4781463398692811,0.777245183080808,0.4869520513071896,0.7910192992424242],"dir":"ltr"},{"str":".","boundary":[0.48695204248366025,0.7715289248737374,0.49183618202614393,0.7853030410353535],"dir":"ltr"},{"str":"Just","boundary":[0.14529517973856224,0.8056198339646464,0.1809101732026145,0.8193939501262626],"dir":"ltr"},{"str":"as","boundary":[0.18581199346405242,0.8056198339646464,0.20401165212418312,0.8193939501262626],"dir":"ltr"},{"str":"O","boundary":[0.2089134640522877,0.8113360921717171,0.22242506176470603,0.8251102083333333],"dir":"ltr"},{"str":"(\u0001)","boundary":[0.22301321895424847,0.8110330616161615,0.24158719673202622,0.8251102083333333],"dir":"ltr"},{"str":"is","boundary":[0.24668521241830074,0.8056198339646464,0.2556693264705883,0.8193939501262626],"dir":"ltr"},{"str":"an","boundary":[0.26547295751634,0.8056198339646464,0.2864177165032681,0.8193939501262626],"dir":"ltr"},{"str":"analog","boundary":[0.2911234477124184,0.8056198339646464,0.34611458088235303,0.8193939501262626],"dir":"ltr"},{"str":"of","boundary":[0.350820343137255,0.8056198339646464,0.3654905870915034,0.8193939501262626],"dir":"ltr"},{"str":"\u0014","boundary":[0.37058864379084977,0.8110330616161615,0.38449239869281054,0.8248071777777776],"dir":"ltr"},{"str":"we","boundary":[0.39427841503267985,0.8056198339646464,0.4169878813725491,0.8193939501262626],"dir":"ltr"},{"str":"can","boundary":[0.42208593137254913,0.8056198339646464,0.45085600882352955,0.8193939501262626],"dir":"ltr"},{"str":"also","boundary":[0.45556174836601315,0.8056198339646464,0.488235572385621,0.8193939501262626],"dir":"ltr"},{"str":"de\u0002ne","boundary":[0.4931374019607844,0.8056198339646464,0.542852238398693,0.8193939501262626],"dir":"ltr"},{"str":"analogs","boundary":[0.5479501470588236,0.8056198339646464,0.611158755882353,0.8193939501262626],"dir":"ltr"},{"str":"of","boundary":[0.615864526143791,0.8056198339646464,0.6305347700980393,0.8193939501262626],"dir":"ltr"},{"str":"\u0015","boundary":[0.6356328267973858,0.8110330616161615,0.6495365816993465,0.8248071777777776],"dir":"ltr"},{"str":"and","boundary":[0.6544385457516341,0.8056198339646464,0.6855615663398694,0.8193939501262626],"dir":"ltr"},{"str":"=","boundary":[0.6902674673202616,0.8113360921717171,0.7041712222222223,0.8251102083333333],"dir":"ltr"},{"str":"as","boundary":[0.7090730228758171,0.8056198339646464,0.7272726815359478,0.8193939501262626],"dir":"ltr"},{"str":"follows:","boundary":[0.7321744934640524,0.8056198339646464,0.7939927267973858,0.8193939501262626],"dir":"ltr"},{"str":"f","boundary":[0.39725619281045765,0.838154273989899,0.40606190424836613,0.8519283901515151],"dir":"ltr"},{"str":"=","boundary":[0.4127285294117648,0.838154273989899,0.421730320261438,0.8519283901515151],"dir":"ltr"},{"str":"(","boundary":[0.44445761029411773,0.838154273989899,0.4513025357843138,0.8519283901515151],"dir":"ltr"},{"str":"g","boundary":[0.45130254901960803,0.838154273989899,0.459716103267974,0.8519283901515151],"dir":"ltr"},{"str":")","boundary":[0.4603042810457518,0.838154273989899,0.4671492065359478,0.8519283901515151],"dir":"ltr"},{"str":"means","boundary":[0.4724433006535949,0.8324380157828283,0.5262757875816996,0.8462121319444444],"dir":"ltr"},{"str":"g","boundary":[0.5309815359477126,0.838154273989899,0.5393950901960786,0.8519283901515151],"dir":"ltr"},{"str":"=","boundary":[0.5450812908496734,0.838154273989899,0.5589850457516341,0.8519283901515151],"dir":"ltr"},{"str":"O","boundary":[0.5638870098039217,0.838154273989899,0.57739860751634,0.8519283901515151],"dir":"ltr"},{"str":"(","boundary":[0.5779867647058825,0.838154273989899,0.5848316901960786,0.8519283901515151],"dir":"ltr"},{"str":"f","boundary":[0.5848316830065361,0.838154273989899,0.5936373944444446,0.8519283901515151],"dir":"ltr"},{"str":")","boundary":[0.595598120915033,0.838154273989899,0.6024430464052289,0.8519283901515151],"dir":"ltr"},{"str":"f","boundary":[0.3386291666666669,0.8590633648989899,0.3474348781045754,0.8728374810606061],"dir":"ltr"},{"str":"=","boundary":[0.3542975653594773,0.8590633648989899,0.36329935620915055,0.8728374810606061],"dir":"ltr"},{"str":"\u0002(","boundary":[0.3731032843137257,0.8590633648989899,0.3938519647058826,0.8728374810606061],"dir":"ltr"},{"str":"g","boundary":[0.39385197712418324,0.8590633648989899,0.4022655313725492,0.8728374810606061],"dir":"ltr"},{"str":")","boundary":[0.40285370915032703,0.8590633648989899,0.4096986346405231,0.8728374810606061],"dir":"ltr"},{"str":"means","boundary":[0.41479665032679763,0.8533471066919193,0.4686291372549022,0.8671212228535354],"dir":"ltr"},{"str":"f","boundary":[0.4735309640522878,0.8590633648989899,0.4823366754901962,0.8728374810606061],"dir":"ltr"},{"str":"=","boundary":[0.48900330065359493,0.8590633648989899,0.5029070555555557,0.8728374810606061],"dir":"ltr"},{"str":"O","boundary":[0.5078090196078433,0.8590633648989899,0.5213206173202616,0.8728374810606061],"dir":"ltr"},{"str":"(","boundary":[0.5219087745098041,0.8590633648989899,0.5287537000000001,0.8728374810606061],"dir":"ltr"},{"str":"g","boundary":[0.5287536928104577,0.8590633648989899,0.5371672470588237,0.8728374810606061],"dir":"ltr"},{"str":")","boundary":[0.5377554248366014,0.8590633648989899,0.5446003503267975,0.8728374810606061],"dir":"ltr"},{"str":"and","boundary":[0.5498944444444446,0.8533471066919193,0.5810174650326799,0.8671212228535354],"dir":"ltr"},{"str":"f","boundary":[0.5857232026143792,0.8590633648989899,0.5945289140522877,0.8728374810606061],"dir":"ltr"},{"str":"=","boundary":[0.6013916013071897,0.8590633648989899,0.6103933921568628,0.8728374810606061],"dir":"ltr"},{"str":"(","boundary":[0.6331206821895426,0.8590633648989899,0.6399656076797388,0.8728374810606061],"dir":"ltr"},{"str":"g","boundary":[0.6399656209150328,0.8590633648989899,0.6483791751633988,0.8728374810606061],"dir":"ltr"},{"str":"):","boundary":[0.6489673529411766,0.8590633648989899,0.6608924728758171,0.8728374810606061],"dir":"ltr"}],"boundary":[0.11764,0.44562,0.88244,0.87284],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":16,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/c1ea0611ffc9372b1878a17823c6a6c7.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/98705832ca7983751e6d66a64044e353.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11781,0.53853]},"elements":[{"words":[{"str":"S","boundary":[0.11764705882352941,0.08979153426128839,0.1293939594771242,0.10356565042290454],"dir":"ltr"},{"str":"Dasgupta,","boundary":[0.13800351307189543,0.08979153426128839,0.2225490380718954,0.10356565042290454],"dir":"ltr"},{"str":"C.H.","boundary":[0.22745089869281046,0.08979153426128839,0.26443845637254904,0.10356565042290454],"dir":"ltr"},{"str":"Papadimitriou,","boundary":[0.2693402777777778,0.08979153426128839,0.3932084790849673,0.10356565042290454],"dir":"ltr"},{"str":"and","boundary":[0.39771821895424836,0.08979153426128839,0.42884123954248365,0.10356565042290454],"dir":"ltr"},{"str":"U.V","boundary":[0.43374305555555553,0.08979153426128839,0.4664347251633986,0.10356565042290454],"dir":"ltr"},{"str":"Vazirani","boundary":[0.47190697712418295,0.08979153426128839,0.5419605168300654,0.10356565042290454],"dir":"ltr"},{"str":"17","boundary":[0.8617647058823529,0.09001376073232323,0.8817290718954248,0.10378787689393938],"dir":"ltr"},{"str":"In","boundary":[0.11764705882352941,0.12880163952020204,0.13584671748366012,0.1425757556818182],"dir":"ltr"},{"str":"the","boundary":[0.1407485294117647,0.12880163952020204,0.1673617423202614,0.1425757556818182],"dir":"ltr"},{"str":"preceding","boundary":[0.17226356209150326,0.12880163952020204,0.2521032008169935,0.1425757556818182],"dir":"ltr"},{"str":"example","boundary":[0.2573972222222222,0.12880163952020204,0.32629211029411764,0.1425757556818182],"dir":"ltr"},{"str":",","boundary":[0.32589983660130717,0.12880163952020204,0.33078397614379085,0.1425757556818182],"dir":"ltr"},{"str":"f","boundary":[0.3358819934640523,0.13451789772727277,0.34468770490196077,0.1482920138888889],"dir":"ltr"},{"str":"=","boundary":[0.3576468464052287,0.13451789772727277,0.36664863725490193,0.1482920138888889],"dir":"ltr"},{"str":"\u0002(","boundary":[0.3764525653594771,0.13451789772727277,0.39720124575163396,0.1482920138888889],"dir":"ltr"},{"str":"f","boundary":[0.39720125816993457,0.13451789772727277,0.40600696960784305,0.1482920138888889],"dir":"ltr"},{"str":")","boundary":[0.4137253758169934,0.13451789772727277,0.42057030130718953,0.1482920138888889],"dir":"ltr"},{"str":"and","boundary":[0.4254722058823529,0.12880163952020204,0.4565952264705882,0.1425757556818182],"dir":"ltr"},{"str":"f","boundary":[0.4614970424836601,0.13451789772727277,0.4703027539215685,0.1482920138888889],"dir":"ltr"},{"str":"=","boundary":[0.48294099673202606,0.13451789772727277,0.49194278758169924,0.1482920138888889],"dir":"ltr"},{"str":"(","boundary":[0.514670077614379,0.13451789772727277,0.5215150031045751,0.1482920138888889],"dir":"ltr"},{"str":"f","boundary":[0.5215150163398692,0.13451789772727277,0.5303207277777776,0.1482920138888889],"dir":"ltr"},{"str":").","boundary":[0.538039133986928,0.12880163952020204,0.5497681918300653,0.1482920138888889],"dir":"ltr"},{"str":"2","boundary":[0.3450978267973856,0.1394222190656566,0.35194795401960777,0.14948548926767682],"dir":"ltr"},{"str":"3","boundary":[0.406078316993464,0.1394222190656566,0.4129284442156862,0.14948548926767682],"dir":"ltr"},{"str":"1","boundary":[0.4703919771241829,0.1394222190656566,0.4772421043464051,0.14948548926767682],"dir":"ltr"},{"str":"3","boundary":[0.5303920751633986,0.1394222190656566,0.5372422023856208,0.14948548926767682],"dir":"ltr"},{"str":"Big-O","boundary":[0.14529418300653585,0.1630440637626263,0.1928521859477123,0.18253443813131315],"dir":"ltr"},{"str":"notation","boundary":[0.19951869281045742,0.1630440637626263,0.2683957555555555,0.17681817992424245],"dir":"ltr"},{"str":"lets","boundary":[0.2744740849673202,0.1630440637626263,0.30401065147058814,0.17681817992424245],"dir":"ltr"},{"str":"us","boundary":[0.31028503267973845,0.1630440637626263,0.3294650843137254,0.17681817992424245],"dir":"ltr"},{"str":"focus","boundary":[0.33573944444444437,0.1630440637626263,0.37741505849673196,0.17681817992424245],"dir":"ltr"},{"str":"on","boundary":[0.38368944444444436,0.1630440637626263,0.40345773186274503,0.17681817992424245],"dir":"ltr"},{"str":"the","boundary":[0.40953617647058815,0.1630440637626263,0.43614938937908493,0.17681817992424245],"dir":"ltr"},{"str":"big","boundary":[0.44242375816993457,0.1630440637626263,0.46766442091503263,0.17681817992424245],"dir":"ltr"},{"str":"picture","boundary":[0.4737428758169934,0.1630440637626263,0.5318534411764706,0.17681817992424245],"dir":"ltr"},{"str":"When","boundary":[0.546345294117647,0.1630440637626263,0.594509327124183,0.17681817992424245],"dir":"ltr"},{"str":"faced","boundary":[0.6007836928104575,0.1630440637626263,0.6434396998366013,0.17681817992424245],"dir":"ltr"},{"str":"with","boundary":[0.6497140849673203,0.1630440637626263,0.687093795261438,0.17681817992424245],"dir":"ltr"},{"str":"a","boundary":[0.693172091503268,0.1630440637626263,0.6970758366013072,0.17681817992424245],"dir":"ltr"},{"str":"complicated","boundary":[0.7092327124183007,0.1630440637626263,0.806879852614379,0.17681817992424245],"dir":"ltr"},{"str":"function","boundary":[0.8131542810457516,0.1630440637626263,0.8810509508169935,0.17681817992424245],"dir":"ltr"},{"str":"like","boundary":[0.11764611111111109,0.18016527588383835,0.14835914918300652,0.19393939204545452],"dir":"ltr"},{"str":"3n2","boundary":[0.15365330065359475,0.1836646559343434,0.18018256186274506,0.1996556502525252],"dir":"ltr"},{"str":"+","boundary":[0.1850971405228758,0.18588153409090905,0.1948832450980392,0.1996556502525252],"dir":"ltr"},{"str":"4n","boundary":[0.20311854575163396,0.18588153409090905,0.22269074575163395,0.1996556502525252],"dir":"ltr"},{"str":"+","boundary":[0.22700444444444443,0.18588153409090905,0.2367905490196078,0.1996556502525252],"dir":"ltr"},{"str":"5","boundary":[0.2450258496732026,0.18588153409090905,0.2538315611111111,0.1996556502525252],"dir":"ltr"},{"str":"we","boundary":[0.26420584967320265,0.18016527588383835,0.2869153160130719,0.19393939204545452],"dir":"ltr"},{"str":"just","boundary":[0.29220944444444447,0.18016527588383835,0.32351071830065364,0.19393939204545452],"dir":"ltr"},{"str":"replace","boundary":[0.328804705882353,0.18016527588383835,0.38789566421568633,0.19393939204545452],"dir":"ltr"},{"str":"it","boundary":[0.393385751633987,0.18016527588383835,0.4006049941176471,0.19393939204545452],"dir":"ltr"},{"str":"with","boundary":[0.41119326797385625,0.18016527588383835,0.44857297826797393,0.19393939204545452],"dir":"ltr"},{"str":"O","boundary":[0.45367088235294123,0.18588153409090905,0.4671824800653595,0.1996556502525252],"dir":"ltr"},{"str":"(","boundary":[0.46777063725490203,0.18588153409090905,0.4746155627450981,0.1996556502525252],"dir":"ltr"},{"str":"f","boundary":[0.4746155555555556,0.18588153409090905,0.4834212669934641,0.1996556502525252],"dir":"ltr"},{"str":"(","boundary":[0.4853819934640524,0.18588153409090905,0.49222691895424847,0.1996556502525252],"dir":"ltr"},{"str":"n","boundary":[0.49222691176470607,0.18588153409090905,0.502993409150327,0.1996556502525252],"dir":"ltr"},{"str":"))","boundary":[0.5029933986928106,0.18588153409090905,0.5166832496732028,0.1996556502525252],"dir":"ltr"},{"str":"where","boundary":[0.5270575163398694,0.18016527588383835,0.5773605885620916,0.19393939204545452],"dir":"ltr"},{"str":"f","boundary":[0.5828506535947714,0.18588153409090905,0.5916563650326798,0.1996556502525252],"dir":"ltr"},{"str":"(","boundary":[0.5936170915032681,0.18588153409090905,0.6004620169934642,0.1996556502525252],"dir":"ltr"},{"str":"n","boundary":[0.6004620098039217,0.18588153409090905,0.6112285071895427,0.1996556502525252],"dir":"ltr"},{"str":")","boundary":[0.6112284967320264,0.18588153409090905,0.6180734222222224,0.1996556502525252],"dir":"ltr"},{"str":"is","boundary":[0.6231714379084969,0.18016527588383835,0.6317632316993466,0.19393939204545452],"dir":"ltr"},{"str":"as","boundary":[0.6423515032679741,0.18016527588383835,0.6605511619281048,0.19393939204545452],"dir":"ltr"},{"str":"simple","boundary":[0.6656492156862747,0.18016527588383835,0.7200521130718956,0.19393939204545452],"dir":"ltr"},{"str":"as","boundary":[0.7253461111111112,0.18016527588383835,0.743545769771242,0.19393939204545452],"dir":"ltr"},{"str":"possible","boundary":[0.7488397385620916,0.18016527588383835,0.8143834651960786,0.19393939204545452],"dir":"ltr"},{"str":"In","boundary":[0.8261303431372551,0.18016527588383835,0.8443300017973857,0.19393939204545452],"dir":"ltr"},{"str":"this","boundary":[0.8494280555555557,0.18016527588383835,0.8811214866013073,0.19393939204545452],"dir":"ltr"},{"str":"particular","boundary":[0.11764700980392169,0.19728648800505041,0.20041000212418314,0.21106060416666655],"dir":"ltr"},{"str":"example","boundary":[0.2062922712418302,0.19728648800505041,0.27518715931372567,0.21106060416666655],"dir":"ltr"},{"str":"we'd","boundary":[0.28126547385620926,0.19728648800505041,0.31139037941176484,0.21106060416666655],"dir":"ltr"},{"str":"use","boundary":[0.323154934640523,0.19728648800505041,0.3511406977124184,0.21106060416666655],"dir":"ltr"},{"str":"O","boundary":[0.35721915032679746,0.2030027462121211,0.3707307480392158,0.21677686237373728],"dir":"ltr"},{"str":"(","boundary":[0.37131890522875827,0.2030027462121211,0.3781638307189543,0.21677686237373728],"dir":"ltr"},{"str":"n2","boundary":[0.37816382352941186,0.20078593118686855,0.3962618919281046,0.21677686237373728],"dir":"ltr"},{"str":")","boundary":[0.39705882352941185,0.2030027462121211,0.4039037490196079,0.21677686237373728],"dir":"ltr"},{"str":"because","boundary":[0.4152584313725491,0.19728648800505041,0.47983959035947726,0.21106060416666655],"dir":"ltr"},{"str":"the","boundary":[0.4859179084967321,0.19728648800505041,0.5125311214052288,0.21106060416666655],"dir":"ltr"},{"str":"quadratic","boundary":[0.5186095751633988,0.19728648800505041,0.5978609781045752,0.21106060416666655],"dir":"ltr"},{"str":"portion","boundary":[0.6035471568627452,0.19728648800505041,0.6626381151960785,0.21106060416666655],"dir":"ltr"},{"str":"of","boundary":[0.6689125163398694,0.19728648800505041,0.6835827602941177,0.21106060416666655],"dir":"ltr"},{"str":"the","boundary":[0.6898572875816994,0.19728648800505041,0.7164705004901961,0.21106060416666655],"dir":"ltr"},{"str":"sum","boundary":[0.7225487908496733,0.19728648800505041,0.7575933833333334,0.21106060416666655],"dir":"ltr"},{"str":"dominates","boundary":[0.7634757516339871,0.19728648800505041,0.8488055910130721,0.21106060416666655],"dir":"ltr"},{"str":"the","boundary":[0.8548839215686276,0.19728648800505041,0.8814971344771243,0.21106060416666655],"dir":"ltr"},{"str":"rest.","boundary":[0.11764699346405236,0.21425618497474744,0.15422456405228765,0.2280303011363636],"dir":"ltr"},{"str":"Here","boundary":[0.16324405228758176,0.21425618497474744,0.20356494150326804,0.2280303011363636],"dir":"ltr"},{"str":"are","boundary":[0.20964323529411774,0.21425618497474744,0.2362564482026145,0.2280303011363636],"dir":"ltr"},{"str":"some","boundary":[0.24213866013071905,0.21425618497474744,0.28383209950980404,0.2280303011363636],"dir":"ltr"},{"str":"commonsense","boundary":[0.2897143137254903,0.21425618497474744,0.4028516629084969,0.2280303011363636],"dir":"ltr"},{"str