一个AVL树是其每个节点的左子树和右子树的高度差最多差1的二叉查找树；AVL树是一种最古老的平衡查找树

上代码：

package com.itany.avlshu;

public class AVLTree<T extends Comparable<?super T>>
{
    private static class AvlNode<T>
    {
        private int height;
        private T element;
        private AvlNode<T> left;
        private AvlNode<T> right;
        public AvlNode(T element)
        {
            this(element,null,null);
        }
        public AvlNode(T element,AvlNode<T> left,AvlNode right)
        {
            this.element=element;
            this.left=left;
            this.right=right;
            height=0;
        }
    }
    private int height(AvlNode<T> node)
    {
        return (node==null)?-1:node.height;
    }
    private int compare(T x, T element)
    {
        return x.compareTo(element);
    }
    private AvlNode<T> insert(T x,AvlNode<T> t)
    {
        if(t==null)
            return new AvlNode<T>(x,null,null);//创造出来时 默认height=0
        int compareResult=compare(x,t.element);
        if(compareResult<0)
        {
            t.left=insert(x,t.left);
            //做完了插入之后 立马比较t的左右儿子的高度差是否等于2 若是 则进行相应旋转 若不是那么下一步  直接更新这个t的height值
            //此时左边儿子高度比较大
            if(height(t.left)-height(t.right)==2)
                
            {
                //下面分两种旋转情况 一种是单旋转 另一种是双旋转
                if(compare(x,t.left.element)<0)
                    t=rotateWithLeftChild(t);
                else
                    t=doubleRotateWithLeftChild(t);
            }
        }
        else if(compareResult>0)
        {
            t.right=insert(x,t.right);
            //做完了插入之后 立马比较t的左右儿子的高度差是否等于2 若是 则进行相应旋转 若不是那么下一步  直接更新这个t的height值
            //此时右边儿子高度比较大
            if(height(t.right)-height(t.left)==2)
            {
                //下面分两种旋转情况 一种是单旋转 另一种是双旋转
                if(compare(x,t.right.element)<0)
                    t=doubleRotateWithRightChild(t);
                else
                    t=rotateWithRightChild(t);
            }
        }
        else
            ;
        t.height=Math.max(height(t.left), height(t.right))+1;//+1是加一个自己 
        return t;
    }
    private AvlNode<T> rotateWithRightChild(AvlNode<T> k1)
    {
        AvlNode<T> k2=k1.right;
        k1.right=k2.left;
        k2.left=k1;
        k2.height=Math.max(height(k2.left),height(k2.right))+1;
        k1.height=Math.max(height(k1.left),height(k1.right))+1;
        return k2;
    }
    private AvlNode<T> doubleRotateWithRightChild(AvlNode<T> k3)
    {
        k3.right=rotateWithLeftChild(k3.right);
        return rotateWithRightChild(k3);
    }
    //双旋转是由两次单旋转得来
    private AvlNode<T> doubleRotateWithLeftChild(AvlNode<T> k3)
    {
        k3.left=rotateWithRightChild(k3.left);
        return rotateWithLeftChild(k3);
    }
    private AvlNode<T> rotateWithLeftChild(AvlNode<T> k2)
    {
        AvlNode<T> k1=k2.left;
        k2.left=k1.right;
        k1.right=k2;
        k2.height=Math.max(height(k2.left),height(k2.right))+1;
        k1.height=Math.max(height(k1.left),height(k1.right))+1;
        return k1;
    }
    
}