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<h1 id="42">4.2. &nbsp; 链表<a class="headerlink" href="#42" title="Permanent link">&para;</a></h1> <h1 id="42">4.2. &nbsp; 链表<a class="headerlink" href="#42" title="Permanent link">&para;</a></h1>
<div class="admonition note"> <p>内存空间是所有程序的公共资源，排除已被占用的内存空间，空闲内存空间往往是散落在内存各处的。上节讲到，<strong>存储数组的内存空间必须是连续的</strong>，当我们需要申请一个非常大的数组时，系统不一定能够分配这么大的连续内存空间。</p>
<p class="admonition-title">引言</p> <p>相对地，链表则更加灵活，可以被存储到非连续的内存空间。「链表 Linked List」是一种线性数据结构，其中每个元素都是单独的对象，各个元素（即结点）之间通过指针连接。由于结点中记录了连接关系，因此链表的存储方式相比于数组更加灵活，系统可将结点分散在内存各处，而不必保证内存地址的连续性。</p>
<p>内存空间是所有程序的公共资源，排除已占用的内存，空闲内存往往是散落在内存各处的。我们知道，存储数组需要内存空间连续，当我们需要申请一个很大的数组时，系统不一定存在这么大的连续内存空间。而链表则更加灵活，不需要内存是连续的，只要剩余内存空间大小够用即可。</p>
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<p>「链表 Linked List」是一种线性数据结构，其中每个元素都是单独的对象，各个元素（一般称为结点）之间通过指针连接。由于结点中记录了连接关系，因此链表的存储方式相比于数组更加灵活，系统不必保证内存地址的连续性。</p>
<p>链表的「结点 Node」包含两项数据，一是结点「值 Value」，二是指向下一结点的「指针 Pointer」（或称「引用 Reference」）。</p> <p>链表的「结点 Node」包含两项数据，一是结点「值 Value」，二是指向下一结点的「指针 Pointer」（或称「引用 Reference」）。</p>
<p><img alt="链表定义与存储方式" src="../linked_list.assets/linkedlist_definition.png" /></p> <p><img alt="链表定义与存储方式" src="../linked_list.assets/linkedlist_definition.png" /></p>
<p align="center"> Fig. 链表定义与存储方式 </p> <p align="center"> Fig. 链表定义与存储方式 </p>

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</div> </div>
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<p>结点的两个指针分别指向「左子结点 Left Child Node」和「右子结点 Right Child Node」，并且称该结点为两个子结点的「父结点 Parent Node」。给定二叉树某结点，将左子结点以下的树称为该结点的「左子树 Left Subtree」，右子树同理。</p> <p>结点的两个指针分别指向「左子结点」和「右子结点」，并且称该结点为两个子结点的「父结点」。给定二叉树某结点，将“左子结点及其以下结点形成的树”称为该结点的「左子树」，右子树同理。</p>
<p>除了叶结点外，每个结点都有子结点和子树。例如，若将下图的「结点 2」看作父结点，那么其左子结点和右子结点分别为「结点 4」和「结点 5」，左子树和右子树分别为「结点 4 及其以下结点形成的树」和「结点 5 及其以下结点形成的树」。</p> <p>除了叶结点外，每个结点都有子结点和子树。例如，若将下图的“结点 2”看作父结点，那么其左子结点和右子结点分别为“结点 4”和“结点 5”，左子树和右子树分别为“结点 4 及其以下结点形成的树”和“结点 5 及其以下结点形成的树”。</p>
<p><img alt="父结点、子结点、子树" src="../binary_tree.assets/binary_tree_definition.png" /></p> <p><img alt="父结点、子结点、子树" src="../binary_tree.assets/binary_tree_definition.png" /></p>
<p align="center"> Fig. 父结点、子结点、子树 </p> <p align="center"> Fig. 父结点、子结点、子树 </p>
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</div> </div>
<h2 id="713">7.1.3. &nbsp; 常见二叉树类型<a class="headerlink" href="#713" title="Permanent link">&para;</a></h2> <h2 id="713">7.1.3. &nbsp; 常见二叉树类型<a class="headerlink" href="#713" title="Permanent link">&para;</a></h2>
<h3 id="_1">完美二叉树<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3> <h3 id="_1">完美二叉树<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
<p>「完美二叉树 Perfect Binary Tree」的所有层的结点都被完全填满。在完美二叉树中，所有结点的度 = 2 ；若树高度 <span class="arithmatex">\(= h\)</span> ，则结点总数 <span class="arithmatex">\(= 2^{h+1} - 1\)</span> ，呈标准的指数级关系，反映着自然界中常见的细胞分裂。</p> <p>「完美二叉树 Perfect Binary Tree」的所有层的结点都被完全填满。在完美二叉树中，叶结点的度为 <span class="arithmatex">\(0\)</span> ，其余所有结点的度都为 <span class="arithmatex">\(2\)</span> ；若树高度 <span class="arithmatex">\(= h\)</span> ，则结点总数 <span class="arithmatex">\(= 2^{h+1} - 1\)</span> ，呈标准的指数级关系，反映着自然界中常见的细胞分裂。</p>
<div class="admonition tip"> <div class="admonition tip">
<p class="admonition-title">Tip</p> <p class="admonition-title">Tip</p>
<p>在中文社区中，完美二叉树常被称为「满二叉树」，请注意与完满二叉树区分。</p> <p>在中文社区中，完美二叉树常被称为「满二叉树」，请注意与完满二叉树区分。</p>

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<p align="center"> Fig. 二叉树的层序遍历 </p> <p align="center"> Fig. 二叉树的层序遍历 </p>
<h3 id="_1">算法实现<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3> <h3 id="_1">算法实现<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
<p>广度优先遍历一般借助「队列」来实现。队列的规则是“先进先出”，广度优先遍历的规则是 ”一层层平推“ ，两者背后的思想是一致的。</p> <p>广度优先遍历一般借助「队列」来实现。队列的规则是“先进先出”，广度优先遍历的规则是“一层层平推”，两者背后的思想是一致的。</p>
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