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 = ;
     return node;
 }

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

 void updateHeight(Node* root){
      root -> height = max(getHeight(root -> lchild),getHeight(root -> rchild))+;
 } 

 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) == ){
             if(getBalanceFactor(root -> lchild) == ){
                 R(root);
             }else if(getBalanceFactor(root -> lchild) == -){
                 L(root -> lchild);
                 R(root);
             }
         }
     }else{
         insert(root -> rchild,v);
         updateHeight(root);
         if(getBalanceFactor(root) == -){
             if(getBalanceFactor(root -> rchild) == -){
                 L(root);
             }else if(getBalanceFactor(root -> rchild) == ){
                 R(root -> rchild);
                 L(root);

             }
         }
     }
 }

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