Merge branch 'krahets:master' into master

codes/csharp/chapter_array_and_linkedlist/Array.cs

@@ -0,0 +1,122 @@
+/*
+* File: Array.cs
+* Created Time: 2022-12-14
+* Author: mingXta (1195669834@qq.com)
+*/
+ 
+namespace hello_algo.chapter_array_and_linkedlist
+{
+    public class Array
+    {
+        /* 随机返回一个数组元素 */
+        public static int RandomAccess(int[] nums)
+        {
+            Random random = new();
+            int randomIndex = random.Next(nums.Length);
+            int randomNum = nums[randomIndex];
+            return randomNum;
+        }
+
+        /* 扩展数组长度 */
+        public static int[] Extend(int[] nums, int enlarge)
+        {
+            // 初始化一个扩展长度后的数组
+            int[] res = new int[nums.Length + enlarge];
+            // 将原数组中的所有元素复制到新数组
+            for (int i = 0; i < nums.Length; i++)
+            {
+                res[i] = nums[i];
+            }
+            // 返回扩展后的新数组
+            return res;
+        }
+
+        /* 在数组的索引 index 处插入元素 num */
+        public static void Insert(int[] nums, int num, int index)
+        {
+            // 把索引 index 以及之后的所有元素向后移动一位
+            for (int i = nums.Length - 1; i >= index; i--)
+            {
+                nums[i] = nums[i - 1];
+            }
+            // 将 num 赋给 index 处元素
+            nums[index] = num;
+        }
+
+        /* 删除索引 index 处元素 */
+        public static void Remove(int[] nums, int index)
+        {
+            // 把索引 index 之后的所有元素向前移动一位
+            for (int i = index; i < nums.Length - 1; i++)
+            {
+                nums[i] = nums[i + 1];
+            }
+        }
+
+        /* 遍历数组 */
+        public static void Traverse(int[] nums)
+        {
+            int count = 0;
+            // 通过索引遍历数组
+            for (int i = 0; i < nums.Length; i++)
+            {
+                count++;
+            }
+            // 直接遍历数组
+            foreach (int num in nums)
+            {
+                count++;
+            }
+        }
+
+        /* 在数组中查找指定元素 */
+        public static int Find(int[] nums, int target)
+        {
+            for (int i = 0; i < nums.Length; i++)
+            {
+                if (nums[i] == target)
+                    return i;
+            }
+            return -1;
+        }
+
+        /*辅助函数,数组转字符串 */
+        public static string ToString(int[] nums)
+        {
+            return string.Join(",", nums);
+        }
+
+        /* Driver Code */
+        public static void Main()
+        {
+            /* 初始化数组 */
+            int[] arr = new int[5];
+            Console.WriteLine("数组 arr = " + ToString(arr));
+            int[] nums = { 1, 3, 2, 5, 4 };
+            Console.WriteLine("数组 nums = " + ToString(nums));
+
+            /* 随机访问 */
+            int randomNum = RandomAccess(nums);
+            Console.WriteLine("在 nums 中获取随机元素 " + randomNum);
+
+            /* 长度扩展 */
+            nums = Extend(nums, 3);
+            Console.WriteLine("将数组长度扩展至 8 ，得到 nums = " + ToString(nums));
+
+            /* 插入元素 */
+            Insert(nums, 6, 3);
+            Console.WriteLine("在索引 3 处插入数字 6 ，得到 nums = " + ToString(nums));
+
+            /* 删除元素 */
+            Remove(nums, 2);
+            Console.WriteLine("删除索引 2 处的元素，得到 nums = " + ToString(nums));
+
+            /* 遍历数组 */
+            Traverse(nums);
+
+            /* 查找元素 */
+            int index = Find(nums, 3);
+            Console.WriteLine("在 nums 中查找元素 3 ，得到索引 = " + index);
+        }
+    }
+}

