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krahets/hello-algo
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0. 前言
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0. 前言
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0.1. 关于本书
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0.2. 如何使用本书
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0.3. 小结
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<span class="md-ellipsis">
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1. 初识算法
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1. 初识算法
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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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1.2. 算法是什么
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1.3. 小结
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</span>
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</a>
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</li>
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<span class="md-ellipsis">
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2. 复杂度
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</a>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
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2. 复杂度
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2.1. 算法效率评估
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</span>
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</a>
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</li>
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<span class="md-ellipsis">
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2.2. 时间复杂度
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</span>
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</a>
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</li>
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<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
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<span class="md-ellipsis">
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2.3. 空间复杂度
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</span>
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</a>
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</li>
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2.4. 小结
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</span>
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</a>
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</li>
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3. 数据结构
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3. 数据结构
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<label class="md-nav__link md-nav__link--active" for="__toc">
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<span class="md-ellipsis">
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3.1. 数据结构分类
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</span>
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<span class="md-nav__icon md-icon"></span>
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</label>
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<a href="./" class="md-nav__link md-nav__link--active">
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<span class="md-ellipsis">
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3.1. 数据结构分类
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</span>
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</a>
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<nav class="md-nav md-nav--secondary" aria-label="目录">
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<label class="md-nav__title" for="__toc">
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<span class="md-nav__icon md-icon"></span>
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目录
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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="#311" class="md-nav__link">
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3.1.1. 逻辑结构：线性与非线性
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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="#312" class="md-nav__link">
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3.1.2. 物理结构：连续与离散
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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">
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<a href="../basic_data_types/" class="md-nav__link">
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<span class="md-ellipsis">
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3.2. 基本数据类型
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</span>
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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="../number_encoding/" class="md-nav__link">
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<span class="md-ellipsis">
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3.3. 数字编码 *
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../character_encoding/" class="md-nav__link">
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<span class="md-ellipsis">
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3.4. 字符编码 *
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../summary/" class="md-nav__link">
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<span class="md-ellipsis">
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3.5. 小结
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</span>
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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 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__container">
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<a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
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<span class="md-ellipsis">
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4. 数组与链表
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</span>
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</a>
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<label class="md-nav__link " 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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<span class="md-ellipsis">
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4.1. 数组
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</span>
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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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<span class="md-ellipsis">
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4.2. 链表
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</span>
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</a>
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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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<span class="md-ellipsis">
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4.3. 列表
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</span>
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</a>
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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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<span class="md-ellipsis">
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4.4. 小结
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</span>
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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__container">
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<a href="../../chapter_stack_and_queue/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
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<span class="md-ellipsis">
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5. 栈与队列
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</span>
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</a>
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<label class="md-nav__link " 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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<span class="md-ellipsis">
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5.1. 栈
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</span>
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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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<span class="md-ellipsis">
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5.2. 队列
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</span>
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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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<span class="md-ellipsis">
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5.3. 双向队列
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</span>
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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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<span class="md-ellipsis">
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5.4. 小结
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</span>
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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__container">
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<a href="../../chapter_hashing/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
