算法模板新增 typescript 版本代码

Author: Jerry-306

problems/算法模板.md

@@ -394,7 +394,7 @@ var postorder = function (root, list) {
 ```javascript
 var preorderTraversal = function (root) {
     let res = [];
-    if (root === null) return rs;
+    if (root === null) return res;
     let stack = [root],
         cur = null;
     while (stack.length) {
@@ -536,6 +536,269 @@ function backtracking(参数) {
     }
 ```
 
+TypeScript：
+
+## 二分查找法
+
+使用左闭右闭区间
+
+```typescript
+var search = function (nums: number[], target: number): number {
+    let left: number = 0, right: number = nums.length - 1;
+    // 使用左闭右闭区间
+    while (left <= right) {
+        let mid: number = left + Math.floor((right - left)/2);
+        if (nums[mid] > target) {
+            right = mid - 1;  // 去左面闭区间寻找
+        } else if (nums[mid] < target) {
+            left = mid + 1;   // 去右面闭区间寻找
+        } else {
+            return mid;
+        }
+    }
+    return -1;
+};
+```
+
+使用左闭右开区间
+
+```typescript
+var search = function (nums: number[], target: number): number {
+    let left: number = 0, right: number = nums.length;
+    // 使用左闭右开区间 [left, right)
+    while (left < right) {
+        let mid: number = left + Math.floor((right - left)/2);
+        if (nums[mid] > target) {
+            right = mid;  // 去左面闭区间寻找
+        } else if (nums[mid] < target) {
+            left = mid + 1;   // 去右面闭区间寻找
+        } else {
+            return mid;
+        }
+    }
+    return -1;
+};
+```
+
+## KMP
+
+```typescript
+var kmp = function (next: number[], s: number): void {
+    next[0] = -1;
+    let j: number = -1;
+    for(let i: number = 1; i < s.length; i++){
+        while (j >= 0 && s[i] !== s[j + 1]) {
+            j = next[j];
+        }
+        if (s[i] === s[j + 1]) {
+            j++;
+        }
+        next[i] = j;
+    }
+}
+```
+
+## 二叉树
+
+### 深度优先遍历（递归）
+
+二叉树节点定义：
+
+```typescript
+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)
+        this.left = (left===undefined ? null : left)
+        this.right = (right===undefined ? null : right)
+    }
+}
+```
+
+前序遍历（中左右）：
+
+```typescript
+var preorder = function (root: TreeNode | null, list: number[]): void {
+    if (root === null) return;
+    list.push(root.val);        // 中
+    preorder(root.left, list);  // 左
+    preorder(root.right, list); // 右
+}
+```
+
+中序遍历（左中右）：
+
+```typescript
+var inorder = function (root: TreeNode | null, list: number[]): void {
+    if (root === null) return;
+    inorder(root.left, list);  // 左
+    list.push(root.val);        // 中
+    inorder(root.right, list); // 右
+}
+```
+
+后序遍历（左右中）：
+
+```typescript
+var postorder = function (root: TreeNode | null, list: number[]): void {
+    if (root === null) return;
+    postorder(root.left, list);  // 左
+    postorder(root.right, list); // 右
+    list.push(root.val);        // 中
+}
+```
+
+### 深度优先遍历（迭代）
+
+前序遍历（中左右）：
+
+```typescript
+var preorderTraversal = function (root: TreeNode | null): number[] {
+    let res: number[] = [];
+    if (root === null) return res;
+    let stack: TreeNode[] = [root],
+        cur: TreeNode | null = null;
+    while (stack.length) {
+        cur = stack.pop();
+        res.push(cur.val);
+        cur.right && stack.push(cur.right);
+        cur.left && stack.push(cur.left);
+    }
+    return res;
+};
+```
+
+中序遍历（左中右）：
+
+```typescript
+var inorderTraversal = function (root: TreeNode | null): number[] {
+    let res: number[] = [];
+    if (root === null) return res;
+    let stack: TreeNode[] = [];
+    let cur: TreeNode | null = root;
+    while (stack.length ！== 0 || cur !== null) {
+        if (cur !== null) {
+            stack.push(cur);
+            cur = cur.left;
+        } else {
+            cur = stack.pop();
+            res.push(cur.val);
+            cur = cur.right;
+        }
+    }
+    return res;
+};
+```
+
+后序遍历（左右中）：
+
+```typescript
+var postorderTraversal = function (root: TreeNode | null): number[] {
+    let res: number[] = [];
+    if (root === null) return res;
+    let stack: TreeNode[] = [root];
+    let cur: TreeNode | null = null;
+    while (stack.length) {
+        cur = stack.pop();
+        res.push(cur.val);
+        cur.left && stack.push(cur.left);
+        cur.right && stack.push(cur.right);
+    }
+    return res.reverse()
+};
+```
+
+### 广度优先遍历（队列）
+
+```typescript
+var levelOrder = function (root: TreeNode | null): number[] {
+    let res: number[] = [];
+    if (root === null) return res;
+    let queue: TreeNode[] = [root];
+    while (queue.length) {
+        let n: number = queue.length;
+        let temp: number[] = [];
+        for (let i: number = 0; i < n; i++) {
+            let node: TreeNode = queue.shift();
+            temp.push(node.val);
+            node.left && queue.push(node.left);
+            node.right && queue.push(node.right);
+        }
+        res.push(temp);
+    }
+    return res;
+};
+```
+
+### 二叉树深度
+
+```typescript
+var getDepth = function (node: TreNode | null): number {
+    if (node === null) return 0;
+    return 1 + Math.max(getDepth(node.left), getDepth(node.right));
+}
+```
+
+### 二叉树节点数量
+
+```typescript
+var countNodes = function (root: TreeNode | null): number {
+    if (root === null) return 0;
+    return 1 + countNodes(root.left) + countNodes(root.right);
+}
+```
+
+## 回溯算法 
+
+```typescript
+function backtracking(参数) {
+    if (终止条件) {
+        存放结果;
+        return;
+    }
+
+    for (选择：本层集合中元素（树中节点孩子的数量就是集合的大小）) {
+        处理节点;
+        backtracking(路径，选择列表); // 递归
+        回溯，撤销处理结果
+    }
+}
+
+```
+
+## 并查集 
+
+```typescript
+    let n: number = 1005; // 根据题意而定 
+    let father: number[] = new Array(n).fill(0);
+
+    // 并查集初始化
+    function init () {
+        for (int i: number = 0; i < n; ++i) {
+            father[i] = i;
+        }
+    }
+    // 并查集里寻根的过程
+    function find (u: number): number {
+        return u === father[u] ? u : father[u] = find(father[u]);
+    }
+    // 将v->u 这条边加入并查集
+    function join(u: number, v: number) {
+        u = find(u);
+        v = find(v);
+        if (u === v) return ;
+        father[v] = u;
+    }
+    // 判断 u 和 v是否找到同一个根
+    function same(u: number, v: number): boolean {
+        u = find(u);
+        v = find(v);
+        return u === v;
+    }
+```
+
 Java：