Line Segment Intersection

#include <bits/stdc++.h>

using namespace std;

//Definitions for quicker writing
#define REP(i,a,b) for (int i = a; i < b; i++)
#define clz __builtin_clz
#define ctz __builtin_ctz
#define popct __builtin_popcount
#define PB push_back
#define MP make_pair
#define F first
#define S second
#define X real()
#define Y imag()

//Typedefs for quicker writing
typedef long long ll;
typedef vector<int> vi;
typedef vector<long long> vl;
typedef pair<int,int> pi;
typedef pair<long long, long long> pl;
typedef complex<long long> po;

//Max values
const long long lmx = LLONG_MAX;
const int imx = INT_MAX;

ll cross(po v, po w){
    return v.X * w.Y - v.Y * w.X;
}

//Is c between a and b?
bool between(po a,po b,po c){
    return c.X <= max(a.X,b.X) && c.X >= min(a.X,b.X) &&
           c.Y <= max(a.Y,b.Y) && c.Y >= min(a.Y,b.Y);
}


int main() {
	//IO optimization
	ios::sync_with_stdio(0);
	cin.tie(0);
	
	//Input definition
	ll n;

	//Read In
	cin >> n;

	//Main part
    ll x,y;
    po a,b,c,d;
    bool res = false;
	REP(i,0,n){
        cin >> x >> y;
        a = {x,y};
        cin >> x >> y;
        b = {x,y};
        cin >> x >> y;
        c = {x,y};
        cin >> x >> y;
        d = {x,y};

        //First case:
        //The lines are parallel and the segments overlap
        if(cross(b-a,d-c) == 0 && (cross(c-a,c-b) == 0 || cross(d-a,d-b) == 0)){
            if(between(a,b,c) || between(a,b,d) || between(c,d,a) || between(c,d,b)){
                res = true;
            }
        }

        //Second case:
        //Any of the points match
        if ((a==c) || (b==c) || (a==d) || (b==d)){
            res = true;
        }

        //Third case:
        //Point location
        //a and b have to be on different sides
        //same goes for c and d
        ll c1 = cross(c-a,c-b);
        ll c2 = cross(d-a,d-b);
        ll c3 = cross(a-c,a-d);
        ll c4 = cross(b-c,b-d);
        if(((c1 < 0 && c2 > 0) || (c1 > 0 && c2 < 0)) &&
           ((c3 < 0 && c4 > 0) || (c3 > 0 && c4 < 0))){
            res = true;
        }

        //cout << "c relative to ab: " << c1 << "\n";
        //cout << "d relative to ab: " << c2 << "\n";
        //cout << "a relative to cd: " << c3 << "\n";
        //cout << "b relative to cd: " << c4 << "\n";

        //Fourth case:
        //One of the endpoints is on one of the lines
        if(cross(c-a,c-b) == 0 && between(a,b,c)) res = true;
        if(cross(d-a,d-b) == 0 && between(a,b,d)) res = true;
        if(cross(a-c,a-d) == 0 && between(c,d,a)) res = true;
        if(cross(b-c,b-d) == 0 && between(c,d,b)) res = true;

        //Write out
        cout << (res ? "YES" : "NO") << "\n";

        //Reset
        res = false;
    }
	
	//Return
	return 0;

}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED