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krahets
2023-08-17 05:12:16 +08:00
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<p>「层序遍历 Level-Order Traversal」从顶部到底部逐层遍历二叉树,并在每一层按照从左到右的顺序访问节点。</p>
<p>层序遍历本质上属于「广度优先搜索 Breadth-First Traversal」,它体现了一种“一圈一圈向外扩展”的逐层搜索方式。</p>
<p><img alt="二叉树的层序遍历" src="../binary_tree_traversal.assets/binary_tree_bfs.png" /></p>
<p align="center"> Fig. 二叉树的层序遍历 </p>
<p align="center"> 图:二叉树的层序遍历 </p>
<p>广度优先遍历通常借助「队列」来实现。队列遵循“先进先出”的规则,而广度优先遍历则遵循“逐层推进”的规则,两者背后的思想是一致的。</p>
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<p>相应地,前序、中序和后序遍历都属于「深度优先遍历 Depth-First Traversal」,它体现了一种“先走到尽头,再回溯继续”的遍历方式。</p>
<p>如下图所示,左侧是深度优先遍历的示意图,右上方是对应的递归代码。深度优先遍历就像是绕着整个二叉树的外围“走”一圈,在这个过程中,在每个节点都会遇到三个位置,分别对应前序遍历、中序遍历和后序遍历。</p>
<p><img alt="二叉搜索树的前、中、后序遍历" src="../binary_tree_traversal.assets/binary_tree_dfs.png" /></p>
<p align="center"> Fig. 二叉搜索树的前、中、后序遍历 </p>
<p align="center"> 图:二叉搜索树的前、中、后序遍历 </p>
<p>以下给出了实现代码,请配合上图理解深度优先遍历的递归过程。</p>
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<p align="center"> 图:前序遍历的递归过程 </p>