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chapter_tree/binary_tree.md
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@@ -6,16 +6,15 @@ comments: true
「二叉树 binary tree」是一种非线性数据结构，代表着祖先与后代之间的派生关系，体现着“一分为二”的分治逻辑。与链表类似，二叉树的基本单元是节点，每个节点包含：值、左子节点引用、右子节点引用。
=== "Java"
=== "Python"
```java title=""
/* 二叉树节点类 */
class TreeNode {
int val; // 节点值
TreeNode left; // 左子节点引用
TreeNode right; // 右子节点引用
TreeNode(int x) { val = x; }
}
```python title=""
class TreeNode:
"""二叉树节点类"""
def __init__(self, val: int):
self.val: int = val # 节点值
self.left: Optional[TreeNode] = None # 左子节点引用
self.right: Optional[TreeNode] = None # 右子节点引用
```
=== "C++"
@@ -30,15 +29,28 @@ comments: true
};
```
=== "Python"
=== "Java"
```python title=""
class TreeNode:
"""二叉树节点类"""
def __init__(self, val: int):
self.val: int = val # 节点值
self.left: Optional[TreeNode] = None # 左子节点引用
self.right: Optional[TreeNode] = None # 右子节点引用
```java title=""
/* 二叉树节点类 */
class TreeNode {
int val; // 节点值
TreeNode left; // 左子节点引用
TreeNode right; // 右子节点引用
TreeNode(int x) { val = x; }
}
```
=== "C#"
```csharp title=""
/* 二叉树节点类 */
class TreeNode {
int val; // 节点值
TreeNode? left; // 左子节点引用
TreeNode? right; // 右子节点引用
TreeNode(int x) { val = x; }
}
```
=== "Go"
@@ -60,6 +72,21 @@ comments: true
}
```
=== "Swift"
```swift title=""
/* 二叉树节点类 */
class TreeNode {
var val: Int // 节点值
var left: TreeNode? // 左子节点引用
var right: TreeNode? // 右子节点引用
init(x: Int) {
val = x
}
}
```
=== "JS"
```javascript title=""
@@ -88,6 +115,24 @@ comments: true
}
```
=== "Dart"
```dart title=""
/* 二叉树节点类 */
class TreeNode {
int val; // 节点值
TreeNode? left; // 左子节点引用
TreeNode? right; // 右子节点引用
TreeNode(this.val, [this.left, this.right]);
}
```
=== "Rust"
```rust title=""
```
=== "C"
```c title=""
@@ -114,57 +159,12 @@ comments: true
}
```
=== "C#"
```csharp title=""
/* 二叉树节点类 */
class TreeNode {
int val; // 节点值
TreeNode? left; // 左子节点引用
TreeNode? right; // 右子节点引用
TreeNode(int x) { val = x; }
}
```
=== "Swift"
```swift title=""
/* 二叉树节点类 */
class TreeNode {
var val: Int // 节点值
var left: TreeNode? // 左子节点引用
var right: TreeNode? // 右子节点引用
init(x: Int) {
val = x
}
}
```
=== "Zig"
```zig title=""
```
=== "Dart"
```dart title=""
/* 二叉树节点类 */
class TreeNode {
int val; // 节点值
TreeNode? left; // 左子节点引用
TreeNode? right; // 右子节点引用
TreeNode(this.val, [this.left, this.right]);
}
```
=== "Rust"
```rust title=""
```
每个节点都有两个引用（指针），分别指向「左子节点 left-child node」和「右子节点 right-child node」，该节点被称为这两个子节点的「父节点 parent node」。当给定一个二叉树的节点时，我们将该节点的左子节点及其以下节点形成的树称为该节点的「左子树 left subtree」，同理可得「右子树 right subtree」。
**在二叉树中，除叶节点外，其他所有节点都包含子节点和非空子树**。如图 7-1 所示，如果将“节点 2”视为父节点，则其左子节点和右子节点分别是“节点 4”和“节点 5”，左子树是“节点 4 及其以下节点形成的树”，右子树是“节点 5 及其以下节点形成的树”。
@@ -200,20 +200,21 @@ comments: true
