1066 Root of AVL Tree （25 分）

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

平衡二叉树：http://lib.csdn.net/article/datastructure/9204

https://www.liuchuo.net/archives/2178

#include<iostream>
using namespace std;
struct Node{
	int data;
	struct Node *left,*right;
};
typedef struct Node* AVL;
AVL RightRot(AVL t)
{
	AVL p=t->left;
	t->left=p->right;
	p->right=t;
	return p;
}
AVL LeftRot(AVL t)
{
	AVL p=t->right;
	t->right=p->left;
	p->left=t;
	return p;
}
AVL LeftRightRot(AVL t)
{
	t->left=LeftRot(t->left);
	return RightRot(t);
}
AVL RightLeftRot(AVL t)
{
	t->right=RightRot(t->right);
	return LeftRot(t);
}
int GetHeight(AVL t)
{
	if(t==NULL) return 0;
	return max(GetHeight(t->left),GetHeight(t->right))+1;
}
AVL it(AVL t,int x)
{
	if(t==NULL)
	{
		t=new Node();
		t->data=x;
		t->left=t->right=NULL;
	}
	else if(x<t->data)
	{
		t->left=it(t->left,x);
		if(GetHeight(t->left)-GetHeight(t->right)==2)
		{
			if(x<t->left->data) t=RightRot(t); //
			else t=LeftRightRot(t);
		}
	}
	else 
	{
		t->right=it(t->right,x);
		if(GetHeight(t->left)-GetHeight(t->right)==-2)
		{
			if(x>t->right->data) t=LeftRot(t); //
			else t=RightLeftRot(t);
		}
	}
	return t;
}
int main(void)
{
	int n,i,tp;
	AVL r=NULL;
	scanf("%d",&n);
	for(i=0;i<n;i++)
	{
		scanf("%d",&tp);
		r=it(r,tp);
	}
	printf("%d\n",r->data);
	return 0;
}