PAT Advanced 1066 Root of AVL Tree (25) [平衡⼆叉树（AVL树）]

题目

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node difer by at most one; if at any time they difer 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

题目分析

已知平衡二叉树建树序列，求建树后的根节点

解题思路

1.建树（平衡二叉树insert节点）

2.打印根节点

易错点

左旋、右旋、插入节点方法，参数列表中要用指针引用node *&root，否则是值传递，方法中对root本身的修改不会在main函数中生效

Code

#include <iostream>
using namespace std;
struct node {
	int data;
	int heigh=0;
	node * left=NULL;
	node * right=NULL;
	node() {}
	node(int _data):data(_data) {
		heigh=1;
	}
};
int getHeigh(node * root) {
	if(root==NULL)return 0;
	return root->heigh;
}
void updateHeigh(node * root) {
	root->heigh=max(getHeigh(root->left),getHeigh(root->right))+1;
}
void L(node * &root) {
	//左旋
	node * temp=root->right;
	root->right=temp->left;
	temp->left=root;
	updateHeigh(root);
	updateHeigh(temp);
	root=temp;
}
void R(node * &root) {
	//右旋
	node * temp=root->left;
	root->left=temp->right;
	temp->right=root;
	updateHeigh(root);
	updateHeigh(temp);
	root=temp;
}
int getBalanceFactor(node *root) {
	return getHeigh(root->left)-getHeigh(root->right);
}
void insert(node * &root, int val) {
	if(root==NULL) {
		root=new node(val);
		return;
	}
	if(val<root->data) {
		insert(root->left,val);
		updateHeigh(root);
		if(getBalanceFactor(root)==2) {
			if(getBalanceFactor(root->left)==1) {
				//LL
				R(root);
			} else if(getBalanceFactor(root->left)==-1) {
				//LR
				L(root->left);
				R(root);
			}
		}
	} else {
		insert(root->right,val);
		updateHeigh(root);
		if(getBalanceFactor(root)==-2) {
			if(getBalanceFactor(root->right)==-1) {
				//RR
				L(root);
			} else if(getBalanceFactor(root->right)==1) {
				//RL
				R(root->right);
				L(root);
			}
		}
	}
}
int main(int argc,char * argv[]) {
	int n,m;
	scanf("%d",&n);
	node * root=NULL;
	for(int i=0; i<n; i++) {
		scanf("%d",&m);
		insert(root,m);
	}
	printf("%d",root->data);
	return 0;
}