2022-12-21 17:19:39 +08:00
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comments: true
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---
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2023-01-31 03:37:50 +08:00
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# 7.2. 二叉树遍历
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2022-12-21 17:19:39 +08:00
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非线性数据结构的遍历操作比线性数据结构更加复杂,往往需要使用搜索算法来实现。常见的二叉树遍历方式有层序遍历、前序遍历、中序遍历、后序遍历。
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2023-01-31 03:37:50 +08:00
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## 7.2.1. 层序遍历
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2022-12-21 17:19:39 +08:00
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「层序遍历 Hierarchical-Order Traversal」从顶至底、一层一层地遍历二叉树,并在每层中按照从左到右的顺序访问结点。
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层序遍历本质上是「广度优先搜索 Breadth-First Traversal」,其体现着一种“一圈一圈向外”的层进遍历方式。
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![binary_tree_bfs](binary_tree_traversal.assets/binary_tree_bfs.png)
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<p align="center"> Fig. 二叉树的层序遍历 </p>
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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。
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=== "Java"
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```java title="binary_tree_bfs.java"
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2023-02-07 04:43:52 +08:00
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[class]{binary_tree_bfs}-[func]{hierOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "C++"
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```cpp title="binary_tree_bfs.cpp"
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[class]{}-[func]{hierOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "Python"
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```python title="binary_tree_bfs.py"
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2023-02-06 23:23:21 +08:00
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[class]{}-[func]{hier_order}
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2022-12-21 17:19:39 +08:00
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```
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=== "Go"
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```go title="binary_tree_bfs.go"
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2023-02-09 04:45:06 +08:00
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[class]{}-[func]{hierOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "JavaScript"
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2023-02-08 04:27:55 +08:00
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```javascript title="binary_tree_bfs.js"
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2023-02-08 19:45:06 +08:00
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[class]{}-[func]{hierOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "TypeScript"
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```typescript title="binary_tree_bfs.ts"
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[class]{}-[func]{hierOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "C"
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```c title="binary_tree_bfs.c"
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2023-02-11 18:22:27 +08:00
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[class]{}-[func]{hierOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "C#"
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```csharp title="binary_tree_bfs.cs"
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2023-02-08 22:18:02 +08:00
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[class]{binary_tree_bfs}-[func]{hierOrder}
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2022-12-21 17:19:39 +08:00
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```
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2023-01-08 19:41:05 +08:00
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=== "Swift"
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```swift title="binary_tree_bfs.swift"
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[class]{}-[func]{hierOrder}
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2023-01-08 19:41:05 +08:00
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```
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2023-02-01 22:03:04 +08:00
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=== "Zig"
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```zig title="binary_tree_bfs.zig"
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2023-02-09 22:57:25 +08:00
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[class]{}-[func]{hierOrder}
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2023-02-01 22:03:04 +08:00
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```
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2023-01-31 03:37:50 +08:00
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## 7.2.2. 前序、中序、后序遍历
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2022-12-21 17:19:39 +08:00
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相对地,前、中、后序遍历皆属于「深度优先遍历 Depth-First Traversal」,其体现着一种“先走到尽头,再回头继续”的回溯遍历方式。
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如下图所示,左侧是深度优先遍历的的示意图,右上方是对应的递归实现代码。深度优先遍历就像是绕着整个二叉树的外围“走”一圈,走的过程中,在每个结点都会遇到三个位置,分别对应前序遍历、中序遍历、后序遍历。
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![binary_tree_dfs](binary_tree_traversal.assets/binary_tree_dfs.png)
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<p align="center"> Fig. 二叉树的前 / 中 / 后序遍历 </p>
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<div class="center-table" markdown>
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| 位置 | 含义 | 此处访问结点时对应 |
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| ---------- | ------------------------------------ | ----------------------------- |
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| 橙色圆圈处 | 刚进入此结点,即将访问该结点的左子树 | 前序遍历 Pre-Order Traversal |
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| 蓝色圆圈处 | 已访问完左子树,即将访问右子树 | 中序遍历 In-Order Traversal |
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| 紫色圆圈处 | 已访问完左子树和右子树,即将返回 | 后序遍历 Post-Order Traversal |
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</div>
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=== "Java"
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```java title="binary_tree_dfs.java"
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[class]{binary_tree_dfs}-[func]{preOrder}
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[class]{binary_tree_dfs}-[func]{inOrder}
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[class]{binary_tree_dfs}-[func]{postOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "C++"
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```cpp title="binary_tree_dfs.cpp"
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[class]{}-[func]{preOrder}
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[class]{}-[func]{inOrder}
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[class]{}-[func]{postOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "Python"
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```python title="binary_tree_dfs.py"
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[class]{}-[func]{pre_order}
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[class]{}-[func]{in_order}
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[class]{}-[func]{post_order}
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2022-12-21 17:19:39 +08:00
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```
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=== "Go"
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```go title="binary_tree_dfs.go"
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[class]{}-[func]{preOrder}
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[class]{}-[func]{inOrder}
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[class]{}-[func]{postOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "JavaScript"
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2023-02-08 04:27:55 +08:00
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```javascript title="binary_tree_dfs.js"
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2023-02-08 19:45:06 +08:00
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[class]{}-[func]{preOrder}
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[class]{}-[func]{inOrder}
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[class]{}-[func]{postOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "TypeScript"
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```typescript title="binary_tree_dfs.ts"
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[class]{}-[func]{preOrder}
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[class]{}-[func]{inOrder}
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[class]{}-[func]{postOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "C"
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```c title="binary_tree_dfs.c"
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2023-02-11 18:22:27 +08:00
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[class]{}-[func]{preOrder}
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[class]{}-[func]{inOrder}
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[class]{}-[func]{postOrder}
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2022-12-21 17:19:39 +08:00
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```
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=== "C#"
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```csharp title="binary_tree_dfs.cs"
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2023-02-08 22:18:02 +08:00
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[class]{binary_tree_dfs}-[func]{preOrder}
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2022-12-23 15:42:02 +08:00
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2023-02-08 22:18:02 +08:00
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[class]{binary_tree_dfs}-[func]{inOrder}
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2022-12-23 15:42:02 +08:00
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2023-02-08 22:18:02 +08:00
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[class]{binary_tree_dfs}-[func]{postOrder}
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2022-12-21 17:19:39 +08:00
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```
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2023-01-08 19:41:05 +08:00
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=== "Swift"
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```swift title="binary_tree_dfs.swift"
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2023-02-08 20:30:05 +08:00
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[class]{}-[func]{preOrder}
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2023-01-19 00:12:54 +08:00
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2023-02-08 20:30:05 +08:00
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[class]{}-[func]{inOrder}
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2023-01-08 19:41:05 +08:00
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2023-02-08 20:30:05 +08:00
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[class]{}-[func]{postOrder}
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2023-01-08 19:41:05 +08:00
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```
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2023-02-01 22:03:04 +08:00
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=== "Zig"
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```zig title="binary_tree_dfs.zig"
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2023-02-09 22:57:25 +08:00
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[class]{}-[func]{preOrder}
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2023-02-01 22:03:04 +08:00
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2023-02-09 22:57:25 +08:00
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[class]{}-[func]{inOrder}
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[class]{}-[func]{postOrder}
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2023-02-01 22:03:04 +08:00
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```
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2022-12-21 17:19:39 +08:00
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!!! note
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使用循环一样可以实现前、中、后序遍历,但代码相对繁琐,有兴趣的同学可以自行实现。
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