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.

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：

  1 #include <stdio.h>
  2 #include <stdlib.h>
  3 #include <unistd.h>
  4 
  5 typedef int ElementType;
  6 typedef struct AVLNode *Position;
  7 typedef Position AVLTree;
 
  8 
  9 struct AVLNode {
 10     ElementType Data;
 11     AVLTree Left;
 12     AVLTree Right;
 13     int Height;
 14 };
 15 
 16 int Max(int a, int b)
 17 {
 18     return a>b?a:b;
 19 }
 20 
 21 int GetHeight(AVLTree A)
 22 {
 23     int MaxH, HR, HL;
 24     if(A) {
 25         HL = GetHeight(A->Left);
 26         HR = GetHeight(A->Right);
 27         MaxH = (HL>HR)?HL:HR;
 28         return MaxH+1;
 29     }
 30     return -1;
 31 }
 32 
 33 AVLTree SingleLeftRotation(AVLTree A)
 34 {
 35     AVLTree B = A->Left;
 36     A->Left = B->Right;
 37     B->Right = A;
 38     A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;
 39     B->Height = Max(GetHeight(B->Left), A->Height) + 1;
 40 
 41     return B;
 42 }
 43 
 44 AVLTree SingleRightRotation(AVLTree A)
 45 {
 46     AVLTree B = A->Right;
 47     A->Right = B->Left;
 48     B->Left = A;
 49     A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;
 50     A->Height = Max(GetHeight(B->Right), A->Height) + 1;
 51 
 52     return B;
 53 }
 54 
 55 AVLTree DoubleLeftRightRotation(AVLTree A)
 56 {
 57     A->Left = SingleRightRotation(A->Left);
 58 
 59     return SingleLeftRotation(A);
 60 }
 61 
 62 AVLTree DoubleRightLeftRotation(AVLTree A)
 63 {
 64     A->Right = SingleLeftRotation(A->Right);
 65 
 66     return SingleRightRotation(A);
 67 }
 68 
 69 AVLTree Insert(AVLTree T, ElementType X)
 70 {
 71     if(!T) {
 72         T = (AVLTree)malloc(sizeof(struct AVLNode));
 73         T->Data = X;
 74         T->Height = 0;
 75         T->Left = T->Right = NULL;
 76     } else if(X < T->Data) {
 77         T->Left = Insert(T->Left, X);
 78         if(GetHeight(T->Left) - GetHeight(T->Right) == 2) {
 79             if(X < T->Left->Data)
 80                 T = SingleLeftRotation(T);
 81             else
 82                 T = DoubleLeftRightRotation(T);
 83         }
 84     } else if(X > T->Data) {
 85         T->Right = Insert(T->Right, X);
 86         if(GetHeight(T->Left) - GetHeight(T->Right) == -2) {
 87             if(X > T->Right->Data)
 88                 T = SingleRightRotation(T);
 89             else
 90                 T = DoubleRightLeftRotation(T);
 91         }
 92     }
 93 
 94     T->Height = Max(GetHeight(T->Left), GetHeight(T->Right)) + 1;
 95     return T;
 96 }
 97 
 98 int main()
 99 {
100     int N, i;
101     ElementType data;
102     AVLTree T;
103 
104     scanf("%d\n", &N);
105     for(i=0;i<N;i++) {
106         scanf("%d", &data);
107         T = Insert(T, data);
108     }
109     if(T)
110         printf("%d", T->Data);
111     return 0;
112 }

04-樹5 Root of AVL Tree（25 分）