題目連結:

PAT1066 Root of AVL Tree
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

總體思路：

分為左左，左右，右左，右右四種情況進行調整。

#include <iostream>
 

#include<cstdio>
using namespace std;
struct node{
	int v;
	node *left,*right;
};
int getDepth(node *root){
	if(root==NULL)
		return 0;
	int dep1=getDepth(root->left);
	int dep2=getDepth(root->right);
	int dep=max(dep1,dep2)+1;
	return dep;
}
node *LL(node *k1){
	node *k2=k1->left;
	k1->left=k2->right;
	k2->right=k1;
	return k2;
} 
node *RR(node *k1){
	node *k2=k1->right;
	k1->right=k2->left;
	k2->left=k1;
	return k2;
}
node *LR(node *k1){//先RR再LL 
	k1->left=RR(k1->left);
	return LL(k1);
}
node *RL(node *k1){
	k1->right=LL(k1->right);
	return RR(k1);
}
node *build(node *root,int v){
	if(root==NULL){
		root=new node();
		root->v=v;
		root->left=root->right=NULL;
		return root;
	}else{
		if(v>=root->v){
			root->right=build(root->right,v);
			if(getDepth(root->right)-getDepth(root->left)==2){
				if(v>=root->right->v)
					root=RR(root);
				else
					root=RL(root);
			}
			return root;
		}else{
			root->left=build(root->left,v);
			if(getDepth(root->left)-getDepth(root->right)==2){
				if(v<root->left->v)
					root=LL(root);
				else
					root=LR(root);
			}
			return root;
		}
	}
} 
int main(int argc, char** argv) {
	int n;scanf("%d",&n);
	node *root=NULL;
	for(int i=0;i<n;i++){
		int x;scanf("%d",&x);
		root=build(root,x);
	}
	printf("%d",root->v);
	return 0;
}

參考自：

https://www.cnblogs.com/jackwang822/p/4755442.html