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krahets
2023-09-27 13:47:05 +08:00
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commit f28fb3ea72
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chapter_tree/array_representation_of_tree/index.html
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chapter_tree/avl_tree/index.html
+73 -38
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<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_1">1. &nbsp; 完美二叉树<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
<p>「完美二叉树 perfect binary tree」除了最底层外，其余所有层的节点都被完全填满。在完美二叉树中，叶节点的度为 <span class="arithmatex">\(0\)</span> ，其余所有节点的度都为 <span class="arithmatex">\(2\)</span> ；若树高度为 <span class="arithmatex">\(h\)</span> ，则节点总数为 <span class="arithmatex">\(2^{h+1} - 1\)</span> ，呈现标准的指数级关系，反映了自然界中常见的细胞分裂现象。</p>
<p>「完美二叉树 perfect binary tree」所有层的节点都被完全填满。在完美二叉树中，叶节点的度为 <span class="arithmatex">\(0\)</span> ，其余所有节点的度都为 <span class="arithmatex">\(2\)</span> ；若树高度为 <span class="arithmatex">\(h\)</span> ，则节点总数为 <span class="arithmatex">\(2^{h+1} - 1\)</span> ，呈现标准的指数级关系，反映了自然界中常见的细胞分裂现象。</p>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>请注意，在中文社区中，完美二叉树常被称为「满二叉树」。</p>
@@ -3918,7 +3953,7 @@
<p align="center"> 图 7-7 &nbsp; 平衡二叉树 </p>
<h2 id="714">7.1.4 &nbsp; 二叉树的退化<a class="headerlink" href="#714" title="Permanent link">&para;</a></h2>
<p>当二叉树的每层节点都被填满时，达到“完美二叉树”；而当所有节点都偏向一侧时，二叉树退化为“链表”。</p>
<p>图 7-8 展示了二叉树的理想与退化状态。当二叉树的每层节点都被填满时，达到“完美二叉树”；而当所有节点都偏向一侧时，二叉树退化为“链表”。</p>
<ul>
<li>完美二叉树是理想情况，可以充分发挥二叉树“分治”的优势。</li>
<li>链表则是另一个极端，各项操作都变为线性操作，时间复杂度退化至 <span class="arithmatex">\(O(n)\)</span> 。</li>
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