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0.1. 关于本书
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
|
||
0.2. 如何使用本书
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/installation/" class="md-nav__link">
|
||
0.3. 编程环境安装
|
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</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_preface/contribution/" class="md-nav__link">
|
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0.4. 一起参与创作
|
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</a>
|
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</li>
|
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|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</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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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
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|
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|
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<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
|
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1. 引言
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_2">
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<span class="md-nav__icon md-icon"></span>
|
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1. 引言
|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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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_introduction/algorithms_are_everywhere/" class="md-nav__link">
|
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1.1. 算法无处不在
|
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</a>
|
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</li>
|
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|
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<li class="md-nav__item">
|
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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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</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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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
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|
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|
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|
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<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
|
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2. 计算复杂度
|
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<span class="md-nav__icon md-icon"></span>
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</label>
|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_3">
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<span class="md-nav__icon md-icon"></span>
|
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2. 计算复杂度
|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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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">
|
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<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
|
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2.1. 算法效率评估
|
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</a>
|
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</li>
|
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|
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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_computational_complexity/time_complexity/" class="md-nav__link">
|
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2.2. 时间复杂度
|
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</a>
|
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</li>
|
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|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
|
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2.3. 空间复杂度
|
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</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/space_time_tradeoff/" class="md-nav__link">
|
||
2.4. 权衡时间与空间
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
|
||
2.5. 小结
|
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</a>
|
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</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
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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--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
|
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|
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|
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|
||
|
||
<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
|
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3. 数据结构简介
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
|
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<label class="md-nav__title" for="__nav_4">
|
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<span class="md-nav__icon md-icon"></span>
|
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3. 数据结构简介
|
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</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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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">
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<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
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|
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|
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|
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|
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<label class="md-nav__link md-nav__link--active" for="__toc">
|
||
3.1. 数据与内存
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
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<a href="./" class="md-nav__link md-nav__link--active">
|
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3.1. 数据与内存
|
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</a>
|
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|
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|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
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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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<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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</label>
|
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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
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<a href="#311" class="md-nav__link">
|
||
3.1.1. 基本数据类型
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#312" class="md-nav__link">
|
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3.1.2. 计算机内存
|
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</a>
|
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|
||
</li>
|
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|
||
</ul>
|
||
|
||
</nav>
|
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|
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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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|
||
|
||
|
||
<li class="md-nav__item">
|
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<a href="../classification_of_data_structure/" class="md-nav__link">
|
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3.2. 数据结构分类
|
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</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../summary/" class="md-nav__link">
|
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3.3. 小结
|
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</a>
|
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</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</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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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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|
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|
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|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
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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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|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
|
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4. 数组与链表
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
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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>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
|