":"rules","boundary":[0.40893000000000007,0.21425618497474744,0.45040953545751644,0.2280303011363636],"dir":"ltr"},{"str":"that","boundary":[0.45629176470588245,0.21425618497474744,0.4909263746732027,0.2280303011363636],"dir":"ltr"},{"str":"help","boundary":[0.4968085947712419,0.21425618497474744,0.5324235977124183,0.2280303011363636],"dir":"ltr"},{"str":"simplify","boundary":[0.5381097385620915,0.21425618497474744,0.604829936764706,0.2280303011363636],"dir":"ltr"},{"str":"functions","boundary":[0.6105161111111111,0.21425618497474744,0.6866302565359478,0.2280303011363636],"dir":"ltr"},{"str":"by","boundary":[0.6923164379084968,0.21425618497474744,0.7118886467320262,0.2280303011363636],"dir":"ltr"},{"str":"omitting","boundary":[0.7175747712418301,0.21425618497474744,0.7878243841503269,0.2280303011363636],"dir":"ltr"},{"str":"dominated","boundary":[0.7937066339869281,0.21425618497474744,0.8809972593137255,0.2280303011363636],"dir":"ltr"},{"str":"terms:","boundary":[0.11764617647058824,0.2313773970959595,0.17008828790849673,0.24515151325757564],"dir":"ltr"},{"str":"1.","boundary":[0.13843049019607842,0.2598622455808079,0.15329681274509802,0.27363636174242406],"dir":"ltr"},{"str":"Multiplicative","boundary":[0.16212019607843137,0.2598622455808079,0.27834132679738566,0.27363636174242406],"dir":"ltr"},{"str":"constants","boundary":[0.28304715686274506,0.2598622455808079,0.3617103240196078,0.27363636174242406],"dir":"ltr"},{"str":"can","boundary":[0.3668082679738562,0.2598622455808079,0.39557834542483655,0.27363636174242406],"dir":"ltr"},{"str":"be","boundary":[0.4004801633986928,0.2598622455808079,0.41926805784313725,0.27363636174242406],"dir":"ltr"},{"str":"omitted:","boundary":[0.4241698692810457,0.2598622455808079,0.49206653905228753,0.27363636174242406],"dir":"ltr"},{"str":"14n","boundary":[0.4985370261437908,0.2655785037878786,0.5269149614379085,0.2793526199494948],"dir":"ltr"},{"str":"2","boundary":[0.527646045751634,0.26336162563131293,0.5344961729738562,0.2734248958333331],"dir":"ltr"},{"str":"becomes","boundary":[0.5403911437908496,0.2598622455808079,0.6086977960784313,0.27363636174242406],"dir":"ltr"},{"str":"n2","boundary":[0.6137957189542484,0.26336162563131293,0.6315549474836601,0.2793526199494948],"dir":"ltr"},{"str":".","boundary":[0.6323518790849674,0.2598622455808079,0.637236018627451,0.27363636174242406],"dir":"ltr"},{"str":"2.","boundary":[0.13843031045751647,0.28834709406565634,0.15329663300653606,0.3021212102272725],"dir":"ltr"},{"str":"na","boundary":[0.1621200163398694,0.2918464741161613,0.18019387462418313,0.3078374684343432],"dir":"ltr"},{"str":"dominates","boundary":[0.18607727124183018,0.28834709406565634,0.27140711062091516,0.3021212102272725],"dir":"ltr"},{"str":"nb","boundary":[0.2763089705882354,0.2918464741161613,0.29312717256535953,0.3078374684343432],"dir":"ltr"},{"str":"if","boundary":[0.2988224019607844,0.28834709406565634,0.3103553883986929,0.3021212102272725],"dir":"ltr"},{"str":"a","boundary":[0.31525736928104586,0.294063352272727,0.31955331928104586,0.3078374684343432],"dir":"ltr"},{"str":">","boundary":[0.32974931372549027,0.294063352272727,0.3387511045751635,0.3078374684343432],"dir":"ltr"},{"str":"b","boundary":[0.3485550326797387,0.294063352272727,0.35618427254901974,0.3078374684343432],"dir":"ltr"},{"str":"for","boundary":[0.3671467810457517,0.28834709406565634,0.38964234346405235,0.3021212102272725],"dir":"ltr"},{"str":"instance","boundary":[0.3949364869281046,0.28834709406565634,0.4642057068627452,0.3021212102272725],"dir":"ltr"},{"str":",","boundary":[0.46381344771241834,0.28834709406565634,0.468697587254902,0.3021212102272725],"dir":"ltr"},{"str":"n2","boundary":[0.4735994934640523,0.2918464741161613,0.49155502918300653,0.3078374684343432],"dir":"ltr"},{"str":"dominates","boundary":[0.4972539215686275,0.28834709406565634,0.5825837609477125,0.3021212102272725],"dir":"ltr"},{"str":"n","boundary":[0.5876816993464052,0.294063352272727,0.5984481967320262,0.3078374684343432],"dir":"ltr"},{"str":".","boundary":[0.5984481862745098,0.28834709406565634,0.6033323258169935,0.3021212102272725],"dir":"ltr"},{"str":"3.","boundary":[0.13843021241830067,0.3166804273989897,0.15329653496732026,0.3304545435606059],"dir":"ltr"},{"str":"Any","boundary":[0.1621199183006536,0.3166804273989897,0.19559588202614378,0.3304545435606059],"dir":"ltr"},{"str":"exponential","boundary":[0.20049769607843138,0.3166804273989897,0.29677228611111117,0.3304545435606059],"dir":"ltr"},{"str":"dominates","boundary":[0.30147808823529415,0.3166804273989897,0.3868079276143791,0.3304545435606059],"dir":"ltr"},{"str":"any","boundary":[0.3919058660130719,0.3166804273989897,0.4224406508169935,0.3304545435606059],"dir":"ltr"},{"str":"polynomial:","boundary":[0.4271463888888889,0.3166804273989897,0.5232249003267974,0.3304545435606059],"dir":"ltr"},{"str":"3","boundary":[0.5291071732026144,0.32239668560606044,0.5379128846405228,0.3361708017676766],"dir":"ltr"},{"str":"n","boundary":[0.5386261437908496,0.32017980744949476,0.5470520607352941,0.33024307765151495],"dir":"ltr"},{"str":"dominates","boundary":[0.552939885620915,0.3166804273989897,0.638269725,0.3304545435606059],"dir":"ltr"},{"str":"n5","boundary":[0.6431715849673202,0.32017980744949476,0.660966516111111,0.3361708017676766],"dir":"ltr"},{"str":"(it","boundary":[0.6668614869281045,0.3166804273989897,0.6852393988562091,0.3304545435606059],"dir":"ltr"},{"str":"even","boundary":[0.6901412254901961,0.3166804273989897,0.7283052501633986,0.3304545435606059],"dir":"ltr"},{"str":"dominates","boundary":[0.7334033169934641,0.3166804273989897,0.8187331563725491,0.3304545435606059],"dir":"ltr"},{"str":"2n","boundary":[0.8236350163398692,0.32017980744949476,0.8411697731535948,0.3361708017676766],"dir":"ltr"},{"str":").","boundary":[0.8419596078431372,0.3166804273989897,0.8527082799019606,0.3304545435606059],"dir":"ltr"},{"str":"4.","boundary":[0.13843019607843132,0.3451652758838383,0.15329651862745092,0.35893939204545444],"dir":"ltr"},{"str":"Likewise","boundary":[0.16211990196078424,0.3451652758838383,0.23570285098039215,0.35893939204545444],"dir":"ltr"},{"str":"any","boundary":[0.24882214052287574,0.3451652758838383,0.27935692532679735,0.35893939204545444],"dir":"ltr"},{"str":"polynomial","boundary":[0.2868077614379084,0.3451652758838383,0.3780021333333333,0.35893939204545444],"dir":"ltr"},{"str":"dominates","boundary":[0.3856491013071895,0.3451652758838383,0.47097894068627444,0.35893939204545444],"dir":"ltr"},{"str":"any","boundary":[0.47882197712418295,0.3451652758838383,0.5093567619281045,0.35893939204545444],"dir":"ltr"},{"str":"logarithm:","boundary":[0.5168075980392157,0.3451652758838383,0.6029039264705883,0.35893939204545444],"dir":"ltr"},{"str":"n","boundary":[0.614668545751634,0.35088153409090894,0.625435043137255,0.3646556502525251],"dir":"ltr"},{"str":"dominates","boundary":[0.6330821078431372,0.3451652758838383,0.7184119472222222,0.35893939204545444],"dir":"ltr"},{"str":"(log","boundary":[0.7262549836601306,0.35088153409090894,0.7555954715686274,0.3646556502525251],"dir":"ltr"},{"str":"n","boundary":[0.7591249183006535,0.35088153409090894,0.7698914156862745,0.3646556502525251],"dir":"ltr"},{"str":")","boundary":[0.7698913562091503,0.35088153409090894,0.7767362816993463,0.3646556502525251],"dir":"ltr"},{"str":"3","boundary":[0.7778418790849673,0.34866465593434326,0.7846920063071895,0.35872792613636345],"dir":"ltr"},{"str":"This","boundary":[0.8052750490196078,0.3451652758838383,0.8420665235294118,0.35893939204545444],"dir":"ltr"},{"str":"also","boundary":[0.8495175326797385,0.3451652758838383,0.8821913566993465,0.35893939204545444],"dir":"ltr"},{"str":"means","boundary":[0.16215642156862736,0.36228648800505037,0.21598890849673194,0.3760606041666666],"dir":"ltr"},{"str":"for","boundary":[0.22538266339869273,0.36228648800505037,0.24787822581699337,0.3760606041666666],"dir":"ltr"},{"str":"example","boundary":[0.2529762908496731,0.36228648800505037,0.3218711789215685,0.3760606041666666],"dir":"ltr"},{"str":"that","boundary":[0.33146106209150317,0.36228648800505037,0.36609567205882343,0.3760606041666666],"dir":"ltr"},{"str":"n2","boundary":[0.3709974999999999,0.36578593118686853,0.38900640173202605,0.38177686237373726],"dir":"ltr"},{"str":"dominates","boundary":[0.3949013725490196,0.36228648800505037,0.48023121192810453,0.3760606041666666],"dir":"ltr"},{"str":"n","boundary":[0.4851330718954248,0.36800274621212103,0.4958995692810457,0.38177686237373726],"dir":"ltr"},{"str":"log","boundary":[0.4988406862745097,0.36800274621212103,0.5213362486928104,0.38177686237373726],"dir":"ltr"},{"str":"n","boundary":[0.5246696078431372,0.36800274621212103,0.5354361052287581,0.38177686237373726],"dir":"ltr"},{"str":".","boundary":[0.5354360947712418,0.36228648800505037,0.5403202343137254,0.3760606041666666],"dir":"ltr"},{"str":"Don't","boundary":[0.11764687908496722,0.3906198213383837,0.16187151486928095,0.4043939374999999],"dir":"ltr"},{"str":"misunderstand","boundary":[0.16853805555555545,0.3906198213383837,0.2932083911764705,0.4043939374999999],"dir":"ltr"},{"str":"this","boundary":[0.30007089869281034,0.3906198213383837,0.33176432973856196,0.4043939374999999],"dir":"ltr"},{"str":"cavalier","boundary":[0.33843086601307176,0.3906198213383837,0.403582450490196,0.4043939374999999],"dir":"ltr"},{"str":"attitude","boundary":[0.4104450816993463,0.3906198213383837,0.47657704411764695,0.4043939374999999],"dir":"ltr"},{"str":"toward","boundary":[0.48343968954248356,0.3906198213383837,0.5405877075163399,0.4043939374999999],"dir":"ltr"},{"str":"constants","boundary":[0.5476465522875816,0.3906198213383837,0.6263097194444444,0.4043939374999999],"dir":"ltr"},{"str":"Programmers","boundary":[0.6425663235294117,0.3906198213383837,0.7551154369281045,0.4043939374999999],"dir":"ltr"},{"str":"and","boundary":[0.7621741666666665,0.3906198213383837,0.7932971872549018,0.4043939374999999],"dir":"ltr"},{"str":"algorithm","boundary":[0.7999637091503267,0.3906198213383837,0.8811758980392156,0.4043939374999999],"dir":"ltr"},{"str":"developers","boundary":[0.11764671568627445,0.40774103345959584,0.20452735849673195,0.421515149621212],"dir":"ltr"},{"str":"are","boundary":[0.2100174673202614,0.40774103345959584,0.23663068022875813,0.421515149621212],"dir":"ltr"},{"str":"very","boundary":[0.24192465686274503,0.40774103345959584,0.27557887385620905,0.421515149621212],"dir":"ltr"},{"str":"interested","boundary":[0.2810689379084967,0.40774103345959584,0.36402800882352937,0.421515149621212],"dir":"ltr"},{"str":"in","boundary":[0.3695181209150326,0.40774103345959584,0.3861491508169934,0.421515149621212],"dir":"ltr"},{"str":"constants","boundary":[0.3910509640522875,0.40774103345959584,0.4697141312091503,0.421515149621212],"dir":"ltr"},{"str":"and","boundary":[0.47500815359477117,0.40774103345959584,0.5061311741830065,0.421515149621212],"dir":"ltr"},{"str":"would","boundary":[0.5110329901960783,0.40774103345959584,0.5605517480392156,0.421515149621212],"dir":"ltr"},{"str":"gladly","boundary":[0.565649656862745,0.40774103345959584,0.6163270609477124,0.421515149621212],"dir":"ltr"},{"str":"stay","boundary":[0.6212289052287581,0.40774103345959584,0.6505694797385619,0.421515149621212],"dir":"ltr"},{"str":"up","boundary":[0.6607654411764705,0.40774103345959584,0.6819062787581698,0.421515149621212],"dir":"ltr"},{"str":"nights","boundary":[0.6870041666666665,0.40774103345959584,0.7392501995098039,0.421515149621212],"dir":"ltr"},{"str":"in","boundary":[0.7443481209150326,0.40774103345959584,0.7609791508169933,0.421515149621212],"dir":"ltr"},{"str":"order","boundary":[0.7658811274509802,0.40774103345959584,0.809321448856209,0.421515149621212],"dir":"ltr"},{"str":"to","boundary":[0.8148116830065358,0.40774103345959584,0.8304623199346404,0.421515149621212],"dir":"ltr"},{"str":"make","boundary":[0.8357564542483659,0.40774103345959584,0.8809793083333333,0.421515149621212],"dir":"ltr"},{"str":"an","boundary":[0.11764697712418284,0.4248623718434342,0.13859173611111097,0.4386364880050504],"dir":"ltr"},{"str":"algorithm","boundary":[0.14486625816993445,0.4248623718434342,0.22607844705882335,0.4386364880050504],"dir":"ltr"},{"str":"run","boundary":[0.23254893790849657,0.4248623718434342,0.26229940833333315,0.4386364880050504],"dir":"ltr"},{"str":"faster","boundary":[0.26857377450980374,0.4248623718434342,0.31611392107843117,0.4386364880050504],"dir":"ltr"},{"str":"by","boundary":[0.32297655228758154,0.4248623718434342,0.34254876111111093,0.4386364880050504],"dir":"ltr"},{"str":"a","boundary":[0.3488232843137253,0.4248623718434342,0.3523348725490194,0.4386364880050504],"dir":"ltr"},{"str":"factor","boundary":[0.36527606209150304,0.4248623718434342,0.412424051470588,0.4386364880050504],"dir":"ltr"},{"str":"of","boundary":[0.41928668300653577,0.4248623718434342,0.43395692696078414,0.4386364880050504],"dir":"ltr"},{"str":"2.","boundary":[0.4404275326797384,0.4248623718434342,0.45529385522875804,0.4386364880050504],"dir":"ltr"},{"str":"But","boundary":[0.46607802287581684,0.4248623718434342,0.49680888627450964,0.4386364880050504],"dir":"ltr"},{"str":"understanding","boundary":[0.5032793300653593,0.4248623718434342,0.624420250980392,0.4386364880050504],"dir":"ltr"},{"str":"algorithms","boundary":[0.6306946895424835,0.4248623718434342,0.7201243540849671,0.4386364880050504],"dir":"ltr"},{"str":"at","boundary":[0.7265948529411763,0.4248623718434342,0.7434219614379084,0.4386364880050504],"dir":"ltr"},{"str":"the","boundary":[0.7498924019607842,0.4248623718434342,0.7765056148692809,0.4386364880050504],"dir":"ltr"},{"str":"level","boundary":[0.782976225490196,0.4248623718434342,0.8215145820261437,0.4386364880050504],"dir":"ltr"},{"str":"of","boundary":[0.8279850490196077,0.4248623718434342,0.8426552929738561,0.4386364880050504],"dir":"ltr"},{"str":"this","boundary":[0.8493219771241829,0.4248623718434342,0.8810154081699345,0.4386364880050504],"dir":"ltr"},{"str":"book","boundary":[0.1176471405228757,0.4419835839646463,0.15581116519607832,0.4557577001262625],"dir":"ltr"},{"str":"would","boundary":[0.16090906862745086,0.4419835839646463,0.21042782647058808,0.4557577001262625],"dir":"ltr"},{"str":"be","boundary":[0.21513357843137243,0.4419835839646463,0.23392147287581685,0.4557577001262625],"dir":"ltr"},{"str":"impossible","boundary":[0.23901952614379074,0.4419835839646463,0.3260962475490195,0.4557577001262625],"dir":"ltr"},{"str":"without","boundary":[0.33099812091503256,0.4419835839646463,0.3949910441176469,0.4557577001262625],"dir":"ltr"},{"str":"the","boundary":[0.39969681372549004,0.4419835839646463,0.4263100266339868,0.4557577001262625],"dir":"ltr"},{"str":"simplicity","boundary":[0.43140808823529403,0.4419835839646463,0.5126024517973856,0.4557577001262625],"dir":"ltr"},{"str":"afforded","boundary":[0.5175043300653593,0.4419835839646463,0.5850088426470588,0.4557577001262625],"dir":"ltr"},{"str":"by","boundary":[0.5903028594771241,0.4419835839646463,0.6098750683006535,0.4557577001262625],"dir":"ltr"},{"str":"big-O","boundary":[0.6145809640522876,0.4419835839646463,0.6591977905228757,0.46147395833333316],"dir":"ltr"},{"str":"notation.","boundary":[0.6646879901960784,0.4419835839646463,0.7384491924836601,0.4557577001262625],"dir":"ltr"}],"boundary":[0.11765,0.08979,0.88219,0.46147],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":17,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/31a3832616ec80cf30a3739d5e741bfb.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/032788a88d5e126713d82efefb44e20f.