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3.1.1 &nbsp; 逻辑结构：线性与非线性
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3.1.2 &nbsp; 物理结构：连续与离散
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<h1 id="31">3.1 &nbsp; 数据结构分类<a class="headerlink" href="#31" title="Permanent link">&para;</a></h1>
<p>常见的数据结构包括数组、链表、栈、队列、哈希表、树、堆、图，它们可以从“逻辑结构”和“物理结构”两个维度进行分类。</p>
<h2 id="311">3.1.1 &nbsp; 逻辑结构：线性与非线性<a class="headerlink" href="#311" title="Permanent link">&para;</a></h2>
<p><strong>逻辑结构揭示了数据元素之间的逻辑关系</strong>。在数组和链表中，数据按照顺序依次排列，体现了数据之间的线性关系；而在树中，数据从顶部向下按层次排列，表现出祖先与后代之间的派生关系；图则由节点和边构成，反映了复杂的网络关系。</p>
<p>如图 3-1 所示，逻辑结构可被分为“线性”和“非线性”两大类。线性结构比较直观，指数据在逻辑关系上呈线性排列；非线性结构则相反，呈非线性排列。</p>
<ul>
<li><strong>线性数据结构</strong>：数组、链表、栈、队列、哈希表。</li>
<li><strong>非线性数据结构</strong>：树、堆、图、哈希表。</li>
</ul>
<p><img alt="线性与非线性数据结构" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></p>
<p align="center"> 图 3-1 &nbsp; 线性与非线性数据结构 </p>
<p>非线性数据结构可以进一步被划分为树形结构和网状结构。</p>
<ul>
<li><strong>线性结构</strong>：数组、链表、队列、栈、哈希表，元素之间是一对一的顺序关系。</li>
<li><strong>树形结构</strong>：树、堆、哈希表，元素之间是一对多的关系。</li>
<li><strong>网状结构</strong>：图，元素之间是多对多的关系。</li>
</ul>
<h2 id="312">3.1.2 &nbsp; 物理结构：连续与离散<a class="headerlink" href="#312" title="Permanent link">&para;</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>在算法运行过程中，相关数据都存储在内存中</strong>。图 3-2 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一定大小的数据，在算法运行时，所有数据都被存储在这些单元格中。</p>
<p><strong>系统通过内存地址来访问目标位置的数据</strong>。如图 3-2 所示，计算机根据特定规则为表格中的每个单元格分配编号，确保每个内存空间都有唯一的内存地址。有了这些地址，程序便可以访问内存中的数据。</p>
<p><img alt="内存条、内存空间、内存地址" src="../classification_of_data_structure.assets/computer_memory_location.png" /></p>
<p align="center"> 图 3-2 &nbsp; 内存条、内存空间、内存地址 </p>
<p>内存是所有程序的共享资源，当某块内存被某个程序占用时，则无法被其他程序同时使用了。<strong>因此在数据结构与算法的设计中，内存资源是一个重要的考虑因素</strong>。比如，算法所占用的内存峰值不应超过系统剩余空闲内存；如果缺少连续大块的内存空间，那么所选用的数据结构必须能够存储在离散的内存空间内。</p>
<p>如图 3-3 所示，<strong>物理结构反映了数据在计算机内存中的存储方式</strong>，可分为连续空间存储（数组）和离散空间存储（链表）。物理结构从底层决定了数据的访问、更新、增删等操作方法，同时在时间效率和空间效率方面呈现出互补的特点。</p>
<p><img alt="连续空间存储与离散空间存储" src="../classification_of_data_structure.assets/classification_phisical_structure.png" /></p>
<p align="center"> 图 3-3 &nbsp; 连续空间存储与离散空间存储 </p>
<p>值得说明的是，<strong>所有数据结构都是基于数组、链表或二者的组合实现的</strong>。例如，栈和队列既可以使用数组实现，也可以使用链表实现；而哈希表的实现可能同时包含数组和链表。</p>
<ul>
<li><strong>基于数组可实现</strong>：栈、队列、哈希表、树、堆、图、矩阵、张量（维度 <span class="arithmatex">\(\geq 3\)</span> 的数组）等。</li>
<li><strong>基于链表可实现</strong>：栈、队列、哈希表、树、堆、图等。</li>
</ul>
<p>基于数组实现的数据结构也被称为“静态数据结构”，这意味着此类数据结构在初始化后长度不可变。相对应地，基于链表实现的数据结构被称为“动态数据结构”，这类数据结构在初始化后，仍可以在程序运行过程中对其长度进行调整。</p>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>如果你感觉物理结构理解起来有困难，建议先阅读下一章“数组与链表”，然后再回顾本节内容。</p>
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