上篇介绍了AVL树的概述，这篇把AVL树的java代码实现贴出来
public class AVLTree<K extends Comparable<K>, V> {
private class Node{
public K key;
public V value;
public Node left, right;
public int height; //树的高度
public Node(K key, V value){
this.key = key;
this.value = value;
left = null;
right = null;
height = 1;
}
}
private Node root; //根节点
private int size; //元素个数
public AVLTree(){
root = null;
size = 0;
}
//获取元素个数
public int getSize(){
return size;
}
//判断AVL树是否为空
public boolean isEmpty(){
return size == 0;
}
//获取节点的高度
private int getHeight(Node node){
if(node == null)
return 0;
return node.height;
}
//获得节点的平衡因子
private int getBalanceFactor(Node node){
if(node == null)
return 0;
return getHeight(node.left) - getHeight(node.right);
}
//判断是否是二分搜索树
private 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;
}
//中序遍历
public void inOrder(Node node, ArrayList<K> keys){
if(node == null)
return;
inOrder(node.left,keys);
keys.add(node.key);
inOrder(node.right,keys);
}
//判断二叉树是否是一棵平衡二叉树
public boolean isBalanced(){
return isBalanced(root);
}
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);
}
//右旋转
private Node rightRotate(Node y){
Node x = y.left;
Node T3 = x.right;
//向右旋转
x.right = y;
y.left = T3;
//更新height值，旋转后只有x和y的高度值发生变化
y.height = Math.max(getHeight(y.left),getHeight(y.right)) + 1;
x.height = Math.max(getHeight(x.left),getHeight(x.right)) + 1;
return x;
}
//左旋转
private Node leftRotate(Node y){
Node x = y.right;
Node T3 = x.left;
//向左旋转
x.left = y;
y.right = T3;
//更新height值，旋转后只有x和y的高度值发生变化
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AVL树添加新的元素(key, value)
public void add(K key, V value){
root = add(root, key, value);
}
// 向以node为根的AVL树中插入元素(key, value)，递归算法
// 返回插入新节点后AVL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);
//平衡维护
//LL
if(balanceFactor > 1 && getBalanceFactor(node.left) >= 0)
rightRotate(node);
//RR
if(balanceFactor < -1 && getBalanceFactor(node.right) <= 0)
return leftRotate(node);
//LR
if(balanceFactor > 1 && getBalanceFactor(node.left) < 0){
node.left = leftRotate(node.left);
return rightRotate(node);
}
//RL
if(balanceFactor < -1 && getBalanceFactor(node.right) > 0){
node.right = rightRotate(node.right);
return leftRotate(node);
}
return node;
}
// 返回以node为根节点的AVL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);
}
//判断AVL树中是否包含key
public boolean contains(K key){
return getNode(root, key) != null;
}
//获取AVL树中键为key的value值
public V get(K key){
Node node = getNode(root, key);
return node == null ? null : node.value;
}
//将AVL树中键为key的value值设置成新的newValue值
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AVL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);
}
// 从AVL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; //要返回的node节点，
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 = node;
}
// 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 = node;
}
// 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
else {
Node successor = minimum(node.right);
successor.right = remove(node.right, successor.key);
successor.left = node.left;
node.left = node.right = null;
retNode = node;
}
}
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);
//平衡维护
//LL
if(balanceFactor > 1 && getBalanceFactor(retNode.left) >= 0)
rightRotate(retNode);
//RR
if(balanceFactor < -1 && getBalanceFactor(retNode.right) <= 0)
return leftRotate(retNode);
//LR
if(balanceFactor > 1 && getBalanceFactor(retNode.left) < 0){
retNode.left = leftRotate(retNode.left);
return rightRotate(retNode);
}
//RL
if(balanceFactor < -1 && getBalanceFactor(retNode.right) > 0){
retNode.right = rightRotate(retNode.right);
return leftRotate(retNode);
}
return retNode;
}
public static void main(String[] args) {
int[] arr = {12,8,18,5,11,17,4};
AVLTree avlTree = new AVLTree();
for (int i = 0; i < arr.length; i++) {
avlTree.add(arr[i],arr[i]);
}
System.out.println("AVLTree is balanced: " + avlTree.isBalanced());
avlTree.add(2,2);
avlTree.add(7,7);
System.out.println("AVLTree is balanced: " + avlTree.isBalanced());
avlTree.remove(18);
System.out.println("AVLTree is balanced: " + avlTree.isBalanced());
}
}
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