169 lines
4.4 KiB
Python
Executable file
169 lines
4.4 KiB
Python
Executable file
#!/usr/bin/env python
|
|
|
|
import functools
|
|
import itertools
|
|
import sys
|
|
from dataclasses import dataclass
|
|
from typing import List, Optional, Set, Tuple
|
|
|
|
|
|
@dataclass(eq=True, frozen=True) # Hash-able
|
|
class Vector:
|
|
x: int
|
|
y: int
|
|
z: int
|
|
|
|
def __add__(self, other: "Vector") -> "Vector":
|
|
return Vector(self.x + other.x, self.y + other.y, self.z + other.z)
|
|
|
|
def __sub__(self, other: "Vector") -> "Vector":
|
|
return Vector(self.x - other.x, self.y - other.y, self.z - other.z)
|
|
|
|
|
|
@dataclass(eq=True, frozen=True) # Hash-able
|
|
class Matrix:
|
|
v1: Vector
|
|
v2: Vector
|
|
v3: Vector
|
|
|
|
def __matmul__(self, other: Vector) -> Vector:
|
|
return Vector(
|
|
self.v1.x * other.x + self.v1.y * other.y + self.v1.z * other.z,
|
|
self.v2.x * other.x + self.v2.y * other.y + self.v2.z * other.z,
|
|
self.v3.x * other.x + self.v3.y * other.y + self.v3.z * other.z,
|
|
)
|
|
|
|
|
|
def rotations() -> List[Matrix]:
|
|
def cos(angle: int) -> int:
|
|
if angle == 0:
|
|
return 1
|
|
if angle == 180:
|
|
return -1
|
|
assert angle in (90, 270) # Sanity check
|
|
return 0
|
|
|
|
def sin(angle: int) -> int:
|
|
if angle == 90:
|
|
return 1
|
|
if angle == 270:
|
|
return -1
|
|
assert angle in (0, 180) # Sanity check
|
|
return 0
|
|
|
|
def rotate(x: int, y: int, z: int) -> Matrix:
|
|
v1 = Vector(
|
|
cos(z) * cos(y),
|
|
cos(z) * sin(y) * sin(x) - sin(z) * cos(x),
|
|
cos(z) * sin(y) * cos(x) + sin(z) * sin(x),
|
|
)
|
|
v2 = Vector(
|
|
sin(z) * cos(y),
|
|
sin(z) * sin(y) * sin(x) + cos(z) * cos(x),
|
|
sin(z) * sin(y) * cos(x) - cos(z) * sin(x),
|
|
)
|
|
v3 = Vector(-sin(y), cos(y) * sin(x), cos(y) * cos(x))
|
|
return Matrix(v1, v2, v3)
|
|
|
|
return [
|
|
rotate(0, 0, 0),
|
|
rotate(90, 0, 0),
|
|
rotate(180, 0, 0),
|
|
rotate(270, 0, 0),
|
|
rotate(0, 90, 0),
|
|
rotate(90, 90, 0),
|
|
rotate(180, 90, 0),
|
|
rotate(270, 90, 0),
|
|
rotate(0, 180, 0),
|
|
rotate(90, 180, 0),
|
|
rotate(180, 180, 0),
|
|
rotate(270, 180, 0),
|
|
rotate(0, 270, 0),
|
|
rotate(90, 270, 0),
|
|
rotate(180, 270, 0),
|
|
rotate(270, 270, 0),
|
|
rotate(0, 0, 90),
|
|
rotate(90, 0, 90),
|
|
rotate(180, 0, 90),
|
|
rotate(270, 0, 90),
|
|
rotate(0, 0, 270),
|
|
rotate(90, 0, 270),
|
|
rotate(180, 0, 270),
|
|
rotate(270, 0, 270),
|
|
]
|
|
|
|
|
|
ROTATIONS = rotations()
|
|
|
|
BeaconList = Set[Vector]
|
|
|
|
|
|
def solve(input: List[str]) -> int:
|
|
def parse() -> List[BeaconList]:
|
|
res: List[BeaconList] = []
|
|
|
|
for line in input:
|
|
if "scanner" in line:
|
|
res.append(set())
|
|
continue
|
|
if line == "":
|
|
continue
|
|
x, y, z = map(int, line.split(","))
|
|
res[-1].add(Vector(x, y, z))
|
|
|
|
return res
|
|
|
|
def find_overlap(
|
|
known: BeaconList, other: BeaconList
|
|
) -> Optional[Tuple[Matrix, Vector]]:
|
|
def find_delta(known: BeaconList, other: BeaconList) -> Optional[Vector]:
|
|
for dest, source in itertools.product(known, rotated):
|
|
delta = dest - source
|
|
if sum((v + delta) in known for v in rotated) >= 12:
|
|
return delta
|
|
return None
|
|
|
|
for r in ROTATIONS:
|
|
rotated = set(r @ v for v in other)
|
|
if (delta := find_delta(known, rotated)) is not None:
|
|
return r, delta
|
|
|
|
return None
|
|
|
|
def apply(known: BeaconList, other: BeaconList) -> Tuple[bool, BeaconList]:
|
|
res = find_overlap(known, other)
|
|
if res is None:
|
|
return False, known
|
|
|
|
rot, delta = res
|
|
|
|
new = {(rot @ v) + delta for v in other}
|
|
|
|
# Return whether there are new points in the set
|
|
return not (new <= known), (known | new)
|
|
|
|
def match_all(scans: List[BeaconList]) -> BeaconList:
|
|
# First scan is our basis
|
|
known = scans[0]
|
|
# No need to inspect the first scan in the future
|
|
to_match = scans[1:]
|
|
|
|
while to_match:
|
|
s = to_match.pop(0)
|
|
applied, known = apply(known, s)
|
|
if not applied:
|
|
to_match.append(s)
|
|
return known
|
|
|
|
beacons = parse()
|
|
return len(match_all(beacons))
|
|
|
|
|
|
def main() -> None:
|
|
input = [line.strip() for line in sys.stdin.readlines()]
|
|
print(solve(input))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
main()
|