PAT A1066 Root of AVL Tree (25分)-优快云博客

本文链接：https://blog.youkuaiyun.com/PanYiAn9/article/details/105229147

本文介绍如何通过一系列插入操作构建AVL平衡二叉树，并输出最终树的根节点值。AVL树是一种自平衡的二叉搜索树，确保任意节点的两个子树高度差不超过1。文中提供了一个C++实现的例子。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

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:

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

题意：

输入平衡二叉树的结点数、结点权值序列；输出平衡二叉树的根结点权值.

思路：

(1)依据给定的条件构建平衡二叉树，输出其根结点权值.

代码：

#include <cstdio>
#include <algorithm>
using namespace std;

struct node{//平衡二叉树存储结构 
	int data,height;
	node *lchild,*rchild;
};
node* newNode(int x){//新建一个平衡二叉树 
	node* root = new node;
	root->data = x;
	root->height = 1;
	root->lchild = root->rchild = NULL;
	return root;
}
int getHeight(node* root){//获取结点高度 
	if(root==NULL) return 0;
	return root->height;
}
void updateHeight(node* &root){//更新结点高度 
	root->height = max(getHeight(root->lchild),getHeight(root->rchild))+1;
}
int getBalanceFactor(node* root){//获取结点平衡因子 
	return getHeight(root->lchild)-getHeight(root->rchild); 
}
void R(node* &root){//右旋 
	node* temp = root->lchild;
	root->lchild = temp->rchild;
	temp->rchild = root;
	updateHeight(root);
	updateHeight(temp);
	root = temp;
}
void L(node* &root){//左旋 
	node* temp = root->rchild;
	root->rchild = temp->lchild;
	temp->lchild = root;
	updateHeight(root);
	updateHeight(temp);
	root = temp;
}
void insert(node* &root,int x){//插入权值为x的结点 
	if(root==NULL){
		root = newNode(x);
		return;
	}
	if(root->data>x){
		insert(root->lchild,x);
		updateHeight(root);
		if(getBalanceFactor(root)==2){
			if(getBalanceFactor(root->lchild)==1){
				R(root);
			}else if(getBalanceFactor(root->lchild)==-1){
				L(root->lchild);
				R(root);
			}
		}
	}else{
		insert(root->rchild,x);
		updateHeight(root);
		if(getBalanceFactor(root)==-2){
			if(getBalanceFactor(root->rchild)==-1){
				L(root);
			}else if(getBalanceFactor(root->rchild)==1){
				R(root->rchild);
				L(root);
			}
		}
	}
}
node* createAVL(int data[],int n){//创建平衡二叉树 
	node* root = NULL;
	for(int i=0;i<n;i++) insert(root,data[i]);
	return root;
}

int main(){
	int n;
	scanf("%d",&n);
	int data[n];
	for(int i=0;i<n;i++) scanf("%d",&data[i]);
	node* root = createAVL(data,n);
	printf("%d\n",root->data);
	return 0;
}