【笨方法学PAT】1066 Root of AVL Tree （25 分）

最新推荐文章于 2022-02-07 02:18:28 发布

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最新推荐文章于 2022-02-07 02:18:28 发布

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分类专栏： PAT 文章标签： C PAT甲级

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本文探讨了AVL树的插入操作及根节点求解方法。通过自平衡二叉搜索树的特性，确保每次插入后的树仍保持平衡。文章详细介绍了AVL树的旋转规则，并提供了完整的代码实现，用于解决给定一系列插入操作后AVL树的根节点问题。

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一、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 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:

二、题目大意

求平衡二叉树根节点数值。

三、考点

平衡二叉树

四、注意

1、虽然很基础，但如果之前不了解平衡二叉树，，，

五、代码

#include<iostream>
#include<algorithm>
using namespace std;
struct node {
	int val;
	struct node *right, *left;
};
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 *totateRightLeft(node *root) {
	root->right = rotateRight(root->right);
	return rotateLeft(root);
}
int getHeight(node *root) {
	if (root == NULL)
		return 0;
	else
		return max(getHeight(root->left), getHeight(root->right)) + 1;
}
node *insert(node *root, int val) {
	if (root == NULL) {
		root = new node();
		root->val = val;
		root->left = NULL;
		root->right = NULL;
	}
	else if (root->val > val) {
		root->left = insert(root->left, val);
		if (getHeight(root->left) - getHeight(root->right) == 2) {
			if (val < root->left->val)
				root=rotateRight(root);
			else
				root=rotateLeftRight(root);
		}
	}
	else {
		root->right = insert(root->right, val);
		if (getHeight(root->right) - getHeight(root->left) == 2) {
			if (val > root->right->val)
				root=rotateLeft(root);
			else
				root=totateRightLeft(root);
		}
	}
	return root;
}
int main() {
	//read
	int n;
	cin >> n;
	node *root=NULL;
	for (int i = 0; i < n; ++i) {
		int a;
		cin >> a;
		root=insert(root, a);
	}
	
	//output
	cout << root->val;
	
	system("pause");
	return 0;
}