[SCOI 2008] 奖励关

[题目链接]

https://www.lydsy.com/JudgeOnline/problem.php?id=1076

[算法]

f[i][S]表示当前第i次抛出宝物，目前集合为S，所能获得的最高分值

dp即可

[代码]

#include<bits/stdc++.h>
using namespace std;
#define MAXN 110
const int MAXS =  << ;

int i,j,k,n,x,s;
int S[MAXN],c[MAXN];
double f[MAXN][MAXS];

inline double dp(int now,int s)
{
    int i;
    if (f[now][s] != -) return f[now][s];
    if (now == k)
    {
        f[now][s] = ;
        for (i = ; i < n; i++)
        {
            if ((S[i] & s) == S[i] && c[i] > )
                f[now][s] += c[i];
        }
        f[now][s] /= n;
    } else
    {
        f[now][s] = ;
        for (i = ; i < n; i++)
        {
            if ((S[i] & s) == S[i])
                f[now][s] += max(dp(now + ,s),dp(now + ,s | ( << i)) + c[i]);
            else f[now][s] += dp(now + ,s);
        }
        f[now][s] /= n;
    }
    return f[now][s];
}

int main()
{

    scanf("%d%d",&k,&n);
    for (i = ; i < n; i++)
    {
        scanf("%d",&c[i]);
        s = ;
        while (scanf("%d",&x) && x) s |= ( << (x - ));
        S[i] = s;
    }
    for (i = ; i <= k; i++)
    {
        for (j = ; j < MAXS; j++)
        {
            f[i][j] = -;
        }
    }
    printf("%.6lf\n",dp(,));

    return ;
}