# Card Collector

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1405    Accepted Submission(s): 624
Special Judge

Problem Description
In your childhood, do you crazy for collecting the beautiful cards in the snacks? They said that, for example, if you collect all the 108 people in the famous novel Water Margin, you will win an amazing award.

As a smart boy, you notice that to win the award, you must buy much more snacks than it seems to be. To convince your friends not to waste money any more, you should find the expected number of snacks one should buy to collect a full suit of cards.

Input
The first line of each test case contains one integer N (1 <= N <= 20), indicating the number of different cards you need the collect. The second line contains N numbers p1, p2, ..., pN, (p1 + p2 + ... + pN <= 1), indicating the possibility of each card to appear in a bag of snacks.

Note there is at most one card in a bag of snacks. And it is possible that there is nothing in the bag.

Output
Output one number for each test case, indicating the expected number of bags to buy to collect all the N different cards.

You will get accepted if the difference between your answer and the standard answer is no more that 10^-4.

Sample Input
1 0.1 2 0.1 0.4

Sample Output
10.000 10.500

Source

Recommend
zhoujiaqi2010

/*
HDU 4336

*/
#include<stdio.h>
#include<algorithm>
#include<iostream>
#include<string.h>
using namespace std;
const int MAXN=22;
double p[MAXN];
double dp[1<<MAXN];
int main()
{
int n;
while(scanf("%d",&n)!=EOF)
{
double tt=0;
for(int i=0;i<n;i++)
{
scanf("%lf",&p[i]);
tt+=p[i];
}
tt=1-tt;//tt就表示没有卡片的概率了
dp[(1<<n)-1]=0;
for(int i=(1<<n)-2;i>=0;i--)
{
double x=0,sum=1;
for(int j=0;j<n;j++)
{
if((i&(1<<j)))x+=p[j];
else sum+=p[j]*dp[i|(1<<j)];
}
dp[i]=sum/(1-tt-x);
}
printf("%.5lf\n",dp);

}
return 0;
}

/*
HDU 4336

*/
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;

double p;
int main()
{
int n;
while(scanf("%d",&n)==1)
{
for(int i=0;i<n;i++)scanf("%lf",&p[i]);
double ans=0;
for(int i=1;i<(1<<n);i++)
{
int cnt=0;
double sum=0;
for(int j=0;j<n;j++)
if(i&(1<<j))
{
sum+=p[j];
cnt++;
}
if(cnt&1)ans+=1.0/sum;
else ans-=1.0/sum;
}
printf("%.5lf\n",ans);
}
return 0;
}

posted on 2012-10-06 16:50  kuangbin  阅读(2572)  评论(5编辑  收藏

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