【codeforces 442B】 Andrey and Problem

http://codeforces.com/problemset/problem/442/B (题目链接)

题意

　　n个人，每个人有p[i]的概率出一道题。问如何选择其中s个人使得这些人正好只出1道题的概率最大。

Solution

　　很显然的概率dp，过了样例即可AC。。话说我为什么要刷B题→_→

代码

// codeforces442B
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<cmath>
#define LL long long
#define inf 1<<30
#define Pi acos(-1.0)
#define free(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);
using namespace std;

const int maxn=200;
double f[maxn][maxn],p[maxn][maxn],a[maxn];
int n;

int main() {
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%lf",&a[i]);
	for (int i=1;i<=n;i++) {
		p[i-1][0]=1;
		for (int j=1;j<=i;j++) {
			if (f[i-1][j]<f[i-1][j-1]*(1-a[i])+p[i-1][j-1]*a[i]) {
				f[i][j]=f[i-1][j-1]*(1-a[i])+p[i-1][j-1]*a[i];
				p[i][j]=p[i-1][j-1]*(1-a[i]);
			}
			else f[i][j]=f[i-1][j],p[i][j]=p[i-1][j];
		}
	}
	double ans=0;
	for (int i=1;i<=n;i++) ans=max(ans,f[n][i]);
	printf("%.12lf",ans);
	return 0;
}