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11767,0.11901]},"elements":[{"words":[{"str":"18","boundary":[0.11764705882352941,0.09001376073232323,0.1376114248366013,0.10378787689393938],"dir":"ltr"},{"str":"Algorithms","boundary":[0.7899640522875817,0.08979153426128839,0.8823348957516342,0.10356565042290454],"dir":"ltr"},{"str":"Exercises","boundary":[0.11764705882352941,0.12284010984848488,0.2340341225490196,0.14095399873737377],"dir":"ltr"},{"str":"0.1.","boundary":[0.12607841503267972,0.1623149297979798,0.15313381973856208,0.1748940207070707],"dir":"ltr"},{"str":"In","boundary":[0.16215341503267972,0.1623149297979798,0.17880665150326797,0.1748940207070707],"dir":"ltr"},{"str":"each","boundary":[0.1827280882352941,0.1623149297979798,0.2128929279738562,0.1748940207070707],"dir":"ltr"},{"str":"of","boundary":[0.22112815359477125,0.1623149297979798,0.23091342444444446,0.1748940207070707],"dir":"ltr"},{"str":"the","boundary":[0.23875642156862745,0.1623149297979798,0.26323977215686273,0.1748940207070707],"dir":"ltr"},{"str":"following","boundary":[0.2671613235294118,0.1623149297979798,0.3359230741176471,0.1748940207070707],"dir":"ltr"},{"str":",","boundary":[0.4138941666666667,0.1623149297979798,0.4140897100653595,0.1748940207070707],"dir":"ltr"},{"str":"situations","boundary":[0.3394525,0.1623149297979798,0.4142862517647059,0.1748940207070707],"dir":"ltr"},{"str":"indicate","boundary":[0.42271709150326797,0.1623149297979798,0.4830626903267974,0.1748940207070707],"dir":"ltr"},{"str":"whether","boundary":[0.4871803267973856,0.1623149297979798,0.549853797385621,0.1748940207070707],"dir":"ltr"},{"str":"f","boundary":[0.5533831045751634,0.1675352525252525,0.5614085645751634,0.1801143434343434],"dir":"ltr"},{"str":"=","boundary":[0.5676830392156862,0.1675352525252525,0.5804130792156863,0.1801143434343434],"dir":"ltr"},{"str":"O","boundary":[0.584922908496732,0.1675352525252525,0.597262256732026,0.1801143434343434],"dir":"ltr"},{"str":"(","boundary":[0.597654362745098,0.1675352525252525,0.6039217098039215,0.1801143434343434],"dir":"ltr"},{"str":"g","boundary":[0.6039216830065359,0.1675352525252525,0.6117517971241829,0.1801143434343434],"dir":"ltr"},{"str":"),","boundary":[0.6123399836601306,0.1623149297979798,0.6188028473202614,0.1801143434343434],"dir":"ltr"},{"str":"or","boundary":[0.6274302287581699,0.1623149297979798,0.6428951111111111,0.1748940207070707],"dir":"ltr"},{"str":"f","boundary":[0.6468166666666666,0.1675352525252525,0.6548421266666666,0.1801143434343434],"dir":"ltr"},{"str":"=","boundary":[0.6609205392156863,0.1675352525252525,0.6691407499346405,0.1801143434343434],"dir":"ltr"},{"str":"(","boundary":[0.6899137190849673,0.1675352525252525,0.6961810661437908,0.1801143434343434],"dir":"ltr"},{"str":"g","boundary":[0.696180996732026,0.1675352525252525,0.7040111108496732,0.1801143434343434],"dir":"ltr"},{"str":"),","boundary":[0.7045993790849672,0.1623149297979798,0.7112581414379084,0.1801143434343434],"dir":"ltr"},{"str":"or","boundary":[0.7194935620915032,0.1623149297979798,0.7349584444444444,0.1748940207070707],"dir":"ltr"},{"str":"both","boundary":[0.73888,0.1623149297979798,0.7723818188235294,0.1748940207070707],"dir":"ltr"},{"str":"(in","boundary":[0.7764994444444444,0.1623149297979798,0.7970758773856208,0.1748940207070707],"dir":"ltr"},{"str":"which","boundary":[0.8009973202614379,0.1623149297979798,0.8419396926797386,0.1748940207070707],"dir":"ltr"},{"str":"case","boundary":[0.8497825980392157,0.1623149297979798,0.8817053709803923,0.1748940207070707],"dir":"ltr"},{"str":"f","boundary":[0.16215678104575168,0.18268676767676767,0.17018224104575166,0.19526585858585857],"dir":"ltr"},{"str":"=","boundary":[0.17645671568627455,0.18268676767676767,0.1846769264052288,0.19526585858585857],"dir":"ltr"},{"str":"\u0002(","boundary":[0.19369658496732028,0.18268676767676767,0.21269397202614382,0.19526585858585857],"dir":"ltr"},{"str":"g","boundary":[0.2126939705882353,0.18268676767676767,0.22052408470588236,0.19526585858585857],"dir":"ltr"},{"str":")).","boundary":[0.22111227124183006,0.17746644494949493,0.23737478915032678,0.19526585858585857],"dir":"ltr"},{"str":"f","boundary":[0.2168627614379085,0.2013231313131313,0.2248882214379085,0.2139022222222222],"dir":"ltr"},{"str":"(","boundary":[0.22665287581699345,0.2013231313131313,0.23292022287581696,0.2139022222222222],"dir":"ltr"},{"str":"n","boundary":[0.23292019607843137,0.2013231313131313,0.24272004784313725,0.2139022222222222],"dir":"ltr"},{"str":")","boundary":[0.24272001633986925,0.2013231313131313,0.2489873633986928,0.2139022222222222],"dir":"ltr"},{"str":"g","boundary":[0.3238892973856209,0.2013231313131313,0.33171941150326795,0.2139022222222222],"dir":"ltr"},{"str":"(","boundary":[0.33230759803921567,0.2013231313131313,0.33857494509803915,0.2139022222222222],"dir":"ltr"},{"str":"n","boundary":[0.33857491830065356,0.2013231313131313,0.34837477006535944,0.2139022222222222],"dir":"ltr"},{"str":")","boundary":[0.34837473856209145,0.2013231313131313,0.354642085620915,0.2139022222222222],"dir":"ltr"},{"str":"(a)","boundary":[0.17470643790849671,0.2112543237373737,0.19469683320261436,0.2238334146464646],"dir":"ltr"},{"str":"n","boundary":[0.2168536601307189,0.21647464646464645,0.2266535118954248,0.22905373737373735],"dir":"ltr"},{"str":"\u0000","boundary":[0.2301828594771241,0.21619790646464643,0.24291289947712413,0.22877699737373733],"dir":"ltr"},{"str":"100","boundary":[0.24644227124183,0.21647464646464645,0.27110468888888883,0.22905373737373735],"dir":"ltr"},{"str":"n","boundary":[0.3238497875816993,0.21647464646464645,0.3336496393464052,0.22905373737373735],"dir":"ltr"},{"str":"\u0000","boundary":[0.3371789869281045,0.21619790646464643,0.3499090269281045,0.22877699737373733],"dir":"ltr"},{"str":"200","boundary":[0.3534383986928104,0.21647464646464645,0.3781008163398692,0.22905373737373735],"dir":"ltr"},{"str":"(b)","boundary":[0.17470637254901952,0.22686038434343433,0.1946967678431372,0.23943947525252524],"dir":"ltr"},{"str":"n1","boundary":[0.21685359477124175,0.23036554608585855,0.23312824011437905,0.24465979797979798],"dir":"ltr"},{"str":"=","boundary":[0.233128202614379,0.23036554608585855,0.23979438276143783,0.2391709122474747],"dir":"ltr"},{"str":"2","boundary":[0.23979436274509797,0.23036554608585855,0.2462554296568627,0.2391709122474747],"dir":"ltr"},{"str":"n2","boundary":[0.3239221405228757,0.23036554608585855,0.3401871290032679,0.24465979797979798],"dir":"ltr"},{"str":"=","boundary":[0.34018709150326787,0.23036554608585855,0.3468532716503267,0.2391709122474747],"dir":"ltr"},{"str":"3","boundary":[0.34685325163398684,0.23036554608585855,0.35331431854575157,0.2391709122474747],"dir":"ltr"},{"str":"(c)","boundary":[0.17568658496732018,0.24201189949494947,0.19390258849673195,0.2545909904040404],"dir":"ltr"},{"str":"100n","boundary":[0.21684377450980385,0.24723222222222221,0.2513060445751633,0.2598113131313131],"dir":"ltr"},{"str":"+","boundary":[0.2546393300653594,0.24723222222222221,0.26383999830065347,0.2598113131313131],"dir":"ltr"},{"str":"log","boundary":[0.2708987418300653,0.24723222222222221,0.29184958771241826,0.2598113131313131],"dir":"ltr"},{"str":"n","boundary":[0.3238062581699346,0.24723222222222221,0.33360610993464046,0.2598113131313131],"dir":"ltr"},{"str":"+","boundary":[0.3371354575163398,0.24723222222222221,0.34633612575163386,0.2598113131313131],"dir":"ltr"},{"str":"(log","boundary":[0.35339486928104563,0.24723222222222221,0.38061306222222213,0.2598113131313131],"dir":"ltr"},{"str":"n","boundary":[0.3835541830065359,0.24723222222222221,0.39335403477124176,0.2598113131313131],"dir":"ltr"},{"str":")","boundary":[0.39335400326797376,0.24723222222222221,0.3996213503267973,0.2598113131313131],"dir":"ltr"},{"str":"2","boundary":[0.39980437908496724,0.24551706123737368,0.406265445996732,0.25432242739898986],"dir":"ltr"},{"str":"(d)","boundary":[0.17451026143790843,0.25716341464646464,0.19489134849673195,0.2697425055555555],"dir":"ltr"},{"str":"n","boundary":[0.2168520915032679,0.2623837373737374,0.22665194326797378,0.27496282828282825],"dir":"ltr"},{"str":"log","boundary":[0.22939697712418292,0.2623837373737374,0.2503478230065359,0.27496282828282825],"dir":"ltr"},{"str":"n","boundary":[0.25309289215686265,0.2623837373737374,0.26289274392156853,0.27496282828282825],"dir":"ltr"},{"str":"10n","boundary":[0.3238731209150326,0.2623837373737374,0.35011463934640513,0.27496282828282825],"dir":"ltr"},{"str":"log","boundary":[0.3528596732026143,0.2623837373737374,0.37381051908496726,0.27496282828282825],"dir":"ltr"},{"str":"10n","boundary":[0.37635950980392147,0.2623837373737374,0.40260102823529403,0.27496282828282825],"dir":"ltr"},{"str":"(e)","boundary":[0.17509856209150315,0.27216341464646465,0.19429129503267964,0.2847425055555555],"dir":"ltr"},{"str":"log","boundary":[0.2168402287581698,0.27738373737373734,0.23779107464052276,0.28996282828282827],"dir":"ltr"},{"str":"2n","boundary":[0.24053614379084956,0.27738373737373734,0.2585567962091502,0.28996282828282827],"dir":"ltr"},{"str":"log","boundary":[0.3238508986928103,0.27738373737373734,0.34480174457516327,0.28996282828282827],"dir":"ltr"},{"str":"3n","boundary":[0.34754681372549007,0.27738373737373734,0.3655674661437907,0.28996282828282827],"dir":"ltr"},{"str":"(f)","boundary":[0.1764718627450979,0.2873149297979798,0.1929297533333332,0.29989402070707066],"dir":"ltr"},{"str":"10","boundary":[0.21685127450980382,0.29253525252525253,0.23054789673202603,0.3051143434343434],"dir":"ltr"},{"str":"log","boundary":[0.23603787581699334,0.29253525252525253,0.25698872169934633,0.3051143434343434],"dir":"ltr"},{"str":"n","boundary":[0.25953771241830054,0.29253525252525253,0.2693375641830064,0.3051143434343434],"dir":"ltr"},{"str":"log(n2","boundary":[0.32384735294117634,0.290820091540404,0.36744270089869263,0.3051143434343434],"dir":"ltr"},{"str":")","boundary":[0.3684326307189541,0.29253525252525253,0.37469997777777764,0.3051143434343434],"dir":"ltr"},{"str":"(g)","boundary":[0.17490321895424824,0.30307250555555554,0.19469826836601295,0.31565159646464647],"dir":"ltr"},{"str":"n1","boundary":[0.21685501633986914,0.30657766729797975,0.23312894272875803,0.3208719191919192],"dir":"ltr"},{"str":":","boundary":[0.23312890522875804,0.30657766729797975,0.2370488470588234,0.31538303345959595],"dir":"ltr"},{"str":"01","boundary":[0.2370488398692809,0.30657766729797975,0.24997097369281032,0.31538303345959595],"dir":"ltr"},{"str":"n","boundary":[0.3239226960784312,0.3082928282828283,0.3337225478431371,0.3208719191919192],"dir":"ltr"},{"str":"log2","boundary":[0.33646758169934626,0.30551713699494953,0.36391312573529394,0.3208719191919192],"dir":"ltr"},{"str":"n","boundary":[0.36745205882352927,0.3082928282828283,0.37725191058823515,0.3208719191919192],"dir":"ltr"},{"str":"(h)","boundary":[0.1743148039215685,0.31822402070707073,0.19528192862745083,0.33080311161616166],"dir":"ltr"},{"str":"n2","boundary":[0.21685042483660116,0.32172918244949494,0.23312877933006526,0.3360234343434344],"dir":"ltr"},{"str":"=","boundary":[0.23392259803921556,0.3234443434343435,0.2421434039215685,0.3360234343434344],"dir":"ltr"},{"str":"log","boundary":[0.24488846405228742,0.3234443434343435,0.2658393099346404,0.3360234343434344],"dir":"ltr"},{"str":"n","boundary":[0.2683883006535946,0.3234443434343435,0.2781881524183005,0.3360234343434344],"dir":"ltr"},{"str":"n(log","boundary":[0.3238744117647057,0.3234443434343435,0.3608924249673201,0.3360234343434344],"dir":"ltr"},{"str":"n","boundary":[0.3636374673202613,0.3234443434343435,0.3734373190849672,0.3360234343434344],"dir":"ltr"},{"str":")","boundary":[0.3734372875816992,0.3234443434343435,0.37970463464052273,0.3360234343434344],"dir":"ltr"},{"str":"2","boundary":[0.3798050490196077,0.32172918244949494,0.38626611593137244,0.33053454861111115],"dir":"ltr"},{"str":"(i)","boundary":[0.17666779411764696,0.33337553585858587,0.19273499294117635,0.3459546267676768],"dir":"ltr"},{"str":"n0","boundary":[0.21685259803921558,0.3368806976010101,0.23312887736928098,0.3511749494949496],"dir":"ltr"},{"str":":","boundary":[0.23312883986928093,0.3368806976010101,0.2370487816993463,0.3456860637626263],"dir":"ltr"},{"str":"1","boundary":[0.23704877450980383,0.3368806976010101,0.2435098414215685,0.3456860637626263],"dir":"ltr"},{"str":"(log","boundary":[0.32392263071895416,0.3385958585858586,0.3511408236601306,0.3511749494949496],"dir":"ltr"},{"str":"n","boundary":[0.35408194444444435,0.3385958585858586,0.36388179620915023,0.3511749494949496],"dir":"ltr"},{"str":")","boundary":[0.36388176470588224,0.3385958585858586,0.3701491117647058,0.3511749494949496],"dir":"ltr"},{"str":"10","boundary":[0.3701971405228757,0.3368806976010101,0.38311927434640514,0.3456860637626263],"dir":"ltr"},{"str":"(j)","boundary":[0.17686380718954242,0.348527051010101,0.19273566013071888,0.36110614191919194],"dir":"ltr"},{"str":"(log","boundary":[0.21685318627450975,0.3537473737373738,0.24407137921568622,0.36632646464646473],"dir":"ltr"},{"str":"n","boundary":[0.2468164215686274,0.3537473737373738,0.25661627333333326,0.36632646464646473],"dir":"ltr"},{"str":")","boundary":[0.2566162418300653,0.3537473737373738,0.2628835888888888,0.36632646464646473],"dir":"ltr"},{"str":"log","boundary":[0.2629421568627451,0.3520322127525252,0.27957911928104573,0.3608375789141414],"dir":"ltr"},{"str":"n","boundary":[0.2821281045751634,0.3520322127525252,0.29016170629084964,0.3608375789141414],"dir":"ltr"},{"str":"n=","boundary":[0.3239225490196078,0.3537473737373738,0.34194320666666667,0.36632646464646473],"dir":"ltr"},{"str":"log","boundary":[0.34468823529411763,0.3537473737373738,0.3656390811764706,0.36632646464646473],"dir":"ltr"},{"str":"n","boundary":[0.36818807189542485,0.3537473737373738,0.37798792366013073,0.36632646464646473],"dir":"ltr"},{"str":"p","boundary":[0.21686290849673204,0.35953123979797985,0.23039061084967322,0.3721103307070708],"dir":"ltr"},{"str":"3","boundary":[0.37019622549019604,0.3671838541666666,0.3766572924019608,0.3759892203282828],"dir":"ltr"},{"str":"(k)","boundary":[0.17431388888888888,0.36367856616161615,0.19489032183006536,0.3762576570707071],"dir":"ltr"},{"str":"n","boundary":[0.230390522875817,0.3688990151515152,0.24019037464052287,0.3814781060606061],"dir":"ltr"},{"str":"(log","boundary":[0.3239158496732026,0.3688990151515152,0.3511340426143791,0.3814781060606061],"dir":"ltr"},{"str":"n","boundary":[0.35407516339869277,0.3688990151515152,0.36387501516339865,0.3814781060606061],"dir":"ltr"},{"str":")","boundary":[0.3638749836601307,0.3688990151515152,0.3701423307189542,0.3814781060606061],"dir":"ltr"},{"str":"(l)","boundary":[0.17666681372549015,0.37928487929292926,0.19273401254901956,0.3918639702020202],"dir":"ltr"},{"str":"n1","boundary":[0.21685161764705876,0.38279004103535347,0.23312789697712416,0.397084292929293],"dir":"ltr"},{"str":"=","boundary":[0.23312785947712414,0.38279004103535347,0.23979403962418297,0.39159540719696967],"dir":"ltr"},{"str":"2","boundary":[0.23979401960784308,0.38279004103535347,0.2462550865196078,0.39159540719696967],"dir":"ltr"},{"str":"5log2","boundary":[0.3239217973856209,0.38279004103535347,0.35450578379084957,0.397084292929293],"dir":"ltr"},{"str":"n","boundary":[0.35745120915032674,0.38279004103535347,0.365484810866013,0.39159540719696967],"dir":"ltr"},{"str":"(m)","boundary":[0.17196101307189535,0.3944363944444444,0.19743737189542476,0.4070154853535353],"dir":"ltr"},{"str":"n2n","boundary":[0.2168490849673202,0.3979415561868686,0.24293577491830057,0.4122358080808081],"dir":"ltr"},{"str":"3n","boundary":[0.32392178104575153,0.3979415561868686,0.34019066053921554,0.4122358080808081],"dir":"ltr"},{"str":"(n)","boundary":[0.17431392156862735,0.40958790959595953,0.19528104627450968,0.42216700050505046],"dir":"ltr"},{"str":"2n","boundary":[0.21684954248366003,0.41294153093434344,0.23313178799019596,0.42738732323232326],"dir":"ltr"},{"str":"2n+1","boundary":[0.32392171568627437,0.41294153093434344,0.35664521143790834,0.42738732323232326],"dir":"ltr"},{"str":"(o)","boundary":[0.17509743464052271,0.42458788434343436,0.1942901675816992,0.4371669752525253],"dir":"ltr"},{"str":"n","boundary":[0.21683910130718936,0.4298082070707071,0.22663895307189527,0.4423872979797981],"dir":"ltr"},{"str":"!","boundary":[0.22663892156862728,0.4298082070707071,0.23114815568627436,0.4423872979797981],"dir":"ltr"},{"str":"2n","boundary":[0.32389316993464035,0.4280930460858586,0.3401897781862743,0.4423872979797981],"dir":"ltr"},{"str":"(p)","boundary":[0.17450911764705865,0.44155758131313133,0.19489020470588217,0.45413667222222226],"dir":"ltr"},{"str":"(log","boundary":[0.21685094771241814,0.4467779040404041,0.2440691406535946,0.45935699494949506],"dir":"ltr"},{"str":"n","boundary":[0.2468141830065358,0.4467779040404041,0.2566140347712417,0.45935699494949506],"dir":"ltr"},{"str":")","boundary":[0.2566140032679737,0.4467779040404041,0.2628813503267972,0.45935699494949506],"dir":"ltr"},{"str":"log","boundary":[0.262940473856209,0.44506274305555554,0.27957743627450965,0.45386810921717174],"dir":"ltr"},{"str":"n","boundary":[0.28212642156862733,0.44506274305555554,0.29016002328431356,0.45386810921717174],"dir":"ltr"},{"str":"2(log2","boundary":[0.3239208660130718,0.44506274305555554,0.3596028916339868,0.45935699494949506],"dir":"ltr"},{"str":"n","boundary":[0.3625483169934639,0.44506274305555554,0.3705819187091502,0.45386810921717174],"dir":"ltr"},{"str":")","boundary":[0.37058189542483644,0.44506274305555554,0.3756755407679737,0.45386810921717174],"dir":"ltr"},{"str":"2","boundary":[0.3756855555555554,0.44362715616161613,0.38117151908496716,0.4499167016161616],"dir":"ltr"},{"str":"(q)","boundary":[0.17470516339869266,0.45670909646464647,0.1946955586928103,0.4692881873737374],"dir":"ltr"},{"str":"Pn","boundary":[0.21686202614379071,0.452610966969697,0.24195445138888874,0.46735299558080806],"dir":"ltr"},{"str":"ik","boundary":[0.2586266666666665,0.4602142582070706,0.2711728393790848,0.47450851010101014],"dir":"ltr"},{"str":"nk+1","boundary":[0.3239207843137253,0.4602142582070706,0.3572352931372547,0.47450851010101014],"dir":"ltr"},{"str":"i=1","boundary":[0.23392084967320248,0.468547591540404,0.2548765676470587,0.4773529577020202],"dir":"ltr"},{"str":"0.2.","boundary":[0.1260780392156861,0.48019394494949486,0.15313344392156844,0.4927730358585858],"dir":"ltr"},{"str":"Show","boundary":[0.1621530392156861,0.48019394494949486,0.2032896262745096,0.4927730358585858],"dir":"ltr"},{"str":"that,","boundary":[0.20760336601307172,0.48019394494949486,0.24366096013071875,0.4927730358585858],"dir":"ltr"},{"str":"if","boundary":[0.24836676470588218,0.48019394494949486,0.25894799999999984,0.4927730358585858],"dir":"ltr"},{"str":"c","boundary":[0.26345776143790833,0.4854142676767676,0.27050649202614363,0.4979933585858586],"dir":"ltr"},{"str":"is","boundary":[0.27501625816993447,0.48019394494949486,0.2828451235294116,0.4927730358585858],"dir":"ltr"},{"str":"a","boundary":[0.2922567810457515,0.48019394494949486,0.29676549856209133,0.4927730358585858],"dir":"ltr"},{"str":"positive","boundary":[0.3057849999999998,0.48019394494949486,0.3643562070588233,0.4927730358585858],"dir":"ltr"},{"str":"real","boundary":[0.36866980392156845,0.48019394494949486,0.3982484262745096,0.4927730358585858