An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

 

 

 

 

 

 

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the root of the resulting AVL tree in one line.

Sample Input 1:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

 代码：

#include<iostream>
#include<algorithm>
using namespace std;
int N;
int num[25];
struct node//定义树的结点
{
    int height;//存放树的高度，用以间接获得结点的平衡因子
    int data;
    node* lchild;
    node* rchild;
};
int getheight(node *root)//获得结点的高度
{
    if(root==NULL)
        return 0;
    else 
        return root->height;
}
void updataheight(node *root)//更新结点root的高度，为左右子树中高度高的一个+1
{
    root->height=max(getheight(root->lchild),getheight(root->rchild))+1;
}
int getbalance(node *root)//获得结点的平衡因子（=左子树高度-右子树高度）
{
    return getheight(root->lchild)-getheight(root->rchild);
}
void L(node * &root)//左旋
{
        node *p=root->rchild;
        root->rchild=p->lchild;
        p->lchild=root;
        updataheight(root);
        updataheight(p);
        root=p;
}
void R(node * &root)//右旋
{
        node *p=root->lchild;
        root->lchild=p->rchild;
        p->rchild=root;
        updataheight(root);
        updataheight(p);
        root=p;
}
void insert(node *&root,int x)//插入x,注意root要用引用
{
    if(root==NULL)
    {
        root=new node;
        root->data=x;
        root->lchild=NULL;
        root->rchild=NULL;
        root->height=1;
        return;
    }
    if(root->data>x)
    {
        insert(root->lchild,x);
        updataheight(root);
        if(getbalance(root)==2)//调整树为平衡二叉树
        {
            if(getbalance(root->lchild)==1)//为LL型，进行右旋
                R(root);
            else if(getbalance(root->lchild)==-1)//为LR型，先左旋，在右旋
            {
                L(root->lchild);
                R(root);
            }
        }
    }
    else
    {
        insert(root->rchild,x);
        updataheight(root);
        if(getbalance(root)==-2)
        {
            if(getbalance(root->rchild)==-1)//为RR型，进行左旋
               L(root);
            else if(getbalance(root->rchild)==1)//为RＬ型，先右旋，在左旋
            {
                R(root->rchild);
                L(root);
            }
        }
    }
}
node* creat()
{
    node *root=NULL;
    for(int i=0;i<N;i++)
        insert(root,num[i]);
    return root;
}
int main()
{
    scanf("%d",&N);
    for(int i=0;i<N;i++)
        scanf("%d",num+i);
    node *root=creat();
    printf("%d",root->data);
    return 0;
}