与链表类似，首先初始化节点，然后构建引用（指针）。
=== "Java"
=== "Python"
```java title="binary_tree.java"
// 初始化节点
TreeNode n1 = new TreeNode(1);
TreeNode n2 = new TreeNode(2);
TreeNode n3 = new TreeNode(3);
TreeNode n4 = new TreeNode(4);
TreeNode n5 = new TreeNode(5);
// 构建引用指向（即指针）
n1.left = n2;
n1.right = n3;
n2.left = n4;
n2.right = n5;
```python title="binary_tree.py"
# 初始化二叉树
# 初始化节点
n1 = TreeNode(val=1)
n2 = TreeNode(val=2)
n3 = TreeNode(val=3)
n4 = TreeNode(val=4)
n5 = TreeNode(val=5)
# 构建引用指向（即指针）
n1.left = n2
n1.right = n3
n2.left = n4
n2.right = n5
```
=== "C++"
@@ -233,21 +234,37 @@ comments: true
n2->right = n5;
```
=== "Python"
=== "Java"
```python title="binary_tree.py"
# 初始化二叉树
# 初始化节点
n1 = TreeNode(val=1)
n2 = TreeNode(val=2)
n3 = TreeNode(val=3)
n4 = TreeNode(val=4)
n5 = TreeNode(val=5)
# 构建引用指向（即指针）
n1.left = n2
n1.right = n3
n2.left = n4
n2.right = n5
```java title="binary_tree.java"
// 初始化节点
TreeNode n1 = new TreeNode(1);
TreeNode n2 = new TreeNode(2);
TreeNode n3 = new TreeNode(3);
TreeNode n4 = new TreeNode(4);
TreeNode n5 = new TreeNode(5);
// 构建引用指向（即指针）
n1.left = n2;
n1.right = n3;
n2.left = n4;
n2.right = n5;
```
=== "C#"
```csharp title="binary_tree.cs"
/* 初始化二叉树 */
// 初始化节点
TreeNode n1 = new TreeNode(1);
TreeNode n2 = new TreeNode(2);
TreeNode n3 = new TreeNode(3);
TreeNode n4 = new TreeNode(4);
TreeNode n5 = new TreeNode(5);
// 构建引用指向（即指针）
n1.left = n2;
n1.right = n3;
n2.left = n4;
n2.right = n5;
```
=== "Go"
@@ -267,6 +284,22 @@ comments: true
n2.Right = n5
```
=== "Swift"
```swift title="binary_tree.swift"
// 初始化节点
let n1 = TreeNode(x: 1)
let n2 = TreeNode(x: 2)
let n3 = TreeNode(x: 3)
let n4 = TreeNode(x: 4)
let n5 = TreeNode(x: 5)
// 构建引用指向（即指针）
n1.left = n2
n1.right = n3
n2.left = n4
n2.right = n5
```
=== "JS"
```javascript title="binary_tree.js"
@@ -301,62 +334,6 @@ comments: true
n2.right = n5;
```
=== "C"
```c title="binary_tree.c"
/* 初始化二叉树 */
// 初始化节点
TreeNode *n1 = newTreeNode(1);
TreeNode *n2 = newTreeNode(2);
TreeNode *n3 = newTreeNode(3);
TreeNode *n4 = newTreeNode(4);
TreeNode *n5 = newTreeNode(5);
// 构建引用指向（即指针）
n1->left = n2;
n1->right = n3;
n2->left = n4;
n2->right = n5;
```
=== "C#"
```csharp title="binary_tree.cs"
/* 初始化二叉树 */
// 初始化节点
TreeNode n1 = new TreeNode(1);
TreeNode n2 = new TreeNode(2);
TreeNode n3 = new TreeNode(3);
TreeNode n4 = new TreeNode(4);
TreeNode n5 = new TreeNode(5);
// 构建引用指向（即指针）
n1.left = n2;
n1.right = n3;
n2.left = n4;
n2.right = n5;
```
=== "Swift"
```swift title="binary_tree.swift"
// 初始化节点
let n1 = TreeNode(x: 1)
let n2 = TreeNode(x: 2)
let n3 = TreeNode(x: 3)
let n4 = TreeNode(x: 4)
let n5 = TreeNode(x: 5)
// 构建引用指向（即指针）
n1.left = n2
