学步园

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<string>
#include<queue>
#include<cmath>
#include<memory.h>

using namespace std;

#define inf 1<<20

int base[20];
double p[20],dp[inf];

void clear()
{
	memset(dp,0.0,sizeof(dp));
	memset(p,0.0,sizeof(p));
	int i;
	for(i=0;i<20;i++)
		base[i]=1<<i;
}

int main()
{
	int n,i,maxn,j;
	double sum,t;
	while(cin>>n)
	{
		clear();
		for(i=0;i<n;i++)
			cin>>p[i];
		maxn=1<<n;
		for(i=1;i<maxn;i++)
		{
			sum=t=0.0;
			for(j=0;j<n;j++)
			{
				if(i & base[j])
				{
					t+=p[j]*dp[i-base[j]];
					sum+=p[j];
				}
			}
			dp[i]=(t+1)/sum;
		}
		printf("%.5lf\n",dp[(1<<n)-1]);
	}
	return 0;
}