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chapter_array_and_linkedlist/summary/index.html
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<ul>
<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>
<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>
<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>
<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。</li>
<li>常见的链表类型包括单向链表、循环链表、双向链表，它们分别具有各自的应用场景。</li>
<li>列表是一种支持增删查改的元素有序集合，通常基于动态数组实现，其保留了数组的优势，同时可以灵活调整长度。</li>
<li>列表的出现大幅地提高了数组的实用性，但可能导致部分内存空间浪费。</li>
</ul>
<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
<div class="admonition question">

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</div>
<p align="center"> 图 9-8 &nbsp; 邻接表的初始化、增删边、增删顶点 </p>
<p>以下是基于邻接表实现图的代码示例。细心的同学可能注意到，<strong>我们在邻接表中使用 <code>Vertex</code> 节点类来表示顶点</strong>，而这样做是有原因的。</p>
<ol>
<li>如果我们选择通过顶点值来区分不同顶点，那么值重复的顶点将无法被区分。</li>
<li>如果类似邻接矩阵那样，使用顶点列表索引来区分不同顶点。那么，假设我们想要删除索引为 <span class="arithmatex">\(i\)</span> 的顶点，则需要遍历整个邻接表，将其中 <span class="arithmatex">\(&gt; i\)</span> 的索引全部减 <span class="arithmatex">\(1\)</span> ，这样操作效率较低。</li>
<li>因此我们考虑引入顶点类 <code>Vertex</code> ，使得每个顶点都是唯一的对象，此时删除顶点时就无须改动其余顶点了。</li>
</ol>
<p>以下是邻接表的代码实现。对比图 9-8 ，实际代码有以下不同。</p>
<ul>
<li>为了方便添加与删除顶点，以及简化代码，我们使用列表（动态数组）来代替链表。</li>
<li>使用哈希表来存储邻接表，<code>key</code> 为顶点实例，<code>value</code> 为该顶点的邻接顶点列表（链表）。</li>
</ul>
<p>另外，我们在邻接表中使用 <code>Vertex</code> 类来表示顶点。这是因为如果与邻接矩阵一样用列表索引来区分不同顶点。那么假设想要删除索引为 <span class="arithmatex">\(i\)</span> 的顶点，则需要遍历整个邻接表，将所有大于 <span class="arithmatex">\(i\)</span> 的索引全部减 <span class="arithmatex">\(1\)</span> ，效率很低。而如果每个顶点都是唯一的 <code>Vertex</code> 实例，删除某一顶点之后就无须改动其他顶点了。</p>
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<p align="center"> 图 7-16 &nbsp; 二叉搜索树 </p>
<h2 id="741">7.4.1 &nbsp; 二叉搜索树的操作<a class="headerlink" href="#741" title="Permanent link">&para;</a></h2>
<p>我们将二叉搜索树封装为一个类 <code>ArrayBinaryTree</code> ，并声明一个成员变量 <code>root</code> ，指向树的根节点。</p>
<p>我们将二叉搜索树封装为一个类 <code>BinarySearchTree</code> ，并声明一个成员变量 <code>root</code> ，指向树的根节点。</p>
<h3 id="1">1. &nbsp; 查找节点<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>给定目标节点值 <code>num</code> ，可以根据二叉搜索树的性质来查找。如图 7-17 所示，我们声明一个节点 <code>cur</code> ，从二叉树的根节点 <code>root</code> 出发，循环比较节点值 <code>cur.val</code> 和 <code>num</code> 之间的大小关系。</p>
<ul>

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