],"dir":"ltr"},{"str":",","boundary":[0.4601676797385619,0.48019394494949486,0.46036322313725475,0.4927730358585858],"dir":"ltr"},{"str":"number","boundary":[0.4027582026143789,0.48019394494949486,0.46173638026143776,0.4927730358585858],"dir":"ltr"},{"str":"then","boundary":[0.4689906045751632,0.48019394494949486,0.5034691528104573,0.4927730358585858],"dir":"ltr"},{"str":"g","boundary":[0.5077827614379082,0.4854142676767676,0.5156128755555554,0.4979933585858586],"dir":"ltr"},{"str":"(","boundary":[0.516201062091503,0.4854142676767676,0.5224684091503266,0.4979933585858586],"dir":"ltr"},{"str":"n","boundary":[0.5224683823529409,0.4854142676767676,0.5322682341176468,0.4979933585858586],"dir":"ltr"},{"str":")","boundary":[0.5322682026143789,0.4854142676767676,0.534025805228758,0.4979933585858586],"dir":"ltr"},{"str":"=","boundary":[0.5430452941176468,0.4854142676767676,0.5512655048366011,0.4979933585858586],"dir":"ltr"},{"str":"1","boundary":[0.5602851633986926,0.4854142676767676,0.5649765954248365,0.4979933585858586],"dir":"ltr"},{"str":"+","boundary":[0.5720353431372547,0.4854142676767676,0.5847653831372547,0.4979933585858586],"dir":"ltr"},{"str":"c","boundary":[0.5882947549019605,0.4854142676767676,0.5953434854901958,0.4979933585858586],"dir":"ltr"},{"str":"+","boundary":[0.5988728594771239,0.4854142676767676,0.6116028994771239,0.4979933585858586],"dir":"ltr"},{"str":"c2","boundary":[0.6151322712418298,0.48369910669191907,0.629009596323529,0.4979933585858586],"dir":"ltr"},{"str":"+","boundary":[0.6335289215686272,0.4854142676767676,0.6462589615686272,0.4979933585858586],"dir":"ltr"},{"str":"\u0001","boundary":[0.6497883333333331,0.4851375276767676,0.6515525205228755,0.49771661858585853],"dir":"ltr"},{"str":"\u0001","boundary":[0.6570426143790846,0.4851375276767676,0.6588068015686271,0.49771661858585853],"dir":"ltr"},{"str":"\u0001","boundary":[0.6642968954248363,0.4851375276767676,0.6688061295424833,0.49771661858585853],"dir":"ltr"},{"str":"+","boundary":[0.6723355392156859,0.4854142676767676,0.685065579215686,0.4979933585858586],"dir":"ltr"},{"str":"cn","boundary":[0.688594901960784,0.48369910669191907,0.703719353349673,0.4979933585858586],"dir":"ltr"},{"str":"is:","boundary":[0.7090191013071893,0.48019394494949486,0.7260630295424834,0.4927730358585858],"dir":"ltr"},{"str":"(a)","boundary":[0.17254851307189517,0.5082242479797978,0.1925389083660128,0.5208033388888887],"dir":"ltr"},{"str":"\u0002(1)","boundary":[0.20136240196078406,0.5134445707070706,0.23484794196078407,0.5260236616161615],"dir":"ltr"},{"str":"if","boundary":[0.23935766339869255,0.5082242479797978,0.24993889869281022,0.5208033388888887],"dir":"ltr"},{"str":"c","boundary":[0.2544486601307187,0.5134445707070706,0.25698762457516316,0.5260236616161615],"dir":"ltr"},{"str":"<","boundary":[0.26600715686274484,0.5134445707070706,0.2787371968627449,0.5260236616161615],"dir":"ltr"},{"str":"1","boundary":[0.28324702614379066,0.5134445707070706,0.29146783202614357,0.5260236616161615],"dir":"ltr"},{"str":".","boundary":[0.29146782679738537,0.5082242479797978,0.29597706091503245,0.5208033388888887],"dir":"ltr"},{"str":"(b)","boundary":[0.17254854575163375,0.5280727328282827,0.19253894104575142,0.5406518237373736],"dir":"ltr"},{"str":"\u0002(","boundary":[0.20136243464052264,0.5332930555555555,0.2203598216993462,0.5458721464646464],"dir":"ltr"},{"str":"n","boundary":[0.22035982026143766,0.5332930555555555,0.23015967202614354,0.5458721464646464],"dir":"ltr"},{"str":")","boundary":[0.23015964052287557,0.5332930555555555,0.23642698758169908,0.5458721464646464],"dir":"ltr"},{"str":"if","boundary":[0.24093673202614357,0.5280727328282827,0.2515179673202612,0.5406518237373736],"dir":"ltr"},{"str":"c","boundary":[0.2560277287581697,0.5332930555555555,0.263076459346405,0.5458721464646464],"dir":"ltr"},{"str":"=","boundary":[0.2675862254901959,0.5332930555555555,0.27580643620915013,0.5458721464646464],"dir":"ltr"},{"str":"1","boundary":[0.28482609477124166,0.5332930555555555,0.29304690065359457,0.5458721464646464],"dir":"ltr"},{"str":".","boundary":[0.2930468954248364,0.5280727328282827,0.2975561295424835,0.5406518237373736],"dir":"ltr"},{"str":"(c)","boundary":[0.1745094771241828,0.5480727328282827,0.19272548065359457,0.5606518237373737],"dir":"ltr"},{"str":"\u0002(","boundary":[0.2013529411764704,0.5532930555555555,0.2203503282352939,0.5658721464646465],"dir":"ltr"},{"str":"cn","boundary":[0.22035032679738542,0.5515778945707069,0.23548430433006515,0.5658721464646465],"dir":"ltr"},{"str":")","boundary":[0.2362742320261436,0.5532930555555555,0.24254157908496712,0.5658721464646465],"dir":"ltr"},{"str":"if","boundary":[0.2472474019607841,0.5480727328282827,0.25782863725490174,0.5606518237373737],"dir":"ltr"},{"str":"c","boundary":[0.262142336601307,0.5532930555555555,0.26468130104575144,0.5658721464646465],"dir":"ltr"},{"str":">","boundary":[0.2737008333333331,0.5532930555555555,0.28643087333333317,0.5658721464646465],"dir":"ltr"},{"str":"1","boundary":[0.29094070261437893,0.5532930555555555,0.29916150849673184,0.5658721464646465],"dir":"ltr"},{"str":".","boundary":[0.29916150326797364,0.5480727328282827,0.3036707373856207,0.5606518237373737],"dir":"ltr"},{"str":"The","boundary":[0.16215676470588214,0.5761030358585857,0.1911493494117645,0.5886821267676766],"dir":"ltr"},{"str":"moral:","boundary":[0.19605120915032662,0.5761030358585857,0.24464349738562075,0.5886821267676766],"dir":"ltr"},{"str":"in","boundary":[0.25111411764705865,0.5761030358585857,0.2662045870588233,0.5886821267676766],"dir":"ltr"},{"str":"big-","boundary":[0.27130251633986907,0.5761030358585857,0.299725342222222,0.5886821267676766],"dir":"ltr"},{"str":"\u0002","boundary":[0.29972539215686256,0.5813233585858585,0.31245543215686256,0.5939024494949494],"dir":"ltr"},{"str":"terms","boundary":[0.31716133986928086,0.5761030358585857,0.3608374233986926,0.5886821267676766],"dir":"ltr"},{"str":"the","boundary":[0.3700525816993462,0.5761030358585857,0.3945359322875815,0.5886821267676766],"dir":"ltr"},{"str":"sum","boundary":[0.39943787581699325,0.5761030358585857,0.4313769275816991,0.5886821267676766],"dir":"ltr"},{"str":"of","boundary":[0.43647496732026125,0.5761030358585857,0.45018173673202594,0.5886821267676766],"dir":"ltr"},{"str":"a","boundary":[0.4548875490196077,0.5761030358585857,0.45880801490196066,0.5886821267676766],"dir":"ltr"},{"str":"geometric","boundary":[0.46900401960784294,0.5761030358585857,0.5428447631372547,0.5886821267676766],"dir":"ltr"},{"str":"series","boundary":[0.5473545098039213,0.5761030358585857,0.5910143145098037,0.5886821267676766],"dir":"ltr"},{"str":"is","boundary":[0.5961123529411763,0.5761030358585857,0.6035490614379083,0.5886821267676766],"dir":"ltr"},{"str":"simply","boundary":[0.6137450326797383,0.5761030358585857,0.6641117126797385,0.5886821267676766],"dir":"ltr"},{"str":"the","boundary":[0.6690136601307188,0.5761030358585857,0.6934970107189541,0.5886821267676766],"dir":"ltr"},{"str":"\u0002rst","boundary":[0.6983989542483658,0.5761030358585857,0.7293449977777776,0.5886821267676766],"dir":"ltr"},{"str":"term","boundary":[0.7344429084967319,0.5761030358585857,0.7706795696732024,0.5886821267676766],"dir":"ltr"},{"str":"if","boundary":[0.7755814705882351,0.5761030358585857,0.7812608039215685,0.5886821267676766],"dir":"ltr"},{"str":"the","boundary":[0.7910646078431371,0.5761030358585857,0.8155479584313724,0.5886821267676766],"dir":"ltr"},{"str":"series","boundary":[0.8204499019607842,0.5761030358585857,0.8641097066666664,0.5886821267676766],"dir":"ltr"},{"str":"is","boundary":[0.8690115032679737,0.5761030358585857,0.8815461973856208,0.5886821267676766],"dir":"ltr"},{"str":"strictly","boundary":[0.16215692810457502,0.5911030358585857,0.21563286339869267,0.6036821267676766],"dir":"ltr"},{"str":",","boundary":[0.30046101307189527,0.5911030358585857,0.3006565564705881,0.6036821267676766],"dir":"ltr"},{"str":"decreasing","boundary":[0.22014271241830052,0.5911030358585857,0.30085311947712406,0.6036821267676766],"dir":"ltr"},{"str":"the","boundary":[0.30928393790849656,0.5911030358585857,0.3337672884967319,0.6036821267676766],"dir":"ltr"},{"str":"last","boundary":[0.33808099673202596,0.5911030358585857,0.3659015061437907,0.6036821267676766],"dir":"ltr"},{"str":"term","boundary":[0.3704112254901959,0.5911030358585857,0.4066478866666665,0.6036821267676766],"dir":"ltr"},{"str":"if","boundary":[0.4109615522875815,0.5911030358585857,0.4170330261437907,0.6036821267676766],"dir":"ltr"},{"str":"the","boundary":[0.4260525490196077,0.5911030358585857,0.45053589960784296,0.6036821267676766],"dir":"ltr"},{"str":"series","boundary":[0.45484960784313716,0.5911030358585857,0.4985094125490195,0.6036821267676766],"dir":"ltr"},{"str":"is","boundary":[0.5028231372549018,0.5911030358585857,0.5108480810457515,0.6036821267676766],"dir":"ltr"},{"str":"strictly","boundary":[0.5198675816993463,0.5911030358585857,0.573343516993464,0.6036821267676766],"dir":"ltr"},{"str":",","boundary":[0.6558282026143789,0.5911030358585857,0.6560237460130718,0.6036821267676766],"dir":"ltr"},{"str":"increasing","boundary":[0.5780494444444443,0.5911030358585857,0.6562203550326796,0.6036821267676766],"dir":"ltr"},{"str":"or","boundary":[0.6646511274509802,0.5911030358585857,0.6801160098039215,0.6036821267676766],"dir":"ltr"},{"str":"the","boundary":[0.6842336437908496,0.5911030358585857,0.7087169943790849,0.6036821267676766],"dir":"ltr"},{"str":"number","boundary":[0.7132266176470587,0.5911030358585857,0.7722047952941176,0.6036821267676766],"dir":"ltr"},{"str":"of","boundary":[0.7763223692810456,0.5911030358585857,0.7857154832679738,0.6036821267676766],"dir":"ltr"},{"str":"terms","boundary":[0.794342794117647,0.5911030358585857,0.8380188776470586,0.6036821267676766],"dir":"ltr"},{"str":"if","boundary":[0.8423324999999999,0.5911030358585857,0.8486000032679739,0.6036821267676766],"dir":"ltr"},{"str":"the","boundary":[0.8572274673202613,0.5911030358585857,0.8817108179084968,0.6036821267676766],"dir":"ltr"},{"str":"series","boundary":[0.16215720588235294,0.6062545510101008,0.2058170105882353,0.6188336419191918],"dir":"ltr"},{"str":"is","boundary":[0.2103268137254902,0.6062545510101008,0.21815567908496733,0.6188336419191918],"dir":"ltr"},{"str":"unchanging","boundary":[0.22756733660130718,0.6062545510101008,0.31635131294117647,0.6188336419191918],"dir":"ltr"},{"str":".","boundary":[0.3159591666666667,0.6062545510101008,0.3204684007843137,0.6188336419191918],"dir":"ltr"},{"str":"0.3.","boundary":[0.1260784477124183,0.6286787934343433,0.15313385241830066,0.6412578843434342],"dir":"ltr"},{"str":"The","boundary":[0.1621534477124183,0.6286787934343433,0.19114603241830067,0.6412578843434342],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.19565573529411764,0.6286787934343433,0.2671678783006536,0.6412578843434342],"dir":"ltr"},{"str":"numbers","boundary":[0.2716775816993464,0.6286787934343433,0.33809518169934644,0.6412578843434342],"dir":"ltr"},{"str":";","boundary":[0.36039202614379084,0.6338991161616161,0.36215621333333337,0.646478207070707],"dir":"ltr"},{"str":"F1","boundary":[0.3676463071895425,0.6338991161616161,0.38450015187908493,0.6473529450757575],"dir":"ltr"},{"str":";","boundary":[0.3854900490196078,0.6338991161616161,0.38725423620915034,0.646478207070707],"dir":"ltr"},{"str":"F2","boundary":[0.3927443300653594,0.6338991161616161,0.4095981747549019,0.6473529450757575],"dir":"ltr"},{"str":";","boundary":[0.4103920261437908,0.6338991161616161,0.4121562133333333,0.646478207070707],"dir":"ltr"},{"str":":","boundary":[0.41764630718954243,0.6338991161616161,0.4194104943790849,0.646478207070707],"dir":"ltr"},{"str":":","boundary":[0.4249005882352941,0.6338991161616161,0.42666477542483655,0.646478207070707],"dir":"ltr"},{"str":":","boundary":[0.4321548692810457,0.6338991161616161,0.43391905647058815,0.646478207070707],"dir":"ltr"},{"str":";","boundary":[0.43940915032679734,0.6338991161616161,0.4439183844444444,0.646478207070707],"dir":"ltr"},{"str":"are","boundary":[0.4484281535947712,0.6286787934343433,0.4729115041830065,0.6412578843434342],"dir":"ltr"},{"str":"de\u0002ned","boundary":[0.47742129084967316,0.6286787934343433,0.5326716179084967,0.6412578843434342],"dir":"ltr"},{"str":"by","boundary":[0.5365931862745098,0.6286787934343433,0.5544347768627452,0.6412578843434342],"dir":"ltr"},{"str":"the","boundary":[0.5589444934640523,0.6286787934343433,0.5834278440522875,0.6412578843434342],"dir":"ltr"},{"str":"rule","boundary":[0.5879376307189542,0.6286787934343433,0.6184929824836601,0.6412578843434342],"dir":"ltr"},{"str":"F0","boundary":[0.3424087908496732,0.6338991161616161,0.3594020963235294,0.6473529450757575],"dir":"ltr"},{"str":"F0","boundary":[0.3941173692810458,0.6611718434343433,0.41097060939542485,0.6746256723484848],"dir":"ltr"},{"str":"=","boundary":[0.4164703267973856,0.6611718434343433,0.42469053751633984,0.6737509343434341],"dir":"ltr"},{"str":"0","boundary":[0.43371019607843136,0.6611718434343433,0.4419310019607843,0.6737509343434341],"dir":"ltr"},{"str":"F1","boundary":[0.4534990359477124,0.6611718434343433,0.47038243946078423,0.6746256723484848],"dir":"ltr"},{"str":"=","boundary":[0.47588215686274504,0.6611718434343433,0.4842984460130718,0.6737509343434341],"dir":"ltr"},{"str":"1","boundary":[0.4929259477124182,0.6611718434343433,0.5011467535947711,0.6737509343434341],"dir":"ltr"},{"str":"Fn","boundary":[0.5129108496732026,0.6611718434343433,0.5313668206699347,0.6746256723484848],"dir":"ltr"},{"str":"=","boundary":[0.5368625980392157,0.6611718434343433,0.5495926380392158,0.6737509343434341],"dir":"ltr"},{"str":"Fn","boundary":[0.5539063888888889,0.6611718434343433,0.5723472455065359,0.6746256723484848],"dir":"ltr"},{"str":"\u0000","boundary":[0.5723472222222221,0.6663926549873737,0.5825345129084966,0.6751980211489899],"dir":"ltr"},{"str":"1","boundary":[0.5825345098039215,0.6658203061868687,0.5889955767156861,0.6746256723484848],"dir":"ltr"},{"str":"+","boundary":[0.5935293300653595,0.6611718434343433,0.6062593700653595,0.6737509343434341],"dir":"ltr"},{"str":"Fn","boundary":[0.6097887418300653,0.6611718434343433,0.6282295984477124,0.6746256723484848],"dir":"ltr"},{"str":"\u0000","boundary":[0.6282295751633986,0.6663926549873737,0.638416865849673,0.6751980211489899],"dir":"ltr"},{"str":"2","boundary":[0.6384168627450979,0.6658203061868687,0.6448779296568626,0.6746256723484848],"dir":"ltr"},{"str":":","boundary":[0.6458823039215685,0.6611718434343433,0.6503915380392156,0.6737509343434341],"dir":"ltr"},{"str":"In","boundary":[0.16215681372549007,0.6830727328282828,0.1788100501960783,0.6956518237373737],"dir":"ltr"},{"str":"this","boundary":[0.18508459150326784,0.6830727328282828,0.21388183032679728,0.6956518237373737],"dir":"ltr"},{"str":"problem","boundary":[0.22054848039215674,0.6830727328282828,0.28226150039215675,0.6956518237373737],"dir":"ltr"},{"str":"we","boundary":[0.28833998366013064,0.6830727328282828,0.3092908295424836,0.6956518237373737],"dir":"ltr"},{"str":"will","boundary":[0.31556531045751623,0.6830727328282828,0.3435811657516339,0.6956518237373737],"dir":"ltr"},{"str":"con\u0002rm","boundary":[0.350051748366013,0.6830727328282828,0.40725553424836597,0.6956518237373737],"dir":"ltr"},{"str":"that","boundary":[0.41333393790849665,0.6830727328282828,0.4448822979084967,0.6956518237373737],"dir":"ltr"},{"str":"this","boundary":[0.4513528921568627,0.6830727328282828,0.48015013098039205,0.6956518237373737],"dir":"ltr"},{"str":"sequence","boundary":[0.48662070261437906,0.6830727328282828,0.5549754826143791,0.6956518237373737],"dir":"ltr"},{"str":"grows","boundary":[0.5610538725490195,0.6830727328282828,0.6055113396078431,0.6956518237373737],"dir":"ltr"},{"str":"exponentially","boundary":[0.6117857352941176,0.6830727328282828,0.7140655835294117,0.6956518237373737],"dir":"ltr"},{"str":"fast","boundary":[0.720144068627451,0.6830727328282828,0.7483552698039215,0.6956518237373737],"dir":"ltr"},{"str":"and","boundary":[0.7548257679738561,0.6830727328282828,0.783248593856209,0.6956518237373737],"dir":"ltr"},{"str":"obtain","boundary":[0.7895231535947712,0.6830727328282828,0.8371387124183006,0.6956518237373737],"dir":"ltr"},{"str":"some","boundary":[0.8436092647058823,0.6830727328282828,0.8819947305882352,0.6956518237373737],"dir":"ltr"},{"str":"bounds","boundary":[0.16215665032679738,0.698224247979798,0.21623490209150326,0.7108033388888888],"dir":"ltr"},{"str":"on","boundary":[0.2207447222222222,0.698224247979798,0.23896072575163396,0.7108033388888888],"dir":"ltr"},{"str":"its","boundary":[0.2432744607843137,0.698224247979798,0.2620765019607843,0.7108033388888888],"dir":"ltr"},{"str":"growth.","boundary":[0.2667823039215686,0.698224247979798,0.32457212745098035,0.7108033388888888],"dir":"ltr"},{"str":"(a)","boundary":[0.17254880718954244,0.7226181873737373,0.19253920248366008,0.7351972782828281],"dir":"ltr"},{"str":"Use","boundary":[0.20136269607843132,0.7226181873737373,0.2303552807843137,0.7351972782828281],"dir":"ltr"},{"str":"induction","boundary":[0.23486498366013067,0.7226181873737373,0.3061825095424836,0.7351972782828281],"dir":"ltr"},{"str":"to","boundary":[0.3104961928104575,0.7226181873737373,0.32498434575163393,0.7351972782828281],"dir":"ltr"},{"str":"prove","boundary":[0.32949406862745095,0.7226181873737373,0.3714120392156862,0.7351972782828281],"dir":"ltr"},{"str":"that","boundary":[0.3755296895424836,0.7226181873