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<meta name="description" content="动画图解、一键运行的数据结构与算法教程">
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<meta name="author" content="Krahets">
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Hello 算法
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.4.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
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krahets/hello-algo
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<a href="." title="Hello 算法" class="md-nav__button md-logo" aria-label="Hello 算法" data-md-component="logo">
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Hello 算法
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.4.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
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krahets/hello-algo
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_preface/">0. 前言</a>
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<label for="__nav_1">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_1">
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<span class="md-nav__icon md-icon"></span>
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0. 前言
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_preface/about_the_book/" class="md-nav__link">
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0.1. 关于本书
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</a>
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<li class="md-nav__item">
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<a href="chapter_preface/suggestions/" class="md-nav__link">
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0.2. 如何使用本书
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</a>
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<li class="md-nav__item">
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<a href="chapter_preface/summary/" class="md-nav__link">
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0.3. 小结
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</a>
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_introduction/">1. 初识算法</a>
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_2">
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<span class="md-nav__icon md-icon"></span>
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1. 初识算法
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
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1.1. 算法无处不在
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_introduction/what_is_dsa/" class="md-nav__link">
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1.2. 算法是什么
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</a>
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<li class="md-nav__item">
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<a href="chapter_introduction/summary/" class="md-nav__link">
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1.3. 小结
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</a>
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</nav>
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<li class="md-nav__item md-nav__item--nested">
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_computational_complexity/">2. 复杂度</a>
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_3">
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<span class="md-nav__icon md-icon"></span>
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2. 复杂度
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
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2.1. 算法效率评估
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_computational_complexity/time_complexity/" class="md-nav__link">
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2.2. 时间复杂度
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_computational_complexity/space_complexity/" class="md-nav__link">
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2.3. 空间复杂度
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_computational_complexity/summary/" class="md-nav__link">
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2.4. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_data_structure/">3. 数据结构</a>
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<label for="__nav_4">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_4">
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<span class="md-nav__icon md-icon"></span>
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3. 数据结构
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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3.1. 数据结构分类
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_data_structure/basic_data_types/" class="md-nav__link">
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3.2. 基本数据类型
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_data_structure/number_encoding/" class="md-nav__link">
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3.3. 数字编码 *
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_data_structure/character_encoding/" class="md-nav__link">
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3.4. 字符编码 *
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_data_structure/summary/" class="md-nav__link">
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3.5. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_array_and_linkedlist/">4. 数组与链表</a>
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<label for="__nav_5">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_5">
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<span class="md-nav__icon md-icon"></span>
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4. 数组与链表
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_array_and_linkedlist/array/" class="md-nav__link">
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4.1. 数组
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
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4.2. 链表
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_array_and_linkedlist/list/" class="md-nav__link">
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4.3. 列表
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_array_and_linkedlist/summary/" class="md-nav__link">
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4.4. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_stack_and_queue/">5. 栈与队列</a>
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<label for="__nav_6">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_6">
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<span class="md-nav__icon md-icon"></span>
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5. 栈与队列
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_stack_and_queue/stack/" class="md-nav__link">
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5.1. 栈
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_stack_and_queue/queue/" class="md-nav__link">
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5.2. 队列
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_stack_and_queue/deque/" class="md-nav__link">
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5.3. 双向队列
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_stack_and_queue/summary/" class="md-nav__link">
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5.4. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
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<div class="md-nav__link md-nav__link--index ">
|
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<a href="chapter_hashing/">6. 散列表</a>
|
