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;
}
原文地址：https://blog.csdn.net/fairylyt/article/details/123169499
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