2023-02-05 14:15:05 +08:00
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/**
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2023-02-07 01:21:58 +08:00
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* File: avl_tree.js
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2023-02-05 14:15:05 +08:00
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* Created Time: 2023-02-05
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* Author: what-is-me (whatisme@outlook.jp)
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*/
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2023-04-17 21:58:11 +08:00
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const { TreeNode } = require('../modules/TreeNode');
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const { printTree } = require('../modules/PrintUtil');
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/* AVL 树*/
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class AVLTree {
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/* 构造方法 */
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constructor() {
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this.root = null; //根节点
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}
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/* 获取节点高度 */
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height(node) {
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// 空节点高度为 -1 ,叶节点高度为 0
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return node === null ? -1 : node.height;
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}
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/* 更新节点高度 */
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#updateHeight(node) {
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// 节点高度等于最高子树高度 + 1
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node.height =
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Math.max(this.height(node.left), this.height(node.right)) + 1;
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}
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/* 获取平衡因子 */
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balanceFactor(node) {
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// 空节点平衡因子为 0
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if (node === null) return 0;
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// 节点平衡因子 = 左子树高度 - 右子树高度
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return this.height(node.left) - this.height(node.right);
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}
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/* 右旋操作 */
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#rightRotate(node) {
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const child = node.left;
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const grandChild = child.right;
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// 以 child 为原点,将 node 向右旋转
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child.right = node;
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node.left = grandChild;
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// 更新节点高度
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this.#updateHeight(node);
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this.#updateHeight(child);
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// 返回旋转后子树的根节点
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return child;
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}
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/* 左旋操作 */
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#leftRotate(node) {
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const child = node.right;
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const grandChild = child.left;
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// 以 child 为原点,将 node 向左旋转
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child.left = node;
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node.right = grandChild;
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// 更新节点高度
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this.#updateHeight(node);
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this.#updateHeight(child);
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// 返回旋转后子树的根节点
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return child;
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}
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/* 执行旋转操作,使该子树重新恢复平衡 */
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#rotate(node) {
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// 获取节点 node 的平衡因子
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const balanceFactor = this.balanceFactor(node);
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// 左偏树
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if (balanceFactor > 1) {
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if (this.balanceFactor(node.left) >= 0) {
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// 右旋
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return this.#rightRotate(node);
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} else {
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// 先左旋后右旋
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node.left = this.#leftRotate(node.left);
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return this.#rightRotate(node);
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}
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}
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// 右偏树
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if (balanceFactor < -1) {
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if (this.balanceFactor(node.right) <= 0) {
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// 左旋
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return this.#leftRotate(node);
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} else {
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// 先右旋后左旋
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node.right = this.#rightRotate(node.right);
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return this.#leftRotate(node);
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}
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}
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// 平衡树,无须旋转,直接返回
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return node;
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}
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/* 插入节点 */
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insert(val) {
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this.root = this.#insertHelper(this.root, val);
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}
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/* 递归插入节点(辅助方法) */
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#insertHelper(node, val) {
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if (node === null) return new TreeNode(val);
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/* 1. 查找插入位置,并插入节点 */
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if (val < node.val) node.left = this.#insertHelper(node.left, val);
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else if (val > node.val)
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node.right = this.#insertHelper(node.right, val);
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else return node; // 重复节点不插入,直接返回
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this.#updateHeight(node); // 更新节点高度
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/* 2. 执行旋转操作,使该子树重新恢复平衡 */
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node = this.#rotate(node);
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// 返回子树的根节点
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return node;
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}
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/* 删除节点 */
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remove(val) {
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this.root = this.#removeHelper(this.root, val);
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}
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/* 递归删除节点(辅助方法) */
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#removeHelper(node, val) {
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if (node === null) return null;
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/* 1. 查找节点,并删除之 */
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if (val < node.val) node.left = this.#removeHelper(node.left, val);
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else if (val > node.val)
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node.right = this.#removeHelper(node.right, val);
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else {
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if (node.left === null || node.right === null) {
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const child = node.left !== null ? node.left : node.right;
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// 子节点数量 = 0 ,直接删除 node 并返回
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if (child === null) return null;
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// 子节点数量 = 1 ,直接删除 node
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else node = child;
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} else {
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// 子节点数量 = 2 ,则将中序遍历的下个节点删除,并用该节点替换当前节点
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let temp = node.right;
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while (temp.left !== null) {
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temp = temp.left;
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}
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node.right = this.#removeHelper(node.right, temp.val);
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node.val = temp.val;
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}
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}
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this.#updateHeight(node); // 更新节点高度
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/* 2. 执行旋转操作,使该子树重新恢复平衡 */
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node = this.#rotate(node);
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// 返回子树的根节点
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return node;
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}
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/* 查找节点 */
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search(val) {
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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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// 目标节点在 cur 的右子树中
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if (cur.val < val) 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 > val) 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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}
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function testInsert(tree, val) {
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tree.insert(val);
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console.log('\n插入节点 ' + val + ' 后,AVL 树为');
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printTree(tree.root);
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}
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function testRemove(tree, val) {
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tree.remove(val);
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console.log('\n删除节点 ' + val + ' 后,AVL 树为');
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printTree(tree.root);
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}
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/* Driver Code */
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/* 初始化空 AVL 树 */
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const avlTree = new AVLTree();
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/* 插入节点 */
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// 请关注插入节点后,AVL 树是如何保持平衡的
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testInsert(avlTree, 1);
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testInsert(avlTree, 2);
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testInsert(avlTree, 3);
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testInsert(avlTree, 4);
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testInsert(avlTree, 5);
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testInsert(avlTree, 8);
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testInsert(avlTree, 7);
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testInsert(avlTree, 9);
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testInsert(avlTree, 10);
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testInsert(avlTree, 6);
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/* 插入重复节点 */
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testInsert(avlTree, 7);
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/* 删除节点 */
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// 请关注删除节点后,AVL 树是如何保持平衡的
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testRemove(avlTree, 8); // 删除度为 0 的节点
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testRemove(avlTree, 5); // 删除度为 1 的节点
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testRemove(avlTree, 4); // 删除度为 2 的节点
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/* 查询节点 */
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const node = avlTree.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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