左旋转

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右旋转

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双旋转

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左旋右旋规律

右旋右低，左旋左低，
左高右旋，右高左旋
左旋动左。
右旋动右。
新节点
代替当前根节点。
左旋，新节点右子树=右子树左子节点。
右旋，新节点左子树=左子树右子节点。
根节点
左旋，值=右子节点值，右子树=右子树右子节点，左子树=新节点
右旋，值=左子节点值，左子树=左子树左子节点，右子树=新节点。
最终版口诀：
左旋动右给左（新节点），根=右
右旋动左给右（新节点），根=左

code

Node

package com.pl.arithmetic.binaryTree.avl;

/**
 * <p>
 *
 * @Description: TODO
 * </p>
 * @ClassName Node
 * @Author pl
 * @Date 2020/11/14
 * @Version V1.0.0
 */
public class Node {
    int value;
    Node left;
    Node right;


    public Node(int value) {
        this.value = value;
    }

    // AVLTree ---------------------------------------
    public int leftHeight(){
        if (left == null){
            return  0;
        }
        return left.height();
    }

    public int rightHeight(){
        if (right == null){
            return  0;
        }
        return right.height();
    }

    /**
     * 计算当前节点的树高度
     *
     * @param
     * @return int
     * @exception
     * @author silenter
     * @date 2020/11/20 7:28
    */
    public int height(){
        return Math.max(left == null ?0:left.height(),right == null?0:right.height())+1;
    }

    /**
     *  左旋前提右子树高于左子树
     *  左旋右旋
     *
     *  创建新节点，代替当前根节点，左子树和当前节点一样，右子树变成右子树的左子树
     *  右子树等于当前节点右子树的右子节点，当前节点的值等于右子节点的值，当前节点左子树指向新节点，
     *
     * @param
     * @return void
     * @exception
     * @author silenter
     * @date 2020/11/20 8:13
    */
    public void leftRoute(){
        Node newNode = new Node(this.value);
        newNode.left = this.left;
        newNode.right = this.right.left;
        this.value = right.value;
        this.right = right.right;
        this.left = newNode;
    }

    /**
     * 右旋的前提，左子树高于右子树
     *
     * @param
     * @return void
     * @exception
     * @author silenter
     * @date 2020/11/20 8:14
    */
    public void rightRoute(){
        Node newNode = new Node(this.value);
        newNode.left = left.right;
        newNode.right = right;
        value = left.value;
        left = left.left;
        right = newNode;
    }
    /**
     * 添加节点  和bst相比，只有添加不同
     *
     * @param node
     * @return void
     * @exception
     * @author silenter
     * @date 2020/11/14 9:31
     */
    public void addNode(Node node){
        verifyNode(node);
        if (node.value<this.value){
            if (this.left!=null){
                this.left.addNode(node);
            }else if (this.left == null){
                this.left = node;
            }
        }
        if (node.value>this.value){
            if (this.right!=null){
                this.right.addNode(node);
            }else if (this.right == null){
                this.right = node;
            }
        }
        //左高右旋
        if (leftHeight()-rightHeight()>1){
            if (right != null && left.rightHeight()>left.leftHeight()){
                left.leftRoute();
                rightRoute();
            }else {
                rightRoute();
            }
        }
        //右高左旋
        if (rightHeight()-leftHeight()>1){
            if (right != null && right.leftHeight()>right.rightHeight()){
                right.rightRoute();
                leftRoute();
            }else {
                leftRoute();
            }
        }

    }
// AVLTree ---------------------------------------




    public Node searchRightMixNode(Node node){
        Node tempNode = node;
        while (tempNode.left!=null){
            tempNode = tempNode.left;
        }
        return tempNode;
    }

    /**
     * 查找指定节点
     *
     * @param value
     * @return com.pl.arithmetic.binaryTree.binarySearchTree.Node
     * @exception
     * @author silenter
     * @date 2020/11/14 10:18
    */
    public Node searchNode(int value){
        Node tempNode = null;
        if (this.value == value){
            tempNode = this;
            System.out.println("找到指定节点");
            return tempNode;
        }
        if (tempNode ==null){
            if (value<this.value && this.left!=null){
                tempNode = this.left.searchNode(value);
            }
            if (value>this.value&&this.right!=null){
                tempNode =  this.right.searchNode(value);
            }
        }
        return tempNode;
    }



    /**
     * 查找当前节点的父节点
     *
     * @param value
     * @return com.pl.arithmetic.binaryTree.binarySearchTree.Node
     * @exception
     * @author silenter
     * @date 2020/11/14 9:32
    */
    public Node searchParentNode(int value){
        if ((this.left !=null && this.left.value == value) || (this.right !=null && this.right.value == value)){
            System.out.println("找到该父节点"+this);
            return this;
        }else{
            if (value <this.value && this.left!=null){
                return this.left.searchParentNode(value);
            }else if (value>this.value && this.right!=null) {
                return this.right.searchParentNode(value);
            }
        }
        return null;
    }



    /**
     * 前序遍历
     *
     * @param
     * @return void
     * @exception
     * @author silenter
     * @date 2020/11/14 9:19
    */
    //中序遍历
    public void infixOrder() {
        if(this.left != null) {
            this.left.infixOrder();
        }
        System.out.println(this);
        if(this.right != null) {
            this.right.infixOrder();
        }
    }

    public void verifyNode(Node node){
        if (node ==null){
            throw new RuntimeException("node为空");
        }
    }


    @Override
    public String toString() {
        return "Node{" +
                "value=" + value +
                '}';
    }
}

AVLTree

package com.pl.arithmetic.binaryTree.avl;

/**
 * <p>
 *
 * @Description: TODO
 * </p>
 * @ClassName AVLTree
 * @Author pl
 * @Date 2020/11/20
 * @Version V1.0.0
 */
public class AVLTree {
    private Node root;

    public Node getRoot() {
        return root;
    }

    // 添加结点的方法
    public void add(Node node) {
        if (root == null) {
            root = node;// 如果root为空则直接让root指向node
        } else {
            root.addNode(node);
        }
    }

    // 中序遍历
    public void infixOrder() {
        if (root != null) {
            root.infixOrder();
        } else {
            System.out.println("二叉排序树为空，不能遍历");
        }
    }
}

AVLTreeDemo

package com.pl.arithmetic.binaryTree.avl;

/**
 * <p>
 *
 * @Description: TODO
 * </p>
 * @ClassName AVLTreeDemo
 * @Author pl
 * @Date 2020/11/20
 * @Version V1.0.0
 */
public class AVLTreeDemo {

    public static void main(String[] args) {
        //int[] arr = {4,3,6,5,7,8};
        //int[] arr = { 10, 12, 8, 9, 7, 6 };
        int[] arr = { 10, 11, 7, 6, 8, 9 };
        //创建一个 AVLTree对象
        AVLTree avlTree = new AVLTree();
        //添加结点
        for(int i=0; i < arr.length; i++) {
            avlTree.add(new Node(arr[i]));
        }

        //遍历
        System.out.println("中序遍历");
        avlTree.infixOrder();

        System.out.println("在平衡处理~~");
        System.out.println("树的高度=" + avlTree.getRoot().height()); //3
        System.out.println("树的左子树高度=" + avlTree.getRoot().leftHeight()); // 2
        System.out.println("树的右子树高度=" + avlTree.getRoot().rightHeight()); // 2
        System.out.println("当前的根结点=" + avlTree.getRoot());//8


    }
}