概念: 二叉树存在值顺序插入导致树高度过大的问题、平衡二叉树通过旋转的方式、使二叉树处于平衡状态、子树高度差不能大于1

旋转规则:

        左子树高右旋、右子树高左旋

        右旋时插入节点在最右、则子树先左旋

        左旋时插入节点在最左、则子树先右旋

代码实现: 

package com.info.dataStructure.avl;/*** @author haizhuangbu* @date 2024/3/22 10:47* @mark AvlNode 节点*/
public class AvlNode<T extends Comparable<T>> {AvlNode<T> left;AvlNode<T> right;T key;// 高度int height;public AvlNode(T key) {this.key = key;this.height = 0;}}

package com.info.dataStructure.avl;/*** @author haizhuangbu* @date 2024/3/22 10:45* @mark AvlTree*/
public class AvlTree<T extends Comparable<T>> {// 根节点private AvlNode<T> root;public AvlTree() {this.root = null;}/*** @param node 节点* @return 节点高度(树的高度)*/private int height(AvlNode<T> node) {if (node == null) return -1;return node.height;}private void updateHeight(AvlNode<T> node) {// 当前树的高度为 最大的子树高度 + 1node.height = Math.max(height(node.left), height(node.right)) + 1;}/*** @param avlNode 节点* @return 右旋*/private AvlNode<T> rotateLeft(AvlNode<T> avlNode) {AvlNode<T> right = avlNode.right;avlNode.right = right.left;right.left = avlNode;updateHeight(avlNode);updateHeight(right);return right;}/*** @param node 节点* @return 右旋*/private AvlNode<T> rotateRight(AvlNode<T> node) {AvlNode<T> left = node.left;node.left = left.right;left.right = node;updateHeight(node);updateHeight(left);return left;}private AvlNode<T> insert(AvlNode<T> node, T key) {if (node == null) return new AvlNode<>(key);// 将节点插入 平衡二叉树中if (key.compareTo(node.key) < 0) {node.left = insert(node.left, key);} else if (key.compareTo(node.key) > 0) {node.right = insert(node.right, key);} else {// 键值存在不需要插入return node;}// 不满足 子节点高度差不能大于1if (height(node.left) - height(node.right) == 2) {if (key.compareTo(node.left.key) < 0) {return rotateRight(node);} else {node.left = rotateLeft(node.left);return rotateRight(node);}} else if (height(node.right) - height(node.left) == 2) {if (key.compareTo(node.right.key) > 0) {return rotateLeft(node);} else {node.right = rotateRight(node.right);return rotateLeft(node);}}updateHeight(node);return node;}public void insert(T key) {root = insert(root, key);}}