04-树5 Root of AVL Tree（25 分）

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 (≤20) 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

我的答案：

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

 typedef int ElementType;
 typedef struct AVLNode *Position;
 typedef Position AVLTree;

 struct AVLNode {
     ElementType Data;
     AVLTree Left;
     AVLTree Right;
     int Height;
 };

 int Max(int a, int b)
 {
     return a>b?a:b;
 }

 int GetHeight(AVLTree A)
 {
     int MaxH, HR, HL;
     if(A) {
         HL = GetHeight(A->Left);
         HR = GetHeight(A->Right);
         MaxH = (HL>HR)?HL:HR;
         return MaxH+;
     }
     return -;
 }

 AVLTree SingleLeftRotation(AVLTree A)
 {
     AVLTree B = A->Left;
     A->Left = B->Right;
     B->Right = A;
     A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + ;
     B->Height = Max(GetHeight(B->Left), A->Height) + ;

     return B;
 }

 AVLTree SingleRightRotation(AVLTree A)
 {
     AVLTree B = A->Right;
     A->Right = B->Left;
     B->Left = A;
     A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + ;
     A->Height = Max(GetHeight(B->Right), A->Height) + ;

     return B;
 }

 AVLTree DoubleLeftRightRotation(AVLTree A)
 {
     A->Left = SingleRightRotation(A->Left);

     return SingleLeftRotation(A);
 }

 AVLTree DoubleRightLeftRotation(AVLTree A)
 {
     A->Right = SingleLeftRotation(A->Right);

     return SingleRightRotation(A);
 }

 AVLTree Insert(AVLTree T, ElementType X)
 {
     if(!T) {
         T = (AVLTree)malloc(sizeof(struct AVLNode));
         T->Data = X;
         T->Height = ;
         T->Left = T->Right = NULL;
     } else if(X < T->Data) {
         T->Left = Insert(T->Left, X);
         if(GetHeight(T->Left) - GetHeight(T->Right) == ) {
             if(X < T->Left->Data)
                 T = SingleLeftRotation(T);
             else
                 T = DoubleLeftRightRotation(T);
         }
     } else if(X > T->Data) {
         T->Right = Insert(T->Right, X);
         if(GetHeight(T->Left) - GetHeight(T->Right) == -) {
             if(X > T->Right->Data)
                 T = SingleRightRotation(T);
             else
                 T = DoubleRightLeftRotation(T);
         }
     }

     T->Height = Max(GetHeight(T->Left), GetHeight(T->Right)) + ;
     return T;
 }

 int main()
 {
     int N, i;
     ElementType data;
     AVLTree T;

     scanf("%d\n", &N);
     for(i=;i<N;i++) {
         scanf("%d", &data);
         T = Insert(T, data);
     }
     if(T)
         printf("%d", T->Data);
     return ;
 }