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Add TypeScript code and docs to AVL tree and the coding style for Typ…
…escript and JavaScript (#342) * Add TypeScript code and docs to AVL tree and update JavaScript style * Update the coding style for Typescript and JavaScript
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,228 @@ | ||
| /** | ||
| * File: avl_tree.ts | ||
| * Created Time: 2023-02-06 | ||
| * Author: Justin (xiefahit@gmail.com) | ||
| */ | ||
|
|
||
| import { TreeNode } from "../module/TreeNode"; | ||
| import { printTree } from "../module/PrintUtil"; | ||
|
|
||
| /* AVL 树*/ | ||
| class AVLTree { | ||
| root: TreeNode; | ||
| /*构造函数*/ | ||
| constructor() { | ||
| this.root = null; //根节点 | ||
| } | ||
|
|
||
| /* 获取结点高度 */ | ||
| height(node: TreeNode): number { | ||
| // 空结点高度为 -1 ，叶结点高度为 0 | ||
| return node === null ? -1 : node.height; | ||
| } | ||
|
|
||
| /* 更新结点高度 */ | ||
| updateHeight(node: TreeNode): void { | ||
| // 结点高度等于最高子树高度 + 1 | ||
| node.height = Math.max(this.height(node.left), this.height(node.right)) + 1; | ||
| } | ||
|
|
||
| /* 获取平衡因子 */ | ||
| balanceFactor(node: TreeNode): number { | ||
| // 空结点平衡因子为 0 | ||
| if (node === null) return 0; | ||
| // 结点平衡因子 = 左子树高度 - 右子树高度 | ||
| return this.height(node.left) - this.height(node.right); | ||
| } | ||
|
|
||
| /* 右旋操作 */ | ||
| rightRotate(node: TreeNode): TreeNode { | ||
| const child = node.left; | ||
| const grandChild = child.right; | ||
| // 以 child 为原点，将 node 向右旋转 | ||
| child.right = node; | ||
| node.left = grandChild; | ||
| // 更新结点高度 | ||
| this.updateHeight(node); | ||
| this.updateHeight(child); | ||
| // 返回旋转后子树的根节点 | ||
| return child; | ||
| } | ||
|
|
||
| /* 左旋操作 */ | ||
| leftRotate(node: TreeNode): TreeNode { | ||
| const child = node.right; | ||
| const grandChild = child.left; | ||
| // 以 child 为原点，将 node 向左旋转 | ||
| child.left = node; | ||
| node.right = grandChild; | ||
| // 更新结点高度 | ||
| this.updateHeight(node); | ||
| this.updateHeight(child); | ||
| // 返回旋转后子树的根节点 | ||
| return child; | ||
| } | ||
|
|
||
| /* 执行旋转操作，使该子树重新恢复平衡 */ | ||
| rotate(node: TreeNode): TreeNode { | ||
| // 获取结点 node 的平衡因子 | ||
| const balanceFactor = this.balanceFactor(node); | ||
| // 左偏树 | ||
| if (balanceFactor > 1) { | ||
| if (this.balanceFactor(node.left) >= 0) { | ||
| // 右旋 | ||
| return this.rightRotate(node); | ||
| } else { | ||
| // 先左旋后右旋 | ||
| node.left = this.leftRotate(node.left); | ||
| return this.rightRotate(node); | ||
| } | ||
| } | ||
| // 右偏树 | ||
| if (balanceFactor < -1) { | ||
| if (this.balanceFactor(node.right) <= 0) { | ||
| // 左旋 | ||
| return this.leftRotate(node); | ||
| } else { | ||
| // 先右旋后左旋 | ||
| node.right = this.rightRotate(node.right); | ||
| return this.leftRotate(node); | ||
| } | ||
| } | ||
| // 平衡树，无需旋转，直接返回 | ||
| return node; | ||
| } | ||
|
|
||
| /* 插入结点 */ | ||
| insert(val: number): TreeNode { | ||
| this.root = this.insertHelper(this.root, val); | ||
| return this.root; | ||
| } | ||
|
|
||
| /* 递归插入结点（辅助函数） */ | ||
| insertHelper(node: TreeNode, val: number): TreeNode { | ||
| if (node === null) return new TreeNode(val); | ||
| /* 1. 查找插入位置，并插入结点 */ | ||
| if (val < node.val) { | ||
| node.left = this.insertHelper(node.left, val); | ||
| } else if (val > node.val) { | ||
| node.right = this.insertHelper(node.right, val); | ||
| } else { | ||