codes/typescript/chapter_tree/binary_search_tree.ts

@@ -0,0 +1,172 @@
+/**
+ * File: binary_search_tree.ts
+ * Created Time: 2022-12-14
+ * Author: Justin (xiefahit@gmail.com)
+ */
+
+import { TreeNode } from '../module/TreeNode';
+import { printTree } from '../module/PrintUtil';
+
+/* 二叉搜索树 */
+let root: TreeNode | null;
+
+function BinarySearchTree(nums: number[]): void {
+    nums.sort((a, b) => a - b); // 排序数组
+    root = buildTree(nums, 0, nums.length - 1); // 构建二叉搜索树
+}
+
+/* 获取二叉树根结点 */
+function getRoot(): TreeNode | null {
+    return root;
+}
+
+/* 构建二叉搜索树 */
+function buildTree(nums: number[], i: number, j: number): TreeNode | null {
+    if (i > j) {
+        return null;
+    }
+    // 将数组中间结点作为根结点
+    let mid = Math.floor((i + j) / 2);
+    let root = new TreeNode(nums[mid]);
+    // 递归建立左子树和右子树
+    root.left = buildTree(nums, i, mid - 1);
+    root.right = buildTree(nums, mid + 1, j);
+    return root;
+}
+
+/* 查找结点 */
+function search(num: number): TreeNode | null {
+    let cur = root;
+    // 循环查找，越过叶结点后跳出
+    while (cur !== null) {
+        if (cur.val < num) {
+            cur = cur.right; // 目标结点在 root 的右子树中
+        } else if (cur.val > num) {
+            cur = cur.left; // 目标结点在 root 的左子树中
+        } else {
+            break; // 找到目标结点，跳出循环
+        }
+    }
+    // 返回目标结点
+    return cur;
+}
+
+/* 插入结点 */
+function insert(num: number): TreeNode | null {
+    // 若树为空，直接提前返回
+    if (root === null) {
+        return null;
+    }
+    let cur = root,
+        pre: TreeNode | null = null;
+    // 循环查找，越过叶结点后跳出
+    while (cur !== null) {
+        if (cur.val === num) {
+            return null; // 找到重复结点，直接返回
+        }
+        pre = cur;
+        if (cur.val < num) {
+            cur = cur.right as TreeNode; // 插入位置在 root 的右子树中
+        } else {
+            cur = cur.left as TreeNode; // 插入位置在 root 的左子树中
+        }
+    }
+    // 插入结点 val
+    let node = new TreeNode(num);
+    if (pre!.val < num) {
+        pre!.right = node;
+    } else {
+        pre!.left = node;
+    }
+    return node;
+}
+
+/* 删除结点 */
+function remove(num: number): TreeNode | null {
+    // 若树为空，直接提前返回
+    if (root === null) {
+        return null;
+    }
+    let cur = root,
+        pre: TreeNode | null = null;
+    // 循环查找，越过叶结点后跳出
+    while (cur !== null) {
+        // 找到待删除结点，跳出循环
+        if (cur.val === num) {
+            break;
+        }
+        pre = cur;
+        if (cur.val < num) {
+            cur = cur.right as TreeNode; // 待删除结点在 root 的右子树中
+        } else {
+            cur = cur.left as TreeNode; // 待删除结点在 root 的左子树中
+        }
+    }
+    // 若无待删除结点，则直接返回
+    if (cur === null) {
+        return null;
+    }
+    // 子结点数量 = 0 or 1
+    if (cur.left === null || cur.right === null) {
+        // 当子结点数量 = 0 / 1 时， child = null / 该子结点
+        let child = cur.left !== null ? cur.left : cur.right;
+        // 删除结点 cur
+        if (pre!.left === cur) {
+            pre!.left = child;
+        } else {
+            pre!.right = child;
+        }
+    }
+    // 子结点数量 = 2
+    else {
+        // 获取中序遍历中 cur 的下一个结点
+        let next = min(cur.right);
+        let tmp = next!.val;
+        // 递归删除结点 nex
+        remove(next!.val);
+        // 将 nex 的值复制给 cur
+        cur.val = tmp;
+    }
+    return cur;
+}
+
+/* 获取最小结点 */
+function min(root: TreeNode | null): TreeNode | null {
+    if (root === null) {
+        return null;
+    }
+    // 循环访问左子结点，直到叶结点时为最小结点，跳出
+    while (root.left !== null) {
+        root = root.left;
+    }
+    return root;
+}
+
+/* Driver Code */
+/* 初始化二叉搜索树 */
+const nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15];
+BinarySearchTree(nums);
+console.log('\n初始化的二叉树为\n');
+printTree(getRoot());
+
+/* 查找结点 */
+let node = search(5);
+console.log('\n查找到的结点对象为 ' + node + '，结点值 = ' + node!.val);
+
+/* 插入结点 */
+node = insert(16);
+console.log('\n插入结点 16 后，二叉树为\n');
+printTree(getRoot());
+
+/* 删除结点 */
+remove(1);
+console.log('\n删除结点 1 后，二叉树为\n');
+printTree(getRoot());
+remove(2);
+console.log('\n删除结点 2 后，二叉树为\n');
+printTree(getRoot());
+remove(4);
+console.log('\n删除结点 4 后，二叉树为\n');
+printTree(getRoot());
+
+export {};

