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chapter_tree/array_representation_of_tree.md
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chapter_tree/avl_tree.md
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chapter_tree/binary_search_tree.md
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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。
chapter_tree/binary_tree_traversal.md
+347 -347
View File
@@ -22,26 +22,24 @@ comments: true
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。
=== "Java"
=== "Python"
```java title="binary_tree_bfs.java"
/* 层序遍历 */
List<Integer> levelOrder(TreeNode root) {
// 初始化队列，加入根节点
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
// 初始化一个列表，用于保存遍历序列
List<Integer> list = new ArrayList<>();
while (!queue.isEmpty()) {
TreeNode node = queue.poll(); // 队列出队
list.add(node.val); // 保存节点值
if (node.left != null)
queue.offer(node.left); // 左子节点入队
if (node.right != null)
queue.offer(node.right); // 右子节点入队
}
return list;
}
```python title="binary_tree_bfs.py"
def level_order(root: TreeNode | None) -> list[int]:
"""层序遍历"""
# 初始化队列，加入根节点
queue: deque[TreeNode] = deque()
queue.append(root)
# 初始化一个列表，用于保存遍历序列
res = []
while queue:
node: TreeNode = queue.popleft() # 队列出队
res.append(node.val) # 保存节点值
if node.left is not None:
queue.append(node.left) # 左子节点入队
if node.right is not None:
queue.append(node.right) # 右子节点入队
return res
```
=== "C++"
@@ -67,24 +65,48 @@ comments: true
}
```
=== "Python"
=== "Java"
```python title="binary_tree_bfs.py"
def level_order(root: TreeNode | None) -> list[int]:
"""层序遍历"""
# 初始化队列，加入根节点
queue: deque[TreeNode] = deque()
queue.append(root)
# 初始化一个列表，用于保存遍历序列
res = []
while queue:
node: TreeNode = queue.popleft() # 队列出队
res.append(node.val) # 保存节点值
if node.left is not None:
queue.append(node.left) # 左子节点入队
if node.right is not None:
queue.append(node.right) # 右子节点入队
return res
```java title="binary_tree_bfs.java"
/* 层序遍历 */
List<Integer> levelOrder(TreeNode root) {
// 初始化队列，加入根节点
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
// 初始化一个列表，用于保存遍历序列
List<Integer> list = new ArrayList<>();
while (!queue.isEmpty()) {
TreeNode node = queue.poll(); // 队列出队
list.add(node.val); // 保存节点值
if (node.left != null)
queue.offer(node.left); // 左子节点入队
if (node.right != null)
queue.offer(node.right); // 右子节点入队
}
return list;
}
```
=== "C#"
```csharp title="binary_tree_bfs.cs"
/* 层序遍历 */
List<int> levelOrder(TreeNode root) {
// 初始化队列，加入根节点
Queue<TreeNode> queue = new();
queue.Enqueue(root);
// 初始化一个列表，用于保存遍历序列
List<int> list = new();
while (queue.Count != 0) {
TreeNode node = queue.Dequeue(); // 队列出队
list.Add(node.val); // 保存节点值
if (node.left != null)
queue.Enqueue(node.left); // 左子节点入队
if (node.right != null)
queue.Enqueue(node.right); // 右子节点入队
}
return list;
}
```
=== "Go"
@@ -115,6 +137,29 @@ comments: true
}
```
=== "Swift"
```swift title="binary_tree_bfs.swift"
/* 层序遍历 */
func levelOrder(root: TreeNode) -> [Int] {
// 初始化队列，加入根节点
var queue: [TreeNode] = [root]
// 初始化一个列表，用于保存遍历序列
var list: [Int] = []