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<label for="__nav_7">
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_7">
|
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<span class="md-nav__icon md-icon"></span>
|
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6. 散列表
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_hashing/hash_map/" class="md-nav__link">
|
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6.1. 哈希表（New）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_hashing/hash_collision/" class="md-nav__link">
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6.2. 哈希冲突（New）
|
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_hashing/hash_algorithm/" class="md-nav__link">
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6.3. 哈希算法（New）
|
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_hashing/summary/" class="md-nav__link">
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6.4. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
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<div class="md-nav__link md-nav__link--index ">
|
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<a href="chapter_tree/">7. 树</a>
|
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|
<label for="__nav_8">
|
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|
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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</div>
|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_8">
|
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<span class="md-nav__icon md-icon"></span>
|
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7. 树
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
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<a href="chapter_tree/binary_tree/" class="md-nav__link">
|
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7.1. 二叉树
|
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|
</a>
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</li>
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<li class="md-nav__item">
|
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<a href="chapter_tree/binary_tree_traversal/" class="md-nav__link">
|
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7.2. 二叉树遍历
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
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<a href="chapter_tree/array_representation_of_tree/" class="md-nav__link">
|
|
|
7.3. 二叉树数组表示
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
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<a href="chapter_tree/binary_search_tree/" class="md-nav__link">
|
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7.4. 二叉搜索树
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
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<a href="chapter_tree/avl_tree/" class="md-nav__link">
|
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|
7.5. AVL 树 *
|
|
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</a>
|
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</li>
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<li class="md-nav__item">
|
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<a href="chapter_tree/summary/" class="md-nav__link">
|
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7.6. 小结
|
|
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</a>
|
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</li>
|
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
|
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<div class="md-nav__link md-nav__link--index ">
|
|
|
<a href="chapter_heap/">8. 堆</a>
|
|
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|
|
<label for="__nav_9">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
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|
|
</div>
|
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|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_9">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
8. 堆
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
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|
<a href="chapter_heap/heap/" class="md-nav__link">
|
|
|
8.1. 堆
|
|
|
</a>
|
|
|
</li>
|
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<li class="md-nav__item">
|
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<a href="chapter_heap/build_heap/" class="md-nav__link">
|
|
|
8.2. 建堆操作
|
|
|
</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_heap/top_k/" class="md-nav__link">
|
|
|
8.3. Top-K 问题（New）
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
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<a href="chapter_heap/summary/" class="md-nav__link">
|
|
|
8.4. 小结
|
|
|
</a>
|
|
|
</li>
|
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
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<div class="md-nav__link md-nav__link--index ">
|
|
|
<a href="chapter_graph/">9. 图</a>
|
|
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|
|
<label for="__nav_10">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
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|
|
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</div>
|
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|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_10">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
9. 图
|
|
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</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
|
|
<a href="chapter_graph/graph/" class="md-nav__link">
|
|
|
9.1. 图
|
|
|
</a>
|
|
|
</li>
|
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<li class="md-nav__item">
|
|
|
<a href="chapter_graph/graph_operations/" class="md-nav__link">
|
|
|
9.2. 图基础操作
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
|
|
<a href="chapter_graph/graph_traversal/" class="md-nav__link">
|
|
|
9.3. 图的遍历
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
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|
<a href="chapter_graph/summary/" class="md-nav__link">
|
|
|
9.4. 小结
|
|
|
</a>
|
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|
</li>
|
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
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<div class="md-nav__link md-nav__link--index ">
|
|
|
<a href="chapter_searching/">10. 搜索</a>
|
|
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|
|
<label for="__nav_11">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
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|
|
</div>
|
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|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_11">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
10. 搜索
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
|
|
<a href="chapter_searching/binary_search/" class="md-nav__link">
|
|
|
10.1. 二分查找
|
|
|
</a>
|
|
|
</li>
|
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<li class="md-nav__item">
|
|
|
<a href="chapter_searching/binary_search_edge/" class="md-nav__link">
|
|
|
10.2. 二分查找边界
|
|
|
</a>
|
|
|
</li>
|
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<li class="md-nav__item">
|
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|
<a href="chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
|
|
10.3. 哈希优化策略
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
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<a href="chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
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10.4. 重识搜索算法
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_searching/summary/" class="md-nav__link">
