PAT甲级：1066 Root of AVL Tree (25分)

题干

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

思路

模拟一下AVL树的过程。

四个旋转方法，左单旋，右单旋，左右双旋，右左双旋。具体看代码，函数名写得挺清楚的。

还需要一个高度函数，递归一下就得出来了。

最后再弄一个insert 函数，注意AVL树的特点，左右子树的高度差为2时必须发生平衡旋转。

code

#include <iostream>

using namespace std;

struct node{

	int data;

	node *left, *right;

	node(int data){this->data = data, this->left = this->right = NULL;}

};

node* rotate_left(node* root){

	node* temp = root->left;

	root->left = temp->right;

	temp->right = root;

	return temp;

}

node* rotate_right(node* root){

	node* temp = root->right;

	root->right = temp->left;

	temp->left = root;

	return temp;

}

node* rotate_left_right(node* root){

	root->right = rotate_left(root->right);

	return rotate_right(root);

}

node* rotate_right_left(node* root){

	root->left = rotate_right(root->left);

	return rotate_left(root);

}

int getHeight(node* root){

	if(root == NULL) return 0;

	return max(getHeight(root->right), getHeight(root->left)) + 1;

}

node* insert(int data, node* root){

	if(root == NULL) root = new node(data);

	else if(data > root->data) {

		root->right = insert(data, root->right);

		if(getHeight(root->right) - getHeight(root->left) >= 2)

			root = root->right->data > data ? rotate_left_right(root) : rotate_right(root);

	}

	else {

		root->left = insert(data, root->left);

		if(getHeight(root->left) - getHeight(root->right) >= 2)

			root = root->left->data < data ? rotate_right_left(root) : rotate_left(root);

	}

	return root;

}

int main(){

	int n = 0, temp = 0;

	scanf("%d", &n);

	node *root = NULL;

	for(int i = 0; i < n; i++){

		scanf("%d", &temp);

		root = insert(temp, root);

	}

	printf("%d", root->data);

	return 0;

}