codes/typescript/chapter_tree/binary_tree.ts

@@ -0,0 +1,35 @@
+/**
+ * File: binary_tree.ts
+ * Created Time: 2022-12-13
+ * Author: Justin (xiefahit@gmail.com)
+ */
+
+import { TreeNode } from '../module/TreeNode';
+import { printTree } from '../module/PrintUtil';
+
+/* 初始化二叉树 */
+// 初始化结点
+let n1 = new TreeNode(1),
+    n2 = new TreeNode(2),
+    n3 = new TreeNode(3),
+    n4 = new TreeNode(4),
+    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;
+console.log('\n初始化二叉树\n');
+printTree(n1);
+
+/* 插入与删除结点 */
+const P = new TreeNode(0);
+// 在 n1 -> n2 中间插入结点 P
+n1.left = P;
+P.left = n2;
+console.log('\n插入结点 P 后\n');
+printTree(n1);
+// 删除结点 P
+n1.left = n2;
+console.log('\n删除结点 P 后\n');
+printTree(n1);

codes/typescript/chapter_tree/binary_tree_bfs.ts

@@ -0,0 +1,39 @@
+/**
+ * File: binary_tree_bfs.ts
+ * Created Time: 2022-12-14
+ * Author: Justin (xiefahit@gmail.com)
+ */
+
+import { type TreeNode } from '../module/TreeNode';
+import { arrToTree } from '../module/TreeNode';
+import { printTree } from '../module/PrintUtil';
+
+/* 层序遍历 */
+function hierOrder(root: TreeNode | null): number[] {
+    // 初始化队列，加入根结点
+    const queue = [root];
+    // 初始化一个列表，用于保存遍历序列
+    const list: number[] = [];
+    while (queue.length) {
+        let node = queue.shift() as TreeNode; // 队列出队
+        list.push(node.val); // 保存结点
+        if (node.left) {
+            queue.push(node.left); // 左子结点入队
+        }
+        if (node.right) {
+            queue.push(node.right); // 右子结点入队
+        }
+    }
+    return list;
+}
+
+/* Driver Code */
+/* 初始化二叉树 */
+// 这里借助了一个从数组直接生成二叉树的函数
+var root = arrToTree([1, 2, 3, 4, 5, 6, 7, null, null, null, null, null, null, null, null]);
+console.log('\n初始化二叉树\n');
+printTree(root);
+
+/* 层序遍历 */
+const list = hierOrder(root);
+console.log('\n层序遍历的结点打印序列 = ' + list);

