1066 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:给你一组数,要求生成一个二叉平衡树(AVL),输出根节点

分析: 主要是构建二叉平衡树。
二叉平衡树主要有四种操作:
左旋
右旋
先左后右
先右后左

代码


using namespace std;


struct Node

int data;
int height;
Node* lchild;
Node* rchild;

}*root;
Node *New(int v)
{
Node *node = new Node;
node->data = 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;
//cout<<"temp :"<<temp->data<<endl;
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 val)
{

if(root==NULL)
{
root = New(val);
//cout<<"root: "<<root->data<<" "<<root->height<<endl;
return ;
}
//cout<<"root: "<<root->data<<" "<<root->height<<endl;
if(val<root->data)
{
Insert(root->lchild,val);
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,val);
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 n;
int main()
{
while(scanf("%d",&n)!=EOF)
{
int x;
for(int i=0;i<n;i++)
{
scanf("%d",&x);
Insert(root,x);
}
cout<<root->data<<endl;
}
return 0;
}