96 lines
2.6 KiB
Python
96 lines
2.6 KiB
Python
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#!/usr/bin/env python
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import sys
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from typing import Iterator, NamedTuple, Optional
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class Point(NamedTuple):
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x: int
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y: int
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GardenPoints = set[Point]
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GRID_SIZE = 131
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MID_GRID = 65
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STEPS = 26501365
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def solve(input: list[str]) -> int:
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def parse(input: list[str]) -> tuple[GardenPoints, Point]:
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start: Optional[Point] = None
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points: GardenPoints = set()
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for x, line in enumerate(input):
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for y, c in enumerate(line):
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if c == "#":
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continue
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if c == "S":
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start = Point(x, y)
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points.add(Point(x, y))
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assert start is not None # Sanity check
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return points, start
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def step(points: GardenPoints, positions: set[Point]) -> set[Point]:
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res: set[Point] = set()
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for p in positions:
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for dx, dy in (
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(-1, 0),
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(1, 0),
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(0, -1),
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(0, 1),
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):
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x = p.x + dx
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y = p.y + dy
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# Check if the *wrapped* point is part of the garden
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px = (x + GRID_SIZE) % GRID_SIZE
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py = (y + GRID_SIZE) % GRID_SIZE
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if Point(px, py) not in points:
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continue
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res.add(Point(x, y))
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return res
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def compute_quadratic(points: GardenPoints, start: Point) -> int:
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def iterate() -> Iterator[int]:
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positions = {start}
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while True:
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yield len(positions)
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positions = step(points, positions)
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values: list[tuple[int, int]] = []
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for i, num in enumerate(iterate()):
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if i % GRID_SIZE != MID_GRID:
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continue
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values.append((i, num))
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if len(values) == 3:
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break
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# Lagrange interpolation
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(x1, y1), (x2, y2), (x3, y3) = values
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x = STEPS
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return (
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0
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# Use integer division as it happens to work in our case
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+ ((x - x2) * (x - x3)) * y1 // ((x1 - x2) * (x1 - x3))
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+ ((x - x1) * (x - x3)) * y2 // ((x2 - x1) * (x2 - x3))
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+ ((x - x1) * (x - x2)) * y3 // ((x3 - x1) * (x3 - x2))
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)
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assert len(input) == GRID_SIZE # Sanity check
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assert len(input[0]) == GRID_SIZE # Sanity check
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points, start = parse(input)
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assert start == Point(MID_GRID, MID_GRID) # Sanity check
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return compute_quadratic(points, start)
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def main() -> None:
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input = sys.stdin.read().splitlines()
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print(solve(input))
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if __name__ == "__main__":
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main()
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