Line intersection

struct point
{
    int x, y;

    point(int x, int y) : x(x), y(y) {}

    point operator-(point& other)
    {
        return point(x - other.x, y - other.y);
    }
};

long long cp(point a, point b)
{
    return (long long)a.x * b.y - (long long)a.y * b.x;
}

bool intersect(point a, point b, point c, point d)
{
    // Create change vectors and their cross product
    point r = b - a, s = d - c;
    long long cp_rs = cp(r, s);

    if (cp_rs == 0) // Lines are parallel
    {
        if (cp(c - a, r) == 0) // Lines are colinear
        {
            if (r.x == 0 && s.x == 0) // Check if they're overlaping
            {
                if (a.y > b.y) swap(a, b);
                if (c.y > d.y) swap(c, d);
                return (b.y - c.y >= 0 && d.y - a.y >= 0);
            }

            else
            {
                if (a.x > b.x) swap(a, b);
                if (c.x > d.x) swap(c, d);
                return (b.x - c.x >= 0 && d.x - a.x >= 0);
            }
        }

        return false;
    }

    else // Lines aren't parallel
    {
        // Check where they intersect
        double t = (double)cp(c - a, s) / cp_rs;
        double u = (double)cp(c - a, r) / cp_rs;

        if (t <= 1 && t >= 0 && u <= 1 && u >= 0) return true; // Intersect without prolongation
        return false; // Intersect with prolongation
    }
}