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 (≤) 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

AC代码

#include<stdio.h>
#include<stdlib.h>

typedef struct AVLNode *AVLTree;
struct AVLNode{
  int data;
  AVLTree right;
  AVLTree left;
  //int height;
};
int Max(int a,int b){
  return (a>b?a:b);
} 

int GetTreeHeight(AVLTree T){
  int HL,HR;
  if(T){
    HL = GetTreeHeight(T->left);
    HR = GetTreeHeight(T->right);
    return Max(HL,HR)+1;
  }
  else return 0;
}
AVLTree rotationLL(AVLTree T){
  AVLTree temp = T->left;
  T->left = temp->right;
  temp->right = T;
  return temp;
}
AVLTree rotationRR(AVLTree T){
  
  AVLTree temp = T->right;
  T->right = temp->left;
  temp->left = T;
  return temp;
}
AVLTree rotationLR(AVLTree T){
  T->left = rotationRR(T->left);
  return rotationLL(T);
}
AVLTree rotationRL(AVLTree T){
  T->right = rotationLL(T->right);
  return rotationRR(T);
}

AVLTree InsertAVLNode(AVLTree T,int X){
  if(!T){
    T = (AVLTree)malloc(sizeof(struct AVLNode));
    T->data = X;
    T->right = T->left = NULL;
   // T->hight = 0;
  }else 
    if(X<T->data){
      T->left = InsertAVLNode(T->left,X);
      if(GetTreeHeight(T->left) - GetTreeHeight(T->right) == 2){
        if(X < T->left->data){
          T = rotationLL(T);
        }else
        {
          T = rotationLR(T);
        }
      }
    }else if(X > T->data){
      T->right = InsertAVLNode(T->right,X);
      if(GetTreeHeight(T->right) - GetTreeHeight(T->left)==2){
        if(X < T->right->data){
          T = rotationRL(T);
        }else
        {
          T = rotationRR(T);
        }
      }
    }
  
  //T->height = Max(GetTreeHeight(T->left) , GetTreeHeight(T->right))
  return T;
}
int main(){
  
  int k;
  int Data;
  AVLTree T = NULL;
  scanf("%d",&k);
  for(int i = 0; i <k; i++){
    
    scanf("%d",&Data);
    T = InsertAVLNode(T,Data);
  }
  printf("%d",T->data);
  return 0;
}