1066 Root of AVL Tree (25分)

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

 

 

題解：

#include <iostream>
#include <algorithm>
using namespace std;

struct Node
{
	int v, height;
	Node *lchild, *rchild;
}*root;

Node* newNode(int v) {
	Node* node = new Node;
	node->v = v;
	node->height = 1;
	node->lchild = node->rchild = NULL;
	return node;
}

int getHeight(Node *root) {
	if (root == NULL) return 0;
	return root->height;
}

void updateHeight(Node *root) {
	root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
}

int getBalanceFactor(Node *root) {
	return getHeight(root->lchild) - getHeight(root->rchild);
}

void L(Node* &root) {
	Node* temp = root->rchild;
	root->rchild = temp->lchild;
	temp->lchild = root;
	updateHeight(root);
	updateHeight(temp);
	root = temp;
}

void R(Node* &root) {
	Node* temp = root->lchild;
	root->lchild = temp->rchild;
	temp->rchild = root;
	updateHeight(root);
	updateHeight(temp);
	root = temp;
}

void insert(Node* &root, int v) {
	if (root == NULL)
	{
		root = newNode(v);
		return;
	}
	if (v<root->v)
	{
		insert(root->lchild, v);
		updateHeight(root);
		if (getBalanceFactor(root) == 2)
		{
			if (getBalanceFactor(root->lchild) == 1)
				R(root);
			else if (getBalanceFactor(root->lchild) == -1)
			{
				L(root->lchild);
				R(root);
			}
		}
	}
	else
	{
		insert(root->rchild, v);
		updateHeight(root);
		if (getBalanceFactor(root) == -2)
		{
			if (getBalanceFactor(root->rchild) == -1)
				L(root);
			else if (getBalanceFactor(root->rchild) == 1)
			{
				R(root->rchild);
				L(root);
			}
		}
	}
}

int main() {
	int n, v;
	cin >> n;
	for (int i = 0; i < n; i++)
	{
		cin >> v;
		insert(root, v);
	}
	cout << root->v;
    return 0;
}