动态规划-1-钢条切割（Dynamic Programming-1-rod cutting）

 1 #include <stdio.h>
 2 #define LEN 10
 3 #define NEGINF    -999999
 4 struct r_d {
 5     int r;    //profit
 6     int s;    //distance
 7 };
 8
 9 int price[LEN+1] = {0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 30};
10
11 int cut_rod(int price[], int n)
12 {
13     /*
14     DP-1-cut-rod.c:9:8: error: variable-sized object may not be initialized
15         int r[n+1] = {0, price[1]};
16               ^~~
17     int r[n+1] = {0, price[1]};
18     */
19     int r[LEN+1] = {0, price[1]};
20     int i, j, max;
21
22     for (i = 2; i <= n; i++) {
23         max = NEGINF;
24         for (j = i; j >= 1; j--)
25             max = (max > r[i-j] + price[j]) ? max : (r[i-j]+price[j]);
26         r[i] = max;
27     }
28     return r[n];
29 }
30
31 int extend_cut_rod(int price[], int n)
32 {
33     int r[LEN+1], s[LEN+1];
34     int i, j, max;
35     struct r_d sol;
36
37     r[0] = 0, s[0] = 0;
38     for (i = 1; i <= n; i++) {
39         max = NEGINF;
40         for (j = i; j >= 1; j--) {
41             if (max < r[i-j] + price[j]) {
42                 max = r[i-j] + price[j];
43                 s[i] = j;
44             }
45         }
46         r[i] = max;
47     }
48     for (i = 0; i <= n ; i++)
49         printf("extend_cut_rod.  s[%d] = %d\n", i, s[i]);
50     printf("===========================================\n");
51     for (i = 0; i <= n ; i++)
52         printf("extend_cut_rod.  r[%d] = %d\n", i, r[i]);
53     return r[n];
54 }
55
56 int extend_cut_rod_2(int price[], int n)
57 {
58     int r[LEN+1], s[LEN+1];
59     int i, j, max;
60     struct r_d sol;
61
62     r[0] = 0, s[0] = 0;
63     for (i = 1; i <= n; i++) {
64         max = NEGINF;
65         for (j = 1; j <= i; j++) {
66             if (max < r[i-j] + price[j]) {
67                 max = r[i-j] + price[j];
68                 s[i] = j;
69             }
70         }
71         r[i] = max;
72     }
73     for (i = 0; i <= n ; i++)
74         printf("extend_cut_rod_2.  s[%d] = %d\n", i, s[i]);
75     printf("===========================================\n");
76     for (i = 0; i <= n ; i++)
77         printf("extend_cut_rod_2.  r[%d] = %d\n", i, r[i]);
78     return r[n];
79 }
80
81 int main(int argc, char *argv[])
82 {
83     int r, i;
84
85     for (i = 0; i <= LEN; i++) {
86         r = cut_rod(price, i);
87         printf("cut-rod   r%d = %d\n", i, r);
88     }
89     printf("===========================================\n");
90     extend_cut_rod(price, 10);
91     printf("===========================================\n");
92     extend_cut_rod_2(price, 10);
93
94     return 0;
95 }