Part 1
Operating at these extreme ocean depths has overloaded the submarine's reactor; it needs to be rebooted.
The reactor core is made up of a large 3-dimensional grid made up entirely of cubes, one cube per integer 3-dimensional coordinate (x,y,z). Each cube can be either on or off; at the start of the reboot process, they are all off. (Could it be an old model of a reactor you've seen before?)
To reboot the reactor, you just need to set all of the cubes to either on or off by following a list of reboot steps (your puzzle input). Each step specifies a cuboid (the set of all cubes that have coordinates which fall within ranges for x, y, and z) and whether to turn all of the cubes in that cuboid on or off.
For example, given these reboot steps:
on x=10..12,y=10..12,z=10..12
on x=11..13,y=11..13,z=11..13
off x=9..11,y=9..11,z=9..11
on x=10..10,y=10..10,z=10..10
The first step (on x=10..12,y=10..12,z=10..12) turns on a 3x3x3 cuboid consisting of 27 cubes:
10,10,1010,10,1110,10,1210,11,1010,11,1110,11,1210,12,1010,12,1110,12,1211,10,1011,10,1111,10,1211,11,1011,11,1111,11,1211,12,1011,12,1111,12,1212,10,1012,10,1112,10,1212,11,1012,11,1112,11,1212,12,1012,12,1112,12,12
The second step (on x=11..13,y=11..13,z=11..13) turns on a 3x3x3 cuboid that overlaps with the first. As a result, only 19 additional cubes turn on; the rest are already on from the previous step:
11,11,1311,12,1311,13,1111,13,1211,13,1312,11,1312,12,1312,13,1112,13,1212,13,1313,11,1113,11,1213,11,1313,12,1113,12,1213,12,1313,13,1113,13,1213,13,13
The third step (off x=9..11,y=9..11,z=9..11) turns off a 3x3x3 cuboid that overlaps partially with some cubes that are on, ultimately turning off 8 cubes:
10,10,1010,10,1110,11,1010,11,1111,10,1011,10,1111,11,1011,11,11
The final step (on x=10..10,y=10..10,z=10..10) turns on a single cube, 10,10,10. After this last step, _39_ cubes are on.
The initialization procedure only uses cubes that have x, y, and z positions of at least -50 and at most 50. For now, ignore cubes outside this region.
Here is a larger example:
on x=-20..26,y=-36..17,z=-47..7
on x=-20..33,y=-21..23,z=-26..28
on x=-22..28,y=-29..23,z=-38..16
on x=-46..7,y=-6..46,z=-50..-1
on x=-49..1,y=-3..46,z=-24..28
on x=2..47,y=-22..22,z=-23..27
on x=-27..23,y=-28..26,z=-21..29
on x=-39..5,y=-6..47,z=-3..44
on x=-30..21,y=-8..43,z=-13..34
on x=-22..26,y=-27..20,z=-29..19
off x=-48..-32,y=26..41,z=-47..-37
on x=-12..35,y=6..50,z=-50..-2
off x=-48..-32,y=-32..-16,z=-15..-5
on x=-18..26,y=-33..15,z=-7..46
off x=-40..-22,y=-38..-28,z=23..41
on x=-16..35,y=-41..10,z=-47..6
off x=-32..-23,y=11..30,z=-14..3
on x=-49..-5,y=-3..45,z=-29..18
off x=18..30,y=-20..-8,z=-3..13
on x=-41..9,y=-7..43,z=-33..15
on x=-54112..-39298,y=-85059..-49293,z=-27449..7877
on x=967..23432,y=45373..81175,z=27513..53682
The last two steps are fully outside the initialization procedure area; all other steps are fully within it. After executing these steps in the initialization procedure region, _590784_ cubes are on.
Execute the reboot steps. Afterward, considering only cubes in the region x=-50..50,y=-50..50,z=-50..50, how many cubes are on?
