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@ -8,159 +8,136 @@ import { TreeNode } from '../modules/TreeNode';
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import { printTree } from '../modules/PrintUtil';
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/* 二叉搜索树 */
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let root: TreeNode | null;
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class BinarySearchTree {
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private root: TreeNode | null;
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function BinarySearchTree(nums: number[]): void {
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nums.sort((a, b) => a - b); // 排序数组
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root = buildTree(nums, 0, nums.length - 1); // 构建二叉搜索树
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/* 构造方法 */
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constructor() {
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// 初始化空树
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this.root = null;
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}
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/* 获取二叉树根节点 */
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function getRoot(): TreeNode | null {
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return root;
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}
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/* 构建二叉搜索树 */
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function buildTree(nums: number[], i: number, j: number): TreeNode | null {
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if (i > j) {
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return null;
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}
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// 将数组中间节点作为根节点
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let mid = Math.floor((i + j) / 2);
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let root = new TreeNode(nums[mid]);
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// 递归建立左子树和右子树
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root.left = buildTree(nums, i, mid - 1);
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root.right = buildTree(nums, mid + 1, j);
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return root;
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getRoot(): TreeNode | null {
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return this.root;
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}
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/* 查找节点 */
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function search(num: number): TreeNode | null {
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let cur = root;
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search(num: number): TreeNode | null {
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let cur = this.root;
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// 循环查找,越过叶节点后跳出
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while (cur !== null) {
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if (cur.val < num) {
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cur = cur.right; // 目标节点在 cur 的右子树中
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} else if (cur.val > num) {
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cur = cur.left; // 目标节点在 cur 的左子树中
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} else {
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break; // 找到目标节点,跳出循环
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}
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// 目标节点在 cur 的右子树中
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if (cur.val < num) cur = cur.right;
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// 目标节点在 cur 的左子树中
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else if (cur.val > num) cur = cur.left;
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// 找到目标节点,跳出循环
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else break;
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}
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// 返回目标节点
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return cur;
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}
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/* 插入节点 */
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function insert(num: number): void {
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insert(num: number): void {
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// 若树为空,则初始化根节点
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if (root === null) {
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root = new TreeNode(num);
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if (this.root === null) {
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this.root = new TreeNode(num);
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return;
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}
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let cur = root,
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let cur: TreeNode | null = this.root,
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pre: TreeNode | null = null;
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// 循环查找,越过叶节点后跳出
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while (cur !== null) {
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if (cur.val === num) {
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return; // 找到重复节点,直接返回
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}
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// 找到重复节点,直接返回
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if (cur.val === num) return;
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pre = cur;
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if (cur.val < num) {
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cur = cur.right as TreeNode; // 插入位置在 cur 的右子树中
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} else {
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cur = cur.left as TreeNode; // 插入位置在 cur 的左子树中
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}
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// 插入位置在 cur 的右子树中
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if (cur.val < num) cur = cur.right;
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// 插入位置在 cur 的左子树中
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else cur = cur.left;
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}
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// 插入节点
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let node = new TreeNode(num);
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if (pre!.val < num) {
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pre!.right = node;
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} else {
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pre!.left = node;
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}
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const node = new TreeNode(num);
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if (pre!.val < num) pre!.right = node;
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else pre!.left = node;
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}
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/* 删除节点 */
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function remove(num: number): void {
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remove(num: number): void {
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// 若树为空,直接提前返回
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if (root === null) {
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return;
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}
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let cur = root,
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if (this.root === null) return;
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let cur: TreeNode | null = this.root,
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pre: TreeNode | null = null;
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// 循环查找,越过叶节点后跳出
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while (cur !== null) {
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// 找到待删除节点,跳出循环
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if (cur.val === num) {
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break;
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}
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if (cur.val === num) break;
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pre = cur;
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if (cur.val < num) {
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cur = cur.right as TreeNode; // 待删除节点在 cur 的右子树中
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} else {
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cur = cur.left as TreeNode; // 待删除节点在 cur 的左子树中
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}
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// 待删除节点在 cur 的右子树中
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if (cur.val < num) cur = cur.right;
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// 待删除节点在 cur 的左子树中
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else cur = cur.left;
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}
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// 若无待删除节点,则直接返回
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if (cur === null) {
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return;
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}
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if (cur === null) return;
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// 子节点数量 = 0 or 1
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if (cur.left === null || cur.right === null) {
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// 当子节点数量 = 0 / 1 时, child = null / 该子节点
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let child = cur.left !== null ? cur.left : cur.right;
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const child: TreeNode | null = cur.left !== null ? cur.left : cur.right;
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// 删除节点 cur
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if (cur != root) {
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if (pre!.left === cur) {
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pre!.left = child;
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} else {
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pre!.right = child;
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}
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if (cur !== this.root) {
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if (pre!.left === cur) pre!.left = child;
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else pre!.right = child;
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} else {
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// 若删除节点为根节点,则重新指定根节点
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root = child;
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this.root = child;
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}
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}
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// 子节点数量 = 2
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else {
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// 获取中序遍历中 cur 的下一个节点
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let tmp = cur.right;
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while (tmp.left !== null) {
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tmp = tmp.left;
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let tmp: TreeNode | null = cur.right;
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while (tmp!.left !== null) {
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tmp = tmp!.left;
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}
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// 递归删除节点 tmp
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remove(tmp!.val);
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this.remove(tmp!.val);
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// 用 tmp 覆盖 cur
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cur.val = tmp.val;
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cur.val = tmp!.val;
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}
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}
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}
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/* Driver Code */
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/* 初始化二叉搜索树 */
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const nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15];
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BinarySearchTree(nums);
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const bst = new BinarySearchTree();
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// 请注意,不同的插入顺序会生成不同的二叉树,该序列可以生成一个完美二叉树
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const nums = [8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15];
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for (const num of nums) {
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bst.insert(num);
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}
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console.log('\n初始化的二叉树为\n');
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printTree(getRoot());
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printTree(bst.getRoot());
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/* 查找节点 */
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let node = search(7);
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console.log('\n查找到的节点对象为 ' + node + ',节点值 = ' + node!.val);
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const node = bst.search(7);
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console.log('\n查找到的节点对象为 ' + node + ',节点值 = ' + (node ? node.val : 'null'));
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/* 插入节点 */
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insert(16);
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bst.insert(16);
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console.log('\n插入节点 16 后,二叉树为\n');
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printTree(getRoot());
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printTree(bst.getRoot());
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/* 删除节点 */
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remove(1);
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bst.remove(1);
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console.log('\n删除节点 1 后,二叉树为\n');
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printTree(getRoot());
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remove(2);
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printTree(bst.getRoot());
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bst.remove(2);
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console.log('\n删除节点 2 后,二叉树为\n');
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printTree(getRoot());
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remove(4);
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printTree(bst.getRoot());
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bst.remove(4);
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console.log('\n删除节点 4 后,二叉树为\n');
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printTree(getRoot());
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printTree(bst.getRoot());
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export {};
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