几何向量gcd+暴力枚举——cf552

#include<bits/stdc++.h>
using namespace std;
#define N 2005
map<pair<int,int>,int>mp[N];
pair<int,int>p[N];
int n;
int main(){
    cin>>n;
    for(int i=1;i<=n;i++){
        int x,y;
        scanf("%d%d",&x,&y);
        p[i]=make_pair(x,y);
    }
    for(int i=1;i<=n;i++)
        for(int j=1;j<=n;j++)if(i!=j){
            int dx=p[j].first-p[i].first;
            int dy=p[j].second-p[i].second;
            if(dx==0||dy==0){
                if(dx)dx=1;if(dy)dy=1;
                mp[i][make_pair(dx,dy)]++;
            }
            else {
                int d=__gcd(dx,dy);
                mp[i][make_pair(dx/d,dy/d)]++;
            }
        }
    long long ans=0;
    for(int i=1;i<=n;i++)
        for(int j=1;j<=n;j++)if(i!=j){
            int dx=p[j].first-p[i].first;
            int dy=p[j].second-p[i].second;
            if(dx==0||dy==0){
                if(dx==0){
                    dy=1;
                    ans+=n-2-(mp[i][make_pair(dx,dy)]-1);
                }
                else{
                    dx=1;
                    ans+=n-2-(mp[i][make_pair(dx,dy)]-1);
                }
            }
            else {
                int d=__gcd(dx,dy);
                ans+=n-2-(mp[i][make_pair(dx/d,dy/d)]-1);
            }
        }
    cout<<ans/6<<‘\n‘;
}