0/1背包问题的分支定界法算法

1. #include<stdio.h>
2. #include<stdlib.h>
4. #define MAXNUM 100
6. struct node{
7. int step;
8. double price;
9. double weight;
10. double max, min;
11. unsigned long po;
12. };
14. typedef struct node DataType;
15. struct SeqQueue { /* 顺序队列类型定义 */
16. int f, r;
17. DataType q[MAXNUM];
18. };
19. typedef struct SeqQueue *PSeqQueue;
22. PSeqQueue createEmptyQueue_seq( void ) {
23. PSeqQueue paqu;
24. paqu = (PSeqQueue)malloc(sizeof(struct SeqQueue));
25. if (paqu == NULL)
26. printf("Out of space!! /n");
27. else
28. paqu->f = paqu->r = 0;
30. return paqu;
31. }
33. int isEmptyQueue_seq( PSeqQueue paqu ) {
34. return paqu->f == paqu->r;
35. }
37. /* 在队列中插入一元素x */
38. void enQueue_seq( PSeqQueue paqu, DataType x ) {
39. if( (paqu->r + 1) % MAXNUM == paqu->f )
40. printf( "Full queue./n" );
41. else {
42. paqu->q[paqu->r] = x;
43. paqu->r = (paqu->r + 1) % MAXNUM;
44. }
45. }
47. /* 删除队列头元素 */
48. void deQueue_seq( PSeqQueue paqu ) {
49. if( paqu->f == paqu->r )
50. printf( "Empty Queue./n" );
51. else
52. paqu->f = (paqu->f + 1) % MAXNUM;
53. }
55. /* 对非空队列,求队列头部元素 */
56. DataType frontQueue_seq( PSeqQueue paqu ) {
57. return (paqu->q[paqu->f]);
58. }
60. /* 物品按性价比从新排序*/
61. void sort(int n, double p[], double w[]){
62. int i, j;
63. for (i = 0; i < n-1; i++)
64. for (j = i; j < n-1; j++) {
65. double a = p[j]/w[j];
66. double b = p[j+1]/w[j+1];
67. if (a < b) {
68. double temp = p[j];
69. p[j] = p[j+1];
70. p[j+1] = temp;
71. temp = w[j];
72. w[j] = w[j+1];
73. w[j+1] = temp;
74. }
75. }
76. }
78. /* 求最大可能值*/
79. double up(int k, double m, int n, double p[], double w[]){
80. int i = k;
81. double s = 0;
82. while (i < n && w[i] < m) {
83. m -= w[i];
84. s += p[i];
85. i++;
86. }
87. if (i < n && m > 0) {
88. s += p[i] * m / w[i];
89. i++;
90. }
91. return s;
92. }
94. /* 求最小可能值*/
95. double down(int k, double m, int n, double p[], double w[]){
96. int i = k;
97. double s = 0;
98. while (i < n && w[i] <= m) {
99. m -= w[i];
100. s += p[i];
101. i++;
102. }
103. return s;
104. }
106. /* 用队列实现分支定界算法*/
107. double solve(double m, int n, double p[], double w[], unsigned long* po){
108. double min;
109. PSeqQueue q = createEmptyQueue_seq();
110. DataType x = {0,0,0,0,0,0};
111. sort(n, p, w);
112. x.max = up(0, m, n, p, w);
113. x.min = min = down(0, m, n, p, w);
114. if (min == 0) return -1;
115. enQueue_seq(q, x);
116. while (!isEmptyQueue_seq(q)){
117. int step;
118. DataType y;
119. x = frontQueue_seq(q);
120. deQueue_seq(q);
121. if (x.max < min) continue;
122. step = x.step + 1;
123. if (step == n+1) continue;
124. y.max = x.price + up(step, m - x.weight, n, p, w);
125. if (y.max >= min) {
126. y.min = x.price + down(step, m-x.weight, n, p, w);
127. y.price = x.price;
128. y.weight = x.weight;
129. y.step = step;
130. y.po = x.po << 1;
131. if (y.min >= min) {
132. min = y.min;
133. if (step == n) *po = y.po;
134. }
135. enQueue_seq(q, y);
136. }
137. if (x.weight + w[step-1] <= m) {
138. y.max = x.price + p[step-1] +
139. up(step, m-x.weight-w[step-1], n, p, w);
140. if (y.max >= min) {
141. y.min = x.price + p[step-1] +
142. down(step, m-x.weight-w[step-1], n, p, w);
143. y.price = x.price + p[step-1];
144. y.weight = x.weight + w[step-1];
145. y.step = step;
146. y.po = (x.po << 1) + 1;
147. if (y.min >= min) {
148. min = y.min;
149. if (step == n) *po = y.po;
150. }
151. enQueue_seq(q, y);
152. }
153. }
154. }
155. return min;
156. }
158. #define n 4
160. double m = 15;
161. double p[n] = {10, 10, 12, 18};
162. double w[n] = {2, 4, 6, 9};
164. int main() {
165. int i;
166. double d;
167. unsigned long po;
168. d = solve(m, n, p, w, &po);
169. if (d == -1)
170. printf("No solution!/n");
171. else {
172. for (i = 0; i < n; i++)
173. printf("x%d is %d/n", i + 1, ((po & (1<<(n-i-1))) != 0));
174. printf("The max weight is %f/n", d);
175. }
176. getchar();
177. return 0;
178. }