737373,0.4070780495424836,0.7351972782828281],"dir":"ltr"},{"str":"F","boundary":[0.4115878594771242,0.7278385101010099,0.42197374888888883,0.7404176010101008],"dir":"ltr"},{"str":"\u0015","boundary":[0.4356860130718954,0.7275617701010099,0.4484160530718954,0.7401408610101008],"dir":"ltr"},{"str":"20","boundary":[0.4529258823529411,0.7261233491161616,0.46763734142156854,0.7404176010101008],"dir":"ltr"},{"str":":","boundary":[0.4676373039215686,0.7261233491161616,0.47155724575163405,0.7349287152777777],"dir":"ltr"},{"str":"5n","boundary":[0.4715572385620915,0.7261233491161616,0.48605186968954256,0.7349287152777777],"dir":"ltr"},{"str":"for","boundary":[0.49117629084967324,0.7226181873737373,0.5121271367320261,0.7351972782828281],"dir":"ltr"},{"str":"n","boundary":[0.5166369117647059,0.7278385101010099,0.5264367635294118,0.7404176010101008],"dir":"ltr"},{"str":"\u0015","boundary":[0.5307504411764706,0.7275617701010099,0.5434804811764706,0.7401408610101008],"dir":"ltr"},{"str":"6","boundary":[0.5479903104575163,0.7278385101010099,0.5562111163398693,0.7404176010101008],"dir":"ltr"},{"str":".","boundary":[0.5562111111111111,0.7226181873737373,0.5607203452287582,0.7351972782828281],"dir":"ltr"},{"str":"n","boundary":[0.42215663398692804,0.7324869981060604,0.4301902357026144,0.7412923642676766],"dir":"ltr"},{"str":"(b)","boundary":[0.17254934640522882,0.7424666722222222,0.19253974169934646,0.755045763131313],"dir":"ltr"},{"str":"Find","boundary":[0.2013632352941177,0.7424666722222222,0.23644337124183012,0.755045763131313],"dir":"ltr"},{"str":"a","boundary":[0.24095305555555563,0.7424666722222222,0.24526569464052295,0.755045763131313],"dir":"ltr"},{"str":"constant","boundary":[0.25467735294117655,0.7424666722222222,0.31912521529411775,0.755045763131313],"dir":"ltr"},{"str":"such","boundary":[0.36496789215686287,0.7424666722222222,0.3949358528104576,0.755045763131313],"dir":"ltr"},{"str":"that","boundary":[0.4039553594771243,0.7424666722222222,0.43550371947712435,0.755045763131313],"dir":"ltr"},{"str":"\u0014","boundary":[0.46411800653594776,0.7474102549494948,0.4768480465359478,0.7599893458585857],"dir":"ltr"},{"str":"2cn","boundary":[0.48135787581699346,0.7459718339646463,0.5035217824346405,0.7602660858585857],"dir":"ltr"},{"str":"for","boundary":[0.508823954248366,0.7424666722222222,0.529774800130719,0.755045763131313],"dir":"ltr"},{"str":"all","boundary":[0.5340884967320262,0.7424666722222222,0.5532975084967321,0.755045763131313],"dir":"ltr"},{"str":"n","boundary":[0.5578072875816994,0.7476869949494948,0.5676071393464052,0.7602660858585857],"dir":"ltr"},{"str":"\u0015","boundary":[0.5721168790849673,0.7474102549494948,0.5848469190849673,0.7599893458585857],"dir":"ltr"},{"str":"0","boundary":[0.589356748366013,0.7476869949494948,0.597577554248366,0.7602660858585857],"dir":"ltr"},{"str":"Show","boundary":[0.6075769444444444,0.7424666722222222,0.6487135315032679,0.755045763131313],"dir":"ltr"},{"str":"that","boundary":[0.6530272712418301,0.7424666722222222,0.6845756312418301,0.755045763131313],"dir":"ltr"},{"str":"your","boundary":[0.6892815196078431,0.7424666722222222,0.7235647219607844,0.755045763131313],"dir":"ltr"},{"str":"answer","boundary":[0.7276823366013072,0.7424666722222222,0.7823303471895425,0.755045763131313],"dir":"ltr"},{"str":"is","boundary":[0.7868400163398692,0.7424666722222222,0.794864960130719,0.755045763131313],"dir":"ltr"},{"str":"correct.","boundary":[0.8038844607843137,0.7424666722222222,0.8600789596078432,0.755045763131313],"dir":"ltr"},{"str":"c","boundary":[0.32363503267973864,0.7476869949494948,0.3261739971241831,0.7602660858585857],"dir":"ltr"},{"str":"<","boundary":[0.3351935294117648,0.7476869949494948,0.34792356941176483,0.7602660858585857],"dir":"ltr"},{"str":"1","boundary":[0.352237320261438,0.7476869949494948,0.36045812614379097,0.7602660858585857],"dir":"ltr"},{"str":"Fn","boundary":[0.44020960784313734,0.7476869949494948,0.45881829125817003,0.7611408238636361],"dir":"ltr"},{"str":"(c)","boundary":[0.17451027777777772,0.7624666722222222,0.1927262813071895,0.775045763131313],"dir":"ltr"},{"str":"What","boundary":[0.2013537418300653,0.7624666722222222,0.24250660771241822,0.775045763131313],"dir":"ltr"},{"str":"is","boundary":[0.24721240196078423,0.7624666722222222,0.2550412673202614,0.775045763131313],"dir":"ltr"},{"str":"the","boundary":[0.2644529248366012,0.7624666722222222,0.2889362754248365,0.775045763131313],"dir":"ltr"},{"str":"largest","boundary":[0.2932499836601306,0.7624666722222222,0.34535849777777766,0.775045763131313],"dir":"ltr"},{"str":"c","boundary":[0.34986828431372535,0.7676869949494948,0.35691701490196065,0.7802660858585857],"dir":"ltr"},{"str":"you","boundary":[0.36142678104575154,0.7624666722222222,0.38846590692810445,0.775045763131313],"dir":"ltr"},{"str":"can","boundary":[0.3927795588235293,0.7624666722222222,0.4190373011764704,0.775045763131313],"dir":"ltr"},{"str":"\u0002nd","boundary":[0.42354704248366,0.7624666722222222,0.4529465977777776,0.775045763131313],"dir":"ltr"},{"str":"for","boundary":[0.4572602777777776,0.7624666722222222,0.4782111236601306,0.775045763131313],"dir":"ltr"},{"str":"which","boundary":[0.4825248202614378,0.7624666722222222,0.5273884819607841,0.775045763131313],"dir":"ltr"},{"str":"F","boundary":[0.5318982352941175,0.7676869949494948,0.5422841247058822,0.7802660858585857],"dir":"ltr"},{"str":"=","boundary":[0.5560788725490194,0.7676869949494948,0.5644951616993462,0.7802660858585857],"dir":"ltr"},{"str":"(2cn","boundary":[0.5848759739869279,0.7659718339646463,0.613325720343137,0.7802660858585857],"dir":"ltr"},{"str":")?","boundary":[0.6141180882352939,0.7624666722222222,0.6276294849673201,0.7802660858585857],"dir":"ltr"},{"str":"n","boundary":[0.5425494607843135,0.7723354577020201,0.5505830624999999,0.7811408238636361],"dir":"ltr"},{"str":"0.4.","boundary":[0.12607821895424812,0.7868606116161615,0.15313362366013045,0.7994397025252523],"dir":"ltr"},{"str":"Is","boundary":[0.1621532189542481,0.7868606116161615,0.1762506801307187,0.7994397025252523],"dir":"ltr"},{"str":"there","boundary":[0.18193687908496706,0.7868606116161615,0.22188511202614355,0.7994397025252523],"dir":"ltr"},{"str":"a","boundary":[0.2273752777777775,0.7868606116161615,0.23090360313725464,0.7994397025252523],"dir":"ltr"},{"str":"faster","boundary":[0.2418838888888886,0.7868606116161615,0.2855599724183004,0.7994397025252523],"dir":"ltr"},{"str":"way","boundary":[0.2912461437908494,0.7868606116161615,0.3161315224836598,0.7994397025252523],"dir":"ltr"},{"str":"to","boundary":[0.3267196568627448,0.7868606116161615,0.3412078098039213,0.7994397025252523],"dir":"ltr"},{"str":"compute","boundary":[0.3468940032679736,0.7868606116161615,0.41075582797385596,0.7994397025252523],"dir":"ltr"},{"str":"the","boundary":[0.41604988562091477,0.7868606116161615,0.4405332362091501,0.7994397025252523],"dir":"ltr"},{"str":"nth","boundary":[0.4460234150326795,0.7868606116161615,0.4720857799999998,0.804660025252525],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.4775758496732024,0.7868606116161615,0.5490879926797384,0.7994397025252523],"dir":"ltr"},{"str":"number","boundary":[0.5547741666666665,0.7868606116161615,0.6137523443137254,0.7994397025252523],"dir":"ltr"},{"str":"than","boundary":[0.6190463888888887,0.7868606116161615,0.654322599477124,0.7994397025252523],"dir":"ltr"},{"str":"by","boundary":[0.6600088071895424,0.7868606116161615,0.6778503977777777,0.7994397025252523],"dir":"ltr"},{"str":"(page","boundary":[0.7280300490196078,0.7868606116161615,0.7689875690196077,0.7994397025252523],"dir":"ltr"},{"str":"13)?","boundary":[0.7742816830065359,0.7868606116161615,0.8050486594771241,0.7994397025252523],"dir":"ltr"},{"str":"One","boundary":[0.8138722058823529,0.7868606116161615,0.8448182494117646,0.7994397025252523],"dir":"ltr"},{"str":"idea","boundary":[0.8503083169934639,0.7868606116161615,0.8820520228758167,0.7994397025252523],"dir":"ltr"},{"str":"fib2","boundary":[0.6833405065359476,0.7952257070707069,0.7224096830065357,0.8078047979797978],"dir":"ltr"},{"str":"involves","boundary":[0.16215635620915014,0.8018606116161615,0.22386937620915012,0.8144397025252523],"dir":"ltr"},{"str":"matrices","boundary":[0.22818299019607824,0.8018606116161615,0.29224016078431353,0.8144397025252523],"dir":"ltr"},{"str":".","boundary":[0.2914558660130717,0.8018606116161615,0.2959651001307188,0.8144397025252523],"dir":"ltr"},{"str":"in","boundary":[0.6137250653594768,0.8206484904040403,0.6288155347712414,0.8332275813131311],"dir":"ltr"},{"str":"matrix","boundary":[0.6333252287581695,0.8206484904040403,0.6842779464052283,0.8332275813131311],"dir":"ltr"},{"str":"notation:","boundary":[0.6887878104575159,0.8206484904040403,0.7563774857516335,0.8332275813131311],"dir":"ltr"},{"str":"and","boundary":[0.4813720915032677,0.8206484904040403,0.5097949173856207,0.8332275813131311],"dir":"ltr"},{"str":"+","boundary":[0.575097581699346,0.8258688131313129,0.5878276216993461,0.8384479040404038],"dir":"ltr"},{"str":"F1","boundary":[0.5913569934640519,0.8258688131313129,0.6082253479575159,0.8393226420454543],"dir":"ltr"},{"str":"We","boundary":[0.16215635620915017,0.8206484904040403,0.1807588503267972,0.8332275813131311],"dir":"ltr"},{"str":"start","boundary":[0.189778382352941,0.8206484904040403,0.2260150435294116,0.8332275813131311],"dir":"ltr"},{"str":"by","boundary":[0.23072086601307173,0.8206484904040403,0.24856245660130705,0.8332275813131311],"dir":"ltr"},{"str":"writing","boundary":[0.2530721732026142,0.8206484904040403,0.30832250026143776,0.8332275813131311],"dir":"ltr"},{"str":"the","boundary":[0.31283230392156847,0.8206484904040403,0.3373156545098037,0.8332275813131311],"dir":"ltr"},{"str":"equations","boundary":[0.34162936274509786,0.8206484904040403,0.4149003474509802,0.8332275813131311],"dir":"ltr"},{"str":"F","boundary":[0.4194100816993462,0.8258688131313129,0.4297959711111109,0.8384479040404038],"dir":"ltr"},{"str":"=","boundary":[0.4419602614379083,0.8258688131313129,0.4546903014379083,0.8384479040404038],"dir":"ltr"},{"str":"F1","boundary":[0.45900405228758145,0.8258688131313129,0.4758723741013069,0.8393226420454543],"dir":"ltr"},{"str":"F2","boundary":[0.5143046078431369,0.8258688131313129,0.5311664263888886,0.8393226420454543],"dir":"ltr"},{"str":"=","boundary":[0.5364700653594767,0.8258688131313129,0.5492001053594768,0.8384479040404038],"dir":"ltr"},{"str":"F0","boundary":[0.5537099346405224,0.8258688131313129,0.570578256454248,0.8393226420454543],"dir":"ltr"},{"str":"1","boundary":[0.4299994771241828,0.8305172758838382,0.4364605440359475,0.8393226420454543],"dir":"ltr"},{"str":"\u0012","boundary":[0.43196101307189505,0.8424594391919191,0.4439096695424833,0.8550385301010099],"dir":"ltr"},{"str":"\u0013","boundary":[0.46176493464052243,0.8424594391919191,0.47371359111111067,0.8550385301010099],"dir":"ltr"},{"str":"\u0012","boundary":[0.4952943464052283,0.8424594391919191,0.5072430028758166,0.8550385301010099],"dir":"ltr"},{"str":"\u0013","boundary":[0.5400002124183001,0.8424594644444443,0.5519488688888884,0.8550385553535351],"dir":"ltr"},{"str":"\u0012","boundary":[0.5637256862745094,0.8424594644444443,0.5756743427450975,0.8550385553535351],"dir":"ltr"},{"str":"\u0013","boundary":[0.5933335294117642,0.8424594644444443,0.6052821858823525,0.8550385553535351],"dir":"ltr"},{"str":"F","boundary":[0.44392179738562054,0.8523839898989898,0.45430768679738526,0.8649630808080806],"dir":"ltr"},{"str":"0","boundary":[0.5074512254901955,0.8523839898989898,0.5156720313725485,0.8649630808080806],"dir":"ltr"},{"str":"1","boundary":[0.5317504084967315,0.8523839898989898,0.5399712143790845,0.8649630808080806],"dir":"ltr"},{"str":"F0","boundary":[0.5756864705882347,0.852384015151515,0.5925397107026138,0.8658378440656563],"dir":"ltr"},{"str":":","boundary":[0.6080394117647054,0.8601112626262624,0.6125486458823525,0.8726903535353532],"dir":"ltr"},{"str":"1","boundary":[0.45431393790849633,0.857032452651515,0.460775004820261,0.8658378188131312],"dir":"ltr"},{"str":"=","boundary":[0.4782355228758165,0.8601112373737372,0.49096556287581655,0.872690328282828],"dir":"ltr"},{"str":"\u0001","boundary":[0.555490375816993,0.8598345226262624,0.55999960993464,0.8724136135353532],"dir":"ltr"},{"str":"F2","boundary":[0.44392179738562054,0.8675354924242422,0.460775004820261,0.8809893213383837],"dir":"ltr"},{"str":"1","boundary":[0.5074512254901955,0.8675355050505049,0.5156720313725485,0.8801145959595957],"dir":"ltr"},{"str":"1","boundary":[0.5317504084967315,0.8675355050505049,0.5399712143790845,0.8801145959595957],"dir":"ltr"},{"str":"F1","boundary":[0.5756864705882347,0.8675355176767675,0.5925397107026138,0.8809893465909089],"dir":"ltr"}],"boundary":[0.11765,0.08979,0.88233,0.88099],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":18,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/4289bb49229e36a1e71e5b3f21553650.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/696bf16bb0187e9487b356876302c91a.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11772,0.24504]},"elements":[{"words":[{"str":"S","boundary":[0.11764705882352941,0.08979153426128839,0.1293939594771242,0.10356565042290454],"dir":"ltr"},{"str":"Dasgupta,","boundary":[0.13800351307189543,0.08979153426128839,0.2225490380718954,0.10356565042290454],"dir":"ltr"},{"str":"C.H.","boundary":[0.22745089869281046,0.08979153426128839,0.26443845637254904,0.10356565042290454],"dir":"ltr"},{"str":"Papadimitriou,","boundary":[0.2693402777777778,0.08979153426128839,0.3932084790849673,0.10356565042290454],"dir":"ltr"},{"str":"and","boundary":[0.39771821895424836,0.08979153426128839,0.42884123954248365,0.10356565042290454],"dir":"ltr"},{"str":"U.V","boundary":[0.43374305555555553,0.08979153426128839,0.4664347251633986,0.10356565042290454],"dir":"ltr"},{"str":"Vazirani","boundary":[0.47190697712418295,0.08979153426128839,0.5419605168300654,0.10356565042290454],"dir":"ltr"},{"str":"19","boundary":[0.8617647058823529,0.09001376073232323,0.8817290718954248,0.10378787689393938],"dir":"ltr"},{"str":"Similarly","boundary":[0.16215686274509797,0.13019384393939398,0.23231859215686265,0.14277293484848488],"dir":"ltr"},{"str":",","boundary":[0.23035784313725483,0.13019384393939398,0.2348670772549019,0.14277293484848488],"dir":"ltr"},{"str":"\u0012","boundary":[0.366078431372549,0.14245930030303025,0.3780270878431372,0.15503839121212118],"dir":"ltr"},{"str":"\u0013","boundary":[0.3958823529411764,0.14245936343434323,0.4078310094117647,0.15503845434343416],"dir":"ltr"},{"str":"\u0012","boundary":[0.4294117647058824,0.14245936343434323,0.4413604211764706,0.15503845434343416],"dir":"ltr"},{"str":"\u0013","boundary":[0.4741176470588236,0.14245932555555546,0.4860663035294118,0.15503841646464636],"dir":"ltr"},{"str":"\u0012","boundary":[0.49784312091503274,0.14245932555555546,0.509791777385621,0.15503841646464636],"dir":"ltr"},{"str":"\u0013","boundary":[0.5274509640522875,0.14245938868686842,0.5393996205228758,0.15503847959595934],"dir":"ltr"},{"str":"\u0012","boundary":[0.5611764542483659,0.14245938868686842,0.5731251107189542,0.15503847959595934],"dir":"ltr"},{"str":"\u0013","boundary":[0.6056862745098038,0.14245935080808064,0.6176349309803921,0.15503844171717157],"dir":"ltr"},{"str":"2","boundary":[0.6176470588235293,0.1477899147727271,0.624108125735294,0.15659528093434325],"dir":"ltr"},{"str":"\u0012","boundary":[0.6368627287581698,0.14245933818181805,0.6488113852287581,0.15503842909090895],"dir":"ltr"},{"str":"\u0013","boundary":[0.6664705718954248,0.142459401313131,0.678419228366013,0.15503849222222194],"dir":"ltr"},{"str":"0","boundary":[0.5731372385620914,0.15238387626262603,0.5813580444444444,0.16496296717171693],"dir":"ltr"},{"str":"1","boundary":[0.5976325,0.15238387626262603,0.6058533058823529,0.16496296717171693],"dir":"ltr"},{"str":"F0","boundary":[0.6488235457516339,0.15238382575757567,0.6656767531862744,0.16583771780303014],"dir":"ltr"},{"str":"F","boundary":[0.37803921568627447,0.1523837878787879,0.3884251050980392,0.1649628787878788],"dir":"ltr"},{"str":"0","boundary":[0.4413725490196079,0.15238385101010085,0.4495933549019608,0.16496294191919175],"dir":"ltr"},{"str":"1","boundary":[0.46586781045751635,0.15238385101010085,0.4740886163398693,0.16496294191919175],"dir":"ltr"},{"str":"F1","boundary":[0.5098039052287582,0.15238381313131308,0.5266571126633987,0.16583770517676755],"dir":"ltr"},{"str":"=","boundary":[0.5441176307189542,0.16011118686868656,0.5568476707189542,0.17269027777777746],"dir":"ltr"},{"str":"\u0001","boundary":[0.6286274509803921,0.1598343963636362,0.6331366850980392,0.17241348727272712],"dir":"ltr"},{"str":"2","boundary":[0.38843135620915026,0.1570323137626262,0.394892423120915,0.16583767992424236],"dir":"ltr"},{"str":"=","boundary":[0.4123529411764706,0.16011116161616137,0.42508298117647053,0.17269025252525227],"dir":"ltr"},{"str":"\u0001","boundary":[0.4896078104575164,0.1598343837373736,0.4941170445751635,0.1724134746464645],"dir":"ltr"},{"str":"F3","boundary":[0.37803921568627447,0.16753535353535343,0.394892423120915,0.1809892455808079],"dir":"ltr"},{"str":"1","boundary":[0.4413725490196079,0.16753536616161602,0.4495933549019608,0.18011445707070692],"dir":"ltr"},{"str":"1","boundary":[0.46586781045751635,0.16753536616161602,0.4740886163398693,0.18011445707070692],"dir":"ltr"},{"str":"F2","boundary":[0.5098039052287582,0.1675353787878786,0.5266571126633987,0.18098927