PAT甲级-1066-Root of AVL Tree(平衡二叉树)

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
8 10 11 8 6 7 5

Sample Output 2:

88

分析：

1、左旋（右子树过高）：

补充：结点3是忍痛割爱，将自己的左子树砍断，而将紫色集团植入。
2、右旋（左子树过高）：正好和左旋相反，此处不详述。
3、右左旋（往左子树的右子树上插入了新结点）：先右旋，再左旋

4、左右旋（往右子树的左子树上插入了新结点）：先左旋，再右旋，正好和右左旋相反，此处不详述。

代码如下

#include<iostream>
#include<cmath>
using namespace std;
struct node{
	int val;
	struct node *left,*right;
};
node *L(node *root)
{
	node *temp = root->right;
	root->right = temp->left;
	temp->left = root;
	return temp;
}
node *R(node *root)
{
	node *temp = root->left;
	root->left = temp->right;
	temp->right = root;
	return temp;
}
node *RL(node *root)
{
	root->right = R(root->right);
	return L(root);
}
node *LR(node *root)
{
	root->left = L(root->left);
	return R(root);
}
int height(node *root)
{
	if(root == NULL) return 0;
	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->left = root->right = NULL;
	}else if(val < root->val){
		root->left = insert(root->left, val);
		if(height(root->left)-height(root->right)==2)
			root = val<root->left->val?R(root):LR(root);
		
	}else{
		root->right = insert(root->right, val);
		if(height(root->right)-height(root->left)==2)
			root = val>root->right->val?L(root):RL(root);
	}
	return root;
}
int main()
{
	int n,val;
	cin>>n;
	node *root = NULL;
	for(int i = 0; i < n; i++){
		cin>>val;
		root = insert(root, val); 
	}
	cout<<root->val;
	return 0;
}