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tianqing.liang
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‎21-Hash-Table/AVLTree.dart

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import 'dart:math';
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import 'FileOperator.dart';
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/**
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* AVL树
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* 第一个自平衡的树
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*
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* 添加，删除
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* LL,RR,RL,LR
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*
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* 平衡二叉树
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* 每个节点的左右子树高度相差1
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*/
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class AVLTree<K extends Comparable<K>, V> {
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_Node? root;
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int? size;
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AVLTree() {
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root = null;
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size = 0;
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}
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@override
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add(key, value) {
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root = _addNode(root, key, value);
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}
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_Node? _addNode(_Node? node, K key, V value) {
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if (node == null) {
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size = size! + 1;
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return new _Node(key, value);
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}
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if (key.compareTo(node._key) < 0) {
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node.left = _addNode(node.left, key, value);
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} else if (key.compareTo(node._key) > 0) {
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node.right = _addNode(node.right, key, value);
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} else {
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// key.compareTo(node.key) == 0
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node._value = value;
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}
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//更新height
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node.height =
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1 + [_getHeight(node.left), _getHeight(node.right)].reduce(max);
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// 计算平衡因子
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int balanceFactor = getBalanceFactor(node);
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if (balanceFactor > 1 && getBalanceFactor(node.left) >= 0) {
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return _rightRotate(node);
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}
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//
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if (balanceFactor < -1 && getBalanceFactor(node.right) <= 0) {
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return _leftRotate(node);
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}
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if (balanceFactor > 1 && getBalanceFactor(node.left) < 0) {
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node.left = _leftRotate(node.left!);
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return _rightRotate(node);
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}
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if (balanceFactor < -1 && getBalanceFactor(node.right) > 0) {
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node.right = _rightRotate(node.right!);
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return _leftRotate(node);
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}
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return node;
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}
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// 对节点y进行向右旋转操作，返回旋转后新的根节点x
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// y x
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// / \ / \
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// x T4 向右旋转 (y) z y
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// / \ - - - - - - - -> / \ / \
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// z T3 T1 T2 T3 T4
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// / \
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// T1 T2
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_Node? _rightRotate(_Node y) {
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_Node? x = y.left;
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_Node? T3 = x?.right;
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// 向右旋转过程
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x?.right = y;
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y.left = T3;
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// 更新height
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y.height = [_getHeight(y.left), _getHeight(y.right)].reduce(max) + 1;
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x?.height = [_getHeight(x.left), _getHeight(x.right)].reduce(max) + 1;
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return x;
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}
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// 对节点y进行向左旋转操作，返回旋转后新的根节点x
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// y x
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// / \ / \
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// T1 x 向左旋转 (y) y z
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// / \ - - - - - - - -> / \ / \
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// T2 z T1 T2 T3 T4
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// / \
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// T3 T4
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_Node? _leftRotate(_Node y) {
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_Node? x = y.right;
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_Node? T2 = x?.left;
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// 向左旋转过程
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x?.left = y;
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y.right = T2;
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// 更新height
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y.height = [_getHeight(y.left), _getHeight(y.right)].reduce(max) + 1;
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x?.height = [_getHeight(x.left), _getHeight(x.right)].reduce(max) + 1;
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return x;
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}
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// 判断该二叉树是否是一棵平衡二叉树
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bool isBalanced() {
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return _isBalancedDetail(root);
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}
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// 判断以Node为根的二叉树是否是一棵平衡二叉树，递归算法
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bool _isBalancedDetail(_Node? node) {
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if (node == null) return true;
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int balanceFactor = getBalanceFactor(node);
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if (balanceFactor.abs() > 1) return false;
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return _isBalancedDetail(node.left) && _isBalancedDetail(node.right);
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}
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//获得节点node的平衡因子
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int getBalanceFactor(_Node? node) {
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if (node == null) {
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return 0;
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}
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return _getHeight(node.left) - _getHeight(node.right);
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}
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// 判断该二叉树是否是一棵二分搜索树
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bool isBST() {
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List keys = List.empty(growable: true);
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_inOrder(root, keys);
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for (int i = 1; i < keys.length; i++) {
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if (keys[i - 1].compareTo(keys[i]) > 0) {
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return false;
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}
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}
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return true;
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}
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_inOrder(_Node? node, List? keys) {
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if (node == null) return;
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_inOrder(node.left, keys);
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keys!.add(node._key);
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_inOrder(node.right, keys);
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}
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_Node? _getNode(_Node? node, K key) {
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if (node == null) {
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return null;
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}
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if (key.compareTo(node._key) == 0) {
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return node;
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} else if (key.compareTo(node._key) < 0) {
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return _getNode(node.left, key);
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} else {
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// if(key.compareTo(node.key) > 0)
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return _getNode(node.right, key);
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}
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}
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@override
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bool contains(key) {
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return _getNode(root, key) != null;
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}
