Scala3, Sympy

case class Particle(x: Long, y: Long, z: Long, dx: Long, dy: Long, dz: Long)

def parseParticle(a: String): Option[Particle] = a match
    case s"$x, $y, $z @ $dx, $dy, $dz" => Some(Particle(x.toLong, y.toLong, z.toLong, dx.trim.toLong, dy.trim.toLong, dz.trim.toLong))
    case _ => None

def intersect(min: Double, max: Double)(p: Particle, q: Particle): Boolean =
    val n = p.dx * q.y - p.y * p.dx - q.x * p.dy + p.x * p.dy
    val d = p.dy * q.dx - p.dx * q.dy

    if(d == 0) then false else 
        val k = n.toDouble/d
        val k2 = (q.y + k * q.dy - p.y)/p.dy
        val ix = q.x + k * q.dx
        val iy = q.y + k * q.dy
        k2 >= 0 && k >= 0 && min <= ix && ix <= max && min <= iy && iy <= max

def task1(a: List[String]): Long = 
    val particles = a.flatMap(parseParticle)
    particles.combinations(2).count(l => intersect(2e14, 4e14)(l(0), l(1)))

import re as re2
from sympy import *

p, v, times, eqs = symbols('x y z'), symbols('dx dy dz'), [], []

def parse_eq(i: int, s: str):
    parts = [int(p) for p in re2.split(r'[,\s@]+', s) if p.strip() != '']
    time = Symbol(f't{i}')
    times.append(time)
    for rp, rv, hp, hv in zip(p, v, parts[:3], parts[3:]):
        eqs.append(Eq(rp + time * rv, hp + time * hv))

# need 3 equations for result, everything after that just slows things down
neq = 3
with open('task1.txt', 'r') as fobj:
    for i, s in zip(range(neq), fobj.readlines()):
        parse_eq(i, s)

for sol in solve(eqs, list(p) + list(v) + times):
    x, y, z, *_ = sol
    print(x + y + z)