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<span class="md-ellipsis">
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6. 散列表
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</span>
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</a>
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<label class="md-nav__link " 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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<span class="md-ellipsis">
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6.1. 哈希表
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</span>
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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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<span class="md-ellipsis">
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6.2. 哈希冲突
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</span>
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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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<span class="md-ellipsis">
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6.3. 哈希算法
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</span>
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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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<span class="md-ellipsis">
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6.4. 小结
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<a href="../../chapter_tree/" class="md-nav__link ">
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<span class="md-ellipsis">
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7. 树
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</a>
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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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<span class="md-ellipsis">
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7.1. 二叉树
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</span>
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</a>
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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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<span class="md-ellipsis">
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7.2. 二叉树遍历
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</span>
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</a>
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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">
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<span class="md-ellipsis">
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7.3. 二叉树数组表示
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</span>
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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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<span class="md-ellipsis">
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7.4. 二叉搜索树
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</span>
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</a>
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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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<span class="md-ellipsis">
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7.5. AVL 树 *
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</span>
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</a>
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7.6. 小结
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</span>
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</a>
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</li>
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</nav>
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_heap/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
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<span class="md-ellipsis">
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8. 堆
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</span>
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</a>
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<label class="md-nav__link " for="__nav_9">
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<span class="md-nav__icon md-icon"></span>
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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">
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<label class="md-nav__title" for="__nav_9">
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<span class="md-nav__icon md-icon"></span>
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8. 堆
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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_heap/heap/" class="md-nav__link">
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<span class="md-ellipsis">
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8.1. 堆
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</span>
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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_heap/build_heap/" class="md-nav__link">
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<span class="md-ellipsis">
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8.2. 建堆操作
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</span>
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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_heap/top_k/" class="md-nav__link">
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<span class="md-ellipsis">
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8.3. Top-K 问题
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</span>
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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_heap/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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8.4. 小结
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</span>
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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 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__container">
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<a href="../../chapter_graph/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
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<span class="md-ellipsis">
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9. 图
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</span>
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</a>
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<label class="md-nav__link " for="__nav_10">
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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_10_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_10">
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<span class="md-nav__icon md-icon"></span>
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9. 图
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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_graph/graph/" class="md-nav__link">
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<span class="md-ellipsis">
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9.1. 图
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</span>
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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_graph/graph_operations/" class="md-nav__link">
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<span class="md-ellipsis">
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9.2. 图基础操作
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</span>
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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_graph/graph_traversal/" class="md-nav__link">
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<span class="md-ellipsis">
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9.3. 图的遍历
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</span>
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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_graph/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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9.4. 小结
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</span>
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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_11" >
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<div class="md-nav__link md-nav__container">
|
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<a href="../../chapter_searching/" class="md-nav__link ">
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|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
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<span class="md-ellipsis">
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10. 搜索
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</span>
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</a>
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<label class="md-nav__link " for="__nav_11">
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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_11_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
|
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10. 搜索