codes/typescript/chapter_tree/binary_tree_dfs.ts

@@ -0,0 +1,67 @@
+/**
+ * File: binary_tree_dfs.ts
+ * Created Time: 2022-12-14
+ * Author: Justin (xiefahit@gmail.com)
+ */
+
+import { type TreeNode } from '../module/TreeNode';
+import { arrToTree } from '../module/TreeNode';
+import { printTree } from '../module/PrintUtil';
+
+// 初始化列表，用于存储遍历序列
+const list: number[] = [];
+
+/* 前序遍历 */
+function preOrder(root: TreeNode | null): void {
+    if (root === null) {
+        return;
+    }
+    // 访问优先级：根结点 -> 左子树 -> 右子树
+    list.push(root.val);
+    preOrder(root.left);
+    preOrder(root.right);
+}
+
+/* 中序遍历 */
+function inOrder(root: TreeNode | null): void {
+    if (root === null) {
+        return;
+    }
+    // 访问优先级：左子树 -> 根结点 -> 右子树
+    inOrder(root.left);
+    list.push(root.val);
+    inOrder(root.right);
+}
+
+/* 后序遍历 */
+function postOrder(root: TreeNode | null): void {
+    if (root === null) {
+        return;
+    }
+    // 访问优先级：左子树 -> 右子树 -> 根结点
+    postOrder(root.left);
+    postOrder(root.right);
+    list.push(root.val);
+}
+
+/* Driver Code */
+/* 初始化二叉树 */
+// 这里借助了一个从数组直接生成二叉树的函数
+const root = arrToTree([1, 2, 3, 4, 5, 6, 7, null, null, null, null, null, null, null, null]);
+console.log('\n初始化二叉树\n');
+printTree(root);
+
+/* 前序遍历 */
+list.length = 0;
+preOrder(root);
+console.log('\n前序遍历的结点打印序列 = ' + list);
+
+/* 中序遍历 */
+list.length = 0;
+inOrder(root);
+console.log('\n中序遍历的结点打印序列 = ' + list);
+
+/* 后序遍历 */
+list.length = 0;
+postOrder(root);
+console.log('\n后序遍历的结点打印序列 = ' + list);

codes/typescript/module/PrintUtil.ts

@@ -1,11 +1,26 @@
 /*
  * File: PrintUtil.ts
- * Created Time: 2022-12-10
+ * Created Time: 2022-12-13
  * Author: Justin (xiefahit@gmail.com)
  */
 
 import ListNode from './ListNode';
+import { TreeNode } from './TreeNode';
 
+class Trunk {
+    prev: Trunk | null;
+    str: string;
+
+    constructor(prev: Trunk | null, str: string) {
+        this.prev = prev;
+        this.str = str;
+    }
+}
+
+/**
+ * Print a linked list
+ * @param head
+ */
 function printLinkedList(head: ListNode | null): void {
     const list: string[] = [];
     while (head !== null) {
@@ -15,4 +30,67 @@ function printLinkedList(head: ListNode | null): void {
     console.log(list.join(' -> '));
 }
 
-export { printLinkedList };
+/**
+ * The interface of the tree printer
+ * This tree printer is borrowed from TECHIE DELIGHT
+ * https://www.techiedelight.com/c-program-print-binary-tree/
+ * @param root
+ */
+function printTree(root: TreeNode | null) {
+    printTreeHelper(root, null, false);
+}
+
+/**
+ * Print a binary tree
+ * @param root
+ * @param prev
+ * @param isLeft
+ */
+function printTreeHelper(root: TreeNode | null, prev: Trunk | null, isLeft: boolean) {
+    if (root === null) {
+        return;
+    }
+
+    let prev_str = '    ';
+    const trunk = new Trunk(prev, prev_str);
+
+    printTreeHelper(root.right, trunk, true);
+
+    if (prev === null) {
+        trunk.str = '———';
+    } else if (isLeft) {
+        trunk.str = '/———';
+        prev_str = '   |';
+    } else {
+        trunk.str = '\\———';
+        prev.str = prev_str;
+    }
+
+    showTrunks(trunk);
+    console.log(' ' + root.val);
+
+    if (prev) {
+        prev.str = prev_str;
+    }
+    trunk.str = '   |';
+
+    printTreeHelper(root.left, trunk, false);
+}
+
+/**
+ * Helper function to print branches of the binary tree
+ * @param p
+ */
+function showTrunks(p: Trunk | null) {
+    if (p === null) {
+        return;
+    }
+
+    showTrunks(p.prev);
+    process.stdout.write(p.str);
+    // ts-node to execute, we need to install type definitions for node
+    // solve: npm i --save-dev @types/node
+    // restart the vscode
+}
+
+export { printLinkedList, printTree };