n1.right = n3
n2.left = n4
n2.right = n5
```
=== "Zig"
```zig title="binary_tree.zig"
```
=== "Dart"
```dart title="binary_tree.dart"
@@ -380,6 +357,29 @@ comments: true
```
=== "C"
```c title="binary_tree.c"
/* 初始化二叉树 */
// 初始化节点
TreeNode *n1 = newTreeNode(1);
TreeNode *n2 = newTreeNode(2);
TreeNode *n3 = newTreeNode(3);
TreeNode *n4 = newTreeNode(4);
TreeNode *n5 = newTreeNode(5);
// 构建引用指向（即指针）
n1->left = n2;
n1->right = n3;
n2->left = n4;
n2->right = n5;
```
=== "Zig"
```zig title="binary_tree.zig"
```
### 2.   插入与删除节点
与链表类似，在二叉树中插入与删除节点可以通过修改指针来实现。图 7-3 给出了一个示例。
@@ -388,15 +388,16 @@ comments: true
<p align="center"> 图 7-3 &nbsp; 在二叉树中插入与删除节点 </p>
=== "Java"
=== "Python"
```java title="binary_tree.java"
TreeNode P = new TreeNode(0);
// 在 n1 -> n2 中间插入节点 P
n1.left = P;
P.left = n2;
// 删除节点 P
n1.left = n2;
```python title="binary_tree.py"
# 插入与删除节点
p = TreeNode(0)
# 在 n1 -> n2 中间插入节点 P
n1.left = p
p.left = n2
# 删除节点 P
n1.left = n2
```
=== "C++"
@@ -411,16 +412,27 @@ comments: true
n1->left = n2;
```
=== "Python"
=== "Java"
```python title="binary_tree.py"
# 插入与删除节点
p = TreeNode(0)
# 在 n1 -> n2 中间插入节点 P
n1.left = p
p.left = n2
# 删除节点 P
n1.left = n2
```java title="binary_tree.java"
TreeNode P = new TreeNode(0);
// 在 n1 -> n2 中间插入节点 P
n1.left = P;
P.left = n2;
// 删除节点 P
n1.left = n2;
```
=== "C#"
```csharp title="binary_tree.cs"
/* 插入与删除节点 */
TreeNode P = new TreeNode(0);
// 在 n1 -> n2 中间插入节点 P
n1.left = P;
P.left = n2;
// 删除节点 P
n1.left = n2;
```
=== "Go"
@@ -435,6 +447,17 @@ comments: true
n1.Left = n2
```
=== "Swift"
```swift title="binary_tree.swift"
let P = TreeNode(x: 0)
// 在 n1 -> n2 中间插入节点 P
n1.left = P
P.left = n2
// 删除节点 P
n1.left = n2
```
=== "JS"
```javascript title="binary_tree.js"
@@ -459,47 +482,6 @@ comments: true
n1.left = n2;
```
=== "C"
```c title="binary_tree.c"
/* 插入与删除节点 */
TreeNode *P = newTreeNode(0);
// 在 n1 -> n2 中间插入节点 P
n1->left = P;
P->left = n2;
// 删除节点 P
n1->left = n2;
```
=== "C#"
```csharp title="binary_tree.cs"
/* 插入与删除节点 */
TreeNode P = new TreeNode(0);
// 在 n1 -> n2 中间插入节点 P
n1.left = P;
P.left = n2;
// 删除节点 P
n1.left = n2;
```
=== "Swift"
```swift title="binary_tree.swift"
let P = TreeNode(x: 0)
// 在 n1 -> n2 中间插入节点 P
n1.left = P
P.left = n2
// 删除节点 P
n1.left = n2
```
=== "Zig"
```zig title="binary_tree.zig"
```
=== "Dart"
```dart title="binary_tree.dart"
@@ -518,6 +500,24 @@ comments: true
```
=== "C"
```c title="binary_tree.c"
/* 插入与删除节点 */
TreeNode *P = newTreeNode(0);
// 在 n1 -> n2 中间插入节点 P
n1->left = P;
P->left = n2;
// 删除节点 P
n1->left = n2;
```
=== "Zig"
```zig title="binary_tree.zig"
```
!!! note
需要注意的是，插入节点可能会改变二叉树的原有逻辑结构，而删除节点通常意味着删除该节点及其所有子树。因此，在二叉树中，插入与删除操作通常是由一套操作配合完成的，以实现有实际意义的操作。