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代碼

 1 #include<stdio.h>
 2 #include<stdlib.h>
 3 
 4 typedef struct AVLNode *AVLTree;
 5 struct AVLNode{
 
 6   int data;
 7   AVLTree right;
 8   AVLTree left;
 9   //int height;
10 };
11 int Max(int a,int b){
12   return (a>b?a:b);
13 } 
14 
15 int GetTreeHeight(AVLTree T){
16   int HL,HR;
17   if(T){
18     HL = GetTreeHeight(T->left);
19     HR = GetTreeHeight(T->right);
20     return Max(HL,HR)+1;
21   }
22   else return 0;
23 }
24 AVLTree rotationLL(AVLTree T){
25   AVLTree temp = T->left;
26   T->left = temp->right;
27   temp->right = T;
28   return temp;
29 }
30 AVLTree rotationRR(AVLTree T){
31   
32   AVLTree temp = T->right;
33   T->right = temp->left;
34   temp->left = T;
35   return temp;
36 }
37 AVLTree rotationLR(AVLTree T){
38   T->left = rotationRR(T->left);
39   return rotationLL(T);
40 }
41 AVLTree rotationRL(AVLTree T){
42   T->right = rotationLL(T->right);
43   return rotationRR(T);
44 }
45 
46 AVLTree InsertAVLNode(AVLTree T,int X){
47   if(!T){
48     T = (AVLTree)malloc(sizeof(struct AVLNode));
49     T->data = X;
50     T->right = T->left = NULL;
51    // T->hight = 0;
52   }else 
53     if(X<T->data){
54       T->left = InsertAVLNode(T->left,X);
55       if(GetTreeHeight(T->left) - GetTreeHeight(T->right) == 2){
56         if(X < T->left->data){
57           T = rotationLL(T);
58         }else
59         {
60           T = rotationLR(T);
61         }
62       }
63     }else if(X > T->data){
64       T->right = InsertAVLNode(T->right,X);
65       if(GetTreeHeight(T->right) - GetTreeHeight(T->left)==2){
66         if(X < T->right->data){
67           T = rotationRL(T);
68         }else
69         {
70           T = rotationRR(T);
71         }
72       }
73     }
74   
75   //T->height = Max(GetTreeHeight(T->left) , GetTreeHeight(T->right))
76   return T;
77 }
78 int main(){
79   
80   int k;
81   int Data;
82   AVLTree T = NULL;
83   scanf("%d",&k);
84   for(int i = 0; i <k; i++){
85     
86     scanf("%d",&Data);
87     T = InsertAVLNode(T,Data);
88   }
89   printf("%d",T->data);
90   return 0;
91 }

Root of AVL Tree