CD UVA - 624（背包输出方案）

You have a long drive by car ahead. You have a tape recorder, but unfortunately your best music is on
CDs. You need to have it on tapes so the problem to solve is: you have a tape N minutes long. How
to choose tracks from CD to get most out of tape space and have as short unused space as possible.
Assumptions:
• number of tracks on the CD does not exceed 20
• no track is longer than N minutes
• tracks do not repeat
• length of each track is expressed as an integer number
• N is also integer
Program should find the set of tracks which fills the tape best and print it in the same sequence as
the tracks are stored on the CD
Input
Any number of lines. Each one contains value N, (after space) number of tracks and durations of the
tracks. For example from first line in sample data: N = 5, number of tracks=3, first track lasts for 1
minute, second one 3 minutes, next one 4 minutes
Output
Set of tracks (and durations) which are the correct solutions and string ‘sum:’ and sum of duration
times.
Sample Input
5 3 1 3 4
10 4 9 8 4 2
20 4 10 5 7 4
90 8 10 23 1 2 3 4 5 7
45 8 4 10 44 43 12 9 8 2
Sample Output
1 4 sum:5
8 2 sum:10
10 5 4 sum:19
10 23 1 2 3 4 5 7 sum:55
4 10 12 9 8 2 sum:45

题意： 输出背包方案
思路： 定义数组pre[i][j]代表这个状态是否发生转移。从后往前转移，那么输出的时候就可以从前往后输出。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

int pre[25][10005];
int f[10005],a[25];

int main()
{
	int n,m;
	while(~scanf("%d%d",&m,&n))
	{
		memset(f,0,sizeof(f));memset(pre,0,sizeof(pre));
		for(int i = 1;i <= n;i++)scanf("%d",&a[i]);
		for(int i = n;i >= 1;i--)
		{
			for(int j = m;j >= a[i];j--)
			{
				if(f[j] < f[j - a[i]] + a[i])
				{
					f[j] = f[j - a[i]] + a[i];
					pre[i][j] = 1;
				}
			}
		}
		int num = m;
		for(int i = 1;i <= n;i++)
		{
			if(pre[i][num])
			{
				printf("%d ",a[i]);
				num -= a[i];
			}
		}
		printf("sum:%d\n",f[m]);
	}
	return 0;
}