hdu1712ACboy needs your help【分组背包入门题】

Problem Description

ACboy has N courses this term, and he plans to spend at most M days on study.Of course,the profit he will gain from different course depending on the days he spend on it.How to arrange the M days for the N courses to maximize the profit?

 

Input

The input consists of multiple data sets. A data set starts with a line containing two positive integers N and M, N is the number of courses, M is the days ACboy has.
Next follow a matrix A[i][j], (1<=i<=N<=100,1<=j<=M<=100).A[i][j] indicates if ACboy spend j days on ith course he will get profit of value A[i][j].
N = 0 and M = 0 ends the input.

 

Output

For each data set, your program should output a line which contains the number of the max profit ACboy will gain.

 

Sample Input

   
   
   
   

    
    
    
    2 2
1 2
1 3
2 2
2 1
2 1
2 3
3 2 1
3 2 1
0 0
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    3
4
6
   
   
   
   

 

Source

HDU 2007-Spring Programming Contest

 

昨天晚上开会总结了所有知识点，突然想起来分组背包没做过，果断早上滚来补题~

先说分组背包是什么玩意，分组分组，顾名思义，在背包里面的物品是分成不同组的，每个组只能取一件物品。类似于01背包的做法，很容易想到，背包的容量一定是从大到小递推才能保证每组物品只取一个，这么说来，组间的循环一定是第一层。那么还有第三层的循环是每组内的各个物品的循环。

再说这个题：第一层是不同科间的循环，第二层的循环是v从已知最大天数到0，第三层是组内循环也就是每个课程选几天的付出

/***************
hdu1712
2016.3.13
93MS	1624K	724 B	G++
***************/
#include <iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int num[110][110],n,m;
int dp[110];
int max(int a,int b){if(a>b)return a;return b;}
int main()
{
   // freopen("cin.txt","r",stdin);
    while(~scanf("%d%d",&n,&m))
    {
        if(m==0&&n==0)break;
        for(int i=1;i<=n;i++)
            for(int j=1;j<=m;j++)
                scanf("%d",&num[i][j]);
        memset(dp,0,sizeof(dp));
        for(int k=1;k<=n;k++)//the type of course
            for(int v=m;v>=0;v--)
                for(int j=1;j<=v;j++)
                    dp[v]=max(dp[v],dp[v-j]+num[k][j]);
        printf("%d\n",dp[m]);
    }
    return 0;
}