1066 Root of AVL Tree // AVL平衡二叉搜索树模板

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

 模板：

#include <iostream>
#include <algorithm>
using namespace std;
int n, x;

struct node {
	int val;
	node *left, *right;
};

node *rotateLeft(node *root) {
	node *t = root->right;
	root->right = t->left;
	t->left = root;
	return t;
}

node *rotateRight(node *root) {
	node *t = root->left;
	root->left = t->right;
	t->right = root;
	return t;
}

node *rotateLeftRight(node *root) {
	root->left = rotateLeft(root->left);
	return rotateRight(root);
}

node *rotateRightLeft(node *root) {
	root->right = rotateRight(root->right);
	return rotateLeft(root);
}

int height(node *root) {
	if (root == NULL) {
		return 0;
	} else {
		return max(height(root->left), height(root->right)) + 1;
	}
}

node *insert(node *root, int val) {
	if (root == NULL) {
		root = new node();
		root->val = val;
		root->right = root->left = NULL;
	} else if (val < root->val) {
		root->left = insert(root->left, val);
		if (height(root->left) - height(root->right) == 2) {
			if (val < root->left->val) {
				root = rotateRight(root);
			} else {
				root = rotateLeftRight(root);
			}
		}
	} else {
		root->right = insert(root->right, val);
		if (height(root->right) - height(root->left) == 2) {
			if (val > root->right->val) {
				root = rotateLeft(root);
			} else {
				root = rotateRightLeft(root);
			}
		}
	}
	return root;
}

int main() {
	cin >> n;
	node *root = NULL;
	for (int i = 0; i < n; i++) {
		cin >> x;
		root = insert(root, x);
	}
	cout << root->val;
	return 0;
}

参考博客：1066. Root of AVL Tree (25)-PAT甲级真题_柳婼的博客-CSDN博客 

数据结构图文解析之：AVL树详解及C++模板实现 - 腾讯云开发者社区-腾讯云 (tencent.com)