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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
|
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|
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<span class="md-ellipsis">
|
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第 0 章 前言
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第 0 章 前言
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0.1 关于本书
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|
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|
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|
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</a>
|
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</li>
|
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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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|
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|
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|
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</a>
|
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</li>
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<span class="md-ellipsis">
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0.3 小结
|
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</span>
|
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|
||
|
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</a>
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|
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|
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<span class="md-ellipsis">
|
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第 1 章 初识算法
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第 1 章 初识算法
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1.1 算法无处不在
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</span>
|
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|
||
|
||
</a>
|
||
</li>
|
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1.2 算法是什么
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|
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|
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|
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</a>
|
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</li>
|
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<span class="md-ellipsis">
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1.3 小结
|
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</span>
|
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|
||
|
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</a>
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|
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<span class="md-ellipsis">
|
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第 2 章 复杂度分析
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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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<span class="md-nav__icon md-icon"></span>
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第 2 章 复杂度分析
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|
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2.1 算法效率评估
|
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</span>
|
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|
||
|
||
</a>
|
||
</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
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<span class="md-ellipsis">
|
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2.2 迭代与递归
|
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</span>
|
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|
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|
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|
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|
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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_computational_complexity/time_complexity/" class="md-nav__link">
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<span class="md-ellipsis">
|
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2.3 时间复杂度
|
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</span>
|
||
|
||
|
||
</a>
|
||
</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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|
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|
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<span class="md-ellipsis">
|
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2.4 空间复杂度
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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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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|
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<span class="md-ellipsis">
|
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2.5 小结
|
||
</span>
|
||
|
||
|
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</a>
|
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</li>
|
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|
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|
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</ul>
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</nav>
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</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||
|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
|
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|
||
<span class="md-ellipsis">
|
||
第 3 章 数据结构
|
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|
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</a>
|
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|
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<label class="md-nav__link " for="__nav_4">
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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_4_label" aria-expanded="false">
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第 3 章 数据结构
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|
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3.1 数据结构分类
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
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|
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|
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3.2 基本数据类型
|
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</span>
|
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|
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|
||
</a>
|
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</li>
|
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<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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|
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3.3 数字编码 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
||
|
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|
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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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|
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<span class="md-ellipsis">
|
||
3.4 字符编码 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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<a href="../../chapter_data_structure/summary/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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3.5 小结
|
||
</span>
|
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|
||
|
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</a>
|
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</li>
|
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|
