【HDOJ6693】Valentine's Day（概率）

题意：给定n件物品，每件物品让周驿东开心的概率为a[i]

要求从中选一些，使得周驿东恰好开心一次的概率最大

n<=1e4，0<=a[i]<=1

思路：

 #include<bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef pair<ll,ll> Pll;
 typedef vector<int> VI;
 typedef vector<PII> VII;
 #define N  21000
 #define M  4100000
 #define fi first
 #define se second
 #define MP make_pair
 #define pi acos(-1)
 #define mem(a,b) memset(a,b,sizeof(a))
 #define rep(i,a,b) for(int i=(int)a;i<=(int)b;i++)
 #define per(i,a,b) for(int i=(int)a;i>=(int)b;i--)
 #define lowbit(x) x&(-x)
 #define Rand (rand()*(1<<16)+rand())
 #define id(x) ((x)<=B?(x):m-n/(x)+1)
 #define ls p<<1
 #define rs p<<1|1

 const ll MOD=1e9+,inv2=(MOD+)/;
       double eps=1e-;
       int INF=1e9;
       int dx[]={-,,,};
       int dy[]={,,-,};

       double a[N],b[N],c[N],t1[N],t2[N];

 int read()
 {
    int v=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,c=getchar();
    return v*f;
 }

 int main()
 {
     //freopen("1.in","r",stdin);
     //freopen("1.out","w",stdout);

     int cas;
     scanf("%d",&cas);

     while(cas--)
     {
         int n=read();
         double ans=;
         int m=;
         rep(i,,n)
         {
             scanf("%lf",&a[i]);
             if(a[i]<=0.5) b[++m]=a[i];
             ans=max(ans,a[i]);
         }
         sort(b+,b++m);
         double p=,w=1.0;
         per(i,m,)
         {
             double np=p*(1.0-b[i])+w*b[i];
             double nw=w*(1.0-b[i]);
             if(np<=p) break;
             p=np;
             w=nw;
         }
         ans=max(ans,p);
         printf("%.10f\n",ans);

     }

     return ;
 }