My attempts to work through the 2021 Advent of Code problems.

```commit d838a5e4566e7bb71a52e17946fd296537608752
parent 08e1a707644c3e90cfbcc230a38b6ec8bae4de3a
Date:   Wed, 22 Dec 2021 19:39:50 -0500

Solution to day 22, part 2

Diffstat:
```
```1 file changed, 178 insertions(+), 0 deletions(-)
diff --git a/day22_part2.py b/day22_part2.py
@@ -0,0 +1,178 @@
+#!/usr/bin/env python
+"""Advent of Code 2021, day 22 (part 2): Reactor Reboot
+Apply on/off instructions to a much larger 3D grid of cuboids"""
+
+# Okay so part 2 updated part 1 in the obvious way that I totally expected. No
+# way we can store the on/off status of every coordinate. Insted we'll take a
+# different approach:
+#
+# Since everything starts in an "off" state, and the goal of the problem is to
+# determine how many cubes are "on", we don't need to pay attention to every
+# single coordinate. Instead, we can find the _total on-volume_. The _total
+# on-volume_ is the sum of the volume of every rectangular cuboid (which I will
+# just call "cubes" from now on). We'll process the on/off cuboids one at a
+# time. Each time we add a cube, we'll check its intersection with previous
+# cubes. When there's an intersection between old cube A and new cube B, we'll
+# find the set of cubes corresponding to the volume A not B, and these will
+# replace A in the list of on-cubes. When B is on, it will be added to the
+# list, and when B is off, it won't. This alogirhm is O(n^2) and could probably
+# be beaten by other approaches (I'm wondering about a sweep-plane, for
+# instance), but it's fairly straightforward to code; the hardest function is
+# the A not B cube splitter.
+
+from typing import Tuple, List, Union, NewType
+from functools import reduce
+from operator import mul
+
+from day22_part1 import Instruction, parse_input
+from utils import get_puzzle_input
+
+EXAMPLE_INPUT = \
+"""on x=-5..47,y=-31..22,z=-19..33
+on x=-44..5,y=-27..21,z=-14..35
+on x=-49..-1,y=-11..42,z=-10..38
+on x=-20..34,y=-40..6,z=-44..1
+off x=26..39,y=40..50,z=-2..11
+on x=-41..5,y=-41..6,z=-36..8
+off x=-43..-33,y=-45..-28,z=7..25
+on x=-33..15,y=-32..19,z=-34..11
+off x=35..47,y=-46..-34,z=-11..5
+on x=-14..36,y=-6..44,z=-16..29
+on x=-57795..-6158,y=29564..72030,z=20435..90618
+on x=36731..105352,y=-21140..28532,z=16094..90401
+on x=30999..107136,y=-53464..15513,z=8553..71215
+on x=13528..83982,y=-99403..-27377,z=-24141..23996
+on x=-72682..-12347,y=18159..111354,z=7391..80950
+on x=-1060..80757,y=-65301..-20884,z=-103788..-16709
+on x=-83015..-9461,y=-72160..-8347,z=-81239..-26856
+on x=-52752..22273,y=-49450..9096,z=54442..119054
+on x=-29982..40483,y=-108474..-28371,z=-24328..38471
+on x=-4958..62750,y=40422..118853,z=-7672..65583
+on x=55694..108686,y=-43367..46958,z=-26781..48729
+on x=-98497..-18186,y=-63569..3412,z=1232..88485
+on x=-726..56291,y=-62629..13224,z=18033..85226
+on x=-110886..-34664,y=-81338..-8658,z=8914..63723
+on x=-55829..24974,y=-16897..54165,z=-121762..-28058
+on x=-65152..-11147,y=22489..91432,z=-58782..1780
+on x=-120100..-32970,y=-46592..27473,z=-11695..61039
+on x=-18631..37533,y=-124565..-50804,z=-35667..28308
+on x=-57817..18248,y=49321..117703,z=5745..55881
+on x=14781..98692,y=-1341..70827,z=15753..70151
+on x=-34419..55919,y=-19626..40991,z=39015..114138
+on x=-60785..11593,y=-56135..2999,z=-95368..-26915
+on x=-32178..58085,y=17647..101866,z=-91405..-8878
+on x=-53655..12091,y=50097..105568,z=-75335..-4862
+on x=-111166..-40997,y=-71714..2688,z=5609..50954
+on x=-16602..70118,y=-98693..-44401,z=5197..76897
+on x=16383..101554,y=4615..83635,z=-44907..18747
+off x=-95822..-15171,y=-19987..48940,z=10804..104439
+on x=-89813..-14614,y=16069..88491,z=-3297..45228
+on x=41075..99376,y=-20427..49978,z=-52012..13762
+on x=-21330..50085,y=-17944..62733,z=-112280..-30197
+on x=-16478..35915,y=36008..118594,z=-7885..47086
+off x=-98156..-27851,y=-49952..43171,z=-99005..-8456
+off x=2032..69770,y=-71013..4824,z=7471..94418
+on x=43670..120875,y=-42068..12382,z=-24787..38892
+off x=37514..111226,y=-45862..25743,z=-16714..54663
+off x=25699..97951,y=-30668..59918,z=-15349..69697
+off x=-44271..17935,y=-9516..60759,z=49131..112598
+on x=-61695..-5813,y=40978..94975,z=8655..80240
+off x=-101086..-9439,y=-7088..67543,z=33935..83858
+off x=18020..114017,y=-48931..32606,z=21474..89843
