分组背包问题+求具体方案

$ 时间复杂度O(NMM)，空间复杂度O(NM) $

需要用一维数组来记录每组选的什么

参考文献

算法提高课

AC代码

#include <iostream>
using namespace std;

const int N = 30;

int n,  m;
int g[N][N],f[N][N];
int way[N];

int main(){
    //读入
    cin >> n >> m;
    for (int i = 1 ; i <= n ; i ++)
        for (int j = 1 ; j <= m ; j ++)
            cin >> g[i][j];

    //分组背包
    for (int i = 1 ; i <= n ; i ++){
        for (int j = 0 ; j <= m ; j ++){
            f[i][j] = f[i - 1][j];
            for (int k = 1 ; k <= m ; k ++){
                if (j >= k )f[i][j] = max(f[i][j], f[i - 1][j - k] + g[i][k]);
            }
        }
    }
    cout << f[n][m] << endl;
    //求方案
    int j = m;
    for (int i = n ; i >= 1 ; i --){
        for (int k = 0 ; k <= m ; k ++){
            if (j >= k && f[i][j] == f[i - 1][j - k] + g[i][k]){
                way[i] = k;
                j -= k;
                break;
            }
        }
    }

    for (int i = 1 ; i <= n ; i ++) cout << i << " " << way[i] << endl;;

    return 0;
}