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@override
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get(key) {
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_Node? node = _getNode(root, key);
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return node == null ? null : node._value;
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}
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@override
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int? getSize() {
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return size;
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}
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@override
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bool isEmpty() {
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return size == 0;
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}
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// 获得节点node的高度
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int _getHeight(_Node? node) {
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if (node == null) return 0;
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return node.height;
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}
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@override
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remove(key) {
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_Node? node = _getNode(root, key);
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if (node != null) {
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root = _removeNode(root!, key);
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return node._value;
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}
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return null;
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}
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_Node? _removeNode(_Node node, K key) {
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if (node == null) {
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return null;
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}
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_Node? retNode;
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if (key.compareTo(node._key) < 0) {
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node.left = _removeNode(node.left!, key);
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// return node;
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retNode = node;
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} else if (key.compareTo(node._key) > 0) {
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node.right = _removeNode(node.right!, key);
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// return node;
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retNode = node;
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} else {
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// 待删除节点左子树为空的情况
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if (node.left == null) {
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_Node? rightNode = node.right;
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node.right = null;
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size = size! - 1;
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// return rightNode;
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retNode = rightNode;
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}
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// 待删除节点右子树为空的情况
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if (node.right == null) {
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_Node? leftNode = node.left;
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node.left = null;
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size = size! - 1;
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// return leftNode;
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retNode = leftNode;
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}
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// 待删除节点左右子树均不为空的情况
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// 找到比待删除节点大的最小节点, 即待删除节点右子树的最小节点
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// 用这个节点顶替待删除节点的位置
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_Node successor = _minimum(node.right!);
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//w维持平衡性操作，不再执行removemin
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successor.right = _removeNode(node.right!, successor._key);
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successor.left = node.left;
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node.left = node.right = null;
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// return successor;
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retNode = successor;
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}
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if (retNode == null) {
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return null;
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}
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// 更新height
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retNode.height =
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1 + [_getHeight(retNode.left), _getHeight(retNode.right)].reduce(max);
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// 计算平衡因子
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int balanceFactor = getBalanceFactor(retNode);
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// 平衡维护
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// LL
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if (balanceFactor > 1 && getBalanceFactor(retNode.left) >= 0)
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return _rightRotate(retNode);
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// RR
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if (balanceFactor < -1 && getBalanceFactor(retNode.right) <= 0)
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return _leftRotate(retNode);
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// LR
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if (balanceFactor > 1 && getBalanceFactor(retNode.left) < 0) {
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retNode.left = _leftRotate(retNode.left!);
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return _rightRotate(retNode);
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}
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// RL
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if (balanceFactor < -1 && getBalanceFactor(retNode.right) > 0) {
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retNode.right = _rightRotate(retNode.right!);
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return _leftRotate(retNode);
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}
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return retNode;
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}
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// 删除掉以node为根的二分搜索树中的最小节点
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// 返回删除节点后新的二分搜索树的根
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_Node _removeMin(_Node node) {
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if (node.left == null) {
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_Node? rightNode = node.right;
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node.right = null;
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size = size! - 1;
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return rightNode!;
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}
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node.left = _removeMin(node.left!);
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return node;
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}
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// 返回以node为根的二分搜索树的最小值所在的节点
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_Node _minimum(_Node node) {
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if (node.left == null) {
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return node;
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}
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return _minimum(node.left!);
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}
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@override
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set(key, newValue) {
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_Node? node = _getNode(root, key);
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if (node == null) {
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throw new Exception(" $key + doesn't exist!");
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}
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node._value = newValue;
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}
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}
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class _Node<K, V> {
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K? _key;
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V? _value;
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_Node? left, right;
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int height = 1;
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_Node(K key, V value) {
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this._key = key;
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this._value = value;
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left = null;
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right = null;
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}
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}
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void main() async {
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List result = await FileOperator.getFileString('text2.txt');
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AVLTree<String, int> map = AVLTree();
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for (String word in result) {
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if (map.contains(word))
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map.set(word, map.get(word) + 1);
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else
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map.add(word, 1);
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}
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print("Total different words: ${map.getSize()}");
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print("Frequency of PRIDE: ${map.get("pride")}");
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print("Frequency of PREJUDICE: ${map.get("prejudice")}");
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print("is BST : ${map.isBST()}");
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print("is Balanced : ${map.isBalanced()}");
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}

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