Merge pull request krahets#113 from justin-tse/master

Add the TypeScript code and docs for Chapter of Tree

codes/typescript/chapter_tree/binary_search_tree.ts

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+/**
+ * File: binary_search_tree.ts
+ * Created Time: 2022-12-14
+ * Author: Justin ([email protected])
+ */
+
+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

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+/**
+ * File: binary_tree.ts
+ * Created Time: 2022-12-13
+ * Author: Justin ([email protected])
+ */
+
+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

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+/**
+ * File: binary_tree_bfs.ts
+ * Created Time: 2022-12-14
+ * Author: Justin ([email protected])
+ */
+
+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

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+/**
+ * File: binary_tree_dfs.ts
+ * Created Time: 2022-12-14
+ * Author: Justin ([email protected])
+ */
+
+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);