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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_searching/binary_search/" class="md-nav__link">
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<span class="md-ellipsis">
|
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10.1. 二分查找
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</span>
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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/binary_search_edge/" class="md-nav__link">
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<span class="md-ellipsis">
|
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10.2. 二分查找边界
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</span>
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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/replace_linear_by_hashing/" class="md-nav__link">
|
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<span class="md-ellipsis">
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10.3. 哈希优化策略
|
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</span>
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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/searching_algorithm_revisited/" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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10.4. 重识搜索算法
|
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</span>
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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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<span class="md-ellipsis">
|
|
|
10.5. 小结
|
|
|
</span>
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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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|
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|
|
|
<div class="md-nav__link md-nav__container">
|
|
|
<a href="../../chapter_sorting/" class="md-nav__link ">
|
|
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|
|
|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
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<span class="md-ellipsis">
|
|
|
11. 排序
|
|
|
</span>
|
|
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|
|
</a>
|
|
|
|
|
|
<label class="md-nav__link " for="__nav_12">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
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|
|
|
</div>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_12">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
11. 排序
|
|
|
</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_sorting/sorting_algorithm/" class="md-nav__link">
|
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|
|
<span class="md-ellipsis">
|
|
|
11.1. 排序算法
|
|
|
</span>
|
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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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<span class="md-ellipsis">
|
|
|
11.2. 选择排序
|
|
|
</span>
|
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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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|
<span class="md-ellipsis">
|
|
|
11.3. 冒泡排序
|
|
|
</span>
|
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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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|
<span class="md-ellipsis">
|
|
|
11.4. 插入排序
|
|
|
</span>
|
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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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|
|
<span class="md-ellipsis">
|
|
|
11.5. 快速排序
|
|
|
</span>
|
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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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|
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|
|
<span class="md-ellipsis">
|
|
|
11.6. 归并排序
|
|
|
</span>
|
|
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</a>
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</li>
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.7. 堆排序
|
|
|
</span>
|
|
|
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|
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|
|
</a>
|
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</li>
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.8. 桶排序
|
|
|
</span>
|
|
|
|
|
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|
|
</a>
|
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</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.9. 计数排序
|
|
|
</span>
|
|
|
|
|
|
|
|
|
</a>
|
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</li>
|
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|
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|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.10. 基数排序
|
|
|
</span>
|
|
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|
|
|
|
|
|
</a>
|
|
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</li>
|
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|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.11. 小结
|
|
|
</span>
|
|
|
|
|
|
|
|
|
</a>
|
|
|
</li>
|
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|
|
|
|
</ul>
|
|
|
</nav>
|
|
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|
</li>
|
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|
<li class="md-nav__item md-nav__item--nested">
|
|
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|
|
|
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|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
|
|
|
|
|
|
|
|
|
|
|
|
<div class="md-nav__link md-nav__container">
|
|
|
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
|
|
|
|
|
|
|
|
|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
|
|
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<span class="md-ellipsis">
|
|
|
12. 分治
|
|
|
</span>
|
|
|
|
|
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|
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|
|
<span class="md-status md-status--new" title="最近添加">
|
|
|
</span>
|
|
|
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|
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|
|
|
|
|
|
|
|
|
</a>
|
|
|
|
|
|
<label class="md-nav__link " for="__nav_13">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
</div>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_13">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
12. 分治
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
|
|
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|
|
<span class="md-ellipsis">
|
|
|
12.1. 分治算法
|
|
|
</span>
|
|
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|
<span class="md-status md-status--new" title="最近添加">
|
|
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</span>
|
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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_divide_and_conquer/binary_search_recur/" class="md-nav__link">
|
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|
<span class="md-ellipsis">
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12.2. 分治搜索策略
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<span class="md-status md-status--new" title="最近添加">
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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12.3. 构建树问题
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<span class="md-status md-status--new" title="最近添加">
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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12.4. 汉诺塔问题
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<span class="md-status md-status--new" title="最近添加">
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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12.5. 小结
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</span>
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<span class="md-status md-status--new" title="最近添加">
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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__container">
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<a href="../../chapter_backtracking/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
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<span class="md-ellipsis">
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13. 回溯
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</span>
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</a>
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<label class="md-nav__link " 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. 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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<span class="md-ellipsis">
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13.1. 回溯算法
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</span>
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<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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13.2. 全排列问题
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</span>
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<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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13.3. 子集和问题
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</span>
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<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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13.4. N 皇后问题
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</span>