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|
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|
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|
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</ul>
|
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</nav>
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|
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|
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|
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|
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|
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|
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|
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|
||
|
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|
||
|
||
|
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|
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|
||
|
||
|
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|
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|
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<li class="md-nav__item md-nav__item--active md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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|
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|
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<span class="md-ellipsis">
|
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第 4 章 数组与链表
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</a>
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<label class="md-nav__link " for="__nav_5">
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
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第 4 章 数组与链表
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<li class="md-nav__item">
|
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<a href="../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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|
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|
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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="../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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|
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|
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</a>
|
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</li>
|
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|
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|
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<li class="md-nav__item">
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<a href="../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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|
||
|
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</a>
|
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</li>
|
||
|
||
|
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<label class="md-nav__link md-nav__link--active" for="__toc">
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4.4 小结
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|
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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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|
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|
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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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|
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|
||
</a>
|
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|
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|
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|
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<nav class="md-nav md-nav--secondary" aria-label="目录">
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目录
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1. 重点回顾
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2. Q & A
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|
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</nav>
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|
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第 5 章 栈与队列
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第 5 章 栈与队列
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5.1 栈
|
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|
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|
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|
||
</a>
|
||
</li>
|
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<li class="md-nav__item">
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5.2 队列
|
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|
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|
||
|
||
</a>
|
||
</li>
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<li class="md-nav__item">
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5.3 双向队列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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5.4 小结
|
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|
||
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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|
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|
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<span class="md-ellipsis">
|
||
第 6 章 哈希表
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</a>
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|
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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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
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第 6 章 哈希表
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
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6.1 哈希表
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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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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|
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|
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6.2 哈希冲突
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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|
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<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
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||
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6.3 哈希算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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6.4 小结
|
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</span>
|
||
|
||
|
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|
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|
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|
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||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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第 7 章 树
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第 7 章 树
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|
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7.1 二叉树
|
||
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|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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7.2 二叉树遍历
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
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|
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7.3 二叉树数组表示
