HDU 1712 ACboy needs your help

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

 

解题思路：

转化成01背包问题，利用j天复习第i门课视为一种物品，该物品的体积为j，价值为m[i][j],要注意的是每门课只能选一次

#include<iostream>
#include<math.h>
#include<stdio.h>
#include<string.h>
using namespace std;
int DP[5000],m[5000][5000],N,M;
int w[5000],v[5000];
int max(int x,int y) {
 return (x>y? x:y);
}
int main () {
 while(scanf("%d%d",&N,&M)&&(N||M)) {
  memset(DP,0,sizeof(DP));
  for(int i=1;i<=N;++i)
  for(int j=1;j<=M;++j)
  scanf("%d",&m[i][j]);
  for(int i=1;i<=N;++i)
  for(int j=M;j>=1;--j)
  for(int k=1;k<=j;++k)
  DP[j]=max(DP[j],DP[j-k]+m[i][k]);
  printf("%d\n",DP[M]);
 }
 return 0;
}