import java.util.ArrayList;
public class AVLTree<K extends Comparable<K>, V> {
private class Node{
public K key;
public V value;
public Node left, right;
public int height;
public Node(K key, V value){
this.key = key;
this.value = value;
left = null;
right = null;
height = 1;
}
}
private Node root;
private int size;
public AVLTree(){
root = null;
size = 0;
}
public int getSize(){
return size;
}
public boolean isEmpty(){
return size == 0;
}
// 判断该二叉树是否是一棵二分搜索树
public boolean isBST() {
ArrayList<K> keys = new ArrayList<>();
inOrder(root, keys);
for(int i = 1; i < keys.size(); ++ i) {
if(keys.get(i - 1).compareTo(keys.get(i)) > 0) {
return false;
}
}
return true;
}
private void inOrder(Node node, ArrayList<K> keys) {
if(node == null) {
return ;
}
inOrder(node.left, keys);
keys.add(node.key);
inOrder(node.right, keys);
}
// 判断该二叉树是否是一棵平衡二叉树
public boolean isBalanced() {
return isBalanced(root);
}
// 判断以node为根的二叉树是否是一棵平衡二叉树, 递归算法
private boolean isBalanced(Node node) {
if(node == null) {
return true;
}
int balanceFactor = getBalanceFactor(node);
if(Math.abs(balanceFactor) > 1) {
return false;
}
return isBalanced(node.left) && isBalanced(node.right);
}
// 获得结点node的高度
private int getHeight(Node node) {
if(node == null) {
return 0;
}
return node.height;
}
// 获得结点node的平衡因子
private int getBalanceFactor(Node node) {
if(node == null) {
return 0;
}
return getHeight(node.left) - getHeight(node.right);
}
private Node rightRoate(Node y) {
Node x = y.left;
Node T3 = x.right;
// 向右旋转过程
x.right = y;
y.left = T3;
// 更新height
y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1;
return x;
}
private Node leftRoate(Node y) {
Node x = y.right;
Node T2 = x.left;
// 向左旋转过程
x.left = y;
y.right = T2;
// 更新height
y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1;
return x;
}
// 向二分搜索树中添加新的元素(key, value)
public void add(K key, V value){
root = add(root, key, value);
}
// 向以node为根的二分搜索树中插入元素(key, value)，递归算法
// 返回插入新节点后二分搜索树的根
private Node add(Node node, K key, V value){
if(node == null){
size ++;
return new Node(key, value);
}
if(key.compareTo(node.key) < 0)
node.left = add(node.left, key, value);
else if(key.compareTo(node.key) > 0)
node.right = add(node.right, key, value);
else // key.compareTo(node.key) == 0
node.value = value;
// 更新height
node.height = 1 + Math.max(getHeight(node.left), getHeight(node.right));
// 计算平衡因子
int balanceFactor = getBalanceFactor(node);
// if(Math.abs(balanceFactor) > 1) {
// System.out.println("unbalanced : " + balanceFactor);
// }
// 平衡维护
// LL
if(balanceFactor > 1 && getBalanceFactor(node.left) >= 0) {
return rightRoate(node);
}
// RR
if(balanceFactor < -1 && getBalanceFactor(node.right) <= 0) {
return leftRoate(node);
}
// LR
if(balanceFactor > 1 && getBalanceFactor(node.left) < 0) {
node.left = leftRoate(node.left);
return rightRoate(node);
}
// RL
if(balanceFactor < -1 && getBalanceFactor(node.right) > 0) {
node.right = rightRoate(node.right);
return leftRoate(node);
}
return node;
}
// 返回以node为根节点的二分搜索树中，key所在的节点
private Node getNode(Node node, K key){
if(node == null)
return null;
if(key.equals(node.key))
return node;
else if(key.compareTo(node.key) < 0)
return getNode(node.left, key);
else // if(key.compareTo(node.key) > 0)
return getNode(node.right, key);
}
public boolean contains(K key){
return getNode(root, key) != null;
}
public V get(K key){
Node node = getNode(root, key);
return node == null ? null : node.value;
}
public void set(K key, V newValue){
Node node = getNode(root, key);
if(node == null)
throw new IllegalArgumentException(key + " doesn't exist!");
node.value = newValue;
}
// 返回以node为根的二分搜索树的最小值所在的节点
private Node minimum(Node node){
if(node.left == null)
return node;
return minimum(node.left);
}
// 删除掉以node为根的二分搜索树中的最小节点
// 返回删除节点后新的二分搜索树的根
private Node removeMin(Node node){
if(node.left == null){
Node rightNode = node.right;
node.right = null;
size --;
return rightNode;
}
node.left = removeMin(node.left);
return node;
}
// 从二分搜索树中删除键为key的节点
public V remove(K key){
Node node = getNode(root, key);
if(node != null){
root = remove(root, key);
return node.value;
}
return null;
}
private Node remove(Node node, K key){
if( node == null )
return null;
Node retNode;
if( key.compareTo(node.key) < 0 ){
node.left = remove(node.left , key);
retNode = node;
}
else if(key.compareTo(node.key) > 0 ){
node.right = remove(node.right, key);
retNode = node;
}
else{ // key.compareTo(node.key) == 0
// 待删除节点左子树为空的情况
if(node.left == null){
Node rightNode = node.right;
node.right = null;
size --;
retNode = rightNode;
}
// 待删除节点右子树为空的情况
else if(node.right == null){
Node leftNode = node.left;
node.left = null;
size --;
retNode = leftNode;
}
else { // 待删除节点左右子树均不为空的情况
// 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
// 用这个节点顶替待删除节点的位置
Node successor = minimum(node.right);
successor.right = remove(node.right, successor.key);
successor.left = node.left;
node.left = node.right = null;
retNode = successor;
}
}
if(retNode == null) {
return null;
}
// 更新height
retNode.height = 1 + Math.max(getHeight(retNode.left), getHeight(retNode.right));
// 计算平衡因子
int balanceFactor = getBalanceFactor(retNode);
// if(Math.abs(balanceFactor) > 1) {
// System.out.println("unbalanced : " + balanceFactor);
// }
// 平衡维护
// LL
if(balanceFactor > 1 && getBalanceFactor(retNode.left) >= 0) {
return rightRoate(retNode);
}
// RR
if(balanceFactor < -1 && getBalanceFactor(retNode.right) <= 0) {
return leftRoate(retNode);
}
// LR
if(balanceFactor > 1 && getBalanceFactor(retNode.left) < 0) {
retNode.left = leftRoate(retNode.left);
return rightRoate(retNode);
}
// RL
if(balanceFactor < -1 && getBalanceFactor(retNode.right) > 0) {
retNode.right = rightRoate(retNode.right);
return leftRoate(retNode);
}
return retNode;
}
public static void main(String[] args){
System.out.println("Pride and Prejudice");
ArrayList<String> words = new ArrayList<>();
if(FileOperation.readFile("pride-and-prejudice.txt", words)) {
System.out.println("Total words: " + words.size());
AVLTree<String, Integer> map = new AVLTree<>();
for (String word : words) {
if (map.contains(word))
map.set(word, map.get(word) + 1);
else
map.add(word, 1);
}
System.out.println("Total different words: " + map.getSize());
System.out.println("Frequency of PRIDE: " + map.get("pride"));
System.out.println("Frequency of PREJUDICE: " + map.get("prejudice"));
System.out.println("is BST : " + map.isBST());
System.out.println("is Balanced : " + map.isBalanced());
for(String word : words) {
map.remove(word);
if(!map.isBST() || !map.isBalanced()) {
throw new RuntimeException("ERROR");
}
}
}
System.out.println();
}
}
