129 lines
3.5 KiB
Python
129 lines
3.5 KiB
Python
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#!/usr/bin/env python
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import functools
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import itertools
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import math
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import sys
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from collections import defaultdict
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from copy import deepcopy
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from typing import Dict, Iterator, List, Set, Tuple
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Tile = List[List[str]]
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Tiles = Dict[int, Tile]
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def parse(raw: str) -> Tiles:
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def parse_tile(raw: List[str]) -> Tile:
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return [[line[i] for i in range(len(line))] for line in raw]
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res = {}
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for lines in map(lambda s: s.splitlines(), raw.split("\n\n")):
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if len(lines) == 0:
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continue
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nums = int(lines[0][5:-1])
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res[nums] = parse_tile(lines[1:])
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return res
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def rotations(tile: Tile) -> Iterator[Tile]:
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yield tile
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for __ in range(3):
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prev = deepcopy(tile)
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for i in range(len(tile)):
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for j in range(len(tile[i])):
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prev[i][j] = tile[len(tile) - j - 1][i]
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tile = prev
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yield tile
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def flips(tile: Tile) -> Iterator[Tile]:
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yield tile
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yield tile[::-1]
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yield [line[::-1] for line in tile]
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yield [line[::-1] for line in tile[::-1]]
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def transforms(tile: Tile) -> List[Tile]:
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# Can't use a set with lists...
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res: List[Tile] = functools.reduce(
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lambda l, it: l + [it] if not any(it == other for other in l) else l,
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itertools.chain.from_iterable(map(rotations, flips(tile))),
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[],
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)
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return res
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def borders(tile: Tile) -> Iterator[str]:
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# They should match on same axis (i.e: go clockwise and counter-clockwise)
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return map(
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lambda s: "".join(s),
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[
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tile[0],
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[line[-1] for line in tile],
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tile[-1],
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[line[0] for line in tile],
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],
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)
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Transforms = Dict[int, List[Tile]]
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Tiling = List[List[Tuple[int, int]]] # Which tile, and which transform
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def build_tiling(tiles: Tiles) -> Tuple[Transforms, Tiling]:
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transform_mapping = {num: transforms(tile) for num, tile in tiles.items()}
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trans_borders: Dict[int, Dict[int, List[str]]] = defaultdict(dict)
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for num, trans in transform_mapping.items():
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for i, t in enumerate(trans):
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trans_borders[num][i] = list(borders(t))
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length = math.isqrt(len(tiles))
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tiling = [[(-1, -1)] * length for __ in range(length)]
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def rec(x: int = 0, y: int = 0, used: Set[int] = set()) -> bool:
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if x == length:
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return True
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for num, borders in trans_borders.items():
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if num in used:
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continue
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used |= {num}
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for trans, border in borders.items():
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top, __, __, left = border
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if y > 0:
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nid, ntrans = tiling[x][y - 1]
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__, right, __, __ = trans_borders[nid][ntrans]
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if left != right:
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continue
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if x > 0:
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nid, ntrans = tiling[x - 1][y]
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__, __, bottom, __ = trans_borders[nid][ntrans]
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if top != bottom:
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continue
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tiling[x][y] = num, trans
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next_x, next_y = (x, y + 1) if y < (length - 1) else (x + 1, 0)
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if rec(next_x, next_y, used):
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return True
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used -= {num}
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tiling[x][y] = (-1, -1)
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return False
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assert rec()
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return transform_mapping, tiling
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def solve(tiles: Tiles) -> int:
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transforms, tiling = build_tiling(tiles)
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return tiling[0][0][0] * tiling[0][-1][0] * tiling[-1][0][0] * tiling[-1][-1][0]
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def main() -> None:
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input = parse(sys.stdin.read())
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print(solve(input))
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if __name__ == "__main__":
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main()
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