| return node; // 重复结点不插入，直接返回 | ||
| } | ||
| this.updateHeight(node); // 更新结点高度 | ||
| /* 2. 执行旋转操作，使该子树重新恢复平衡 */ | ||
| node = this.rotate(node); | ||
| // 返回子树的根节点 | ||
| return node; | ||
| } | ||
|
|
||
| /* 删除结点 */ | ||
| remove(val: number): TreeNode { | ||
| this.root = this.removeHelper(this.root, val); | ||
| return this.root; | ||
| } | ||
|
|
||
| /* 递归删除结点（辅助函数） */ | ||
| removeHelper(node: TreeNode, val: number): TreeNode { | ||
| if (node === null) return null; | ||
| /* 1. 查找结点，并删除之 */ | ||
| if (val < node.val) { | ||
| node.left = this.removeHelper(node.left, val); | ||
| } else if (val > node.val) { | ||
| node.right = this.removeHelper(node.right, val); | ||
| } else { | ||
| if (node.left === null || node.right === null) { | ||
| const child = node.left !== null ? node.left : node.right; | ||
| // 子结点数量 = 0 ，直接删除 node 并返回 | ||
| if (child === null) { | ||
| return null; | ||
| } else { | ||
| // 子结点数量 = 1 ，直接删除 node | ||
| node = child; | ||
| } | ||
| } else { | ||
| // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点 | ||
| const temp = this.getInOrderNext(node.right); | ||
| node.right = this.removeHelper(node.right, temp.val); | ||
| node.val = temp.val; | ||
| } | ||
| } | ||
| this.updateHeight(node); // 更新结点高度 | ||
| /* 2. 执行旋转操作，使该子树重新恢复平衡 */ | ||
| node = this.rotate(node); | ||
| // 返回子树的根节点 | ||
| return node; | ||
| } | ||
|
|
||
| /* 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） */ | ||
| getInOrderNext(node: TreeNode): TreeNode { | ||
| if (node === null) return node; | ||
| // 循环访问左子结点，直到叶结点时为最小结点，跳出 | ||
| while (node.left !== null) { | ||
| node = node.left; | ||
| } | ||
| return node; | ||
| } | ||
|
|
||
| /* 查找结点 */ | ||
| search(val: number): TreeNode { | ||
| let cur = this.root; | ||
| // 循环查找，越过叶结点后跳出 | ||
| while (cur !== null) { | ||
| if (cur.val < val) { | ||
| // 目标结点在 cur 的右子树中 | ||
| cur = cur.right; | ||
| } else if (cur.val > val) { | ||
| // 目标结点在 cur 的左子树中 | ||
| cur = cur.left; | ||
| } else { | ||
| // 找到目标结点，跳出循环 | ||
| break; | ||
| } | ||
| } | ||
| // 返回目标结点 | ||
| return cur; | ||
| } | ||
| } | ||
|
|
||
| function testInsert(tree: AVLTree, val: number): void { | ||
| tree.insert(val); | ||
| console.log("\n插入结点 " + val + " 后，AVL 树为"); | ||
| printTree(tree.root); | ||
| } | ||
|
|
||
| function testRemove(tree: AVLTree, val: number): void { | ||
| tree.remove(val); | ||
| console.log("\n删除结点 " + val + " 后，AVL 树为"); | ||
| printTree(tree.root); | ||
| } | ||
|
|
||
| /* Driver Code */ | ||
| /* 初始化空 AVL 树 */ | ||
| const avlTree = new AVLTree(); | ||
| /* 插入结点 */ | ||
| // 请关注插入结点后，AVL 树是如何保持平衡的 | ||
| testInsert(avlTree, 1); | ||
| testInsert(avlTree, 2); | ||
| testInsert(avlTree, 3); | ||
| testInsert(avlTree, 4); | ||
| testInsert(avlTree, 5); | ||
| testInsert(avlTree, 8); | ||
| testInsert(avlTree, 7); | ||
| testInsert(avlTree, 9); | ||
| testInsert(avlTree, 10); | ||
| testInsert(avlTree, 6); | ||
|
|
||
| /* 插入重复结点 */ | ||
| testInsert(avlTree, 7); | ||
|
|
||
| /* 删除结点 */ | ||
| // 请关注删除结点后，AVL 树是如何保持平衡的 | ||
| testRemove(avlTree, 8); // 删除度为 0 的结点 | ||
| testRemove(avlTree, 5); // 删除度为 1 的结点 | ||
| testRemove(avlTree, 4); // 删除度为 2 的结点 | ||
|
|
||
| /* 查询结点 */ | ||
| const node = avlTree.search(7); | ||
| console.log("\n查找到的结点对象为", node, "，结点值 = " + node.val); |
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