while !queue.isEmpty {
let node = queue.removeFirst() // 队列出队
list.append(node.val) // 保存节点值
if let left = node.left {
queue.append(left) // 左子节点入队
}
if let right = node.right {
queue.append(right) // 右子节点入队
}
}
return list
}
```
=== "JS"
```javascript title="binary_tree_bfs.js"
@@ -157,129 +202,6 @@ comments: true
}
```
=== "C"
```c title="binary_tree_bfs.c"
/* 层序遍历 */
int *levelOrder(TreeNode *root, int *size) {
/* 辅助队列 */
int front, rear;
int index, *arr;
TreeNode *node;
TreeNode **queue;
/* 辅助队列 */
queue = (TreeNode **)malloc(sizeof(TreeNode *) * MAX_NODE_SIZE);
// 队列指针
front = 0, rear = 0;
// 加入根节点
queue[rear++] = root;
// 初始化一个列表，用于保存遍历序列
/* 辅助数组 */
arr = (int *)malloc(sizeof(int) * MAX_NODE_SIZE);
// 数组指针
index = 0;
while (front < rear) {
// 队列出队
node = queue[front++];
// 保存节点值
arr[index++] = node->val;
if (node->left != NULL) {
// 左子节点入队
queue[rear++] = node->left;
}
if (node->right != NULL) {
// 右子节点入队
queue[rear++] = node->right;
}
}
// 更新数组长度的值
*size = index;
arr = realloc(arr, sizeof(int) * (*size));
// 释放辅助数组空间
free(queue);
return arr;
}
```
=== "C#"
```csharp title="binary_tree_bfs.cs"
/* 层序遍历 */
List<int> levelOrder(TreeNode root) {
// 初始化队列，加入根节点
Queue<TreeNode> queue = new();
queue.Enqueue(root);
// 初始化一个列表，用于保存遍历序列
List<int> list = new();
while (queue.Count != 0) {
TreeNode node = queue.Dequeue(); // 队列出队
list.Add(node.val); // 保存节点值
if (node.left != null)
queue.Enqueue(node.left); // 左子节点入队
if (node.right != null)
queue.Enqueue(node.right); // 右子节点入队
}
return list;
}
```
=== "Swift"
```swift title="binary_tree_bfs.swift"
/* 层序遍历 */
func levelOrder(root: TreeNode) -> [Int] {
// 初始化队列，加入根节点
var queue: [TreeNode] = [root]
// 初始化一个列表，用于保存遍历序列
var list: [Int] = []
while !queue.isEmpty {
let node = queue.removeFirst() // 队列出队
list.append(node.val) // 保存节点值
if let left = node.left {
queue.append(left) // 左子节点入队
}
if let right = node.right {
queue.append(right) // 右子节点入队
}
}
return list
}
```
=== "Zig"
```zig title="binary_tree_bfs.zig"
// 层序遍历
fn levelOrder(comptime T: type, mem_allocator: std.mem.Allocator, root: *inc.TreeNode(T)) !std.ArrayList(T) {
// 初始化队列，加入根节点
const L = std.TailQueue(*inc.TreeNode(T));
var queue = L{};
var root_node = try mem_allocator.create(L.Node);
root_node.data = root;
queue.append(root_node);
// 初始化一个列表，用于保存遍历序列
var list = std.ArrayList(T).init(std.heap.page_allocator);
while (queue.len > 0) {
var queue_node = queue.popFirst().?; // 队列出队
var node = queue_node.data;
try list.append(node.val); // 保存节点值
if (node.left != null) {
var tmp_node = try mem_allocator.create(L.Node);
tmp_node.data = node.left.?;
queue.append(tmp_node); // 左子节点入队
}
if (node.right != null) {
var tmp_node = try mem_allocator.create(L.Node);
tmp_node.data = node.right.?;
queue.append(tmp_node); // 右子节点入队
}
}
return list;
}
```
=== "Dart"
```dart title="binary_tree_bfs.dart"
@@ -324,6 +246,84 @@ comments: true
}
```
=== "C"
```c title="binary_tree_bfs.c"
/* 层序遍历 */
int *levelOrder(TreeNode *root, int *size) {
/* 辅助队列 */
int front, rear;
int index, *arr;
TreeNode *node;
TreeNode **queue;
/* 辅助队列 */
queue = (TreeNode **)malloc(sizeof(TreeNode *) * MAX_NODE_SIZE);
// 队列指针
front = 0, rear = 0;
// 加入根节点
queue[rear++] = root;
// 初始化一个列表，用于保存遍历序列
/* 辅助数组 */
arr = (int *)malloc(sizeof(int) * MAX_NODE_SIZE);
// 数组指针
index = 0;
while (front < rear) {
// 队列出队
node = queue[front++];
// 保存节点值
arr[index++] = node->val;
if (node->left != NULL) {
// 左子节点入队
queue[rear++] = node->left;
}
if (node->right != NULL) {
// 右子节点入队
queue[rear++] = node->right;
}
}
// 更新数组长度的值
*size = index;
arr = realloc(arr, sizeof(int) * (*size));
// 释放辅助数组空间
free(queue);
return arr;
}
```
=== "Zig"
```zig title="binary_tree_bfs.zig"
// 层序遍历
fn levelOrder(comptime T: type, mem_allocator: std.mem.Allocator, root: *inc.TreeNode(T)) !std.ArrayList(T) {
// 初始化队列，加入根节点
const L = std.TailQueue(*inc.TreeNode(T));
var queue = L{};
var root_node = try mem_allocator.create(L.Node);
root_node.data = root;
queue.append(root_node);
// 初始化一个列表，用于保存遍历序列
var list = std.ArrayList(T).init(std.heap.page_allocator);
while (queue.len > 0) {
var queue_node = queue.popFirst().?; // 队列出队
var node = queue_node.data;
try list.append(node.val); // 保存节点值
if (node.left != null) {
var tmp_node = try mem_allocator.create(L.Node);
tmp_node.data = node.left.?;
queue.append(tmp_node); // 左子节点入队
}
if (node.right != null) {
var tmp_node = try mem_allocator.create(L.Node);
tmp_node.data = node.right.?;
queue.append(tmp_node); // 右子节点入队
}
}
return list;
}
```
### 2. &nbsp; 复杂度分析
- **时间复杂度 $O(n)$** ：所有节点被访问一次，使用 $O(n)$ 时间，其中 $n$ 为节点数量。
@@ -343,38 +343,35 @@ comments: true
深度优先搜索通常基于递归实现：
=== "Java"
=== "Python"
```java title="binary_tree_dfs.java"
/* 前序遍历 */
void preOrder(TreeNode root) {
if (root == null)
return;
// 访问优先级：根节点 -> 左子树 -> 右子树
list.add(root.val);
preOrder(root.left);
preOrder(root.right);
}
```python title="binary_tree_dfs.py"
def pre_order(root: TreeNode | None):
"""前序遍历"""
if root is None:
return
# 访问优先级：根节点 -> 左子树 -> 右子树
res.append(root.val)
pre_order(root=root.left)
pre_order(root=root.right)
/* 中序遍历 */
void inOrder(TreeNode root) {
if (root == null)
return;
// 访问优先级：左子树 -> 根节点 -> 右子树
inOrder(root.left);
list.add(root.val);
inOrder(root.right);
}
def in_order(root: TreeNode | None):
"""中序遍历"""
if root is None:
return
# 访问优先级：左子树 -> 根节点 -> 右子树
in_order(root=root.left)
res.append(root.val)
in_order(root=root.right)
/* 后序遍历 */
void postOrder(TreeNode root) {
if (root == null)
return;
// 访问优先级：左子树 -> 右子树 -> 根节点
postOrder(root.left);
postOrder(root.right);
list.add(root.val);
}
def post_order(root: TreeNode | None):
"""后序遍历"""
if root is None:
return
# 访问优先级：左子树 -> 右子树 -> 根节点
post_order(root=root.left)
post_order(root=root.right)
res.append(root.val)
```
=== "C++"
@@ -411,35 +408,69 @@ comments: true
}
```
=== "Python"
=== "Java"
```python title="binary_tree_dfs.py"
def pre_order(root: TreeNode | None):
"""前序遍历"""
if root is None:
return
# 访问优先级：根节点 -> 左子树 -> 右子树
res.append(root.val)
pre_order(root=root.left)
pre_order(root=root.right)
```java title="binary_tree_dfs.java"
/* 前序遍历 */
void preOrder(TreeNode root) {
if (root == null)
return;
// 访问优先级：根节点 -> 左子树 -> 右子树
list.add(root.val);
preOrder(root.left);
preOrder(root.right);
}
def in_order(root: TreeNode | None):
"""中序遍历"""
if root is None:
return
# 访问优先级：左子树 -> 根节点 -> 右子树
in_order(root=root.left)
res.append(root.val)
in_order(root=root.right)
/* 中序遍历 */
void inOrder(TreeNode root) {
if (root == null)
return;
// 访问优先级：左子树 -> 根节点 -> 右子树
inOrder(root.left);
list.add(root.val);
inOrder(root.right);
}
def post_order(root: TreeNode | None):
"""后序遍历"""
if root is None:
return
# 访问优先级：左子树 -> 右子树 -> 根节点
post_order(root=root.left)
post_order(root=root.right)
res.append(root.val)
/* 后序遍历 */
void postOrder(TreeNode root) {
if (root == null)
return;
// 访问优先级：左子树 -> 右子树 -> 根节点
postOrder(root.left);
postOrder(root.right);
list.add(root.val);
}
```
=== "C#"
```csharp title="binary_tree_dfs.cs"
/* 前序遍历 */
void preOrder(TreeNode? root) {
if (root == null) return;
// 访问优先级：根节点 -> 左子树 -> 右子树
list.Add(root.val);
preOrder(root.left);
preOrder(root.right);
}
/* 中序遍历 */
void inOrder(TreeNode? root) {
if (root == null) return;
// 访问优先级：左子树 -> 根节点 -> 右子树
inOrder(root.left);
list.Add(root.val);
inOrder(root.right);
}
/* 后序遍历 */
void postOrder(TreeNode? root) {
if (root == null) return;
// 访问优先级：左子树 -> 右子树 -> 根节点
postOrder(root.left);
postOrder(root.right);
list.Add(root.val);
}
```
=== "Go"
@@ -479,6 +510,43 @@ comments: true
}
```
=== "Swift"
```swift title="binary_tree_dfs.swift"
/* 前序遍历 */
func preOrder(root: TreeNode?) {
guard let root = root else {
return
}
// 访问优先级：根节点 -> 左子树 -> 右子树
list.append(root.val)
preOrder(root: root.left)
preOrder(root: root.right)
}
/* 中序遍历 */
func inOrder(root: TreeNode?) {
guard let root = root else {
return
}
// 访问优先级：左子树 -> 根节点 -> 右子树
inOrder(root: root.left)
list.append(root.val)
inOrder(root: root.right)
}
/* 后序遍历 */
func postOrder(root: TreeNode?) {
guard let root = root else {
return
}
// 访问优先级：左子树 -> 右子树 -> 根节点
postOrder(root: root.left)
postOrder(root: root.right)
list.append(root.val)
}
```
=== "JS"
```javascript title="binary_tree_dfs.js"
@@ -547,139 +615,6 @@ comments: true
}
```
=== "C"
```c title="binary_tree_dfs.c"
/* 前序遍历 */
void preOrder(TreeNode *root, int *size) {
if (root == NULL)
return;
// 访问优先级：根节点 -> 左子树 -> 右子树
arr[(*size)++] = root->val;
preOrder(root->left, size);
preOrder(root->right, size);
}
/* 中序遍历 */
void inOrder(TreeNode *root, int *size) {
if (root == NULL)
return;
// 访问优先级：左子树 -> 根节点 -> 右子树
inOrder(root->left, size);
arr[(*size)++] = root->val;
inOrder(root->right, size);
}
/* 后序遍历 */
void postOrder(TreeNode *root, int *size) {
if (root == NULL)
return;
// 访问优先级：左子树 -> 右子树 -> 根节点
postOrder(root->left, size);
postOrder(root->right, size);
arr[(*size)++] = root->val;
}
```
=== "C#"
```csharp title="binary_tree_dfs.cs"
/* 前序遍历 */
void preOrder(TreeNode? root) {
if (root == null) return;
// 访问优先级：根节点 -> 左子树 -> 右子树
list.Add(root.val);
preOrder(root.left);
preOrder(root.right);
}
/* 中序遍历 */
void inOrder(TreeNode? root) {
if (root == null) return;
// 访问优先级：左子树 -> 根节点 -> 右子树
inOrder(root.left);
list.Add(root.val);
inOrder(root.right);
}
/* 后序遍历 */
void postOrder(TreeNode? root) {
if (root == null) return;
// 访问优先级：左子树 -> 右子树 -> 根节点
postOrder(root.left);
postOrder(root.right);
list.Add(root.val);
}
```
=== "Swift"
```swift title="binary_tree_dfs.swift"
/* 前序遍历 */
func preOrder(root: TreeNode?) {
guard let root = root else {
return
}
// 访问优先级：根节点 -> 左子树 -> 右子树
list.append(root.val)
preOrder(root: root.left)
preOrder(root: root.right)
}
/* 中序遍历 */
func inOrder(root: TreeNode?) {
guard let root = root else {
return
}
// 访问优先级：左子树 -> 根节点 -> 右子树
inOrder(root: root.left)
list.append(root.val)
inOrder(root: root.right)
}
/* 后序遍历 */
func postOrder(root: TreeNode?) {
guard let root = root else {
return
}
// 访问优先级：左子树 -> 右子树 -> 根节点
postOrder(root: root.left)
postOrder(root: root.right)
list.append(root.val)
}
```
=== "Zig"
```zig title="binary_tree_dfs.zig"
// 前序遍历
fn preOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
if (root == null) return;
// 访问优先级：根节点 -> 左子树 -> 右子树
try list.append(root.?.val);
try preOrder(T, root.?.left);
try preOrder(T, root.?.right);
}
// 中序遍历
fn inOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
if (root == null) return;
// 访问优先级：左子树 -> 根节点 -> 右子树
try inOrder(T, root.?.left);
try list.append(root.?.val);
try inOrder(T, root.?.right);
}
// 后序遍历
fn postOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
if (root == null) return;
// 访问优先级：左子树 -> 右子树 -> 根节点
try postOrder(T, root.?.left);
try postOrder(T, root.?.right);
try list.append(root.?.val);
}
```
=== "Dart"
```dart title="binary_tree_dfs.dart"
@@ -754,6 +689,71 @@ comments: true
}
```
=== "C"
```c title="binary_tree_dfs.c"
/* 前序遍历 */
void preOrder(TreeNode *root, int *size) {
if (root == NULL)
return;
// 访问优先级：根节点 -> 左子树 -> 右子树
arr[(*size)++] = root->val;
preOrder(root->left, size);
preOrder(root->right, size);
}
/* 中序遍历 */
void inOrder(TreeNode *root, int *size) {
if (root == NULL)
return;
// 访问优先级：左子树 -> 根节点 -> 右子树
inOrder(root->left, size);
arr[(*size)++] = root->val;
inOrder(root->right, size);
}
/* 后序遍历 */
void postOrder(TreeNode *root, int *size) {
if (root == NULL)
return;
// 访问优先级：左子树 -> 右子树 -> 根节点
postOrder(root->left, size);
postOrder(root->right, size);
arr[(*size)++] = root->val;
}
```
=== "Zig"
```zig title="binary_tree_dfs.zig"
// 前序遍历
fn preOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
if (root == null) return;
// 访问优先级：根节点 -> 左子树 -> 右子树
try list.append(root.?.val);
try preOrder(T, root.?.left);
try preOrder(T, root.?.right);
}
// 中序遍历
fn inOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
if (root == null) return;
// 访问优先级：左子树 -> 根节点 -> 右子树
try inOrder(T, root.?.left);
try list.append(root.?.val);
try inOrder(T, root.?.right);
}
// 后序遍历
fn postOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
if (root == null) return;
// 访问优先级：左子树 -> 右子树 -> 根节点
try postOrder(T, root.?.left);
try postOrder(T, root.?.right);
try list.append(root.?.val);
}
```
!!! note
深度优先搜索也可以基于迭代实现，有兴趣的同学可以自行研究。