#!/usr/bin/env python import itertools import sys from decimal import Decimal from typing import NamedTuple class Point(NamedTuple): x: int y: int z: int class HailStone(NamedTuple): pos: Point vel: Point def solve(input: list[str]) -> int: def parse_line(line: str) -> HailStone: pos, vel = line.split(" @ ") return HailStone( Point(*map(int, pos.split(", "))), Point(*map(int, vel.split(", "))) ) def parse(input: list[str]) -> list[HailStone]: return [parse_line(line) for line in input] def intersections(hailstones: list[HailStone], boundaries: tuple[int, int]) -> int: def intersects(a: HailStone, b: HailStone) -> bool: # According to wikipedia, if: # x = a_px + t * a_vx = b_px + u * b_vx # y = a_py + t * a_vy = b_py + u * b_vy # then: # t = ((a_px-b_px)*(-b_vy) - (a_py-b_py)*(-b_vx)) / ((-a_vx)*(-b_vy) - (-a_vy)*(-b_vx)) # u = ((a_px-b_px)*(-a_vy) - (a_py-b_py)*(-a_vx)) / ((-a_vx)*(-b_vy) - (-a_vy)*(-b_vx)) (a_px, a_py, _), (a_vx, a_vy, _) = a (b_px, b_py, _), (b_vx, b_vy, _) = b # Use rationals for extra precision, just in case denom = Decimal(a_vx * b_vy - a_vy * b_vx) # Parallel lines if denom == 0: return False t = ((a_px - b_px) * (-b_vy) - (a_py - b_py) * (-b_vx)) / denom u = ((a_px - b_px) * (-a_vy) - (a_py - b_py) * (-a_vx)) / denom # Intersects in the past if t < 0 or u < 0: return False x = a_px + t * a_vx y = a_py + t * a_vy # Outside our observation area if not boundaries[0] <= x <= boundaries[1]: return False if not boundaries[0] <= y <= boundaries[1]: return False return True return sum(intersects(a, b) for a, b in itertools.combinations(hailstones, 2)) hailstones = parse(input) return intersections(hailstones, (200000000000000, 400000000000000)) def main() -> None: input = sys.stdin.read().splitlines() print(solve(input)) if __name__ == "__main__": main()