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10.5. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_sorting/">11. 排序</a>
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<label for="__nav_12">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_12">
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<span class="md-nav__icon md-icon"></span>
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11. 排序
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_sorting/sorting_algorithm/" class="md-nav__link">
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11.1. 排序算法
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/selection_sort/" class="md-nav__link">
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11.2. 选择排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/bubble_sort/" class="md-nav__link">
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11.3. 冒泡排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/insertion_sort/" class="md-nav__link">
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11.4. 插入排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/quick_sort/" class="md-nav__link">
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11.5. 快速排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/merge_sort/" class="md-nav__link">
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11.6. 归并排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/heap_sort/" class="md-nav__link">
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11.7. 堆排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/bucket_sort/" class="md-nav__link">
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11.8. 桶排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/counting_sort/" class="md-nav__link">
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11.9. 计数排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/radix_sort/" class="md-nav__link">
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11.10. 基数排序
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_sorting/summary/" class="md-nav__link">
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11.11. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_backtracking/">12. 回溯</a>
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<label for="__nav_13">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_13">
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<span class="md-nav__icon md-icon"></span>
|
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12. 回溯
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
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12.1. 回溯算法
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_backtracking/permutations_problem/" class="md-nav__link">
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12.2. 全排列问题
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_backtracking/subset_sum_problem/" class="md-nav__link">
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12.3. 子集和问题
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_backtracking/n_queens_problem/" class="md-nav__link">
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12.4. N 皇后问题
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_backtracking/summary/" class="md-nav__link">
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12.5. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="chapter_dynamic_programming/">13. 动态规划</a>
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<label for="__nav_14">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_14">
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<span class="md-nav__icon md-icon"></span>
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13. 动态规划
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
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13.1. 初探动态规划（New）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
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13.2. DP 问题特性（New）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
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13.3. DP 解题思路（New）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
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13.4. 0-1 背包问题（New）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
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13.5. 完全背包问题（New）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
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13.6. 编辑距离问题（New）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_dynamic_programming/summary/" class="md-nav__link">
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13.7. 小结（New）
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
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<label class="md-nav__link" for="__nav_15" id="__nav_15_label" tabindex="0">
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14. 附录
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_15">
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<span class="md-nav__icon md-icon"></span>
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14. 附录
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="chapter_appendix/installation/" class="md-nav__link">
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14.1. 编程环境安装
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</a>
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</li>
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<li class="md-nav__item">
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<a href="chapter_appendix/contribution/" class="md-nav__link">
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14.2. 一起参与创作
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</a>
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</li>
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</ul>
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</nav>
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/index.md" title="编辑此页" class="md-content__button md-icon">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
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</a>
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<h1 align="center"> </h1>
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<p align="center">
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<img src="index.assets/conceptual_rendering.png" width="250">
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<img src="index.assets/hello_algo_knowledge_map_tp.png" width="400">
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</p>
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<h2 align="center"> 《 Hello 算法 》</h2>
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<p align="center"> 动画图解、一键运行的数据结构与算法教程 </p>
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<p align="center">
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<a href="https://github.com/krahets/hello-algo">
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<img alt="GitHub Repo stars" src="https://img.shields.io/github/stars/krahets/hello-algo?style=social&link=https%3A%2F%2Fgithub.com%2Fkrahets%2Fhello-algo">
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</a>
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<a href="https://github.com/krahets/hello-algo">
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<img alt="GitHub contributors" src="https://img.shields.io/github/contributors-anon/krahets/hello-algo?style=social&logo=handshake&logoColor=%23101010">
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</a>
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</p>
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<hr />
