CD(01背包)

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
题目大意：
给定n,m，然后给m个数字，组成尽可能接近n的和，以及组成部分具体数字 
解题思路：
01背包模板，需要进行记录路径.

#include <bits/stdc++.h>
using namespace std;
const int N=1e4+5;
int dp[N],val[25];
int vis[25][N];///记录路径
int main()
{
    int n,m;
    while(cin>>n>>m)
    {
        memset(dp,0,sizeof dp);
        memset(vis,0,sizeof vis);
        for(int i=0;i<m;i++)
            cin>>val[i];
        for(int i=0;i<m;i++)
        {
            for(int j=n;j>=val[i];j--)
            {
                if(dp[j]<=dp[j-val[i]]+val[i])
                    dp[j]=dp[j-val[i]]+val[i],vis[i][j]=1;
            }
        }
        int j=n;
        for(int i=m-1;i>=0;i--)///从后往前的线路是唯一的
        {
            if(vis[i][j])
                cout<<val[i]<<' ',j-=val[i];
        }
        cout<<"sum:"<<dp[n]<<'\n';
    }
}

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