1 #include <stdio.h>
2 #include <stdlib.h>
3 #define FALSE 0
4 #define TRUE 1
5 char chos;
6 int input;
7
8 struct node{
9 int data;
10 int bf;
11 struct node *lchild;
12 struct node *rchild;
13 };
14
15 typedef struct node *BST;
16 BST R = NULL;
17
18 void chose()
19 {
20 printf("i) Insert a point \n"
21 "d) Delete a point \n"
22 "e) exit\n"
23 "Input your choose:");
24 scanf("%c", &chos);
25 }
26
27 int Height(BST T)
28 {
29 if(T == NULL)
30 return -1;
31 else
32 return T->bf;
33 }
34
35 int Max(int a, int b)
36 {
37 return (a > b ? a : b);
38 }
39
40 /*RR旋转*/
41 /* k1指向k2的右子树，沿着k2旋转，使得k1成为根节点，并返回k1*/
42 BST SingleRotatewithRight(BST k2)
43 {
44 BST k1;
45 k1 = k2->rchild;
46 k2->rchild = k1->lchild;
47 k1->lchild = k2;
48 k2->bf = Max(Height(k2->lchild), Height(k2->rchild));
49 k1->bf = Max(Height(k1->lchild), Height(k1->rchild));
50 return k1;
51 }
52
53 /*LL旋转 */
54 /**/
55 BST SingleRotatewithLeft(BST k2)
56 {
57 BST k1;
58 k1 = k2->lchild;
59 k2->lchild = k1->rchild;
60 k1->rchild = k2;
61 k2->bf = Max(Height(k2->lchild), Height(k2->rchild));
62 k1->bf = Max(Height(k1->lchild), Height(k1->rchild));
63 return k1;
64 }
65
66 /* LR旋转 */
67 /**/
68 BST DoubleRotatewithLeft(BST k3)
69 {
70 k3->lchild = SingleRotatewithRight(k3->lchild);
71 return SingleRotatewithLeft(k3);
72 }
73
74 /* RL旋转 */
75 BST DoubleRotatewithRight(BST k3)
76 {
77 k3->rchild = SingleRotatewithLeft(k3->rchild);
78 return SingleRotatewithRight(k3);
79 }
80
81 void OUT(BST T)
82 {
83 if(T->lchild)
84 {
85 printf("Left\t%d[parent:%d]\n", T->lchild->data, T->data);
86 OUT(T->lchild);
87 }
88 if(T->rchild)
89 {
90 printf("Right\t%d[parent:%d]\n", T->rchild->data, T->data);
91 OUT(T->rchild);
92 }
93 }
94
95 /* 调整单个节点，在此定义平衡因子为 Height(lchile) - Height(rchild) */
96 /**/
97 BST Rotate(BST T)
98 {
99 if(Height(T->lchild) - Height(T->rchild) == 2)
100 {
101 if(Height(T->lchild->lchild) >= Height(T->lchild->rchild))
102 T = SingleRotatewithLeft(T);
103 else
104 T = DoubleRotatewithLeft(T);
105 }
106 if(Height(T->rchild) - Height(T->lchild) == 2)
107 {
108 if(Height(T->rchild->rchild) >= Height(T->rchild->lchild))
109 T = SingleRotatewithRight(T);
110 else
111 T = DoubleRotatewithRight(T);
112 }
113 return T;
114 }
115
116 BST AVLInsert(BST T)
117 {
118 if(T == NULL)
119 {/* 若二叉树为空，则创建二叉树 */
120 T = (BST)malloc(sizeof(struct node));
121 if(T == NULL)
122 {
123 perror("malloc");
124 exit(-1);
125 }
126 T->data = input;
127 T->lchild = NULL;
128 T->rchild = NULL;
129 T->bf = 0;
130 }
131 else if(input < T->data)
132 {/* 将节点插入左子树中，采用递归 */
133 T->lchild = AVLInsert(T->lchild);
134 if(Height(T->lchild) - Height(T->rchild) == 2)
135 {
136 if(input < T->lchild->data)
137 T = SingleRotatewithLeft(T);
138 else
139 T = SingleRotatewithLeft(T);
140 }
141 }
142 else if(input > T->data)
143 {
144 T->rchild = AVLInsert(T->rchild);
145 if(Height(T->rchild) - Height(T->lchild) == 2)
146 {
147 if(input > T->rchild->data)
148 T = SingleRotatewithRight(T);
149 else
150 T = DoubleRotatewithRight(T);
151 }
152 }
153 T->bf = Max(Height(T->lchild), Height(T->rchild)) + 1;
154 return T;
155 }
156
157
158 void output(BST T)
159 {
160 if(T == NULL)
161 printf("None\n");
162 else
163 {
164 printf("%d\troot\n", T->data);
165 OUT(T);
166 }
167 }
168
169
170 void Insert()
171 {
172 printf("\nInput the point your want to Insert:");
173 scanf("%d", &input);
174 R = AVLInsert(R);
175 output(R);
176 }
177
178
179 BST AVLDelete(BST T, int key)
180 {
181 if(T == NULL)
182 return NULL;
183 if(key == T->data)
184 {
185 if(T->rchild == NULL)
186 {
187 BST tmp = T;
188 T = T->lchild;
189 free(tmp);
190 }
191 else
192 {/* 选择右子树最左节点作为新二叉树的根节点,并将这个最左节点删除 */
193 BST tmp = T->rchild;
194 while(tmp->lchild != NULL)
195 tmp = tmp->lchild;
196 T->data = tmp->data;
197 T->rchild = AVLDelete(T->rchild, tmp->data);
198 T->bf = Max(Height(T->lchild), Height(T->rchild)) + 1;
199 }
200 return T;
201 }
202 else if(key < T->data)
203 {
204 T->lchild = AVLDelete(T->lchild, key);
205 }
206 else
207 {
208 T->rchild = AVLDelete(T->rchild, key);
209 }
210 T->bf = Max(Height(T->lchild), Height(T->rchild)) + 1;
211 if(T->lchild != NULL)
212 T->lchild = Rotate(T->lchild);
213 if(T->rchild != NULL)
214 T->rchild = Rotate(T->rchild);
215 T = Rotate(T);
216 return T;
217 }
218
219 void Delete()
220 {
221 printf("\nInput the point you want to Delete: ");
222 scanf("%d", &input);
223 R = AVLDelete(R, input);
224 output(R);
225 }
226
227 int main()
228 {
229 while(1)
230 {
231 chose();
232 switch(chos)
233 {
234 case 'i':
235 Insert();
236 break;
237 case 'd':
238 Delete();
239 break;
240 case 'e':
241 exit(0);
242 }
243 }
244 return 0;
245 }