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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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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|
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7.4 二叉搜索树
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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7.5 AVL 树 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
||
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7.6 小结
|
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</span>
|
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|
||
|
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|
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|
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||
|
||
|
||
|
||
|
||
|
||
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<span class="md-ellipsis">
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第 8 章 堆
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|
||
<label class="md-nav__title" for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 8 章 堆
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.1 堆
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.2 建堆操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/top_k/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.3 Top-K 问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.4 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_graph/" class="md-nav__link ">
|
||
|
||
|
||
<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>
|
||
|
||
<span class="md-ellipsis">
|
||
第 9 章 图
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<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>
|
||
第 9 章 图
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.1 图
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.2 图基础操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.3 图的遍历
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.4 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_searching/" class="md-nav__link ">
|
||
|
||
|
||
<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>
|
||
|
||
<span class="md-ellipsis">
|
||
第 10 章 搜索
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<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>
|
||
第 10 章 搜索
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.1 二分查找
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.2 二分查找插入点
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.3 二分查找边界
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.4 哈希优化策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.5 重识搜索算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.6 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_sorting/" class="md-nav__link ">
|
||
|
||
|
||
<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>
|
||
|
||
<span class="md-ellipsis">
|
||
第 11 章 排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</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>
|
||
第 11 章 排序
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.1 排序算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.2 选择排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.3 冒泡排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.4 插入排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.5 快速排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.6 归并排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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<span class="md-ellipsis">
|
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第 12 章 分治
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第 12 章 分治
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12.1 分治算法
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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12.2 分治搜索策略
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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12.3 构建树问题
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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12.4 汉诺塔问题
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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12.5 小结
|
||
</span>
|
||
|
||
|
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</a>
|
||
</li>
|
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|
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|
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|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
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|
||
<span class="md-ellipsis">
|
||
第 13 章 回溯
|
||
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|
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第 13 章 回溯
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<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
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|
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<span class="md-ellipsis">
|
||
13.1 回溯算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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13.2 全排列问题
|
||
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|
||
|
||
|
||
</a>
|
||
</li>
|
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<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
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13.3 子集和问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
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|
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13.4 N 皇后问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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<span class="md-ellipsis">
|
||
13.5 小结
|
||
</span>
|
||
|
||
|
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</a>
|
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|
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|
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|
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||
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||
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||
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||
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||
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||
|
||
|
||
|
||
|
||
|
||
|
||
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|
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|
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<span class="md-ellipsis">
|
||
第 14 章 动态规划
|
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|
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第 14 章 动态规划
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|
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14.1 初探动态规划
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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14.2 DP 问题特性
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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14.3 DP 解题思路
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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<a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
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|
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|
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14.4 0-1 背包问题
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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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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|
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14.5 完全背包问题
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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<a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
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14.6 编辑距离问题