083333308],"dir":"ltr"},{"str":"1","boundary":[0.5731372385620914,0.1675353914141412,0.5813580444444444,0.1801144823232321],"dir":"ltr"},{"str":"1","boundary":[0.5976325,0.1675353914141412,0.6058533058823529,0.1801144823232321],"dir":"ltr"},{"str":"F1","boundary":[0.6488235457516339,0.1675353914141412,0.6656767531862744,0.18098928345959567],"dir":"ltr"},{"str":"and","boundary":[0.16215684640522873,0.1848908767676764,0.19057967228758166,0.1974699676767673],"dir":"ltr"},{"str":"in","boundary":[0.195089362745098,0.1848908767676764,0.21017983215686267,0.1974699676767673],"dir":"ltr"},{"str":"general","boundary":[0.21468952614379078,0.1848908767676764,0.27130727437908486,0.1974699676767673],"dir":"ltr"},{"str":"\u0012","boundary":[0.41843135620915023,0.19518668666666636,0.4303800126797385,0.20776577757575726],"dir":"ltr"},{"str":"\u0013","boundary":[0.4662744444444444,0.19518664878787842,0.4782231009150326,0.20776573969696932],"dir":"ltr"},{"str":"\u0012","boundary":[0.4999999346405228,0.19518664878787842,0.511948591111111,0.20776573969696932],"dir":"ltr"},{"str":"\u0013","boundary":[0.5445097058823528,0.19518663616161583,0.5564583623529411,0.20776572707070673],"dir":"ltr"},{"str":"n","boundary":[0.5564704901960783,0.20051720012626226,0.5645040919117646,0.2093225662878784],"dir":"ltr"},{"str":"\u0012","boundary":[0.577058725490196,0.19518662353535324,0.5890073819607843,0.20776571444444414],"dir":"ltr"},{"str":"\u0013","boundary":[0.6068626797385619,0.1951865856565653,0.6188113362091502,0.2077656765656562],"dir":"ltr"},{"str":"0","boundary":[0.5119607189542482,0.20526267676767637,0.5201815248366012,0.21784176767676727],"dir":"ltr"},{"str":"1","boundary":[0.5362599019607842,0.20526267676767637,0.5444807078431372,0.21784176767676727],"dir":"ltr"},{"str":"F0","boundary":[0.5890195424836601,0.2052626515151512,0.6058727499183005,0.21871648042929254],"dir":"ltr"},{"str":":","boundary":[0.6215685620915031,0.2128383838383834,0.6260777962091502,0.2254174747474743],"dir":"ltr"},{"str":"Fn","boundary":[0.43862743464052284,0.20526271464646428,0.4570532095588235,0.21871654356060566],"dir":"ltr"},{"str":"=","boundary":[0.48274503267973845,0.21283844696969653,0.49547507267973845,0.22541753787878743],"dir":"ltr"},{"str":"\u0001","boundary":[0.5690195098039215,0.21256168171717135,0.5735287439215685,0.22514077262626225],"dir":"ltr"},{"str":"Fn+1","boundary":[0.43039215686274507,0.2202627020202017,0.4652725480392156,0.23371653093434305],"dir":"ltr"},{"str":"1","boundary":[0.5119607189542482,0.22026267676767636,0.5201815248366012,0.23284176767676726],"dir":"ltr"},{"str":"1","boundary":[0.5362599019607842,0.22026267676767636,0.5444807078431372,0.23284176767676726],"dir":"ltr"},{"str":"F1","boundary":[0.5890195424836601,0.22026263888888858,0.6058727499183005,0.23371646780302993],"dir":"ltr"},{"str":"So","boundary":[0.16215679738562072,0.23776957626262582,0.18056814679738545,0.2503486671717167],"dir":"ltr"},{"str":"in","boundary":[0.18939099673202597,0.23776957626262582,0.20448146614379067,0.2503486671717167],"dir":"ltr"},{"str":"order","boundary":[0.20899116013071878,0.23776957626262582,0.2493300848366011,0.2503486671717167],"dir":"ltr"},{"str":"to","boundary":[0.2534476960784312,0.23776957626262582,0.26793584901960765,0.2503486671717167],"dir":"ltr"},{"str":"compute","boundary":[0.2724455718954247,0.23776957626262582,0.33630739660130704,0.2503486671717167],"dir":"ltr"},{"str":"F","boundary":[0.3406210620915031,0.24298989898989856,0.35100695150326783,0.25556898989898946],"dir":"ltr"},{"str":"it","boundary":[0.36901872549019593,0.23776957626262582,0.37567551542483646,0.2503486671717167],"dir":"ltr"},{"str":"suf\u0002ces","boundary":[0.38508717320261426,0.23776957626262582,0.4409072590849672,0.2503486671717167],"dir":"ltr"},{"str":"to","boundary":[0.445220996732026,0.23776957626262582,0.4597091496732024,0.2503486671717167],"dir":"ltr"},{"str":"raise","boundary":[0.4642188725490194,0.23776957626262582,0.5012369172549017,0.2503486671717167],"dir":"ltr"},{"str":"this","boundary":[0.5057466503267972,0.23776957626262582,0.5345438891503266,0.2503486671717167],"dir":"ltr"},{"str":"2","boundary":[0.5392497549019606,0.24298989898989856,0.5474705607843136,0.25556898989898946],"dir":"ltr"},{"str":"\u0002","boundary":[0.5509999346405227,0.24271315898989856,0.5637299746405227,0.25529224989898947],"dir":"ltr"},{"str":"2","boundary":[0.5672593464052286,0.24298989898989856,0.5754801522875814,0.25556898989898946],"dir":"ltr"},{"str":"matrix,","boundary":[0.5799899183006534,0.23776957626262582,0.6354518700653593,0.2503486671717167],"dir":"ltr"},{"str":"call","boundary":[0.6399616503267972,0.23776957626262582,0.6664147385620913,0.2503486671717167],"dir":"ltr"},{"str":"it","boundary":[0.6709245588235292,0.23776957626262582,0.6822871776470586,0.2503486671717167],"dir":"ltr"},{"str":"X","boundary":[0.6867968954248364,0.24298989898989856,0.7003245977777774,0.25556898989898946],"dir":"ltr"},{"str":"to","boundary":[0.7107161437908494,0.23776957626262582,0.7252042967320258,0.2503486671717167],"dir":"ltr"},{"str":"the","boundary":[0.7297140196078429,0.23776957626262582,0.7541973701960782,0.2503486671717167],"dir":"ltr"},{"str":"nth","boundary":[0.7585110784313723,0.23776957626262582,0.7845733943790847,0.25556898989898946],"dir":"ltr"},{"str":"power","boundary":[0.7890832352941174,0.23776957626262582,0.8349081235294116,0.2503486671717167],"dir":"ltr"},{"str":".","boundary":[0.8333394444444443,0.23776957626262582,0.8378486785620912,0.2503486671717167],"dir":"ltr"},{"str":"n","boundary":[0.35117619281045737,0.24763836174242376,0.3592097945261436,0.2564437279040399],"dir":"ltr"},{"str":"(a)","boundary":[0.17254859477124163,0.2661029095959592,0.1925389900653593,0.27868200050505015],"dir":"ltr"},{"str":"Show","boundary":[0.20136248366013054,0.2661029095959592,0.24249907071895407,0.27868200050505015],"dir":"ltr"},{"str":"that","boundary":[0.24681281045751616,0.2661029095959592,0.2783611704575161,0.27868200050505015],"dir":"ltr"},{"str":"two","boundary":[0.2830670588235292,0.2661029095959592,0.3102852517647057,0.27868200050505015],"dir":"ltr"},{"str":"2","boundary":[0.3147949999999998,0.27132323232323197,0.32301580588235274,0.2839023232323229],"dir":"ltr"},{"str":"\u0002","boundary":[0.32634911764705865,0.27104649232323197,0.33907915764705865,0.28362558323232284],"dir":"ltr"},{"str":"2","boundary":[0.3426085294117645,0.27132323232323197,0.3508293352941175,0.2839023232323229],"dir":"ltr"},{"str":"matrices","boundary":[0.3553391013071894,0.2661029095959592,0.4203730013071894,0.27868200050505015],"dir":"ltr"},{"str":"can","boundary":[0.42488272875816974,0.2661029095959592,0.45114047111111094,0.27868200050505015],"dir":"ltr"},{"str":"be","boundary":[0.4556502124183005,0.2661029095959592,0.4728894865359476,0.27868200050505015],"dir":"ltr"},{"str":"multiplied","boundary":[0.47739923202614365,0.2661029095959592,0.5555864214379084,0.27868200050505015],"dir":"ltr"},{"str":"using","boundary":[0.5599000490196077,0.2661029095959592,0.6012482607843136,0.27868200050505015],"dir":"ltr"},{"str":"4","boundary":[0.6057580555555554,0.27132323232323197,0.6139788614379083,0.2839023232323229],"dir":"ltr"},{"str":"additions","boundary":[0.6182925653594769,0.2661029095959592,0.6882426700653592,0.27868200050505015],"dir":"ltr"},{"str":"and","boundary":[0.6927523692810454,0.2661029095959592,0.7211751951633985,0.27868200050505015],"dir":"ltr"},{"str":"8","boundary":[0.7256848856209147,0.27132323232323197,0.7339056915032677,0.2839023232323229],"dir":"ltr"},{"str":"multiplications","boundary":[0.7382193464052285,0.2661029095959592,0.8520571593464049,0.27868200050505015],"dir":"ltr"},{"str":".","boundary":[0.8516650980392154,0.2661029095959592,0.8561743321568624,0.27868200050505015],"dir":"ltr"},{"str":"But","boundary":[0.1621569281045749,0.2942847277777775,0.19017278339869256,0.3068638186868684],"dir":"ltr"},{"str":"how","boundary":[0.19468258169934616,0.2942847277777775,0.2256286252287579,0.3068638186868684],"dir":"ltr"},{"str":"many","boundary":[0.2299423856209148,0.2942847277777775,0.2722836056209148,0.3068638186868684],"dir":"ltr"},{"str":"matrix","boundary":[0.27679336601307164,0.2942847277777775,0.32774608366013047,0.3068638186868684],"dir":"ltr"},{"str":"multiplications","boundary":[0.33225578431372527,0.2942847277777775,0.4460935972549018,0.3068638186868684],"dir":"ltr"},{"str":"does","boundary":[0.4506033333333331,0.2942847277777775,0.4838935274509802,0.3068638186868684],"dir":"ltr"},{"str":"it","boundary":[0.48820725490196054,0.2942847277777775,0.49486404483660107,0.3068638186868684],"dir":"ltr"},{"str":"take","boundary":[0.5042757026143788,0.2942847277777775,0.5373868296732024,0.3068638186868684],"dir":"ltr"},{"str":"to","boundary":[0.5418966176470585,0.2942847277777775,0.556384770588235,0.3068638186868684],"dir":"ltr"},{"str":"compute","boundary":[0.5608944934640521,0.2942847277777775,0.6247563181699345,0.3068638186868684],"dir":"ltr"},{"str":"X","boundary":[0.628873905228758,0.2995050505050502,0.6424016075816992,0.3120841414141411],"dir":"ltr"},{"str":"n","boundary":[0.6441177287581697,0.2977898895202017,0.6521513304738561,0.30659525568181784],"dir":"ltr"},{"str":"?","boundary":[0.6529412581699344,0.2942847277777775,0.6601853346405228,0.3068638186868684],"dir":"ltr"},{"str":"(b)","boundary":[0.17254910130718937,0.31883018232323207,0.19253949660130704,0.33140927323232305],"dir":"ltr"},{"str":"Show","boundary":[0.20136299019607826,0.31883018232323207,0.24249957725490182,0.33140927323232305],"dir":"ltr"},{"str":"that","boundary":[0.24916625816993448,0.31883018232323207,0.2807146181699345,0.33140927323232305],"dir":"ltr"},{"str":"O(log","boundary":[0.287381290849673,0.32405050505050487,0.32733093803921554,0.3366295959595958],"dir":"ltr"},{"str":"n","boundary":[0.3302720588235293,0.32405050505050487,0.34007191058823516,0.3366295959595958],"dir":"ltr"},{"str":")","boundary":[0.34007187908496717,0.32405050505050487,0.3463392261437907,0.3366295959595958],"dir":"ltr"},{"str":"matrix","boundary":[0.3532018954248365,0.31883018232323207,0.40415461307189526,0.33140927323232305],"dir":"ltr"},{"str":"multiplications","boundary":[0.4108211764705881,0.31883018232323207,0.5246589894117646,0.33140927323232305],"dir":"ltr"},{"str":"suf\u0002ce","boundary":[0.531325588235294,0.31883018232323207,0.5797062517647058,0.33140927323232305],"dir":"ltr"},{"str":"for","boundary":[0.5861767320261436,0.31883018232323207,0.6071275779084966,0.33140927323232305],"dir":"ltr"},{"str":"computing","boundary":[0.6135981372549018,0.31883018232323207,0.6931527478431371,0.33140927323232305],"dir":"ltr"},{"str":"X","boundary":[0.6996233006535946,0.32405050505050487,0.7131510030065358,0.3366295959595958],"dir":"ltr"},{"str":"n","boundary":[0.7149021078431371,0.32233534406565634,0.7229357095588235,0.3311407102272725],"dir":"ltr"},{"str":"(","boundary":[0.7401956209150325,0.31883018232323207,0.7456815844444443,0.33140927323232305],"dir":"ltr"},{"str":"Hint:","boundary":[0.7456816013071894,0.31883018232323207,0.7848810083660129,0.33140927323232305],"dir":"ltr"},{"str":"Think","boundary":[0.7876260457516339,0.31883018232323207,0.8330927998692809,0.33140927323232305],"dir":"ltr"},{"str":"about","boundary":[0.8397593790849672,0.31883018232323207,0.8822796661437908,0.33140927323232305],"dir":"ltr"},{"str":"computing","boundary":[0.2013721241830065,0.33398169747474726,0.2809267347712418,0.3465607883838382],"dir":"ltr"},{"str":"X","boundary":[0.2852404248366013,0.33920202020202,0.2987681271895425,0.35178111111111093],"dir":"ltr"},{"str":"8","boundary":[0.30019563725490195,0.3374868592171715,0.3066567041666667,0.3462922253787877],"dir":"ltr"},{"str":".)","boundary":[0.30725449346405226,0.33398169747474726,0.3172496911111111,0.3465607883838382],"dir":"ltr"},{"str":"Thus","boundary":[0.16215645424836603,0.3585271520202018,0.2003628530718954,0.37110624292929273],"dir":"ltr"},{"str":"the","boundary":[0.2046765522875817,0.3585271520202018,0.229159902875817,0.37110624292929273],"dir":"ltr"},{"str":"number","boundary":[0.23327753267973855,0.3585271520202018,0.29225571032679737,0.37110624292929273],"dir":"ltr"},{"str":"of","boundary":[0.2961772058823529,0.3585271520202018,0.30596247673202615,0.37110624292929273],"dir":"ltr"},{"str":"arithmetic","boundary":[0.31380547385620916,0.3585271520202018,0.3927577679738562,0.37110624292929273],"dir":"ltr"},{"str":"operations","boundary":[0.396875408496732,0.3585271520202018,0.4760067696732026,0.37110624292929273],"dir":"ltr"},{"str":"needed","boundary":[0.4799281862745098,0.3585271520202018,0.5334041215686275,0.37110624292929273],"dir":"ltr"},{"str":"by","boundary":[0.537129656862745,0.3585271520202018,0.5549712474509804,0.37110624292929273],"dir":"ltr"},{"str":"our","boundary":[0.5590888071895425,0.3585271520202018,0.5845488871895425,0.37110624292929273],"dir":"ltr"},{"str":"matrix-based","boundary":[0.5884703431372549,0.3585271520202018,0.6880153490196078,0.37110624292929273],"dir":"ltr"},{"str":"algorithm,","boundary":[0.6921329248366013,0.3585271520202018,0.7709061518954249,0.37110624292929273],"dir":"ltr"},{"str":"call","boundary":[0.7750237745098039,0.3585271520202018,0.801476862745098,0.37110624292929273],"dir":"ltr"},{"str":"it","boundary":[0.8057906045751634,0.3585271520202018,0.8171532233986928,0.37110624292929273],"dir":"ltr"},{"str":",","boundary":[0.8604702287581698,0.3585271520202018,0.860861834248366,0.37110624292929273],"dir":"ltr"},{"str":"is","boundary":[0.8690970915032679,0.3585271520202018,0.8816317856209148,0.37110624292929273],"dir":"ltr"},{"str":"fib3","boundary":[0.8212708823529411,0.3668922474747473,0.8603400588235294,0.37947133838383823],"dir":"ltr"},{"str":"for","boundary":[0.4205663398692808,0.37352715202020176,0.4415171857516338,0.38610624292929274],"dir":"ltr"},{"str":".","boundary":[0.48522630718954235,0.37352715202020176,0.4897355413071894,0.38610624292929274],"dir":"ltr"},{"str":"Have","boundary":[0.49503022875816977,0.37352715202020176,0.5336273193464051,0.38610624292929274],"dir":"ltr"},{"str":"we","boundary":[0.5381370915032678,0.37352715202020176,0.5581112079738559,0.38610624292929274],"dir":"ltr"},{"str":"broken","boundary":[0.5626209150326795,0.37352715202020176,0.613362007973856,0.38610624292929274],"dir":"ltr"},{"str":"another","boundary":[0.6176756535947712,0.37352715202020176,0.6754654771241829,0.38610624292929274],"dir":"ltr"},{"str":"exponential","boundary":[0.679779248366013,0.37352715202020176,0.7661709648366012,0.38610624292929274],"dir":"ltr"},{"str":"barrier?","boundary":[0.7700924836601306,0.37352715202020176,0.8302264577777777,0.38610624292929274],"dir":"ltr"},{"str":"just","boundary":[0.16215591503267954,0.37352715202020176,0.19075780797385603,0.38610624292929274],"dir":"ltr"},{"str":"O(log","boundary":[0.19526751633986908,0.37874747474747456,0.23521716352941158,0.3913265656565655],"dir":"ltr"},{"str":"n","boundary":[0.2381582843137253,0.37874747474747456,0.2479581360784312,0.3913265656565655],"dir":"ltr"},{"str":")","boundary":[0.2479581045751632,0.37874747474747456,0.25422545163398674,0.3913265656565655],"dir":"ltr"},{"str":"as","boundary":[0.26344049019607824,0.37352715202020176,0.27989838078431356,0.38610624292929274],"dir":"ltr"},{"str":"compared","boundary":[0.28440813725490177,0.37352715202020176,0.35767912196078416,0.38610624292929274],"dir":"ltr"},{"str":"to","boundary":[0.361796699346405,0.37352715202020176,0.3762848522875815,0.38610624292929274],"dir":"ltr"},{"str":"O","boundary":[0.3807945751633985,0.37874747474747456,0.39313392339869263,0.3913265656565655],"dir":"ltr"},{"str":"(","boundary":[0.3935260294117645,0.37874747474747456,0.39979337647058805,0.3913265656565655],"dir":"ltr"},{"str":"n","boundary":[0.3997933496732024,0.37874747474747456,0.40959320143790834,0.3913265656565655],"dir":"ltr"},{"str":")","boundary":[0.40959316993464034,0.37874747474747456,0.4158605169934638,0.3913265656565655],"dir":"ltr"},{"str":"fib2","boundary":[0.44602696078431353,0.38189224747474726,0.48509613725490175,0.3944713383838382],"dir":"ltr"},{"str":"The","boundary":[0.1621562091503267,0.39246654595959574,0.19114879385620906,0.40504563686868666],"dir":"ltr"},{"str":"catch","boundary":[0.19683496732026134,0.39246654595959574,0.23072189856209138,0.40504563686868666],"dir":"ltr"},{"str":"is","boundary":[0.24209431372549012,0.39246654595959574,0.2546290078431372,0.40504563686868666],"dir":"ltr"},{"str":"that","boundary":[0.2603152287581698,0.39246654595959574,0.2918635887581698,0.40504563686868666],"dir":"ltr"},{"str":"our","boundary":[0.29754986928104565,0.39246654595959574,0.32300994928104565,0.40504563686868666],"dir":"ltr"},{"str":"new","boundary":[0.32850019607843123,0.39246654595959574,0.359446239607843,0.40504563686868666],"dir":"ltr"},{"str":"algorithm","boundary":[0.3647403921568626,0.39246654595959574,0.4390043850980391,0.40504563686868666],"dir":"ltr"},{"str":"involves","boundary":[0.4444944771241829,0.39246654595959574,0.506207497124183,0.40504563686868666],"dir":"ltr"},{"str":"multiplication,","boundary":[0.5115015032679738,0.39246654595959574,0.6224091279738562,0.40504563686868666],"dir":"ltr"},{"str":"not","boundary":[0.6282913725490196,0.39246654595959574,0.6527747231372548,0.40504563686868666],"dir":"ltr"},{"str":"just","boundary":[0.6584609803921567,0.39246654595959574,0.6870628733333333,0.40504563686868666],"dir":"ltr"},{"str":"addition;","boundary":[0.6925