04-树5 Root of AVL Tree

Posted 2021-01-13 shin0324

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

 

 1 #include<stdio.h>
 2 #include<stdlib.h>
 3 
 4 typedef struct AVLNode *PtrToAVLNode;
 5 struct AVLNode {
 6     int Data;
 7     PtrToAVLNode Left, Right;
 8     int Height;
 9 };
10 typedef PtrToAVLNode AVL;
11 
12 int Max(int a, int b) {
13     if (a > b) return a;
14     else return b;
15 }
16 
17 int GetHeight(AVL BT) {
18     int HL, HR, MAXH;
19     if(!BT) return 0;                 //空树高度为0 
20     else {
21         HL = GetHeight(BT->Left);     
22         HR = GetHeight(BT->Right);
23         MAXH = Max(HL, HR);           //递归求出左子树和右子树的高度，选其中较大的那个 
24         return (MAXH + 1);            //树的高度等于较大一边的字数高度+根结点 
25     }
26 }
27 
28 //左单旋 
29 AVL SingleLeftRotation(AVL A) {
30     AVL B = A->Left;
31     A->Left = B->Right;
32     B->Right = A;
33     A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;
34     B->Height = Max(GetHeight(B->Left), GetHeight(B->Right)) + 1;
35     return B;
36 }
37 
38 //右单旋 
39 AVL SingleRightRotation(AVL A) {
40     AVL B = A->Right;
41     A->Right = B->Left;
42     B->Left = A;
43     A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;
44     B->Height = Max(GetHeight(B->Left), GetHeight(B->Right)) + 1;
45     return B;
46 }
47 
48 //左-右双旋 
49 AVL DoubleLeftRightRotation(AVL A) {
50     A->Left = SingleRightRotation(A->Left) ;
51     return SingleLeftRotation(A);
52 }
53 
54 //右-左双旋 
55 AVL DoubleRightLeftRotation(AVL A) {
56     A->Right = SingleLeftRotation(A->Right);
57     return SingleRightRotation(A);
58 }
59 
60 //插入新结点函数，在高度差大于1时做出调整 
61 AVL Insert(AVL T1, int data) {
62     if (!T1) {
63         T1 = (AVL)malloc(sizeof(struct AVLNode));
64         T1->Data = data;
65         T1->Left = T1->Right = NULL;
66     }
67     else if (T1->Data > data) {
68         T1->Left = Insert(T1->Left, data);
69         if (GetHeight(T1->Left) - GetHeight(T1->Right) == 2) {
70             if (data < T1->Left->Data) {
71                 T1 = SingleLeftRotation(T1);
72             }
73             else T1 = DoubleLeftRightRotation(T1);
74         }
75     }
76     else if (T1->Data < data) {
77         T1->Right = Insert(T1->Right, data);
78         if (GetHeight(T1->Right) - GetHeight(T1->Left) == 2) {
79             if (data > T1->Right->Data) {
80                 T1 = SingleRightRotation(T1);
81             }
82             else T1 = DoubleRightLeftRotation(T1);
83         }
84     }
85     T1->Height = GetHeight(T1);                  //更新树高度 
86     return T1;
87 }
88 
89 int main() {
90     int N, data;
91     scanf("%d", &N);
92     AVL T = NULL;
93     while (N--) {
94         scanf("%d", &data);
95         T = Insert(T, data);
96     }
97     printf("%d", T->Data);          //打印头结点data 
98     return 0;
99 }