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AVL Tree.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>AVL(平衡树)</title>
</head>
<body>
<script>
class Node {
constructor(key, value) {
this.key = key;
this.value = value;
this.left = null;
this.right = null;
this.height = 1;
}
}
class AVLTree {
constructor() {
this.root = null;
this.size = 0;
}
add(key, value) {
this.root = this._add(this.root, key, value)
}
_add(node, key, value) {
if (node === null) {
this.size++;
return new Node(key, value)
}
if (value < node.value) {
node.left = this._add(node.left, key, value)
} else if (value > node.value) {
node.right = this._add(node.right, key, value)
} else {
node.key = key;
node.value = value
}
node.height = 1 + Math.max(this.getHeight(node.left), this.getHeight(node.right));
//计算平衡因子
let balanceFactor = this.getBalanceFactor(node);
//平衡维护
//LL
if (balanceFactor > 1 && this.getBalanceFactor(node.left) >= 0) {
return this.rightRotate(node)
}
//RR
if (balanceFactor < -1 && this.getBalanceFactor(node.right) <= 0) {
return this.leftRotate(node)
}
//LR
//region 图示
// y y z
// / \ / \ / \
// x T4 向左旋转 (x) z T4 向右旋转（y） x y
// / \ - - - - - - - -> / \ - - - - - - - -> / \ / \
// T1 z x T3 T1 T2 T3 T4
// / \ / \
// T2 T3 T1 T2
//endregion
if (balanceFactor > 1 && this.getBalanceFactor(node.left) < 0) {
node.left = this.leftRotate(node.left);
return this.rightRotate(node)
}
//RL
//region 图示
// y y z
// / \ / \ / \
// T1 x 向右旋转 (x) T1 z 向右旋转（y） y x
// / \ - - - - - - - -> / \ - - - - - - - -> / \ / \
// z T4 T2 x T1 T2 T3 T4
// / \ / \
// T2 T3 T3 T4
//endregion
if (balanceFactor < -1 && this.getBalanceFactor(node.right) > 0) {
node.right = this.rightRotate(node.right);
return this.leftRotate(node)
}
return node
}
// 对节点y进行向右旋转操作，返回旋转后新的根节点x
// y x
// / \ / \
// x T4 向右旋转 (y) z y
// / \ - - - - - - - -> / \ / \
// z T3 T1 T2 T3 T4
// / \
// T1 T2
rightRotate(y) {
let x = y.left,
T3 = x.right;
x.right = y;
y.left = T3;
y.height = 1 + Math.max(this.getHeight(y.left), this.getHeight(y.right));
x.height = 1 + Math.max(this.getHeight(x.left), this.getHeight(x.right));
return x
}
// 对节点y进行向左旋转操作，返回旋转后新的根节点x
// y x
// / \ / \
// T1 x 向左旋转 (y) y z
// / \ - - - - - - - -> / \ / \
// T2 z T1 T2 T3 T4
// / \
// T3 T4
leftRotate(y) {
let x = y.right,
T2 = x.left;
x.left = y;
y.right = T2;
y.height = 1 + Math.max(this.getHeight(y.left), this.getHeight(y.right));
x.height = 1 + Math.max(this.getHeight(x.left), this.getHeight(x.right));
return x
}
remove(key) {
let node = this.getNode(this.root, key);
if (node) {
this.root = this._remove(this.root, key);
return node.value
}
return null
}
_remove(node, key) {
if (!node) return null;
let retNode;
if (key < node.key) {
node.left = this._remove(node.left, key)
retNode = node
} else if (key > node.key) {
node.right = this._remove(node.right, key)
retNode = node
} else {
if (node.left === null) {
let rightNode = node.right;
node.right = null;
this.size--;
retNode = rightNode
} else if (node.right === null) {
let leftNode = node.left;
node.left = null;
this.size--;
retNode = leftNode;
} else {
let successor = this.minNum(node);
successor.right = this._remove(node.right, successor.key);
successor.left = node.left;
retNode = successor
}
}
if (retNode === null) return null;
retNode.height = 1 + Math.max(this.getHeight(retNode.left), this.getHeight(retNode.right));
//计算平衡因子
let balanceFactor = this.getBalanceFactor(retNode);
//平衡维护
//LL
if (balanceFactor > 1 && this.getBalanceFactor(retNode.left) >= 0) {
return this.rightRotate(retNode)
}
//RR
if (balanceFactor < -1 && this.getBalanceFactor(retNode.right) <= 0) {
return this.leftRotate(retNode)
}
//LR
if (balanceFactor > 1 && this.getBalanceFactor(retNode.left) < 0) {
retNode.left = this.leftRotate(retNode.left);
return this.rightRotate(retNode)
}
//RL
if (balanceFactor < -1 && this.getBalanceFactor(retNode.right) > 0) {
retNode.right = this.rightRotate(retNode.right);
return this.leftRotate(retNode)
}
return retNode
}
isBST() {
let keys = [];
this.inOrder(this.root, keys);
for (let i = 1; i < keys.length; i++) {
if (keys[i - 1] > keys[i]) return false
}
return true
}
contains(key) {
return this.getNode(this.root, key) !== null
}
set(key, val) {
let node = this.getNode(this.root, key);
if (!node) {
throw new Error(`${key} doesn't exist!`)
}
node.value = val
}
//获取节点平衡因子
getBalanceFactor(node) {
if (node === null) return 0;
return this.getHeight(node.left) - this.getHeight(node.right)
}
getHeight(node) {
if (node === null) return 0;
return node.height;
}
getNode(node, key) {
if (!node) return null;
if (key === node.key) {
return node
}
if (node.key < key) {
return this.getNode(node.right, key)
} else {
return this.getNode(node.left, key)
}
}
getSize() {
return this.size
}
isBalanced() {
return this._isBalanced(this.root)
}
_isBalanced(node) {
if (!node) return true;
let balanceFactor = this.getBalanceFactor(node);
if (Math.abs(balanceFactor) > 1) {
return false
}
return this._isBalanced(node.left) && this._isBalanced(node.right)
}
minNum(node) {
if (!node) return null;
while (node) {
if (!node.left) {
return node
}
node = node.left
}
}
inOrder(node, keys) {
if (!node) return null;
let pre;
while (node) {
if (!node.left) {
keys.push(node.key);
node = node.right
} else {
pre = node.left;
while (pre.right && pre.right !== node) {
pre = pre.right
}
if (!pre.right) {
pre.right = node;
node = node.left
} else {
keys.push(node)
node = node.right
}
}
}
}
}
let avl = new AVLTree();
avl.add(12, 12);
avl.add(8, 8);
avl.add(18, 18);
avl.add(5, 5);
avl.add(11, 11);
// // avl.add(7,7); //添加7后需进行右旋转
//RL
// avl.add(14,14);
// avl.add(8,8);
// avl.add(18,18);
// avl.add(5,5);
// avl.add(11,11);
// avl.add(17,17);
// avl.add(10,10);
console.log(avl)
</script>
</body>
</html>