【BZOJ】1914: [Usaco2010 OPen]Triangle Counting 数三角形

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define ll long long
using namespace std;
const int maxn=100010,eps=1e-8;
int n;
long long ans;
struct point{
    ll x,y;double angle;
    ll operator *(const point a)const{
        return x*a.y-a.x*y;//
    }
}a[maxn];
bool cmp(point a,point b){return fabs(a.angle-b.angle)<eps?a.x<b.x:a.angle<b.angle;}
int main(){
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%lld%lld",&a[i].x,&a[i].y);
        a[i].angle=atan2(a[i].y,a[i].x);
    }
    sort(a,a+n,cmp);
    int r=1,num=0;ans=0;
    for(int i=0;i<n;i++){
        while(r!=i&&a[i]*a[r]>=0)r=(r+1)%n,num++;
        ans+=1ll*num*(num-1)/2;
        num--;
    }
    printf("%lld",1ll*n*(n-1)*(n-2)/6-ans);
    return 0;
}