hihoCoder #1040 （判断是否为矩形）

# include<iostream>
# include<cstdio>
# include<cmath>
# include<set>
# include<cstring>
# include<algorithm>
using namespace std;
# define LL long long

const double inf=1e20;
const double eps=1e-20;

struct Edge
{
    LL x,y;
    double k;
};
Edge e[4];
set<LL>s;

double getK(int i)
{
    if(e[i].x==0) return inf;
    return (double)e[i].y/(double)e[i].x;
}

bool ok(int i,int j)
{
    return e[i].x*e[j].x+e[i].y*e[j].y==0ll;
}

bool judge()
{
	if(s.size()!=4) return false;
    int cnt1=0,cnt2=0;
	for(int i=1;i<4;++i){
		if(ok(0,i)) ++cnt1;
		if(e[0].k==e[i].k) ++cnt2;
	}
    return cnt1==2&&cnt2==1;
}

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        LL a,b,c,d;
		s.clear();
        for(int i=0;i<4;++i){
            scanf("%lld%lld%lld%lld",&a,&b,&c,&d);
			s.insert(a*100000ll+b);
			s.insert(c*100000ll+d);
			e[i].x=c-a;
            e[i].y=d-b;
            e[i].k=getK(i);
        }
        if(judge()) printf("YES\n");
        else printf("NO\n");
    }
    return 0;
}