[AcWing 9] 分组背包问题

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点击查看代码

#include<iostream>

using namespace std;
const int N = 110;
int n, m;
int v[N][N], w[N][N], s[N];
int f[N];

int main()
{
    cin >> n >> m;
    for (int i = 1; i <= n; i ++) {
        cin >> s[i];
        for (int j = 1; j <= s[i]; j ++)
            cin >> v[i][j] >> w[i][j];
    }
    for (int i = 1; i <= n; i ++)
        for (int j = m; j >= 0; j --)
            for (int k = 0; k <= s[i]; k ++)
                if (v[i][k] <= j)
                    f[j] = max(f[j], f[j - v[i][k]] + w[i][k]);
    cout << f[m] << endl;
    return 0;
}

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1. 状态转移：$f[i][j] = max( \ (f[i - 1][j - v[i][k]) + w[i][k] \ )$
   含义为：从 $i - 1$ 组中选第 $k$ 件物品