529738562091,0.39246654595959574,0.7595728903267973,0.40504563686868666],"dir":"ltr"},{"str":"and","boundary":[0.7656513398692809,0.39246654595959574,0.7940741657516339,0.40504563686868666],"dir":"ltr"},{"str":"multiplica-","boundary":[0.799564248366013,0.39246654595959574,0.8818699801307189,0.40504563686868666],"dir":"ltr"},{"str":"tions","boundary":[0.16215575163398688,0.4076180611111109,0.19917379633986923,0.4201971520202018],"dir":"ltr"},{"str":"of","boundary":[0.2034874509803921,0.4076180611111109,0.21307664339869273,0.4201971520202018],"dir":"ltr"},{"str":"large","boundary":[0.22131179738562085,0.4076180611111109,0.2597135420915032,0.4201971520202018],"dir":"ltr"},{"str":"numbers","boundary":[0.2638312418300653,0.4076180611111109,0.3302488418300653,0.4201971520202018],"dir":"ltr"},{"str":"are","boundary":[0.3343665359477123,0.4076180611111109,0.3588498865359476,0.4201971520202018],"dir":"ltr"},{"str":"slower","boundary":[0.3629675163398692,0.4076180611111109,0.41191793869281035,0.4201971520202018],"dir":"ltr"},{"str":"than","boundary":[0.41603549019607833,0.4076180611111109,0.4513117007843136,0.4201971520202018],"dir":"ltr"},{"str":"additions","boundary":[0.45542928104575153,0.4076180611111109,0.5253793857516339,0.4201971520202018],"dir":"ltr"},{"str":"We","boundary":[0.5349866830065357,0.4076180611111109,0.5537852392156862,0.4201971520202018],"dir":"ltr"},{"str":"have","boundary":[0.5624126470588234,0.4076180611111109,0.5982742223529409,0.4201971520202018],"dir":"ltr"},{"str":"already","boundary":[0.6023918954248363,0.4076180611111109,0.6592212683660128,0.4201971520202018],"dir":"ltr"},{"str":"seen","boundary":[0.6631427124183004,0.4076180611111109,0.6970189441830063,0.4201971520202018],"dir":"ltr"},{"str":"that,","boundary":[0.7011366666666664,0.4076180611111109,0.7371942607843134,0.4201971520202018],"dir":"ltr"},{"str":"when","boundary":[0.7417039869281044,0.4076180611111109,0.7826452281045749,0.4201971520202018],"dir":"ltr"},{"str":"the","boundary":[0.7865667320261436,0.4076180611111109,0.8110500826143788,0.4201971520202018],"dir":"ltr"},{"str":"complex-","boundary":[0.8151677124183004,0.4076180611111109,0.8821713500653593,0.4201971520202018],"dir":"ltr"},{"str":"ity","boundary":[0.16215627450980374,0.4226180611111109,0.18234201568627434,0.4351971520202018],"dir":"ltr"},{"str":"of","boundary":[0.18685169934640505,0.4226180611111109,0.20055846875816977,0.4351971520202018],"dir":"ltr"},{"str":"arithmetic","boundary":[0.2050682026143789,0.4226180611111109,0.28402049673202595,0.4351971520202018],"dir":"ltr"},{"str":"operations","boundary":[0.2885302941176469,0.4226180611111109,0.36766165529411743,0.4351971520202018],"dir":"ltr"},{"str":"is","boundary":[0.37177931372549,0.4226180611111109,0.37960817908496713,0.4351971520202018],"dir":"ltr"},{"str":"taken","boundary":[0.389019836601307,0.4226180611111109,0.43212616130718934,0.4351971520202018],"dir":"ltr"},{"str":"into","boundary":[0.4366358496732024,0.4226180611111109,0.4662144720261436,0.4351971520202018],"dir":"ltr"},{"str":"account,","boundary":[0.47072424836601284,0.4226180611111109,0.5332186518954247,0.4351971520202018],"dir":"ltr"},{"str":"the","boundary":[0.5375322549019605,0.4226180611111109,0.5620156054901959,0.4351971520202018],"dir":"ltr"},{"str":"running","boundary":[0.5665253921568626,0.4226180611111109,0.6276686533333332,0.4351971520202018],"dir":"ltr"},{"str":"time","boundary":[0.6317861764705881,0.4226180611111109,0.6658740329411763,0.4351971520202018],"dir":"ltr"},{"str":"of","boundary":[0.6703837254901959,0.4226180611111109,0.6840904949019605,0.4351971520202018],"dir":"ltr"},{"str":"becomes","boundary":[0.7321133006535946,0.4226180611111109,0.7949821171241829,0.4351971520202018],"dir":"ltr"},{"str":"O","boundary":[0.7992958169934639,0.42783838383838363,0.811635165228758,0.44041747474747456],"dir":"ltr"},{"str":"(","boundary":[0.8120272712418298,0.42783838383838363,0.8182946183006534,0.44041747474747456],"dir":"ltr"},{"str":"n2","boundary":[0.8182945915032678,0.4261232228535351,0.8350876682189541,0.44041747474747456],"dir":"ltr"},{"str":").","boundary":[0.8360775980392154,0.4226180611111109,0.846854070718954,0.44041747474747456],"dir":"ltr"},{"str":"fib2","boundary":[0.6884041503267971,0.43098315656565633,0.7274733267973854,0.4435622474747473],"dir":"ltr"},{"str":"(c)","boundary":[0.17450823529411744,0.4509513944444442,0.1927242388235292,0.46353048535353514],"dir":"ltr"},{"str":"Show","boundary":[0.20135169934640504,0.4509513944444442,0.24248828640522854,0.46353048535353514],"dir":"ltr"},{"str":"that","boundary":[0.24680202614379063,0.4509513944444442,0.2783503861437906,0.46353048535353514],"dir":"ltr"},{"str":"all","boundary":[0.2830562745098037,0.4509513944444442,0.3022652862745096,0.46353048535353514],"dir":"ltr"},{"str":"intermediate","boundary":[0.30697114379084944,0.4509513944444442,0.40453013320261416,0.46353048535353514],"dir":"ltr"},{"str":"results","boundary":[0.40864777777777755,0.4509513944444442,0.46034932130718936,0.46353048535353514],"dir":"ltr"},{"str":"of","boundary":[0.4650551307189541,0.4509513944444442,0.4787619001307188,0.46353048535353514],"dir":"ltr"},{"str":"are","boundary":[0.5265886274509802,0.4509513944444442,0.5510719780392155,0.46353048535353514],"dir":"ltr"},{"str":"O","boundary":[0.5555817647058823,0.45617171717171695,0.5679211129411763,0.4687508080808079],"dir":"ltr"},{"str":"(","boundary":[0.5683132189542482,0.45617171717171695,0.5745805660130717,0.4687508080808079],"dir":"ltr"},{"str":"n","boundary":[0.5745805392156862,0.45617171717171695,0.584380390980392,0.4687508080808079],"dir":"ltr"},{"str":")","boundary":[0.5843803594771241,0.45617171717171695,0.5906477065359477,0.4687508080808079],"dir":"ltr"},{"str":"bits","boundary":[0.5953535294117646,0.4509513944444442,0.6231740388235293,0.46353048535353514],"dir":"ltr"},{"str":"long","boundary":[0.6278798366013071,0.4509513944444442,0.6600142342483659,0.46353048535353514],"dir":"ltr"},{"str":".","boundary":[0.6596219934640521,0.4509513944444442,0.6641312275816992,0.46353048535353514],"dir":"ltr"},{"str":"fib3","boundary":[0.48307555555555537,0.4593164898989897,0.5221447320261436,0.47189558080808064],"dir":"ltr"},{"str":"(d)","boundary":[0.17235075163398683,0.4711029095959593,0.19273183869281035,0.4836820005050503],"dir":"ltr"},{"str":"Let","boundary":[0.20135924836601296,0.4711029095959593,0.22662398248366,0.4836820005050503],"dir":"ltr"},{"str":"M","boundary":[0.2319180718954247,0.4763232323232321,0.24778992483660117,0.488902323232323],"dir":"ltr"},{"str":"(","boundary":[0.24955450980392144,0.4763232323232321,0.25582185686274495,0.488902323232323],"dir":"ltr"},{"str":"n","boundary":[0.25582183006535936,0.4763232323232321,0.26562168183006524,0.488902323232323],"dir":"ltr"},{"str":")","boundary":[0.26562165032679724,0.4763232323232321,0.2718889973856208,0.488902323232323],"dir":"ltr"},{"str":"be","boundary":[0.27698699346405214,0.4711029095959593,0.29422626758169923,0.4836820005050503],"dir":"ltr"},{"str":"the","boundary":[0.29932424836601296,0.4711029095959593,0.3238075989542482,0.4836820005050503],"dir":"ltr"},{"str":"running","boundary":[0.32890562091503256,0.4711029095959593,0.3900488820915031,0.4836820005050503],"dir":"ltr"},{"str":"time","boundary":[0.39495071895424827,0.4711029095959593,0.4290385754248365,0.4836820005050503],"dir":"ltr"},{"str":"of","boundary":[0.4341365032679737,0.4711029095959593,0.4478432726797384,0.4836820005050503],"dir":"ltr"},{"str":"an","boundary":[0.4527451633986927,0.4711029095959593,0.4717588292810456,0.4836820005050503],"dir":"ltr"},{"str":"algorithm","boundary":[0.4768567647058823,0.4711029095959593,0.5511207576470587,0.4836820005050503],"dir":"ltr"},{"str":"for","boundary":[0.5562188562091502,0.4711029095959593,0.5771697020915032,0.4836820005050503],"dir":"ltr"},{"str":"multiplying","boundary":[0.582071633986928,0.4711029095959593,0.6702702998692809,0.4836820005050503],"dir":"ltr"},{"str":"n-bit","boundary":[0.6751721241830064,0.4711029095959593,0.7108390277124181,0.488902323232323],"dir":"ltr"},{"str":"numbers","boundary":[0.716133088235294,0.4711029095959593,0.782550688235294,0.4836820005050503],"dir":"ltr"},{"str":"and","boundary":[0.7917658333333332,0.4711029095959593,0.8201886592156862,0.4836820005050503],"dir":"ltr"},{"str":"assume","boundary":[0.8252865849673201,0.4711029095959593,0.8819043332026143,0.4836820005050503],"dir":"ltr"},{"str":"that","boundary":[0.20136991830065348,0.4861029095959593,0.23291827830065345,0.49868200050505024],"dir":"ltr"},{"str":"M","boundary":[0.23880063725490183,0.4913232323232321,0.2546724901960783,0.503902323232323],"dir":"ltr"},{"str":"(","boundary":[0.2564370751633986,0.4913232323232321,0.26270442222222207,0.503902323232323],"dir":"ltr"},{"str":"n","boundary":[0.2627043954248365,0.4913232323232321,0.27250424718954236,0.503902323232323],"dir":"ltr"},{"str":"=","boundary":[0.28524209150326785,0.4913232323232321,0.29797213150326785,0.503902323232323],"dir":"ltr"},{"str":"O","boundary":[0.3044427450980391,0.4913232323232321,0.31678209333333324,0.503902323232323],"dir":"ltr"},{"str":"(","boundary":[0.3171741993464051,0.4913232323232321,0.3234415464052286,0.503902323232323],"dir":"ltr"},{"str":"n2","boundary":[0.323441519607843,0.4896080713383835,0.33979183488562076,0.503902323232323],"dir":"ltr"},{"str":")","boundary":[0.34078176470588223,0.4913232323232321,0.34704911176470576,0.503902323232323],"dir":"ltr"},{"str":"(the","boundary":[0.3527353267973855,0.4861029095959593,0.3827046409150326,0.49868200050505024],"dir":"ltr"},{"str":"school","boundary":[0.3883908823529411,0.4861029095959593,0.4344103491503267,0.49868200050505024],"dir":"ltr"},{"str":"method","boundary":[0.4399004901960783,0.4861029095959593,0.4965182384313724,0.49868200050505024],"dir":"ltr"},{"str":"for","boundary":[0.5020083333333332,0.4861029095959593,0.5229591792156861,0.49868200050505024],"dir":"ltr"},{"str":"multiplication,","boundary":[0.5284493464052286,0.4861029095959593,0.639356971111111,0.49868200050505024],"dir":"ltr"},{"str":"recalled","boundary":[0.6454352941176469,0.4861029095959593,0.7049832305882351,0.49868200050505024],"dir":"ltr"},{"str":"in","boundary":[0.7102772875816992,0.4861029095959593,0.7253677569934639,0.49868200050505024],"dir":"ltr"},{"str":"Chapter","boundary":[0.7310539215686274,0.4861029095959593,0.7929622874509803,0.49868200050505024],"dir":"ltr"},{"str":"1,","boundary":[0.7986485294117646,0.4861029095959593,0.8121762317647058,0.49868200050505024],"dir":"ltr"},{"str":"achieves","boundary":[0.8182545751633986,0.4861029095959593,0.8821156552941175,0.49868200050505024],"dir":"ltr"},{"str":"this).","boundary":[0.20137004901960776,0.5012544247474745,0.240162485490196,0.5138335156565654],"dir":"ltr"},{"str":"Prove","boundary":[0.24584864379084959,0.5012544247474745,0.28913403555555545,0.5138335156565654],"dir":"ltr"},{"str":"that","boundary":[0.2934476633986927,0.5012544247474745,0.3249960233986927,0.5138335156565654],"dir":"ltr"},{"str":"the","boundary":[0.32970191176470576,0.5012544247474745,0.35418526235294107,0.5138335156565654],"dir":"ltr"},{"str":"running","boundary":[0.35849897058823516,0.5012544247474745,0.4196422317647057,0.5138335156565654],"dir":"ltr"},{"str":"time","boundary":[0.4239558333333332,0.5012544247474745,0.4580436898039214,0.5138335156565654],"dir":"ltr"},{"str":"of","boundary":[0.462553382352941,0.5012544247474745,0.4762601517647057,0.5138335156565654],"dir":"ltr"},{"str":"is","boundary":[0.5240868790849672,0.5012544247474745,0.5366215732026142,0.5138335156565654],"dir":"ltr"},{"str":"O","boundary":[0.5413274019607841,0.5064747474747472,0.5536667501960783,0.5190538383838382],"dir":"ltr"},{"str":"(","boundary":[0.5540588562091502,0.5064747474747472,0.5603262032679737,0.5190538383838382],"dir":"ltr"},{"str":"M","boundary":[0.560326176470588,0.5064747474747472,0.5761980294117646,0.5190538383838382],"dir":"ltr"},{"str":"(","boundary":[0.5779626143790848,0.5064747474747472,0.5842299614379083,0.5190538383838382],"dir":"ltr"},{"str":"n","boundary":[0.5842299346405226,0.5064747474747472,0.5940297864052285,0.5190538383838382],"dir":"ltr"},{"str":")","boundary":[0.5940297549019606,0.5064747474747472,0.5975520633986926,0.5190538383838382],"dir":"ltr"},{"str":"log","boundary":[0.6030421405228756,0.5064747474747472,0.6239929864052286,0.5190538383838382],"dir":"ltr"},{"str":"n","boundary":[0.626934133986928,0.5064747474747472,0.6367339857516338,0.5190538383838382],"dir":"ltr"},{"str":").","boundary":[0.6367339542483659,0.5012544247474745,0.6475105086274509,0.5190538383838382],"dir":"ltr"},{"str":"fib3","boundary":[0.48057380718954235,0.50961952020202,0.5196429836601306,0.5221986111111109],"dir":"ltr"},{"str":"(e)","boundary":[0.1735274183006535,0.5214059398989896,0.19272015124182998,0.5339850308080806],"dir":"ltr"},{"str":"Can","boundary":[0.2013475163398692,0.5214059398989896,0.2321144928104574,0.5339850308080806],"dir":"ltr"},{"str":"you","boundary":[0.2370163071895424,0.5214059398989896,0.26405543307189533,0.5339850308080806],"dir":"ltr"},{"str":"prove","boundary":[0.2689573202614378,0.5214059398989896,0.3108752908496731,0.5339850308080806],"dir":"ltr"},{"str":"that","boundary":[0.3153850980392156,0.5214059398989896,0.3469334580392156,0.5339850308080806],"dir":"ltr"},{"str":"the","boundary":[0.3520315032679738,0.5214059398989896,0.3765148538562091,0.5339850308080806],"dir":"ltr"},{"str":"running","boundary":[0.38141679738562084,0.5214059398989896,0.4425600585620914,0.5339850308080806],"dir":"ltr"},{"str":"time","boundary":[0.4470697385620915,0.5214059398989896,0.4811575950326797,0.5339850308080806],"dir":"ltr"},{"str":"of","boundary":[0.48625552287581697,0.5214059398989896,0.49996229228758166,0.5339850308080806],"dir":"ltr"},{"str":"is","boundary":[0.5487694117647058,0.5214059398989896,0.5613041058823529,0.5339850308080806],"dir":"ltr"},{"str":"O","boundary":[0.5662060130718954,0.5266262626262623,0.5785453613071896,0.5392053535353533],"dir":"ltr"},{"str":"(","boundary":[0.5789374673202614,0.5266262626262623,0.585204814379085,0.5392053535353533],"dir":"ltr"},{"str":"M","boundary":[0.5852047875816994,0.5266262626262623,0.6010766405228758,0.5392053535353533],"dir":"ltr"},{"str":"(","boundary":[0.602841225490196,0.5266262626262623,0.6091085725490196,0.5392053535353533],"dir":"ltr"},{"str":"n","boundary":[0.609108545751634,0.5266262626262623,0.6189083975163399,0.5392053535353533],"dir":"ltr"},{"str":"))","boundary":[0.618908366013072,0.5266262626262623,0.6314430601307189,0.5392053535353533],"dir":"ltr"},{"str":"(","boundary":[0.6459419934640523,0.5214059398989896,0.6514279569934641,0.5339850308080806],"dir":"ltr"},{"str":"Hint:","boundary":[0.6514279411764706,0.5214059398989896,0.6906273482352941,0.5339850308080806],"dir":"ltr"},{"str":"The","boundary":[0.6996468954248366,0.5214059398989896,0.728639480130719,0.5339850308080806],"dir":"ltr"},{"str":"lengths","boundary":[0.7335415032679738,0.5214059398989896,0.7893778679738561,0.5339850308080806],"dir":"ltr"},{"str":"of","boundary":[0.7942797385620914,0.5214059398989896,0.8079865079738562,0.5339850308080806],"dir":"ltr"},{"str":"the","boundary":[0.8126923202614379,0.5214059398989896,0.8371756708496733,0.5339850308080806],"dir":"ltr"},{"str":"num-","boundary":[0.8420776143790849,0.5214059398989896,0.8820584049673202,0.5339850308080806],"dir":"ltr"},{"str":"fib3","boundary":[0.5046681045751634,0.5297710353535351,0.5437372810457516,0.542350126262626],"dir":"ltr"},{"str":"bers","boundary":[0.20137009803921566,0.5365574550505048,0.23329287098039211,0.5491365459595957],"dir":"ltr"},{"str":"being","boundary":[0.23780261437908493,0.5365574550505048,0.2789554802614379,0.5491365459595957],"dir":"ltr"},{"str":"multiplied","boundary":[0.28346519607843135,0.5365574550505048,0.36165238549019607,0.5491365459595957],"dir":"ltr"},{"str":"get","boundary":[0.3659660130718954,0.5365574550505048,0.38927728836601305,0.5491365459595957],"dir":"ltr"},{"str":"doubled","boundary":[0.39359101307189537,0.5365574550505048,0.4529598824836601,0.5491365459595957],"dir":"ltr"},{"str":"with","boundary":[0.45727352941176463,0.5365574550505048,0.49136138588235284,0.5491365459595957],"dir":"ltr"},{"str":"every","boundary":[0.49587107843137246,0.5365574550505048,0.5372030113725489,0.5491365459595957],"dir":"ltr"},{"str":"squaring","boundary":[0.541320588235294,0.5365574550505048,0.6079498129411764,0.5491365459595957],"dir":"ltr"},{"str":".)","boundary":[0.607557679738562,0.5365574550505048,0.6175528773856209,0.5491365459595957],"dir":"ltr"},{"str":"In","boundary":[0.16215408496732023,0.5647392732323229,0.17880732143790845,0.5773183641414139],"dir":"ltr"},{"str":"conclusion,","boundary":[0.1858661764705882,0.5647392732323229,0.2687245841830065,0.5773183641414139],"dir":"ltr"},{"str":"whether","boundary":[0.2761754901960784,0.5647392732323229,0.3388489607843137,0.5773183641414139],"dir":"ltr"},{"str":"is","boundary":[0.39177369281045754,0.5647392732323229,0.4043083869281046,0.5773183641414139],"dir":"ltr"},{"str":"faster","boundary":[0.4113671568627451,0.5647392732323229,0.4550432403921569,0.5773183641414139],"dir":"ltr"},{"str":"than","boundary":[0.4621021241830065,0.5647392732323229,0.4973783347712418,0.5773183641414139],"dir":"ltr"},{"str":"depends","boundary":[0.5504991830065359,0.5647392732323229,0.6126028947712419,0.5773183641414139],"dir":"ltr"},{"str":"on","boundary":[0.6192694444444