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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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<span class="md-ellipsis">
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13.5. 小结
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</span>
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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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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_dynamic_programming/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
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<span class="md-ellipsis">
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14. 动态规划
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</span>
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<span class="md-status md-status--new" title="最近添加">
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</a>
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<label class="md-nav__link " for="__nav_15">
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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_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. 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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<span class="md-ellipsis">
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14.1. 初探动态规划
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</span>
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<span class="md-status md-status--new" title="最近添加">
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</a>
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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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<span class="md-ellipsis">
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14.2. DP 问题特性
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</span>
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<span class="md-status md-status--new" title="最近添加">
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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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<span class="md-ellipsis">
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14.3. DP 解题思路
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</span>
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<span class="md-status md-status--new" title="最近添加">
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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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<span class="md-ellipsis">
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14.4. 0-1 背包问题
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</span>
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<span class="md-status md-status--new" title="最近添加">
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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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<span class="md-ellipsis">
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14.5. 完全背包问题
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</span>
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<span class="md-status md-status--new" title="最近添加">
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</span>
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</a>
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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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<span class="md-ellipsis">
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14.6. 编辑距离问题
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</span>
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<span class="md-status md-status--new" title="最近添加">
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</span>
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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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<span class="md-ellipsis">
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14.7. 小结
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</span>
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<span class="md-status md-status--new" title="最近添加">
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</span>
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</a>
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</ul>
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</nav>
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
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<div class="md-nav__link md-nav__container">
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15.1. 贪心算法
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15.2. 分数背包问题
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15.3. 最大容量问题
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15.4. 最大切分乘积问题
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16. 附录
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16.1. 编程环境安装
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16.2. 一起参与创作
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参考文献
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3.1.1. 逻辑结构：线性与非线性
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3.1.2. 物理结构：连续与离散
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<h1 id="31">3.1. 数据结构分类<a class="headerlink" href="#31" title="Permanent link">¶</a></h1>
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<p>数据结构可以从逻辑结构和物理结构两个维度进行分类。</p>
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<h2 id="311">3.1.1. 逻辑结构：线性与非线性<a class="headerlink" href="#311" title="Permanent link">¶</a></h2>
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<p><strong>「逻辑结构」揭示了数据元素之间的逻辑关系</strong>。在数组和链表中，数据按照顺序依次排列，体现了数据之间的线性关系；而在树中，数据从顶部向下按层次排列，表现出祖先与后代之间的派生关系；图则由节点和边构成，反映了复杂的网络关系。</p>
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<p>逻辑结构通常分为“线性”和“非线性”两类。线性结构比较直观，指数据在逻辑关系上呈线性排列；非线性结构则相反，呈非线性排列。</p>
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<ul>
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<li><strong>线性数据结构</strong>：数组、链表、栈、队列、哈希表；</li>
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<li><strong>非线性数据结构</strong>：树、堆、图、哈希表；</li>
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</ul>
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<p><img alt="线性与非线性数据结构" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></p>
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<p align="center"> Fig. 线性与非线性数据结构 </p>
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<p>非线性数据结构可以进一步被划分为树形结构和网状结构。</p>
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<ul>
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<li><strong>线性结构</strong>：数组、链表、队列、栈、哈希表，元素存在一对一的顺序关系；</li>
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<li><strong>树形结构</strong>：树、堆、哈希表，元素存在一对多的关系；</li>
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<li><strong>网状结构</strong>：图，元素存在多对多的关系；</li>
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</ul>
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<h2 id="312">3.1.2. 物理结构：连续与离散<a class="headerlink" href="#312" title="Permanent link">¶</a></h2>
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<p>在计算机中，内存和硬盘是两种主要的存储硬件设备。硬盘主要用于长期存储数据，容量较大（通常可达到 TB 级别）、速度较慢。内存用于运行程序时暂存数据，速度较快，但容量较小（通常为 GB 级别）。</p>
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<p><strong>在算法运行过程中，相关数据都存储在内存中</strong>。下图展示了一个计算机内存条，其中每个黑色方块都包含一块内存空间。我们可以将内存想象成一个巨大的 Excel 表格，其中每个单元格都可以存储 1 byte 的数据，在算法运行时，所有数据都被存储在这些单元格中。</p>
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<p><strong>系统通过「内存地址 Memory Location」来访问目标内存位置的数据</strong>。计算机根据特定规则为表格中的每个单元格分配编号，确保每个内存空间都有唯一的内存地址。有了这些地址，程序便可以访问内存中的数据。</p>
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<p><img alt="内存条、内存空间、内存地址" src="../classification_of_data_structure.assets/computer_memory_location.png" /></p>
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<p align="center"> Fig. 内存条、内存空间、内存地址 </p>
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<p>内存是所有程序的共享资源，当内存被某个程序占用时，其他程序无法同时使用。<strong>因此，在数据结构与算法的设计中，内存资源是一个重要的考虑因素</strong>。例如，算法所占用的内存峰值不应超过系统剩余空闲内存；如果运行的程序很多并且缺少大量连续的内存空间，那么所选用的数据结构必须能够存储在离散的内存空间内。</p>
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<p><strong>「物理结构」反映了数据在计算机内存中的存储方式</strong>，可分为数组的连续空间存储和链表的离散空间存储。物理结构从底层决定了数据的访问、更新、增删等操作方法，同时在时间效率和空间效率方面呈现出互补的特点。</p>
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<p><img alt="连续空间存储与离散空间存储" src="../classification_of_data_structure.assets/classification_phisical_structure.png" /></p>
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<p align="center"> Fig. 连续空间存储与离散空间存储 </p>
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<p><strong>所有数据结构都是基于数组、链表或二者的组合实现的</strong>。例如，栈和队列既可以使用数组实现，也可以使用链表实现；而哈希表的实现可能同时包含数组和链表。</p>
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<ul>
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<li><strong>基于数组可实现</strong>：栈、队列、哈希表、树、堆、图、矩阵、张量（维度 <span class="arithmatex">\(\geq 3\)</span> 的数组）等；</li>
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<li><strong>基于链表可实现</strong>：栈、队列、哈希表、树、堆、图等；</li>
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</ul>
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<p>基于数组实现的数据结构也被称为“静态数据结构”，这意味着此类数据结构在初始化后长度不可变。相对应地，基于链表实现的数据结构被称为“动态数据结构”，这类数据结构在初始化后，仍可以在程序运行过程中对其长度进行调整。</p>
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