79 lines
2.2 KiB
Python
Executable file
79 lines
2.2 KiB
Python
Executable file
#!/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()
|