codes/typescript/module/TreeNode.ts

@@ -0,0 +1,51 @@
+/*
+ * File: TreeNode.ts
+ * Created Time: 2022-12-13
+ * Author: Justin (xiefahit@gmail.com)
+ */
+
+/**
+ * Definition for a binary tree node.
+ */
+class TreeNode {
+    val: number;
+    left: TreeNode | null;
+    right: TreeNode | null;
+
+    constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
+        this.val = val === undefined ? 0 : val; // 结点值
+        this.left = left === undefined ? null : left; // 左子结点指针
+        this.right = right === undefined ? null : right; // 右子结点指针
+    }
+}
+
+/**
+ * Generate a binary tree with an array
+ * @param arr
+ * @return
+ */
+function arrToTree(arr: (number | null)[]): TreeNode | null {
+    if (arr.length === 0) {
+        return null;
+    }
+
+    const root = new TreeNode(arr[0] as number);
+    const queue = [root];
+    let i = 1;
+    while (queue.length) {
+        let node = queue.shift() as TreeNode;
+        if (arr[i] !== null) {
+            node.left = new TreeNode(arr[i] as number);
+            queue.push(node.left);
+        }
+        i++;
+        if (arr[i] !== null) {
+            node.right = new TreeNode(arr[i] as number);
+            queue.push(node.right);
+        }
+        i++;
+    }
+    return root;
+}
+
+export { TreeNode, arrToTree };

deploy.sh

@@ -1,3 +1,4 @@
+rm -rf ./site
 mkdocs build --clean
 cd site
 git init

docs/chapter_array_and_linkedlist/array.md

@@ -71,7 +71,12 @@ comments: true
 === "C#"
 
     ```csharp title="array.cs"
+    /* 初始化数组 */
+    int[] arr = new int[5]; // { 0, 0, 0, 0, 0 }
+    int[] nums = { 1, 3, 2, 5, 4 };
     
+    var arr2=new int[5]; // { 0, 0, 0, 0, 0 }
+    var nums2=new int[]{1,2,3,4,5};
     ```
 
 ## 数组优点
@@ -169,7 +174,14 @@ elementAddr = firtstElementAddr + elementLength * elementIndex
 === "C#"
 
     ```csharp title="array.cs"
-    
+    /* 随机返回一个数组元素 */
+    int RandomAccess(int[] nums)
+    {
+        Random random=new();
+        int randomIndex = random.Next(nums.Length);
+        int randomNum = nums[randomIndex];
+        return randomNum;
+    }
     ```
 
 ## 数组缺点
@@ -271,7 +283,19 @@ elementAddr = firtstElementAddr + elementLength * elementIndex
 === "C#"
 
     ```csharp title="array.cs"
-    
+    /* 扩展数组长度 */
+    int[] Extend(int[] nums, int enlarge)
+    {
+        // 初始化一个扩展长度后的数组
+        int[] res = new int[nums.Length + enlarge];
+        // 将原数组中的所有元素复制到新数组
+        for (int i = 0; i < nums.Length; i++)
+        {
+            res[i] = nums[i];
+        }
+        // 返回扩展后的新数组
+        return res;
+    }
     ```
 
 **数组中插入或删除元素效率低下。** 假设我们想要在数组中间某位置插入一个元素，由于数组元素在内存中是 “紧挨着的” ，它们之间没有空间再放任何数据。因此，我们不得不将此索引之后的所有元素都向后移动一位，然后再把元素赋值给该索引。删除元素也是类似，需要把此索引之后的元素都向前移动一位。总体看有以下缺点：
@@ -405,7 +429,26 @@ elementAddr = firtstElementAddr + elementLength * elementIndex
 === "C#"
 
     ```csharp title="array.cs"
-    
+    /* 在数组的索引 index 处插入元素 num */
+    void Insert(int[] nums, int num, int index)
+    {
+        // 把索引 index 以及之后的所有元素向后移动一位
+        for (int i = nums.Length - 1; i >= index; i--)
+        {
+            nums[i] = nums[i - 1];
+        }
+        // 将 num 赋给 index 处元素
+        nums[index] = num;
+    }
+    /* 删除索引 index 处元素 */
+    void Remove(int[] nums, int index)
+    {
+        // 把索引 index 之后的所有元素向前移动一位
+        for (int i = index; i < nums.Length - 1; i++)
+        {
+            nums[i] = nums[i + 1];
+        }
+    }
     ```
 
