我真是服了这个数学期望了，打卡代码里满满debug的痕迹（4009.收集卡牌）

#include <iostream>
#include <cstring>
using namespace std;
const int N = 16, M = 1 << N;
int n, K;
double p[N];
double f[M][N * 5 + 1]; //表示卡牌的数量，抽了多少次
int G[M];
//int rrr;
//int aaa, ttt;
int get(int x)
{
    //aaa++;
    if (G[x] != -1) return G[x];
    int res = 0;
    //ttt++;
    int o = x;
    while (x)
    {
        //rrr++;
        res++;
        x -= x & -x;
    }
    G[o] = res;
    return res;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    memset(G, -1, sizeof G);
    cin >> n >> K;
    for (int i = 0; i < n; i++) cin >> p[i];
    f[0][0] = 1;
    double res = 0;
    for (int i = 1; i < 1 << n; i++)
    {
        for (int j = get(i); j <= n * K; j++)
        {
            for (int k = 0; k < n; k++)
            {
                //rrr++;
                if (i >> k & 1)
                {
                    if (i + 1 != 1 << n && 
                        (n - get(i)) * K > j - 1 - get(i)) 
                        f[i][j] += f[i][j - 1] * p[k];
                    if ((n - get(i - (1 << k))) * K > j - 1 - get(i - (1 << k)))
                    f[i][j] += f[i - (1 << k)][j - 1] * p[k];
                }
            }
            if (i + 1 == 1 << n || (n - get(i)) * K <= j - get(i))
            {
                //rrr++;
                //if (f[i][j])cout << i << ' ' << j << ' ' << f[i][j] << endl;
                res += j * f[i][j];
            }
            //cout << f[i][j] << ' ';
        }
        //cout << endl;
    }
    //cout << aaa << ' ' << ttt << ' ' << rrr << endl;
    cout << res << endl;
}