My attempts to work through the 2021 Advent of Code problems.
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commit d838a5e4566e7bb71a52e17946fd296537608752
parent 08e1a707644c3e90cfbcc230a38b6ec8bae4de3a
Author: Eamon Caddigan <>
Date:   Wed, 22 Dec 2021 19:39:50 -0500

Solution to day 22, part 2

Diffstat: | 178+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 178 insertions(+), 0 deletions(-)

diff --git a/ b/ @@ -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""" + return reduce(add_cube, instructions[1:], [Cube(instructions[0][1:])]) + +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()