444,0.5647392732323229,0.6374854479738562,0.5773183641414139],"dir":"ltr"},{"str":"whether","boundary":[0.6443482026143791,0.5647392732323229,0.7070216732026144,0.5773183641414139],"dir":"ltr"},{"str":"we","boundary":[0.7138843137254902,0.5647392732323229,0.7348351596078432,0.5773183641414139],"dir":"ltr"},{"str":"can","boundary":[0.7416978758169935,0.5647392732323229,0.7679556181699346,0.5773183641414139],"dir":"ltr"},{"str":"multiply","boundary":[0.7748183006535948,0.5647392732323229,0.8391033747712419,0.5773183641414139],"dir":"ltr"},{"str":"n-bit","boundary":[0.8461622549019608,0.5647392732323229,0.8818290767320263,0.5825386868686866],"dir":"ltr"},{"str":"fib3","boundary":[0.345515522875817,0.5731043686868684,0.3845846993464052,0.5856834595959594],"dir":"ltr"},{"str":"fib2","boundary":[0.5044370915032679,0.5731043686868684,0.5435062679738561,0.5856834595959594],"dir":"ltr"},{"str":"integers","boundary":[0.1621548366013073,0.5798907883838381,0.223460886013072,0.592469879292929],"dir":"ltr"},{"str":"faster","boundary":[0.22777460784313738,0.5798907883838381,0.2714506913725491,0.592469879292929],"dir":"ltr"},{"str":"than","boundary":[0.27596039215686285,0.5798907883838381,0.3112366027450982,0.592469879292929],"dir":"ltr"},{"str":"O","boundary":[0.31574633986928113,0.5851111111111108,0.3280856881045753,0.5976902020202017],"dir":"ltr"},{"str":"(","boundary":[0.32847779411764716,0.5851111111111108,0.3347451411764707,0.5976902020202017],"dir":"ltr"},{"str":"n2","boundary":[0.33474511437908505,0.5833959501262623,0.3511648414215687,0.5976902020202017],"dir":"ltr"},{"str":")","boundary":[0.35215473856209156,0.5851111111111108,0.3584220856209151,0.5976902020202017],"dir":"ltr"},{"str":"Do","boundary":[0.3686175163398694,0.5798907883838381,0.38956836222222235,0.592469879292929],"dir":"ltr"},{"str":"you","boundary":[0.39407813725490204,0.5798907883838381,0.421117263137255,0.592469879292929],"dir":"ltr"},{"str":"think","boundary":[0.4252348366013073,0.5798907883838381,0.46619235660130726,0.592469879292929],"dir":"ltr"},{"str":"this","boundary":[0.4708982352941178,0.5798907883838381,0.49969547411764714,0.592469879292929],"dir":"ltr"},{"str":"is","boundary":[0.5042052614379086,0.5798907883838381,0.5120341267973857,0.592469879292929],"dir":"ltr"},{"str":"possible?","boundary":[0.5214457843137256,0.5798907883838381,0.588628489019608,0.592469879292929],"dir":"ltr"},{"str":"(The","boundary":[0.594118660130719,0.5798907883838381,0.6285972083660132,0.592469879292929],"dir":"ltr"},{"str":"answer","boundary":[0.6331068954248367,0.5798907883838381,0.687754906013072,0.592469879292929],"dir":"ltr"},{"str":"is","boundary":[0.692068660130719,0.5798907883838381,0.6998975254901961,0.592469879292929],"dir":"ltr"},{"str":"in","boundary":[0.709309183006536,0.5798907883838381,0.7243996524183007,0.592469879292929],"dir":"ltr"},{"str":"Chapter","boundary":[0.7289093464052289,0.5798907883838381,0.7908177122875818,0.592469879292929],"dir":"ltr"},{"str":"2.)","boundary":[0.7951314052287582,0.5798907883838381,0.8141450711111111,0.592469879292929],"dir":"ltr"},{"str":"Finally","boundary":[0.16215428104575166,0.598830182323232,0.21585739111111113,0.611409273232323],"dir":"ltr"},{"str":"there","boundary":[0.22311161764705886,0.598830182323232,0.26305985058823533,0.611409273232323],"dir":"ltr"},{"str":"is","boundary":[0.267373545751634,0.598830182323232,0.2753984895424837,0.611409273232323],"dir":"ltr"},{"str":"a","boundary":[0.28441799019607844,0.598830182323232,0.28892670771241835,0.611409273232323],"dir":"ltr"},{"str":"formula","boundary":[0.2979462091503269,0.598830182323232,0.35751042444444453,0.611409273232323],"dir":"ltr"},{"str":"for","boundary":[0.36182415032679743,0.598830182323232,0.3827749962091504,0.611409273232323],"dir":"ltr"},{"str":"the","boundary":[0.3870886928104575,0.598830182323232,0.4115720433986928,0.611409273232323],"dir":"ltr"},{"str":"Fibonacci","boundary":[0.4160818300653595,0.598830182323232,0.48759397307189545,0.611409273232323],"dir":"ltr"},{"str":"numbers:","boundary":[0.49210367647058817,0.598830182323232,0.5630305105882353,0.611409273232323],"dir":"ltr"},{"str":"p","boundary":[0.4884313725490195,0.6239253180808081,0.5019590749019607,0.636504408989899],"dir":"ltr"},{"str":"!","boundary":[0.5119607843137255,0.6217017624242425,0.5248861701960784,0.6342808533333334],"dir":"ltr"},{"str":"n","boundary":[0.5249019607843137,0.6270323516414141,0.5329355625000001,0.6358377178030303],"dir":"ltr"},{"str":"p","boundary":[0.62490204248366,0.6239253180808081,0.6384297448366012,0.636504408989899],"dir":"ltr"},{"str":"!","boundary":[0.6484313725490196,0.6217017624242425,0.6613567584313725,0.6342808533333334],"dir":"ltr"},{"str":"n","boundary":[0.6613725490196078,0.6270323516414141,0.6694061507352942,0.6358377178030303],"dir":"ltr"},{"str":"1","boundary":[0.42587964052287575,0.6345050378787875,0.4341004464052287,0.6470841287878785],"dir":"ltr"},{"str":"1","boundary":[0.4603921895424837,0.6345050757575758,0.4650836215686275,0.6470841666666667],"dir":"ltr"},{"str":"+","boundary":[0.4721423692810457,0.6345050757575758,0.48487240928104575,0.6470841666666667],"dir":"ltr"},{"str":"5","boundary":[0.5019591503267974,0.6345050757575758,0.5101799562091504,0.6470841666666667],"dir":"ltr"},{"str":"1","boundary":[0.5623529411764706,0.6345050757575758,0.5705737470588236,0.6470841666666667],"dir":"ltr"},{"str":"1","boundary":[0.5968628594771241,0.6345050757575758,0.6050836653594771,0.6470841666666667],"dir":"ltr"},{"str":"\u0000","boundary":[0.6086130392156862,0.6342283357575758,0.6213430792156862,0.6468074266666667],"dir":"ltr"},{"str":"5","boundary":[0.6384297385620915,0.6345050757575758,0.6466505444444445,0.6470841666666667],"dir":"ltr"},{"str":"F","boundary":[0.3670561274509804,0.6431414141414139,0.3774420168627451,0.6557205050505048],"dir":"ltr"},{"str":"=","boundary":[0.3954874836601307,0.6431414141414139,0.4082175236601307,0.6557205050505048],"dir":"ltr"},{"str":"p","boundary":[0.41901960784313724,0.6424101539393939,0.4325473101960784,0.654989244848485],"dir":"ltr"},{"str":"\u0000","boundary":[0.5374509803921569,0.642864712020202,0.5501810203921569,0.6554438029292929],"dir":"ltr"},{"str":"p","boundary":[0.5556862745098039,0.6424101539393939,0.569213976862745,0.654989244848485],"dir":"ltr"},{"str":":","boundary":[0.6729411437908496,0.643141452020202,0.6774503779084967,0.655720542929293],"dir":"ltr"},{"str":"n","boundary":[0.37744826797385617,0.6477898768939392,0.38548186968954246,0.6565952430555553],"dir":"ltr"},{"str":"2","boundary":[0.6176470588235294,0.6517778030303031,0.6258678647058824,0.6643568939393939],"dir":"ltr"},{"str":"5","boundary":[0.4327450980392156,0.6531414393939393,0.4409659039215686,0.6657205303030302],"dir":"ltr"},{"str":"2","boundary":[0.4811764705882353,0.6517778030303031,0.4893972764705883,0.6643568939393939],"dir":"ltr"},{"str":"5","boundary":[0.5692140522875817,0.6531414393939393,0.5774348581699346,0.6657205303030302],"dir":"ltr"},{"str":"So","boundary":[0.1621568300653594,0.6767090080808081,0.1805681794771241,0.6892880989898991],"dir":"ltr"},{"str":"it","boundary":[0.18997928104575154,0.6767090080808081,0.19624389777777768,0.6892880989898991],"dir":"ltr"},{"str":"would","boundary":[0.20643990196078424,0.6767090080808081,0.2518903772549019,0.6892880989898991],"dir":"ltr"},{"str":"appear","boundary":[0.2565962745098038,0.6767090080808081,0.3089164133333332,0.6892880989898991],"dir":"ltr"},{"str":"that","boundary":[0.31362225490196066,0.6767090080808081,0.34517061490196066,0.6892880989898991],"dir":"ltr"},{"str":"we","boundary":[0.35026866013071883,0.6767090080808081,0.3712195060130718,0.6892880989898991],"dir":"ltr"},{"str":"only","boundary":[0.3761214379084966,0.6767090080808081,0.40825583555555545,0.6892880989898991],"dir":"ltr"},{"str":"need","boundary":[0.41315771241830057,0.6767090080808081,0.4490036818300653,0.6892880989898991],"dir":"ltr"},{"str":"to","boundary":[0.45351343137254896,0.6767090080808081,0.4680015843137254,0.6892880989898991],"dir":"ltr"},{"str":"raise","boundary":[0.47309954248366004,0.6767090080808081,0.5101175871895424,0.6892880989898991],"dir":"ltr"},{"str":"a","boundary":[0.515019477124183,0.6767090080808081,0.5189399430065359,0.6892880989898991],"dir":"ltr"},{"str":"couple","boundary":[0.5291359477124182,0.6767090080808081,0.577321265359477,0.6892880989898991],"dir":"ltr"},{"str":"of","boundary":[0.5820271241830065,0.6767090080808081,0.5957338935947711,0.6892880989898991],"dir":"ltr"},{"str":"numbers","boundary":[0.6006357843137254,0.6767090080808081,0.6670533843137255,0.6892880989898991],"dir":"ltr"},{"str":"to","boundary":[0.6717591503267973,0.6767090080808081,0.6862473032679738,0.6892880989898991],"dir":"ltr"},{"str":"the","boundary":[0.6913454248366012,0.6767090080808081,0.7158287754248366,0.6892880989898991],"dir":"ltr"},{"str":"nth","boundary":[0.7207305555555555,0.6767090080808081,0.7467929532026143,0.6945084217171716],"dir":"ltr"},{"str":"power","boundary":[0.7516947875816993,0.6767090080808081,0.7975196758169935,0.6892880989898991],"dir":"ltr"},{"str":"in","boundary":[0.8022255065359477,0.6767090080808081,0.8173159759477123,0.6892880989898991],"dir":"ltr"},{"str":"order","boundary":[0.8222178267973855,0.6767090080808081,0.8625567515032678,0.6892880989898991],"dir":"ltr"},{"str":"to","boundary":[0.8672625980392156,0.6767090080808081,0.8817507509803921,0.6892880989898991],"dir":"ltr"},{"str":"compute","boundary":[0.1621563888888888,0.6918605232323234,0.22601821359477117,0.7044396141414142],"dir":"ltr"},{"str":"The","boundary":[0.2592146241830065,0.6918605232323234,0.28820720888888884,0.7044396141414142],"dir":"ltr"},{"str":"problem","boundary":[0.29232491830065355,0.6918605232323234,0.35403793830065355,0.7044396141414142],"dir":"ltr"},{"str":"is","boundary":[0.35795939542483657,0.6918605232323234,0.36618041764705883,0.7044396141414142],"dir":"ltr"},{"str":"that","boundary":[0.37480776143790845,0.6918605232323234,0.40635612143790845,0.7044396141414142],"dir":"ltr"},{"str":"these","boundary":[0.4106698529411764,0.6918605232323234,0.45081343176470584,0.7044396141414142],"dir":"ltr"},{"str":"numbers","boundary":[0.45473488562091496,0.6918605232323234,0.521152485620915,0.7044396141414142],"dir":"ltr"},{"str":"are","boundary":[0.525270179738562,0.6918605232323234,0.5497535303267973,0.7044396141414142],"dir":"ltr"},{"str":"irrational,","boundary":[0.5536750816993463,0.6918605232323234,0.630478571111111,0.7044396141414142],"dir":"ltr"},{"str":"and","boundary":[0.6347922385620914,0.6918605232323234,0.6632150644444444,0.7044396141414142],"dir":"ltr"},{"str":"computing","boundary":[0.6673325980392156,0.6918605232323234,0.746887208627451,0.7044396141414142],"dir":"ltr"},{"str":"them","boundary":[0.7506126633986927,0.6918605232323234,0.7896004457516339,0.7044396141414142],"dir":"ltr"},{"str":"to","boundary":[0.7937180555555554,0.6918605232323234,0.8082062084967319,0.7044396141414142],"dir":"ltr"},{"str":"suf\u0002cient","boundary":[0.8123237745098039,0.6918605232323234,0.8820622545098038,0.7044396141414142],"dir":"ltr"},{"str":"Fn","boundary":[0.22993972222222217,0.697080845959596,0.24842530106209146,0.7105346748737373],"dir":"ltr"},{"str":"accuracy","boundary":[0.16215710784313722,0.7070120383838385,0.22798867019607835,0.7195911292929293],"dir":"ltr"},{"str":"is","boundary":[0.23426315359477118,0.7070120383838385,0.24679784771241825,0.7195911292929293],"dir":"ltr"},{"str":"nontrivial.","boundary":[0.25326838235294113,0.7070120383838385,0.3326276470588235,0.7195911292929293],"dir":"ltr"},{"str":"In","boundary":[0.34380400326797383,0.7070120383838385,0.36045723973856203,0.7195911292929293],"dir":"ltr"},{"str":"fact,","boundary":[0.36692785947712414,0.7070120383838385,0.3994529488888888,0.7195911292929293],"dir":"ltr"},{"str":"our","boundary":[0.40631560457516336,0.7070120383838385,0.4317756845751633,0.7195911292929293],"dir":"ltr"},{"str":"matrix","boundary":[0.4380502450980392,0.7070120383838385,0.489002962745098,0.7195911292929293],"dir":"ltr"},{"str":"method","boundary":[0.49527736928104577,0.7070120383838385,0.5518951175163399,0.7195911292929293],"dir":"ltr"},{"str":"can","boundary":[0.6036433823529412,0.7070120383838385,0.6299011247058823,0.7195911292929293],"dir":"ltr"},{"str":"be","boundary":[0.6361755718954248,0.7070120383838385,0.653414846013072,0.7195911292929293],"dir":"ltr"},{"str":"seen","boundary":[0.6598853758169935,0.7070120383838385,0.6937616075816994,0.7195911292929293],"dir":"ltr"},{"str":"as","boundary":[0.7000360294117647,0.7070120383838385,0.71649392,0.7195911292929293],"dir":"ltr"},{"str":"a","boundary":[0.7229644607843138,0.7070120383838385,0.7255123449673202,0.7195911292929293],"dir":"ltr"},{"str":"roundabout","boundary":[0.7384535130718954,0.7070120383838385,0.8258382377777778,0.7195911292929293],"dir":"ltr"},{"str":"way","boundary":[0.8319165849673203,0.7070120383838385,0.8558216041830067,0.7195911292929293],"dir":"ltr"},{"str":"of","boundary":[0.8683704575163399,0.7070120383838385,0.8820772269281046,0.7195911292929293],"dir":"ltr"},{"str":"fib3","boundary":[0.5581695261437909,0.7153771338383839,0.5972387026143791,0.7279562247474748],"dir":"ltr"},{"str":"raising","boundary":[0.16215640522875824,0.7220120383838384,0.21486723581699352,0.7345911292929294],"dir":"ltr"},{"str":"these","boundary":[0.22016130718954252,0.7220120383838384,0.26030488601307195,0.7345911292929294],"dir":"ltr"},{"str":"irrational","boundary":[0.26520673202614387,0.7220120383838384,0.3375009873202615,0.7345911292929294],"dir":"ltr"},{"str":"numbers","boundary":[0.34259905228758175,0.7220120383838384,0.4090166522875818,0.7345911292929294],"dir":"ltr"},{"str":"to","boundary":[0.4141147385620916,0.7220120383838384,0.4286028915032681,0.7345911292929294],"dir":"ltr"},{"str":"the","boundary":[0.43370084967320266,0.7220120383838384,0.45818420026143797,0.7345911292929294],"dir":"ltr"},{"str":"nth","boundary":[0.46328222222222226,0.7220120383838384,0.48934458718954255,0.7398114520202019],"dir":"ltr"},{"str":"power","boundary":[0.49444266339869286,0.7220120383838384,0.540267551633987,0.7345911292929294],"dir":"ltr"},{"str":"If","boundary":[0.5502669117647059,0.7220120383838384,0.5575090014379085,0.7345911292929294],"dir":"ltr"},{"str":"you","boundary":[0.5673128267973856,0.7220120383838384,0.5943519526797385,0.7345911292929294],"dir":"ltr"},{"str":"know","boundary":[0.5992538398692809,0.7220120383838384,0.6398043892810458,0.7345911292929294],"dir":"ltr"},{"str":"your","boundary":[0.6447062908496731,0.7220120383838384,0.6789894932026144,0.7345911292929294],"dir":"ltr"},{"str":"linear","boundary":[0.6838914215686274,0.7220120383838384,0.7285605133333332,0.7345911292929294],"dir":"ltr"},{"str":"algebra,","boundary":[0.7336585784313724,0.7220120383838384,0.79460649372549,0.7345911292929294],"dir":"ltr"},{"str":"you","boundary":[0.7999005718954246,0.7220120383838384,0.8269396977777776,0.7345911292929294],"dir":"ltr"},{"str":"should","boundary":[0.8318415849673201,0.7220120383838384,0.8819966402614376,0.7345911292929294],"dir":"ltr"},{"str":"see","boundary":[0.16215694444444426,0.7371635535353537,0.1860379785620913,0.7497426444444445],"dir":"ltr"},{"str":"why","boundary":[0.19054779411764688,0.7371635535353537,0.2220961541176469,0.7497426444444445],"dir":"ltr"},{"str":"(","boundary":[0.22993929738562072,0.7371635535353537,0.23542526091503246,0.7497426444444445],"dir":"ltr"},{"str":"Hint:","boundary":[0.23542524509803905,0.7371635535353537,0.2746246521568626,0.7497426444444445],"dir":"ltr"},{"str":"What","boundary":[0.28285988562091485,0.7371635535353537,0.3240127515032678,0.7497426444444445],"dir":"ltr"},{"str":"are","boundary":[0.3287185457516338,0.7371635535353537,0.3532018963398691,0.7497426444444445],"dir":"ltr"},{"str":"the","boundary":[0.3575156045751632,0.7371635535353537,0.3819989551633985,0.7497426444444445],"dir":"ltr"},{"str":"eigenvalues","boundary":[0.3865087418300651,0.7371635535353537,0.475456233594771,0.7497426444444445],"dir":"ltr"},{"str":"of","boundary":[0.4795737745098037,0.7371635535353537,0.48896688849673187,0.7497426444444445],"dir":"ltr"},{"str":"the","boundary":[0.49759419934640503,0.7371635535353537,0.5220775499346403,0.7497426444444445],"dir":"ltr"},{"str":"matrix","boundary":[0.5265873366013071,0.7371635535353537,0.5775400542483659,0.7497426444444445],"dir":"ltr"},{"str":"X","boundary":[0.5820497549019606,0.7423838762626263,0.5955774572549017,0.7549629671717172],"dir":"ltr"},{"str":"?)","boundary":[0.5969499509803919,0.7371635535353537,0.609679990980392,0.7497426444444445],"dir":"ltr"}],"boundary":[0.11765,0.08979,0.88228,0.75496],"dir":"ltr","type":"paragraph"}]},{"token":null,"index":19,"image":{"jpeg":"/storage/books/4f1eb51f4f5b6edb/pages/050849bc1b35668350917e3cdaf6dcd6.jpg","blurred":"/storage/books/4f1eb51f4f5b6edb/pages/900f182b2bdba2104ae8eb4676f3da02.jpg"},"info":{"width":612,"height":792,"margin":[0.11765,0.08979,0.11767,0.89621]},"elements":[{"words":[{"str":"20","boundary":[0.11764705882352941,0.09001376073232323,0.1376114248366013,0.10378787689393938],"dir":"ltr"}],"boundary":[0.11765,0.09001,0.13761,0.10379],"dir":"ltr","type":"paragraph"},{"words":[{"str":"Algorithms","boundary":[0.7899640522875817,0.08979153426128839,0.8823348957516342,0.10356565042290454],"dir":"ltr"}],"boundary":[0.78996,0.08979,0.88233,0.10357],"dir":"ltr","type":"paragraph"}]}],"words":[]}
خرید یا کرایه
cancel
19