2021: d22: ex2: add solution

2021/d22/ex2/ex2.py

@@ -0,0 +1,167 @@
+#!/usr/bin/env python
+
+import functools
+import itertools
+import sys
+from typing import Iterator, List, NamedTuple, Optional, Set, Tuple, cast
+
+
+class Point(NamedTuple):
+    x: int
+    y: int
+    z: int
+
+
+class Cuboid(NamedTuple):
+    min: Point
+    max: Point
+
+
+class Step(NamedTuple):
+    state: bool
+    bounds: Cuboid
+
+
+Grid = Set[Cuboid]
+
+MAX_BOUND = 10000000000000000000000000000000000000000000  # Just a very large integer
+MIN_BOUND = -MAX_BOUND
+
+
+def solve(input: List[str]) -> int:
+    def parse() -> List[Step]:
+        def parse_step(line: str) -> Step:
+            state, cuboid = line.split(" ")
+
+            xs, ys, zs = cuboid.split(",")
+
+            min_x, max_x = map(int, xs[2:].split(".."))
+            min_y, max_y = map(int, ys[2:].split(".."))
+            min_z, max_z = map(int, zs[2:].split(".."))
+
+            # Sanity check
+            assert min_x <= max_x
+            assert min_y <= max_y
+            assert min_z <= max_z
+
+            bounds = Cuboid(Point(min_x, min_y, min_z), Point(max_x, max_y, max_z))
+
+            return Step(state == "on", bounds)
+
+        return [parse_step(line) for line in input]
+
+    def overlapping_range(
+        min_a: int, max_a: int, min_b: int, max_b: int
+    ) -> Optional[Tuple[int, int]]:
+        if max_a < min_b or min_a > max_b:
+            return None
+        return max(min_a, min_b), min(max_a, max_b)
+
+    def overlapping_cube(cube: Cuboid, other: Cuboid) -> Optional[Cuboid]:
+        xs = overlapping_range(cube.min.x, cube.max.x, other.min.x, other.max.x)
+        ys = overlapping_range(cube.min.y, cube.max.y, other.min.y, other.max.y)
+        zs = overlapping_range(cube.min.z, cube.max.z, other.min.z, other.max.z)
+
+        if xs is None or ys is None or zs is None:
+            return None
+        return Cuboid(Point(xs[0], ys[0], zs[0]), Point(xs[1], ys[1], zs[1]))
+
+    def overlaps(cube: Cuboid, other: Cuboid) -> bool:
+        return overlapping_cube(cube, other) is not None
+
+    def carve_out(grid: Grid, hole: Cuboid) -> Grid:
+        from itertools import filterfalse
+
+        def do_carve(c: Cuboid) -> Set[Cuboid]:
+            cubes: Set[Cuboid] = set()
+
+            min, max = c
+
+            rightside = overlapping_range(hole.max.x + 1, MAX_BOUND, min.x, max.x)
+            leftside = overlapping_range(MIN_BOUND, hole.min.x - 1, min.x, max.x)
+            xs = overlapping_range(hole.min.x, hole.max.x, min.x, max.x)
+            if rightside is not None:
+                min_r, max_r = rightside
+                cubes.add(
+                    Cuboid(Point(min_r, min.y, min.z), Point(max_r, max.y, max.z))
+                )
+            if leftside is not None:
+                min_l, max_l = leftside
+                cubes.add(
+                    Cuboid(Point(min_l, min.y, min.z), Point(max_l, max.y, max.z))
+                )
+
+            backside = overlapping_range(hole.max.y + 1, MAX_BOUND, min.y, max.y)
+            frontside = overlapping_range(MIN_BOUND, hole.min.y - 1, min.y, max.y)
+            ys = overlapping_range(hole.min.y, hole.max.y, min.y, max.y)
+            if backside is not None and xs is not None:
+                min_x, max_x = xs
+                min_b, max_b = backside
+                cubes.add(
+                    Cuboid(Point(min_x, min_b, min.z), Point(max_x, max_b, max.z))
+                )
+            if frontside is not None and xs is not None:
+                min_x, max_x = xs
+                min_f, max_f = frontside
+                cubes.add(
+                    Cuboid(Point(min_x, min_f, min.z), Point(max_x, max_f, max.z))
+                )
+
+            topside = overlapping_range(hole.max.z + 1, MAX_BOUND, min.z, max.z)
+            bottomside = overlapping_range(MIN_BOUND, hole.min.z - 1, min.z, max.z)
+            if topside is not None and xs is not None and ys is not None:
+                min_x, max_x = xs
+                min_y, max_y = ys
+                min_t, max_t = topside
+                cubes.add(
+                    Cuboid(Point(min_x, min_y, min_t), Point(max_x, max_y, max_t))
+                )
+            if bottomside is not None and xs is not None and ys is not None:
+                min_x, max_x = xs
+                min_y, max_y = ys
+                min_b, max_b = bottomside
+                cubes.add(
+                    Cuboid(Point(min_x, min_y, min_b), Point(max_x, max_y, max_b))
+                )
+
+            return cubes
+
+        overlaps_us = lambda c: overlaps(c, hole)
+
+        of_interest, other = filter(overlaps_us, grid), filterfalse(overlaps_us, grid)
+
+        return set(other) | set(
+            itertools.chain.from_iterable(do_carve(c) for c in of_interest)
+        )
+
+    def apply(grid: Grid, step: Step) -> Grid:
+        cuboid = step.bounds
+
+        # Remove that cube from the grid, potentially splitting cubes that overlap
+        grid = carve_out(grid, cuboid)
+
+        # Add it back in if we want to turn on those cubes
+        if step.state:
+            grid.add(cuboid)
+
+        return grid
+
+    def count_cubes(c: Cuboid) -> int:
+        min, max = c
+        return (max.x + 1 - min.x) * (max.y + 1 - min.y) * (max.z + 1 - min.z)
+
+    def score(grid: Grid) -> int:
+        return sum(map(count_cubes, grid))
+
+    steps = parse()
+    grid: Grid = functools.reduce(apply, steps, set())
+    return score(grid)
+
+
+def main() -> None:
+    input = [line.strip() for line in sys.stdin.readlines()]
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()