 ## 数组常用操作
@@ -505,7 +548,21 @@ elementAddr = firtstElementAddr + elementLength * elementIndex
 === "C#"
 
     ```csharp title="array.cs"
-    
+    /* 遍历数组 */
+    void Traverse(int[] nums)
+    {
+        int count = 0;
+        // 通过索引遍历数组
+        for (int i = 0; i < nums.Length; i++)
+        {
+            count++;
+        }
+        // 直接遍历数组
+        foreach (int num in nums)
+        {
+            count++;
+        }
+    }
     ```
 
 **数组查找。** 通过遍历数组，查找数组内的指定元素，并输出对应索引。
@@ -588,7 +645,16 @@ elementAddr = firtstElementAddr + elementLength * elementIndex
 === "C#"
 
     ```csharp title="array.cs"
-    
+    /* 在数组中查找指定元素 */
+    int Find(int[] nums, int target)
+    {
+        for (int i = 0; i < nums.Length; i++)
+        {
+            if (nums[i] == target)
+                return i;
+        }
+        return -1;
+    }
     ```
 
 ## 数组典型应用

docs/chapter_tree/binary_search_tree.md

@@ -132,7 +132,22 @@ comments: true
 === "TypeScript"
 
     ```typescript title="binary_search_tree.ts"
-
+    /* 查找结点 */
+    function search(num: number): TreeNode | null {
+        let cur = root;
+        // 循环查找，越过叶结点后跳出
+        while (cur !== null) {
+            if (cur.val < num) {
+                cur = cur.right; // 目标结点在 root 的右子树中
+            } else if (cur.val > num) {
+                cur = cur.left; // 目标结点在 root 的左子树中
+            } else {
+                break; // 找到目标结点，跳出循环
+            }
+        }
+        // 返回目标结点
+        return cur;
+    }
     ```
 
 === "C"
@@ -280,7 +295,35 @@ comments: true
 === "TypeScript"
 
     ```typescript title="binary_search_tree.ts"
-
+    /* 插入结点 */
+    function insert(num: number): TreeNode | null {
+        // 若树为空，直接提前返回
+        if (root === null) {
+            return null;
+        }
+        let cur = root,
+            pre: TreeNode | null = null;
+        // 循环查找，越过叶结点后跳出
+        while (cur !== null) {
+            if (cur.val === num) {
+                return null; // 找到重复结点，直接返回
+            }
+            pre = cur;
+            if (cur.val < num) {
+                cur = cur.right as TreeNode; // 插入位置在 root 的右子树中
+            } else {
+                cur = cur.left as TreeNode; // 插入位置在 root 的左子树中
+            }
+        }
+        // 插入结点 val
+        let node = new TreeNode(num);
+        if (pre!.val < num) {
+            pre!.right = node;
+        } else {
+            pre!.left = node;
+        }
+        return node;
+    }
     ```
 
 === "C"
@@ -547,7 +590,54 @@ comments: true
 === "TypeScript"
 
     ```typescript title="binary_search_tree.ts"
-
+    /* 删除结点 */
+    function remove(num: number): TreeNode | null {
+        // 若树为空，直接提前返回
+        if (root === null) {
+            return null;
+        }
+        let cur = root,
+            pre: TreeNode | null = null;
+        // 循环查找，越过叶结点后跳出
+        while (cur !== null) {
+            // 找到待删除结点，跳出循环
+            if (cur.val === num) {
+                break;
+            }
+            pre = cur;
+            if (cur.val < num) {
+                cur = cur.right as TreeNode; // 待删除结点在 root 的右子树中
+            } else {
+                cur = cur.left as TreeNode; // 待删除结点在 root 的左子树中
+            }
+        }
+        // 若无待删除结点，则直接返回
+        if (cur === null) {
+            return null;
+        }
+        // 子结点数量 = 0 or 1
+        if (cur.left === null || cur.right === null) {
+            // 当子结点数量 = 0 / 1 时， child = null / 该子结点
+            let child = cur.left !== null ? cur.left : cur.right;
+            // 删除结点 cur
+            if (pre!.left === cur) {
+                pre!.left = child;
+            } else {
+                pre!.right = child;
+            }
+        }
+        // 子结点数量 = 2
+        else {
+            // 获取中序遍历中 cur 的下一个结点
+            let next = min(cur.right);
+            let tmp = next!.val;
+            // 递归删除结点 nex
+            remove(next!.val);
+            // 将 nex 的值复制给 cur
+            cur.val = tmp;
+        }
+        return cur;
+    }
     ```
 
 === "C"

docs/chapter_tree/binary_tree.md

@@ -74,7 +74,18 @@ comments: true
 === "TypeScript"
 
     ```typescript title=""
+    /* 链表结点类 */
+    class TreeNode {
+        val: number;
+        left: TreeNode | null;
+        right: TreeNode | null;
 
+        constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
+            this.val = val === undefined ? 0 : val; // 结点值
+            this.left = left === undefined ? null : left; // 左子结点指针
+            this.right = right === undefined ? null : right; // 右子结点指针
+        }
+    }
     ```
 
 === "C"
@@ -215,7 +226,18 @@ comments: true
 === "TypeScript"
 
     ```typescript title="binary_tree.ts"
-
+    /* 初始化二叉树 */
+    // 初始化结点
+    let n1 = new TreeNode(1),
+        n2 = new TreeNode(2),
+        n3 = new TreeNode(3),
+        n4 = new TreeNode(4),
+        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"
@@ -273,7 +295,6 @@ comments: true
     p := NewTreeNode(0)
     n1.Left = p
     p.Left = n2
-
     // 删除结点 P
     n1.Left = n2
     ```
@@ -286,7 +307,6 @@ comments: true
     // 在 n1 -> n2 中间插入结点 P
     n1.left = P;
     P.left = n2;
-
     // 删除结点 P
     n1.left = n2;
     ```
@@ -294,7 +314,13 @@ comments: true
 === "TypeScript"
 
     ```typescript title="binary_tree.ts"
-
+    /* 插入与删除结点 */
+    const P = new TreeNode(0);
+    // 在 n1 -> n2 中间插入结点 P
+    n1.left = P;
+    P.left = n2;
+    // 删除结点 P
+    n1.left = n2;
     ```
 
 === "C"
@@ -423,7 +449,6 @@ comments: true
                 queue.push(node.left);    // 左子结点入队
             if (node.right)
                 queue.push(node.right);   // 右子结点入队
-            
         }
         return list;
     }
@@ -432,7 +457,24 @@ comments: true
 === "TypeScript"
 
     ```typescript title="binary_tree_bfs.ts"
-
+    /* 层序遍历 */
+    function hierOrder(root: TreeNode | null): number[] {
+        // 初始化队列，加入根结点
+        const queue = [root];
+        // 初始化一个列表，用于保存遍历序列
+        const list: number[] = [];
+        while (queue.length) {
+            let node = queue.shift() as TreeNode; // 队列出队
+            list.push(node.val); // 保存结点
+            if (node.left) {
+                queue.push(node.left); // 左子结点入队
+            }
+            if (node.right) {
+                queue.push(node.right); // 右子结点入队
+            }
+        }
+        return list;
+    }
     ```
 
 === "C"
@@ -606,7 +648,38 @@ comments: true
 === "TypeScript"
 
     ```typescript title="binary_tree_dfs.ts"
+    /* 前序遍历 */
+    function preOrder(root: TreeNode | null): void {
+        if (root === null) {
+            return;
+        }
+        // 访问优先级：根结点 -> 左子树 -> 右子树
+        list.push(root.val);
+        preOrder(root.left);
+        preOrder(root.right);
+    }
 
+    /* 中序遍历 */
+    function inOrder(root: TreeNode | null): void {
+        if (root === null) {
+            return;
+        }
+        // 访问优先级：左子树 -> 根结点 -> 右子树
+        inOrder(root.left);
+        list.push(root.val);
+        inOrder(root.right);
+    }
+
+    /* 后序遍历 */
+    function postOrder(root: TreeNode | null): void {
+        if (root === null) {
+            return;
+        }
+        // 访问优先级：左子树 -> 右子树 -> 根结点
+        postOrder(root.left);
+        postOrder(root.right);
+        list.push(root.val);
+    }
     ```
 
 === "C"

mkdocs.yml

@@ -33,6 +33,7 @@ theme:
     # - navigation.tabs
     # - navigation.tabs.sticky
     # - navigation.top
+    - navigation.footer
     - navigation.tracking
     - search.highlight
     - search.share