[SCOI2008]奖励关 + 状压动归 + 数学期望

 

Code：

#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn = 20;
double f[102][1 << maxn];
int score[maxn], state[maxn], pos[maxn],n, m, tmp ;
int main(){
    for(int i = 1;i <= 16; ++i) pos[i] = (1 << (i - 1));
    scanf("%d%d",&n,&m);
    for(int i = 1;i <= m; ++i)
    {
        scanf("%d%d",&score[i],&tmp);
        while(tmp){ state[i] += pos[tmp]; scanf("%d",&tmp); }
    }
    for(int i = n;i >= 1; --i)
        for(int j = 0;j <= pos[m + 1]; ++j)
        {
            for(int k = 1;k <= m; ++k) 
                if((state[k] & j) == state[k])  
                    f[i][j] += max(f[i+1][j], f[i+1][j|pos[k]] + score[k]);
                else  f[i][j] += f[i + 1][j];
            f[i][j] /= m;
        }
    printf("%.6lf",f[1][0]);
    return 0;
}