+off x=-77139..10506,y=-89994..-18797,z=-80..59318
+off x=8476..79288,y=-75520..11602,z=-96624..-24783
+on x=-47488..-1262,y=24338..100707,z=16292..72967
+off x=-84341..13987,y=2429..92914,z=-90671..-1318
+off x=-37810..49457,y=-71013..-7894,z=-105357..-13188
+off x=-27365..46395,y=31009..98017,z=15428..76570
+off x=-70369..-16548,y=22648..78696,z=-1892..86821
+on x=-53470..21291,y=-120233..-33476,z=-44150..38147
+off x=-93533..-4276,y=-16170..68771,z=-104985..-24507
+"""
+
+# We'll represent cubes using a 3-tuple of 2-tuples giving the X, Y, and Z
+# extents
+Cube = NewType(
+    'Cube',
+    Tuple[Tuple[int, int], Tuple[int, int], Tuple[int, int]]
+)
+
+def cleave_cube(on_cube: Cube, value: int,
+                axis: int) -> Tuple[Union[None, Cube], Union[None, Cube]]:
+    """Split a cube along the given axis, returning two cubes (or one cube and
+    `None`), corresponding to the cube strictly greater than `value` along
+    `axis`, and the cube less than or equal to `value` along `axis`"""
+    if on_cube[axis][0] > value:
+        return (None, on_cube)
+    if on_cube[axis][1] <= value:
+        return (on_cube, None)
+    # We actually have to cleave the cube. First we create a list of lists of
+    # lists representing two copies of the cube.
+    new_cubes_list = [[list(e) for e in on_cube] for _ in range(2)]
+    new_cubes_list[0][axis][1] = value
+    new_cubes_list[1][axis][0] = value + 1
+    # I don't know why but this is giving me Lisp flashbacks
+    return tuple(Cube(tuple(tuple(e) for e in c)) for c in new_cubes_list)
+
+def split_cube(old_cube: Cube, new_cube: Cube) -> List[Cube]:
+    """Return a list containing one or more cubes representing the volume of
+    `old_cube` that doesn't intersect with `new_cube`"""
+    # This is the hard part. If this doesn't work I'm sunk!
+    new_cubes = []
+    intersection_cube = old_cube
+    for axis in range(3):
+        # First check if the cubes intersect along this axis. If they don't,
+        # we're done: no splitting necessary!
+        if old_cube[axis][0] > new_cube[axis][1] \
+                or old_cube[axis][1] < new_cube[axis][0]:
+            return [old_cube]
+        # So they may intersect somehow. We'll cleave the cube into as many as
+        # three new cubes: the part "above" `new_cube`, the part "below" it,
+        # and the intersection; above and below could either or both be `None`,
+        # but intersection better not be. Note that this can create way more
+        # cubes than necessary; I'm hoping that the number of cubes doesn't
+        # explode.
+        intersection_cube, above_cube = cleave_cube(intersection_cube,
+                                                    new_cube[axis][1],
+                                                    axis)
+        below_cube, intersection_cube = cleave_cube(intersection_cube,
+                                                    new_cube[axis][0]-1,
+                                                    axis)
+        if above_cube is not None:
+            new_cubes.append(above_cube)
+        if below_cube is not None:
+            new_cubes.append(below_cube)
+    return new_cubes
+
+def add_cube(on_cubes: List[Cube], instruction: Instruction) -> List[Cube]:
+    """Apply a single step of the instructions to the list of on-cubes and
+    return a new list of cubes"""
+    new_cube = Cube(instruction[1:])
+    new_on_cubes = []
+    for old_cube in on_cubes:
+        new_on_cubes.extend(split_cube(old_cube, new_cube))
+    if instruction[0]:
+        new_on_cubes.append(new_cube)
+    return new_on_cubes
+
+def create_on_cube_list(instructions: List[Instruction]) -> List[Cube]:
+    """Build a list of on-cubes by following the instructions"""
+
+def cube_volume(on_cube: Cube) -> int:
+    """Return the volume of a single cube"""
+    return reduce(mul, [e[1] - e[0] + 1 for e in on_cube])
+
+def solve_puzzle(input_string: str) -> int:
+    """Return the numeric solution to the puzzle"""
+    return sum(map(cube_volume,
+                   create_on_cube_list(parse_input(input_string))))
+
+def main() -> None:
+    """Run when the file is called as a script"""
+    assert solve_puzzle(EXAMPLE_INPUT) == 2758514936282235
+    print("Number of cubes turned on:",
+          solve_puzzle(get_puzzle_input(22)))
+
+if __name__ == "__main__":
+    main()
```