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4.1. 数组（Array）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
|
||
4.2. 链表（LinkedList）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
|
||
4.3. 列表（List）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
|
||
4.4. 小结
|
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</a>
|
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</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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|
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|
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|
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|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
|
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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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|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
|
||
5. 栈与队列
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_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>
|
||
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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|
||
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
|
||
5.1. 栈（Stack）
|
||
</a>
|
||
</li>
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
|
||
5.2. 队列（Queue）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
||
5.3. 双向队列（Deque）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
|
||
5.4. 小结
|
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</a>
|
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</li>
|
||
|
||
|
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|
||
|
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</ul>
|
||
</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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|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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|
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|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
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|
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|
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|
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|
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<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
|
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6. 散列表
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
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|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_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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|
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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">
|
||
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
|
||
6.1. 哈希表（HashMap）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
|
||
6.2. 哈希冲突处理
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
||
6.3. 小结
|
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</a>
|
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</li>
|
||
|
||
|
||
|
||
|
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</ul>
|
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</nav>
|
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</li>
|
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|
||
|
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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--section md-nav__item--nested">
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|
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|
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|
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|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
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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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|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
|
||
7. 二叉树
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
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|
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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. 二叉树
|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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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">
|
||
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
|
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7.1. 二叉树（Binary Tree）
|
||
</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">
|
||
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
|
||
7.2. 二叉树遍历
|
||
</a>
|
||
</li>
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
|
||
7.3. 二叉搜索树
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
|
||
7.4. AVL 树 *
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/summary/" class="md-nav__link">
|
||
7.5. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
|
||
8. 堆
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
8. 堆
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
||
8.1. 堆（Heap）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
|
||
9. 图
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
9. 图
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
||
9.1. 图（Graph）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
||
9.2. 图基础操作
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
||
9.3. 图的遍历
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
|
||
10. 查找算法
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
10. 查找算法
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/linear_search/" class="md-nav__link">
|
||
10.1. 线性查找
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
||
10.2. 二分查找
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/hashing_search/" class="md-nav__link">
|
||
10.3. 哈希查找
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
10.4. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
|
||
11. 排序算法
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<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. 排序算法
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/intro_to_sort/" class="md-nav__link">
|
||
11.1. 排序简介
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
11.2. 冒泡排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
||
11.3. 插入排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
||
11.4. 快速排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
||
11.5. 归并排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
||
11.6. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
|
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|
||
|
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|
||
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__link--index ">
|
||
<a href="../../chapter_reference/">参考文献</a>
|
||
|
||
</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">
|
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<span class="md-nav__icon md-icon"></span>
|
||
参考文献
|
||
</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
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|
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</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
|
||
<div class="md-sidebar__scrollwrap">
|
||
<div class="md-sidebar__inner">
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
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|
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|
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|
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|
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|
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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
|
||
</label>
|
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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#311" class="md-nav__link">
|
||
3.1.1. 基本数据类型
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#312" class="md-nav__link">
|
||
3.1.2. 计算机内存
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="md-content" data-md-component="content">
|
||
<article class="md-content__inner md-typeset">
|
||
|
||
|
||
|
||
|
||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_data_structure/data_and_memory.md" title="编辑此页" class="md-content__button md-icon">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
|
||
</a>
|
||
|
||
|
||
|
||
|
||
|
||
<h1 id="31">3.1. 数据与内存<a class="headerlink" href="#31" title="Permanent link">¶</a></h1>
|
||
<h2 id="311">3.1.1. 基本数据类型<a class="headerlink" href="#311" title="Permanent link">¶</a></h2>
|
||
<p>谈到计算机中的数据，我们能够想到文本、图片、视频、语音、3D 模型等等，这些数据虽然组织形式不同，但是有一个共同点，即都是由各种基本数据类型构成的。</p>
|
||
<p><strong>「基本数据类型」是 CPU 可以直接进行运算的类型，在算法中直接被使用。</strong></p>
|
||
<ul>
|
||
<li>「整数」根据不同的长度分为 byte, short, int, long ，根据算法需求选用，即在满足取值范围的情况下尽量减小内存空间占用；</li>