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<h2 align="center"> 推荐语 </h2>
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<div class="admonition quote">
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<p class="admonition-title">Quote</p>
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<p>“一本通俗易懂的数据结构与算法入门书，引导读者手脑并用地学习，强烈推荐算法初学者阅读。”</p>
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<p><strong>—— 邓俊辉，清华大学计算机系教授</strong></p>
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</div>
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<div class="admonition quote">
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<p class="admonition-title">Quote</p>
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<p>“如果我当年学数据结构与算法的时候有《Hello 算法》，学起来应该会简单 10 倍！”</p>
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<p><strong>—— 李沐，亚马逊资深首席科学家</strong></p>
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</div>
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<hr />
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<h3 align="center"> 全书动画图解 </h3>
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<p align="center"> 内容清晰易懂、学习曲线平滑</br>电脑、平板、手机全终端阅读 </p>
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<p><img alt="algorithm_animation" src="index.assets/animation.gif" /></p>
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<div class="admonition quote">
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<p><p align="center"> "A picture is worth a thousand words." </p>
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<p align="center"> “一图胜千言” </p></p>
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</div>
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<hr />
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<h3 align="center"> 代码一键运行 </h3>
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<p align="center"> 提供各个算法与数据结构的简洁实现与测试样例，皆可直接运行</br>支持 Java, C++, Python, Go, JS, TS, C#, Swift, Zig 等语言 </p>
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<p><img alt="running_code" src="index.assets/running_code.gif" /></p>
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<div class="admonition quote">
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<p><p align="center"> "Talk is cheap. Show me the code." </p>
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<p align="center"> “少吹牛，看代码” </p></p>
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</div>
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<hr />
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<h3 align="center"> 可讨论与提问 </h3>
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<p align="center"> 鼓励小伙伴们互帮互助、共同成长</br>提问与评论一般能在两日内得到回复 </p>
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<p><img alt="comment" src="index.assets/comment.gif" /></p>
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<div class="admonition quote">
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<p><p align="center"> “追风赶月莫停留，平芜尽处是春山” </p>
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<p align="center"> 一起加油！ </p></p>
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</div>
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<hr />
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<h2 align="center"> 序 </h2>
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<p>两年前，我在力扣上分享了《剑指 Offer》系列题解，受到了许多朋友的喜爱与支持。在此期间，我回答了众多读者的评论问题，其中最常见的一个问题是“如何入门学习算法”。我逐渐也对这个问题产生了浓厚的兴趣。</p>
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<p>两眼一抹黑地刷题似乎是最受欢迎的方法，简单直接且有效。然而，刷题就如同玩“扫雷”游戏，自学能力强的同学能够顺利地将地雷逐个排掉，而基础不足的同学很可能被炸的满头是包，并在挫折中步步退缩。通读教材书籍也是一种常见做法，但对于面向求职的同学来说，毕业季、投递简历、准备笔试面试已经占据了大部分精力，厚重的书籍往往变成了一项艰巨的挑战。</p>
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<p>如果你也面临类似的困扰，那么很幸运这本书找到了你。本书是我对此问题的给出的答案，虽然不一定正确，但至少是一次积极的尝试。这本书虽然不足以让你直接拿到 Offer ，但会引导你探索数据结构与算法的“知识地图”，带你了解不同“地雷”的形状大小和分布位置，让你掌握各种“排雷方法”。有了这些本领，相信你可以更加自如地应对刷题和阅读文献，逐步构建起完整的知识体系。</p>
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<h3 align="left"> 作者简介 </h3>
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<p>靳宇栋 (<a href="https://leetcode.cn/u/jyd/">Krahets</a>)，大厂高级算法工程师，上海交通大学硕士。力扣（LeetCode）全网阅读量最高博主，其 LeetBook《图解算法数据结构》已被订阅 24 万本。</p>
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<hr />
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<h2 align="center"> 致谢 </h2>
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<p>本书在开源社区众多贡献者的共同努力下不断成长。感谢每一位投入时间与精力的撰稿人，是他们无私奉献使这本书越变越好，他们是（按照 GitHub 自动生成的顺序排列）：</p>
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<p align="center">
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<a href="https://github.com/krahets/hello-algo/graphs/contributors">
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<img width="550" src="https://contrib.rocks/image?repo=krahets/hello-algo" />
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</a>
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</p>
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<p>本书的代码审阅工作由 Gonglja, gvenusleo, justin‐tse, krahets, nuomi1, Reanon, sjinzh 完成（按照首字母顺序排列）。感谢他们付出的时间与精力，正是他们确保了各语言代码的规范与统一。</p>
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<div class="center-table">
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<table>
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<tbody>
|
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<td align="center"><a href="https://github.com/Gonglja"><img src="https://avatars.githubusercontent.com/u/39959756?v=4" width="50px;" alt="Gonglja"/><br /><sub><b>Gonglja</b></sub></a><br /><sub>C / C++</sub></td>
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<td align="center"><a href="https://github.com/gvenusleo"><img src="https://avatars.githubusercontent.com/u/79075347?v=4" width="50px;" alt="gvenusleo"/><br /><sub><b>gvenusleo</b></sub></a><br /><sub>Dart</sub></td>
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<td align="center"><a href="https://github.com/hpstory"><img src="https://avatars.githubusercontent.com/u/33348162?v=4" width="50px;" alt="hpstory"/><br /><sub><b>hpstory</b></sub></a><br /><sub>C#</sub></td>
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<td align="center"><a href="https://github.com/justin-tse"><img src="https://avatars.githubusercontent.com/u/24556310?v=4" width="50px;" alt="justin-tse"/><br /><sub><b>justin-tse</b></sub></a><br /><sub>JS / TS</sub></td>
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<td align="center"><a href="https://github.com/krahets"><img src="https://avatars.githubusercontent.com/u/26993056?v=4" width="50px;" alt="krahets"/><br /><sub><b>krahets</b></sub></a><br /><sub>Java / Python</sub></td>
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<td align="center"><a href="https://github.com/nuomi1"><img src="https://avatars.githubusercontent.com/u/3739017?v=4" width="50px;" alt="nuomi1"/><br /><sub><b>nuomi1</b></sub></a><br /><sub>Swift</sub></td>
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<td align="center"><a href="https://github.com/Reanon"><img src="https://avatars.githubusercontent.com/u/22005836?v=4" width="50px;" alt="Reanon"/><br /><sub><b>Reanon</b></sub></a><br /><sub>Go / C</sub></td>
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<td align="center"><a href="https://github.com/sjinzh"><img src="https://avatars.githubusercontent.com/u/99076655?v=4" width="50px;" alt="sjinzh"/><br /><sub><b>sjinzh</b></sub></a><br /><sub>Rust / Zig</sub></td>
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</tbody>
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