1066 Root of AVL Tree (25）

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 Ndistinct 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

#include<cstdio>
#include<algorithm>
using namespace std;
struct Node{
     int v,height;
     Node* lchild,*rchild;
}*root;

Node* newNode(int v){
    Node* node = new Node;
    node -> v = v;
    node -> lchild = node -> rchild = NULL;
    node -> height = 1;
    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 R(Node* &root){
    Node* temp =  root -> lchild;
    root -> lchild = temp -> rchild;
    temp -> rchild = root;
    updateHeight(root);
    updateHeight(temp);
    root = temp;
}
void L(Node* &root){
    Node* temp = root -> rchild;
    root -> rchild = temp -> lchild;
    temp -> lchild = root;
    updateHeight(root);  //先更新root（子树）的高度
    updateHeight(temp);
    root = temp;
}

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){
                R(root);
            }else if(getBalanceFactor(root -> lchild) == -1){
                L(root -> lchild);
                R(root);
            }
        }
    }else{
        insert(root -> rchild,v);
        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 main(){
    int n,v;
    scanf("%d",&n);
    for(int i = 0; i < n; i++){
        scanf("%d",&v);
        insert(root,v);
    }
    printf("%d",root -> v);
    return 0;
}