|
||
<li>「浮点数」代表小数，根据长度分为 float, double ，同样根据算法的实际需求选用；</li>
|
||
<li>「字符」在计算机中是以字符集的形式保存的，char 的值实际上是数字，代表字符集中的编号，计算机通过字符集查表来完成编号到字符的转换。占用空间与具体编程语言有关，通常为 2 bytes 或 1 byte ；</li>
|
||
<li>「布尔」代表逻辑中的 “是” 与 “否” ，其占用空间需要具体根据编程语言确定，通常为 1 byte 或 1 bit ；</li>
|
||
</ul>
|
||
<div class="admonition note">
|
||
<p class="admonition-title">字节与比特</p>
|
||
<p>1 字节 (byte) = 8 比特 (bit) ， 1 比特即最基本的 1 个二进制位</p>
|
||
</div>
|
||
<p align="center"> Table. Java 的基本数据类型 </p>
|
||
|
||
<div class="center-table">
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>类别</th>
|
||
<th>符号</th>
|
||
<th>占用空间</th>
|
||
<th>取值范围</th>
|
||
<th>默认值</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>整数</td>
|
||
<td>byte</td>
|
||
<td>1 byte</td>
|
||
<td><span class="arithmatex">\(-2^7\)</span> ~ <span class="arithmatex">\(2^7 - 1\)</span> ( <span class="arithmatex">\(-128\)</span> ~ <span class="arithmatex">\(127\)</span> )</td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td>short</td>
|
||
<td>2 bytes</td>
|
||
<td><span class="arithmatex">\(-2^{15}\)</span> ~ <span class="arithmatex">\(2^{15} - 1\)</span></td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td><strong>int</strong></td>
|
||
<td>4 bytes</td>
|
||
<td><span class="arithmatex">\(-2^{31}\)</span> ~ <span class="arithmatex">\(2^{31} - 1\)</span></td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td>long</td>
|
||
<td>8 bytes</td>
|
||
<td><span class="arithmatex">\(-2^{63}\)</span> ~ <span class="arithmatex">\(2^{63} - 1\)</span></td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>浮点数</td>
|
||
<td><strong>float</strong></td>
|
||
<td>4 bytes</td>
|
||
<td><span class="arithmatex">\(-3.4 \times 10^{38}\)</span> ~ <span class="arithmatex">\(3.4 \times 10^{38}\)</span></td>
|
||
<td><span class="arithmatex">\(0.0\)</span> f</td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td>double</td>
|
||
<td>8 bytes</td>
|
||
<td><span class="arithmatex">\(-1.7 \times 10^{308}\)</span> ~ <span class="arithmatex">\(1.7 \times 10^{308}\)</span></td>
|
||
<td><span class="arithmatex">\(0.0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>字符</td>
|
||
<td><strong>char</strong></td>
|
||
<td>2 bytes / 1 byte</td>
|
||
<td><span class="arithmatex">\(0\)</span> ~ <span class="arithmatex">\(2^{16} - 1\)</span></td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>布尔</td>
|
||
<td><strong>bool</strong></td>
|
||
<td>1 byte / 1 bit</td>
|
||
<td><span class="arithmatex">\(\text{true}\)</span> 或 <span class="arithmatex">\(\text{false}\)</span></td>
|
||
<td><span class="arithmatex">\(\text{false}\)</span></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<div class="admonition tip">
|
||
<p class="admonition-title">Tip</p>
|
||
<p>以上表格中，加粗项在「算法题」中最为常用。此表格无需硬背，大致理解即可，需要时可以通过查表来回忆。</p>
|
||
</div>
|
||
<p><strong>「基本数据类型」与「数据结构」之间的联系与区别</strong></p>
|
||
<p>我们知道，数据结构是在计算机中 <strong>组织与存储数据的方式</strong>，它的主语是“结构”，而不是“数据”。比如，我们想要表示“一排数字”，自然应该使用「数组」这个数据结构。数组的存储方式使之可以表示数字的相邻关系、先后关系等一系列我们需要的信息，但至于其中存储的是整数 int ，还是小数 float ，或是字符 char ，<strong>则与所谓的数据的结构无关了</strong>。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:10"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 使用多种「基本数据类型」来初始化「数组」 */</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="kt">float</span><span class="o">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="kt">char</span><span class="o">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">booleans</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 使用多种「基本数据类型」来初始化「数组」 */</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">numbers</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">decimals</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kt">char</span><span class="w"> </span><span class="n">characters</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">booleans</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="sd">""" Python 的 list 可以自由存储各种基本数据类型和对象 """</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="nb">list</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="s1">'a'</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// 使用多种「基本数据类型」来初始化「数组」</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">var</span><span class="w"> </span><span class="nx">numbers</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">int</span><span class="p">{}</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kd">var</span><span class="w"> </span><span class="nx">decimals</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">float64</span><span class="p">{}</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="kd">var</span><span class="w"> </span><span class="nx">characters</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">byte</span><span class="p">{}</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="kd">var</span><span class="w"> </span><span class="nx">booleans</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">bool</span><span class="p">{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* JavaScript 的数组可以自由存储各种基本数据类型和对象 */</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">array</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="s1">'a'</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">];</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 使用多种「基本数据类型」来初始化「数组」 */</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">numbers</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">characters</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">booleans</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 使用多种「基本数据类型」来初始化「数组」 */</span>
|
||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">numbers</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
|
||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">decimals</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="kt">char</span><span class="w"> </span><span class="n">characters</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">booleans</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 使用多种「基本数据类型」来初始化「数组」 */</span>
|
||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="m">5</span><span class="p">];</span>
|
||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kt">float</span><span class="p">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="p">[</span><span class="m">5</span><span class="p">];</span>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="kt">char</span><span class="p">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="p">[</span><span class="m">5</span><span class="p">];</span>
|
||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">booleans</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">bool</span><span class="p">[</span><span class="m">5</span><span class="p">];</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 使用多种「基本数据类型」来初始化「数组」 */</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">let</span> <span class="nv">numbers</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Int</span><span class="p">(),</span> <span class="bp">count</span><span class="p">:</span> <span class="mi">5</span><span class="p">)</span>
|
||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="kd">let</span> <span class="nv">decimals</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Double</span><span class="p">(),</span> <span class="bp">count</span><span class="p">:</span> <span class="mi">5</span><span class="p">)</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="kd">let</span> <span class="nv">characters</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Character</span><span class="p">(</span><span class="s">"a"</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="mi">5</span><span class="p">)</span>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="kd">let</span> <span class="nv">booleans</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Bool</span><span class="p">(),</span> <span class="bp">count</span><span class="p">:</span> <span class="mi">5</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h2 id="312">3.1.2. 计算机内存<a class="headerlink" href="#312" title="Permanent link">¶</a></h2>
|
||
<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>
|
||
<p><strong>算法运行中，相关数据都被存储在内存中</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>
|
||
<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给表格中每个单元格编号，保证每块内存空间都有独立的内存地址。自此，程序便通过这些地址，访问内存中的数据。</p>
|
||
<p><img alt="computer_memory_location" src="../data_and_memory.assets/computer_memory_location.png" /></p>
|
||
<p align="center"> Fig. 内存条、内存空间、内存地址 </p>
|
||
|
||
<p><strong>内存资源是设计数据结构与算法的重要考虑因素</strong>。内存是所有程序的公共资源，当内存被某程序占用时，不能被其它程序同时使用。我们需要根据剩余内存资源的情况来设计算法。例如，若剩余内存空间有限，则要求算法占用的峰值内存不能超过系统剩余内存；若运行的程序很多、缺少大块连续的内存空间，则要求选取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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