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;
}

1066 root of avl tree

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