Yandex Cup 2020(Catherine the developer works from home-给n个整点问能构成几个至少有一对平行边的四边形)

给n个整点问能构成几个至少有一对平行边的四边形

通过枚举2个平行的边来数至少有一对平行边的四边形，由于平行四边形会被计算2遍需要去重

#include<bits/stdc++.h>
using namespace std;
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#pragma
#define
#define
#define
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 

ll gcd(ll a,ll b){if (!b) return a; return gcd(b,a%b);}
#define
ll sqr(ll a){return a*a;}
ld sqr(ld a){return a*a;}
double sqr(double a){return a*a;}

struct Rat{
    ll s,m;
    Rat(ll _s=0,ll _m=1) {
        s=_s,m=_m;
        ll d=gcd(s,m);
        s/=d,m/=d;
        if (m<0) s=-s,m=-m;
    } 
    Rat operator+ (const Rat &u) {ll d = gcd(m,u.m); return Rat(u.m/d*s+ m/d*u.s, m/d*u.m);    }
    Rat operator- (const Rat &u) {ll d = gcd(m,u.m); return Rat(u.m/d*s- m/d*u.s, m/d*u.m);    }
    Rat operator* (const Rat &u) {return Rat(s*u.s, m*u.m);    }
    
    bool operator < (const Rat& u) const { return s*u.m < u.s*m; }  
    bool operator == (const Rat& u) const { return s*u.m == u.s*m; }  
    friend inline int dcmp(Rat u) {return (u.s==0)?0:(u.s>0?1:-1);}
    void print() {
        cout<<s<<'/'<<m<<endl;
    }
};
ll x[MAXN],y[MAXN];
vector<pair<Rat,Rat> > q;
vector<ll> v;
struct Point
{
    int x, y;
    Point(){}
    Point(int x, int y):x(x), y(y){}
    bool operator<(const Point &rhs)const{
        if(this->x<rhs.x){
            return true;
        }   
        else if(this->x==rhs.x){
            return this->y > rhs.y;
        }
        else{
            return false;
        }
    }
}A[MAXN];
ll work(int n) {
    
    sort(A, A+n);
    int cnt = 0;

    for(int i=0; i<n-1; ++i){
        for(int j=i+1; j<n; ++j){

            int x1 = A[i].x+(A[j].y-A[i].y); int y1 = A[i].y-(A[j].x-A[i].x);
            int x2 = A[j].x+(A[j].y-A[i].y); int y2 = A[j].y-(A[j].x-A[i].x);
            Point a(x1, y1), b(x2, y2);
            int pos1 = lower_bound(A, A+n, a) - A;
            int pos2 = lower_bound(A, A+n, b) - A;
                if(A[pos1].x==a.x&&A[pos1].y==a.y && A[pos2].x==b.x && A[pos2].y==b.y){
                    ++cnt;
                }

        }
    }
    return cnt/2;
}

ll wk(int n) {
    vector<pair<pair<Rat,ll> ,Rat> > q;
    vector<pair<ll,ll> > v;
    For(i,n) {
        Fork(j,i+1,n) {
            ll t=y[i]-y[j],p=x[i]-x[j];
            ll len=t*t+p*p;
            
            if(!p) v.pb(mp(len,x[i]));
            else {
                Rat k=Rat(t,p);
                Rat c=Rat(y[j],1)+Rat(-x[j] *t,p);
                q.pb(mp(mp(k,len),c));
            }
        }
    } 
    
    sort(ALL(q));
    
    sort(ALL(v));
    ll ans=0;
    ll l=-1,sz=SI(v);
    map<ll , ll> h2;
    Rep(i,sz) {
        if(h2.count(v[i].fi) ) h2[v[i].fi]++;
        else h2[v[i].fi]=1;
    }

    for(int i=1;i<=sz;i++) {
        if(i==sz|| v[i]!=v[i-1]) {
            ll len=i-1-l;
            ans+=len*(h2[v[i-1].fi]-len);
            l=i-1;
        }
    }
    ans/=2;
    
    ll ans2=0;
    l=-1,sz=SI(q);
    map<pair<Rat,ll> , ll> h;
    Rep(i,sz) {
        if(h.count(q[i].fi) ) h[q[i].fi]++;
        else h[q[i].fi]=1;
    }
    
    for(int i=1;i<=sz;i++) {
        if(i==sz|| q[i]!=q[i-1]) {
            ll len=i-1-l;
            ans2+=len*(h[q[i-1].fi]-len);
            l=i-1;
        }
    }
    ans2/=2;
    return (ans+ans2)/2;
}


int main()
{
//  freopen("A.in","r",stdin);
//  freopen(".out","w",stdout);
    int n=read();
    For(i,n) {
        cin>>x[i]>>y[i];
        A[i-1].x=x[i],A[i-1].y=y[i];
    }
    
    For(i,n) {
        Fork(j,i+1,n) {
            ll t=y[i]-y[j],p=x[i]-x[j];
            if(!p) v.pb(x[i]);
            else {
                Rat k=Rat(t,p);
                Rat c=Rat(y[j],1)+Rat(-x[j] *t,p);
                q.pb(mp(k,c));
            }
        }
    } 
    
    sort(ALL(q));
    
    sort(ALL(v));
    ll ans=0;
    ll l=-1,sz=SI(v);
    for(int i=1;i<=sz;i++) {
        if(i==sz|| v[i]!=v[i-1]) {
            ll len=i-1-l;
            ans+=len*(sz-len);
            l=i-1;
        }
    }
    ans/=2;
    
    ll ans2=0;
    l=-1,sz=SI(q);
    map<Rat,ll> h;
    Rep(i,sz) {
        if(h.count(q[i].fi)) h[q[i].fi]++;
        else h[q[i].fi]=1;
    }
    
    for(int i=1;i<=sz;i++) {
        if(i==sz|| q[i]!=q[i-1]) {
            ll len=i-1-l;
            ans2+=len*(h[q[i-1].fi]-len);
            l=i-1;
        }
    }
    ans2/=2;
    ll ans3=wk(n);
    cout<<ans+ans2-ans3<<endl;
    return 0;
}