bzoj1913: [Apio2010]signaling 信号覆盖

传送门

题解传送门

//Achen
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<vector>
#include<cstdio>
#include<queue>
#include<cmath>
#define pi acos(-1)
#define eps 1e-15
const int N=1e5+;
#define For(i,a,b) for(int i=(a);i<=(b);i++)
#define Rep(i,a,b) for(int i=(a);i>=(b);i--)
typedef long long LL;
typedef double db;
using namespace std;
int n,cnt;
LL c1,c2,tp;
db a[N],ans;

template<typename T>void read(T &x)  {
    char ch=getchar(); x=; T f=;
    while(ch!='-'&&(ch<''||ch>'')) ch=getchar();
    if(ch=='-') f=-,ch=getchar();
    for(;ch>=''&&ch<='';ch=getchar()) x=x*+ch-''; x*=f;
}

struct pt {
    db x,y;
}p[N];

LL C(int n,int m) {
    LL rs=;
    Rep(i,n,n-m+) rs*=i;
    For(i,,m) rs/=i;
    return rs;
}

int main() {
    read(n); tp=C(n-,);
    For(i,,n) scanf("%lf%lf",&p[i].x,&p[i].y);
    For(i,,n) {
        cnt=;
        For(j,,n) if(j!=i)
            a[++cnt]=atan2(p[j].y-p[i].y,p[j].x-p[i].x);
        For(i,,cnt) {
            if(a[i]<) a[i]+=pi*;
            a[cnt+i]=a[i]+pi*;
        }
        sort(a+,a+*cnt+);
        int r=; c1=;
        For(l,,cnt) {
            while(r<*cnt&&a[r+]-a[l]<pi)
                r++;
            if(r-l) c1+=C(r-l,);
        }
        c2+=tp-c1;
    }
    ans=(db)(c2+(C(n,)-c2)*)/(db)C(n,)+;
    printf("%.6lf\n",ans);
    return ;
}