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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14.7 小结
|
||
</span>
|
||
|
||
|
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|
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|
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|
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||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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<span class="md-ellipsis">
|
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第 15 章 贪心
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第 15 章 贪心
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<a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
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|
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15.1 贪心算法
|
||
</span>
|
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|
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|
||
</a>
|
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</li>
|
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15.2 分数背包问题
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
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15.3 最大容量问题
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
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15.4 最大切分乘积问题
|
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</span>
|
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|
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|
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</a>
|
||
</li>
|
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<span class="md-ellipsis">
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15.5 小结
|
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</span>
|
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|
||
|
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</a>
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</li>
|
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|
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<h1 id="44">4.4 小结<a class="headerlink" href="#44" title="Permanent link">¶</a></h1>
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<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
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<ul>
|
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<li>数组和链表是两种基本的数据结构，分别代表数据在计算机内存中的两种存储方式：连续空间存储和分散空间存储。两者的特点呈现出互补的特性。</li>
|
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<li>数组支持随机访问、占用内存较少；但插入和删除元素效率低，且初始化后长度不可变。</li>
|
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<li>链表通过更改引用（指针）实现高效的节点插入与删除，且可以灵活调整长度；但节点访问效率低、占用内存较多。常见的链表类型包括单向链表、循环链表、双向链表。</li>
|
||
<li>动态数组，又称列表，是基于数组实现的一种数据结构。它保留了数组的优势，同时可以灵活调整长度。列表的出现极大地提高了数组的易用性，但可能导致部分内存空间浪费。</li>
|
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<h3 id="2-q-a">2. Q & A<a class="headerlink" href="#2-q-a" title="Permanent link">¶</a></h3>
|
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<div class="admonition question">
|
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<p class="admonition-title">数组存储在栈上和存储在堆上，对时间效率和空间效率是否有影响？</p>
|
||
<p>存储在栈上和堆上的数组都被存储在连续内存空间内，数据操作效率是基本一致的。然而，栈和堆具有各自的特点，从而导致以下不同点。</p>
|
||
<ol>
|
||
<li>分配和释放效率：栈是一块较小的内存，分配由编译器自动完成；而堆内存相对更大，可以在代码中动态分配，更容易碎片化。因此，堆上的分配和释放操作通常比栈上的慢。</li>
|
||
<li>大小限制：栈内存相对较小，堆的大小一般受限于可用内存。因此堆更加适合存储大型数组。</li>
|
||
<li>灵活性：栈上的数组的大小需要在编译时确定，而堆上的数组的大小可以在运行时动态确定。</li>
|
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</ol>
|
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|
||
<div class="admonition question">
|
||
<p class="admonition-title">为什么数组要求相同类型的元素，而在链表中却没有强调同类型呢？</p>
|
||
<p>链表由结点组成，结点之间通过引用（指针）连接，各个结点可以存储不同类型的数据，例如 int、double、string、object 等。</p>
|
||
<p>相对地，数组元素则必须是相同类型的，这样才能通过计算偏移量来获取对应元素位置。例如，如果数组同时包含 int 和 long 两种类型，单个元素分别占用 4 bytes 和 8 bytes ，那么此时就不能用以下公式计算偏移量了，因为数组中包含了两种长度的元素。</p>
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 元素内存地址 = 数组内存地址 + 元素长度 * 元素索引</span>
|
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</code></pre></div>
|
||
</div>
|
||
<div class="admonition question">
|
||
<p class="admonition-title">删除节点后，是否需要把 <code>P.next</code> 设为 <span class="arithmatex">\(\text{None}\)</span> 呢？</p>
|
||
<p>不修改 <code>P.next</code> 也可以。从该链表的角度看，从头结点遍历到尾结点已经遇不到 <code>P</code> 了。这意味着结点 <code>P</code> 已经从链表中删除了，此时结点 <code>P</code> 指向哪里都不会对这条链表产生影响了。</p>
|
||
<p>从垃圾回收的角度看，对于 Java、Python、Go 等拥有自动垃圾回收的语言来说，节点 <code>P</code> 是否被回收取决于是否有仍存在指向它的引用，而不是 <code>P.next</code> 的值。在 C 和 C++ 等语言中，我们需要手动释放节点内存。</p>
|
||
</div>
|
||
<div class="admonition question">
|
||
<p class="admonition-title">在链表中插入和删除操作的时间复杂度是 <span class="arithmatex">\(O(1)\)</span> 。但是增删之前都需要 <span class="arithmatex">\(O(n)\)</span> 查找元素，那为什么时间复杂度不是 <span class="arithmatex">\(O(n)\)</span> 呢？</p>
|
||
<p>如果是先查找元素、再删除元素，确实是 <span class="arithmatex">\(O(n)\)</span> 。然而，链表的 <span class="arithmatex">\(O(1)\)</span> 增删的优势可以在其他应用上得到体现。例如，双向队列适合使用链表实现，我们维护一个指针变量始终指向头结点、尾结点，每次插入与删除操作都是 <span class="arithmatex">\(O(1)\)</span> 。</p>
|
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|
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<div class="admonition question">
|
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<p class="admonition-title">图片“链表定义与存储方式”中，浅蓝色的存储结点指针是占用一块内存地址吗？还是和结点值各占一半呢？</p>
|
||
<p>文中的示意图只是定性表示，定量表示需要根据具体情况进行分析。</p>
|
||
<ul>
|
||
<li>不同类型的结点值占用的空间是不同的，比如 int、long、double 和实例对象等。</li>
|
||
<li>指针变量占用的内存空间大小根据所使用的操作系统及编译环境而定，大多为 8 字节或 4 字节。</li>
|
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<div class="admonition question">
|
||
<p class="admonition-title">在列表末尾添加元素是否时时刻刻都为 <span class="arithmatex">\(O(1)\)</span> ？</p>
|
||
<p>如果添加元素时超出列表长度，则需要先扩容列表再添加。系统会申请一块新的内存，并将原列表的所有元素搬运过去，这时候时间复杂度就会是 <span class="arithmatex">\(O(n)\)</span> 。</p>
|
||
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|
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<div class="admonition question">
|
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<p class="admonition-title">“列表的出现大大提升了数组的实用性，但副作用是会造成部分内存空间浪费”，这里的空间浪费是指额外增加的变量如容量、长度、扩容倍数所占的内存吗？</p>
|
||
<p>这里的空间浪费主要有两方面含义：一方面，列表都会设定一个初始长度，我们不一定需要用这么多。另一方面，为了防止频繁扩容，扩容一般都会乘以一个系数，比如 <span class="arithmatex">\(\times 1.5\)</span> 。这样一来，也会出现很多空位，我们通常不能完全填满它们。</p>
|
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</div>
|
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<div class="admonition question">
|
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<p class="admonition-title">在 Python 中初始化 <code>n = [1, 2, 3]</code> 后，这 3 个元素的地址是相连的，但是初始化 <code>m = [2, 1, 3]</code> 会发现它们每个元素的 id 并不是连续的，而是分别跟 <code>n</code> 中的相同。这些元素地址不连续，那么 <code>m</code> 还是数组吗？</p>
|
||
<p>假如把列表元素换成链表节点 <code>n = [n1, n2, n3, n4, n5]</code> ，通常情况下这五个节点对象也是被分散存储在内存各处的。然而，给定一个列表索引，我们仍然可以在 <span class="arithmatex">\(O(1)\)</span> 时间内获取到节点内存地址，从而访问到对应的节点。这是因为数组中存储的是节点的引用，而非节点本身。</p>
|
||
<p>与许多语言不同的是，在 Python 中数字也被包装为对象，列表中存储的不是数字本身，而是对数字的引用。因此，我们会发现两个数组中的相同数字拥有同一个 id ，并且这些数字的内存地址是无须连续的。</p>
|
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|
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<div class="admonition question">
|
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<p class="admonition-title">C++ STL 里面的 std::list 已经实现了双向链表，但好像一些算法的书上都不怎么直接用这个，是不是有什么局限性呢?</p>
|
||
<p>一方面，我们往往更青睐使用数组实现算法，而只有在必要时才使用链表，主要有两个原因。</p>
|
||
<ul>
|
||
<li>空间开销：由于每个元素需要两个额外的指针（一个用于前一个元素，一个用于后一个元素），所以 <code>std::list</code> 通常比 <code>std::vector</code> 更占用空间。</li>
|
||
<li>缓存不友好：由于数据不是连续存放的，<code>std::list</code> 对缓存的利用率较低。一般情况下，<code>std::vector</code> 的性能会更好。</li>
|
||
</ul>
|
||
<p>另一方面，必要使用链表的情况主要是二叉树和图。栈和队列往往会使用编程语言提供的 <code>stack</code> 和 <code>queue</code> ，而非链表。</p>
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