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Update AVL Tree.

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This commit is contained in:
Yudong Jin
2022-12-11 02:44:48 +08:00
parent 2a2c0b74e8
commit 5e9a5524d4
3 changed files with 283 additions and 271 deletions
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docs/chapter_tree/avl_tree.md
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@@ -1,4 +1,8 @@
# AVL 树
---
comments: true
---
# AVL 树 *
在「二叉搜索树」章节中提到，在进行多次插入与删除操作后，二叉搜索树可能会退化为链表。此时所有操作的时间复杂度都会由 $O(\log n)$ 劣化至 $O(n)$ 。
@@ -38,43 +42,43 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
=== "C++"
```cpp title="avl_tree.cpp"
```
=== "Python"
```python title="avl_tree.py"
```
=== "Go"
```go title="avl_tree.go"
```
=== "JavaScript"
```js title="avl_tree.js"
```
=== "TypeScript"
```typescript title="avl_tree.ts"
```
=== "C"
```c title="avl_tree.c"
```
=== "C#"
```csharp title="avl_tree.cs"
```
「结点高度」是最远叶结点到该结点的距离，即走过的「边」的数量。需要特别注意，**叶结点的高度为 0 ，空结点的高度为 -1** 。我们封装两个工具函数，分别用于获取与更新结点的高度。
@@ -98,43 +102,43 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
=== "C++"
```cpp title="avl_tree.cpp"
```
=== "Python"
```python title="avl_tree.py"
```
=== "Go"
```go title="avl_tree.go"
```
=== "JavaScript"
```js title="avl_tree.js"
```
=== "TypeScript"
```typescript title="avl_tree.ts"
```
=== "C"
```c title="avl_tree.c"
```
=== "C#"
```csharp title="avl_tree.cs"
```
### 结点平衡因子
@@ -156,43 +160,43 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
=== "C++"
```cpp title="avl_tree.cpp"
```
=== "Python"
```python title="avl_tree.py"
```
=== "Go"
```go title="avl_tree.go"
```
=== "JavaScript"
```js title="avl_tree.js"
```
=== "TypeScript"
```typescript title="avl_tree.ts"
```
=== "C"
```c title="avl_tree.c"
```
=== "C#"
```csharp title="avl_tree.cs"
```
!!! note
@@ -237,7 +241,7 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
// 更新结点高度
updateHeight(node);
updateHeight(child);
// 返回旋转后的根节点
// 返回旋转后子树的根节点
return child;
}
```
@@ -245,43 +249,43 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
=== "C++"
```cpp title="avl_tree.cpp"
```
=== "Python"
```python title="avl_tree.py"
```
=== "Go"
```go title="avl_tree.go"
```
=== "JavaScript"
```js title="avl_tree.js"
```
=== "TypeScript"
```typescript title="avl_tree.ts"
```
=== "C"
```c title="avl_tree.c"
```
=== "C#"
```csharp title="avl_tree.cs"
```
### Case 2 - 左旋
@@ -303,7 +307,7 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
// 更新结点高度
updateHeight(node);
updateHeight(child);
// 返回旋转后的根节点
// 返回旋转后子树的根节点
return child;
}
```
@@ -311,43 +315,43 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
=== "C++"
```cpp title="avl_tree.cpp"
```
=== "Python"
```python title="avl_tree.py"
```
=== "Go"
```go title="avl_tree.go"
```
=== "JavaScript"
```js title="avl_tree.js"
```
=== "TypeScript"
```typescript title="avl_tree.ts"
```
=== "C"
```c title="avl_tree.c"
```
=== "C#"
```csharp title="avl_tree.cs"
```
### Case 3 - 先左后右
@@ -420,43 +424,43 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
=== "C++"
```cpp title="avl_tree.cpp"
```
=== "Python"
```python title="avl_tree.py"
```
=== "Go"
```go title="avl_tree.go"
```
=== "JavaScript"
```js title="avl_tree.js"
```
=== "TypeScript"
```typescript title="avl_tree.ts"
```
=== "C"
```c title="avl_tree.c"
```
=== "C#"
```csharp title="avl_tree.cs"
```
## AVL 树常用操作
@@ -495,43 +499,43 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
=== "C++"
```cpp title="avl_tree.cpp"
```
=== "Python"
```python title="avl_tree.py"
```
=== "Go"
```go title="avl_tree.go"
```
=== "JavaScript"
```js title="avl_tree.js"
```
=== "TypeScript"
```typescript title="avl_tree.ts"
```
=== "C"
```c title="avl_tree.c"
```
=== "C#"
```csharp title="avl_tree.cs"
```
### 删除结点
@@ -592,43 +596,43 @@ AVL 树的独特之处在于「旋转 Rotation」的操作，其可 **在不影
=== "C++"
```cpp title="avl_tree.cpp"
```
=== "Python"
```python title="avl_tree.py"
```
=== "Go"
```go title="avl_tree.go"
```
=== "JavaScript"
```js title="avl_tree.js"
```
=== "TypeScript"
```typescript title="avl_tree.ts"
```
=== "C"
```c title="avl_tree.c"
```
=== "C#"
```csharp title="avl_tree.cs"
```
### 查找结点