版权声明:本文为博主原创文章,未经博主允许不得转载。 https://blog.csdn.net/u012292754/article/details/86886030
1 右旋转
- 左子树的高度比右子树的高度高,并且高度差比 1 大。同时它的左孩子也是,左子树高度大于等于右子树;
x.right = y
y.left = T3
2 左旋转
- 插入的元素在不平衡的节点的右侧的右侧;
- y 的右子树的高度值比左子树高度值大于 1
- T4 < y < T3 < x < T1 < z < T2
x.left = y
y.right = T3
3 测试
AVLTree.java
package avltree;
import java.util.ArrayList;
public class AVLTree<K extends Comparable<K>, V> {
public 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颗二分搜索树
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);
}
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);
}
public int getHeight(Node node) {
if (node == null) {
return 0;
}
return node.height;
}
// 获得节点 node 的平衡因子
private int getBalanceFactor(Node node) {
if (node == null) {
return 0;
}
return getHeight(node.left) - getHeight(node.right);
}
// 对节点 y 进行向右旋转操作,返回旋转后新的根节点 x
private Node rightRotate(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));
x.height = Math.max(getHeight(x.left), getHeight(x.right));
return x;
}
// 对 y 进行左旋转操作,返回旋转后新的根节点
// y x
// / \ / \
// T1 x y z
// / \ / \ / \
// T2 z T1 T2 T3 T4
// / \
// T3 T4
private Node leftRotate(Node y) {
Node x = y.right;
Node T2 = x.left;
// 向左旋转的过程
x.left = y;
y.right = T2;
y.height = Math.max(getHeight(y.left),getHeight(y.right));
x.height = Math.max(getHeight(x.left),getHeight(x.right));
return x;
}
public void add(K key, V value) {
root = add(root, key, value);
}
// 以 node 为根的二分搜索树中插入元素 (key,value)
// 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 {
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
if (balanceFactor > 1 && getBalanceFactor(node.left) >= 0) {
return rightRotate(node);
}
if(balanceFactor < -1 && getBalanceFactor(node.right) <= 0){
return leftRotate(node);
}
return node;
}
}