Line Segment Intersection

#include <bits/stdc++.h>
#include <cmath>

using namespace std;
using ll = long long;
typedef long long C;
typedef complex<C> P;
#define X real()
#define Y imag()

// Debug printing
#ifdef DEBUG
#define deb(fmt, args...) printf("DEBUG: %d: " fmt, __LINE__, ##args)
#define debug_print(fmt, args...) printf(fmt, ##args)
#else
#define deb(fmt, args...)
#define debug_print(fmt, args...)
#endif

void print_array(vector<int> in, const string title = "Vector")
{
	debug_print("DEBUG: %s [\nDEBUG: ", title.c_str());
	for (unsigned int i = 0; i < in.size(); i++) {
		debug_print("%d ", in[i]);
	}
	debug_print("\nDEBUG: ] END\n");
}

void print_matrix(vector<vector<int> > in, const string title = "Matrix")
{
	debug_print("DEBUG: %s [\nDEBUG: ", title.c_str());
	for (unsigned int i = 0; i < in.size(); i++) {
		for (unsigned int j = 0; j < in[i].size(); j++) {
			debug_print("%d ", in[i][j]);
		}
		debug_print("\nDEBUG: ");
	}
	debug_print("DEBUG: ] END\n");
}

double angle(int x1, int y1, int x2, int y2) {
	double dot = x1*x2 + y1*y2;
	double cross = x1*y2 - y1*x2;
	return atan2(cross, dot);
}

double dist(int x1, int y1, int x2, int y2) {
	return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}

int main(int argc, char *argv[])
{
	ios::sync_with_stdio(0);
	cin.tie(0);

	// Read the input parameters
	int n;
	cin >> n;

	double err = 0.00000000000001;

	for (int i = 0; i < n; i++) {
		ll x1, y1, x2, y2;
		ll x3, y3, x4, y4;
		cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3 >> x4 >> y4;
		P a = {x1, y1};
		P b = {x2, y2};
		P c = {x3, y3};
		P d = {x4, y4};
		P v1 = b - a;
		P v2 = d - c;
		// deb("round: %d\n",i);
		// Same endpoints
		if (a == c || a == d || b == c || b == d) {
			cout << "YES\n";
			continue;
		}

		// double k = 1.0 * (y2 - y1) / (x2 - x1);
		// double k2 = 1.0 * (y4 - y3) / (x4 - x3);
		// deb("k: %f, k2: %f\n", k, k2);
		ll cross = (conj(v1)*v2).Y;

		// Same slopes, check if they overlap
		if (cross == 0) {
			// deb("vittu\n");
			double ac = dist(x1, y1, x3, y3);
			double cb = dist(x3, y3, x2, y2);
			double ab = dist(x1, y1, x2, y2);
			double ad = dist(x1, y1, x4, y4);
			double db = dist(x4, y4, x2, y2);
			// deb("%f %f %f\n", ac, cb, ab);
			if (abs(ac + cb - ab) <= err) {
				cout << "YES\n";
				continue;
			}
			// deb("%f %f %f\n", ad, db, ab);
			if (abs(ad + db - ab) <= err) {
				cout << "YES\n";
				continue;
			}
			double ca = dist(x1, y1, x3, y3);
			double cd = dist(x3, y3, x4, y4);
			double bd = dist(x2, y2, x4, y4);
			// deb("%f %f %f\n", ca, ad, cd);
			if (abs(ca + ad - cd) <= err) {
				cout << "YES\n";
				continue;
			}
			// deb("%f %f %f\n", cb, bd, cd);
			if (abs(cb + bd - cd) <= err) {
				cout << "YES\n";
				continue;
			}
		}
		// deb("%d %d %d %d %d %d %d %d\n", x1, y1, x2, y2, x3, y3, x4, y4);
		double t1 = (1.0 * (x1 - x3) * (y3 - y4) - (y1 - y3) * (x3 - x4));
		double t2 = (1.0 * (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4));
		double u1 = -(1.0 * (x1 - x2) * (y1 - y3) - (y1 - y2) * (x1 - x3));
		double u2 = (1.0 * (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4));
		// deb("t1: %f, u1: %f, t2: %f, u2: %f\n", t1, u1, t2, u2);
		// if (abs(t1) <= err && abs(t2) <= err && abs(u1) <= err && abs(u2) <= err) {

		// segments are parallel
		// if (abs(t1) <= err || abs(u1) <= err) {
		if (abs(t1) <= err && abs(t2) <= err && abs(u1) <= err && abs(u2) <= err) {
			// deb("paskaa\n");
			int ac = dist(x1, y1, x3, y3);
			int cb = dist(x3, y3, x2, y2);
			int ab = dist(x1, y1, x2, y2);
			if (abs(ac + cb - ab) <= err) {
				cout << "YES\n";
				continue;
			}
		}
		double t = t1 / t2;
		double u = u1 / u2;
		// deb("t: %f, u: %f\n", t, u);
		if (u >= -err && u <= 1.0 + err && t >= -err && t <= 1.0 + err) {
			cout << "YES\n";
			continue;
		}
		cout << "NO\n";
	}
	}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED