Raucous rockers-two-dimensional backpack

Raucous rockers

DescriptionYou just inherited the copyright of the unpublished N (1 <= n <= 20) songs recorded by the popular "rock and rock" band. You plan to select some songs from them and release m (1 <= m <= 20) CDs. Each CD can contain up to T (1 <= T <= 20) Minutes of music. A song cannot be divided into two CDs. Unfortunately, you are a fan of classical music and do not know how to determine the artistic value of these songs. Therefore, you decided to choose the following criteria: (1) the song must appear on the CD disk in the order of creation time. (2) select as many songs as possible. InputThe first row: Three integers n, T, M; the second row: N integers, indicating the length of each song, arranged in the order of creation time. OutputAn integer that represents the maximum number of music records that can be loaded into m CD disks. Sample Input4 5 2 4 4 2 Sample output3. Conclusion: although it looks like a two-dimensional backpack problem, it still takes a lot of time to compile it. The reason is that you are not clear about the idea and cannot calm down and look at the routine. Fortunately, I finally understood the routine and completed myself.

Code

  1 #include<stdio.h>
 2 #include<stdlib.h>
 3 #include<string.h>
 4 int n,m,t,f[21][21][21];
 5 int a[21];
 6 int main(){
 7     memset(f,0,sizeof(f));
 8     FILE *in,*out;
 9     in=fopen("input1.txt","r");
10     out=fopen("output.txt","w");
11     fscanf(in,"%d%d%d",&n,&t,&m);
12     int i,j,k;
13     for(i=1;i<=n;i++)
14     fscanf(in,"%d",&a[i]);
15     memset(f,0,sizeof(f));
16     
17     for(i=1;i<=m;i++)
18     for(j=1;j<=n;j++)
19     for(k=0;k<=t;k++)
20     if(k>=a[j])
21     {
22       f[i][j][k]=f[i][j-1][k-a[j]]+1;
23       if(f[i][j][k]<f[i-1][j][t])
24       f[i][j][k]=f[i-1][j][t];
25                }
26     else 
27     {       
28      f[i][j][k]=f[i-1][j][t]; 
29      if(f[i][j][k]<f[i][j-1][k])
30      f[i][j][k]=f[i][j-1][k];
31      }
32      
33     
34      fprintf(out,"%d\n",f[m][n][t]);
35        fclose(in);
36        fclose(out);
37        return 0;
38        }
39 

F [I] [J] [k] stands for: I am a CD, I am a j song, and I am a CD with K space available, up to the number of tracks to be recorded. A [J] is the length of song J. It can be transferred by the following States:

If (k> = A [J]) f [I] [J] [k] = max {f [I] [J-1] [k-A [J] + 1, f [I-1] [J] [T]);

Else f [I] [J] [k] = max {f [I-1] [J] [T], F [I] [J-1] [k]};

F [I] [J-1] [k-A [J] + 1 -- add the song J to the maximum number of recorded tracks on the I CD;

F [I-1] [J] [T] -- do not put the song J into the I disk, then look at the previous I-1 CD put J the maximum number of recorded songs;

F [I] [J-1] [k] -- the maximum number of recorded tracks for the first J-1 song on the first I CD.