PAT 甲级 A1066 Root of AVL Tree

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

题意：

这个一颗AVL（平衡二叉）树，依次给出n个插入结点的权，求建完树后的根节点的权值是多少？

思路：
直接建立一颗AVL树，AVL树比二叉查找树多了一个高度，还有调平衡。

	#include
	using namespace std;
	const int maxn=55;
	int weight[maxn];
	int n;
	struct node {
		int height;
		int data;
		node* lchild;
		node* rchild;
	};
	
	node* newNode(int x){
	 	node* Node=new node;
	 	Node->height=1;//新节点初始化高度为1,空结点高度为0; 
	 	Node->data=x;
	 	Node->lchild=NULL;
	 	Node->rchild=NULL;
	 	return Node;
	}
	
	int getHeight(node* root){
		if(root == NULL) return 0;//空树的高度为0;
		return root->height; 
	}
	
	
	void  updateHeight(node* root){//算出该结点的高度; 
		root->height = max(getHeight(root->lchild),getHeight(root->rchild)) + 1;
		return ;
	} 
	
	int getBalanceFactor(node* root){//算出该结点的平衡因子; 
		return getHeight(root->lchild) - getHeight(root->rchild); 
	}
	
	void L(node* &root){//左旋; 
		node* temp = root->rchild;
		root->rchild = temp->lchild;
		temp->lchild = root;
		updateHeight(root);//旋转后记得更新旋转后结点的高度； 
		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 x){
		if(root == NULL){
			root = newNode(x);
			return;
		}
		if(x data){
			insert(root->lchild,x);
			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,x);
			updateHeight(root);
			if(getBalanceFactor(root) == -2){
				if(getBalanceFactor(root->rchild) == -1){
					L(root);
				}
				else if(getBalanceFactor(root->rchild) == 1){
					R(root->rchild);
					L(root);
				}
			}
		}
	}
	
	//左旋右旋和插入都是需要改变二叉树结构的，所以需要用到引用; 
	
	int main( ){
		node* root = NULL;
		scanf("%d",&n);
		for(int i=0;i"%d",&weight[i]);//pat里面数组尽量不要叫做data；
		for(int i=0;i
			insert(root,weight[i]);
		}
		printf("%d",root->data);
		return 0;
	}