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:

Sample Input 2:

7

88 70 61 96 120 90 65

Sample Output 2:

 #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 ;

 }

巴特西