1066 Root of AVL Tree （模拟AVL建树）

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 (≤) 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

　

标准的模板题，为方便记忆，对7个函数的返回类型归纳如下：

1个node* （newNode）

2个int（getHeight， getBalance）

4个void （updateHeight，L，R，insert ）

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

struct node{
    int data,height;
    node *left,*right;
}*root;

node* newNode(int x){
    node *ret=new node;
    ret->data=x;
    ret->height=1;
    ret->left=ret->right=NULL;
    return ret;
}

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

int getBalance(node *root){
    return getHeight(root->left)-getHeight(root->right);
}

void updateHeight(node *root){
    int hleft=getHeight(root->left);
    int hright=getHeight(root->right);
    root->height=max(hleft,hright)+1;
}

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

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

void insert(node* &root,int x){
    if(root==NULL){
        root=newNode(x);
        return;//空return更简洁，不用else 
    }
    if(x<root->data){
        insert(root->left,x);
        updateHeight(root);//* 
        if(getBalance(root)==2){
            if(getBalance(root->left)==1){
                R(root);
            }else if(getBalance(root->left)==-1){
                L(root->left);//* 
                R(root);//* 
            }
        }
    }else{
        insert(root->right,x);
        updateHeight(root);
        if(getBalance(root)==-2){
            if(getBalance(root->right)==-1){
                L(root);
            }else if(getBalance(root->right)==1){
                R(root->right);
                L(root);
            }
        }
    }    
}

int main(){
    int n,v;
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d",&v);
        insert(root,v);
    }
    printf("%d",root->data);
    return 0;
}