1066 Root of AVL Tree

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
题意：给出N个正整数，将它们依次插入初始状态为空的AVL树上，求插入后根结点的值
左旋

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

右旋

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

总结

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)
			{
				//LL型
				R(root); 
			}
			else if(getBalanceFactor(root->lchild)==-1)
			{
				//LR型
				L(root->lchild);
				R(root); 
			}
		} 
	}
	else{
		insert(root->rchild,v);
		updateHeight(root);
		if(getBalanceFactor(root)==-2)
		{
			if(getBalanceFactor(root->rchild)==-1)
			{
				//RR型
				L(root); 
			}
			else if(getBalanceFactor(root->rchild)==1)
			{
				//RL型
				R(root->rchild);
				L(root); 
			}
		}
	}
} 

整道题代码

#include<cstdio>
#include<algorithm>
using namespace std;
struct node
{
	int v,height;//v为结点权值，height为当前子树高度
	node *lchild,*rchild; 
}*root;
//生成一个新结点，v为结点权值
node* newNode(int v)
{
	node* Node=new node;
	Node->v=v;
	Node->height=1;
	Node->lchild=Node->rchild=NULL;
	return Node; 
} 
//获取以root为根结点的子树的当前height
int getHeight(node* root)
{
	if(root==NULL)return 0;
	return root->height;
} 
//更新结点root的height
void updateHeight(node* root)
{
	root->height=max(getHeight(root->lchild),getHeight(root->rchild))+1;
} 
//计算结点root的平衡因子
int getBalanceFactor(node* root)
{
	return getHeight(root->lchild)-getHeight(root->rchild);
}
//左旋
void L(node* &root)
{
    node* temp=root->rchild;
    root->rchild=temp->lchild;
    temp->lchild=root;
    updateHeight(root);
    updateHeight(temp);
    root=temp;
}
//右旋 
void R(node* &root)
{
	node* temp=root->lchild;
	root->lchild=temp->rchild;
	temp->rchild=root;
	updateHeight(root);
	updateHeight(temp);
	root=temp;
} 
//插入权值为v的结点
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)
			{
				//LL型
				R(root); 
			}
			else if(getBalanceFactor(root->lchild)==-1)
			{
				//LR型
				L(root->lchild);
				R(root); 
			}
		} 
	}
	else{
		insert(root->rchild,v);
		updateHeight(root);
		if(getBalanceFactor(root)==-2)
		{
			if(getBalanceFactor(root->rchild)==-1)
			{
				//RR型
				L(root); 
			}
			else if(getBalanceFactor(root->rchild)==1)
			{
				//RL型
				R(root->rchild);
				L(root); 
			}
		}
	}
} 
//AVL树的建立
node* Create(int data[],int n)
{
	node* root=NULL;
	for(int i=0;i<n;i++)
	{
		insert(root,data[i]);
	}
	return root;
} 
int main()
{
	int n,v;
	scanf("%d",&n);
	for(int i=0;i<n;i++)
	{
		scanf("%d",&v);
		insert(root,v);
	}
	printf("%d\n",root->v);
	return 0;
}