Proposed solution: brute force seems to be achievable for part 1 but probably not for part 2, I do it anyway – using a set of size-3 tuples for the coordinates
Time complexity: O(V) where V is the "volume" or the total number of points/cubes in the input
Space complexity: O(V)
#!/usr/bin/env python3
import sys
if len(sys.argv) != 2:
print("Usage: {} <input file>".format(sys.argv[0]))
sys.exit(1)
file_input = open(sys.argv[1], "r").read().strip().split("\n")
cubes = set()
init_range = range(-50,51)
for line in file_input:
if line == "":
continue
instr, ranges = line.split()
_x, _y, _z = ranges.split(",")
x1, x2 = [int(x) for x in _x.split("=")[1].split("..")]
y1, y2 = [int(y) for y in _y.split("=")[1].split("..")]
z1, z2 = [int(z) for z in _z.split("=")[1].split("..")]
for x in range(x1, x2+1):
if x < -50 or x > 50:
break
for y in range(y1, y2+1):
for z in range(z1, z2+1):
if instr == "on":
cubes.add((x,y,z))
else:
cubes.discard((x,y,z))
print("Number of cubes lit: {}".format(len(cubes)))
❯ python3 solution22.py input22
Number of cubes lit: 588120
Part 2
Now that the initialization procedure is complete, you can reboot the reactor.
Starting with all cubes off, run all of the reboot steps for all cubes in the reactor.
Consider the following reboot steps:
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
After running the above reboot steps, _2758514936282235_ cubes are on. (Just for fun, 474140 of those are also in the initialization procedure region.)
Starting again with all cubes off, execute all reboot steps. Afterward, considering all cubes, how many cubes are on?
Proposed solution: instead of counting individual "cubes," or points, use the dimensions of the cubes and split the cubes as they intersect to make sure that the volumes are not overlapping – this is important when calculating the final volume
Time complexity: O(n) where n is the number of instructions
Space complexity: O(n)
#!/usr/bin/env python3
from math import prod
import sys
if len(sys.argv) != 2:
print("Usage: {} <input file>".format(sys.argv[0]))
sys.exit(1)
file_input = open(sys.argv[1], "r").read().strip().split("\n")
class Cube:
def __init__(self, dims):
self.dims = dims
def intersects(self, other):
return not (other.dims[0] < self.dims[0] and other.dims[1] < self.dims[0]) \
and not (other.dims[0] > self.dims[1] and other.dims[1] > self.dims[1]) \
and not (other.dims[2] < self.dims[2] and other.dims[3] < self.dims[2]) \
and not (other.dims[2] > self.dims[3] and other.dims[3] > self.dims[3]) \
and not (other.dims[4] < self.dims[4] and other.dims[5] < self.dims[4]) \
and not (other.dims[4] > self.dims[5] and other.dims[5] > self.dims[5])
def volume(self):
return prod([self.dims[i+1] - self.dims[i] + 1 for i in range(0, 6, 2)])
def __str__(self):
return str(self.dims)
def split(cubes, cube1, cube2):
"""
If cube2 intersects cube1, this functions splits cube1 into new cubes
and adds them to the cubes set.
"""
x_start, y_start, z_start = cube1.dims[0], cube1.dims[2], cube1.dims[4]
x_end, y_end, z_end = cube1.dims[1], cube1.dims[3], cube1.dims[5]
if x_start < cube2.dims[0]:
cubes.add(Cube((x_start, cube2.dims[0]-1, y_start, y_end, z_start, z_end)))
x_start = cube2.dims[0]
if y_start < cube2.dims[2]:
cubes.add(Cube((x_start, x_end, y_start, cube2.dims[2]-1, z_start, z_end)))
y_start = cube2.dims[2]
if z_start < cube2.dims[4]:
cubes.add(Cube((x_start, x_end, y_start, y_end, z_start, cube2.dims[4]-1)))
z_start = cube2.dims[4]
x_start2, y_start2, z_start2 = cube2.dims[1] + 1, cube2.dims[3] + 1, cube2.dims[5] + 1
if x_start2 <= x_end:
cubes.add(Cube((x_start2, x_end, y_start, y_end, z_start, z_end)))
x_end = cube2.dims[1]
if y_start2 <= y_end:
cubes.add(Cube((x_start, x_end, y_start2, y_end, z_start, z_end)))
y_end = cube2.dims[3]
if z_start2 <= z_end:
cubes.add(Cube((x_start, x_end, y_start, y_end, z_start2, z_end)))
z_end = cube2.dims[5]
cubes = set()
for line in file_input:
if line == "":
continue
instr, ranges = line.split()
_x, _y, _z = ranges.split(",")
x1, x2 = [int(x) for x in _x.split("=")[1].split("..")]
y1, y2 = [int(y) for y in _y.split("=")[1].split("..")]
z1, z2 = [int(z) for z in _z.split("=")[1].split("..")]
new_cube = Cube((x1, x2, y1, y2, z1, z2))
for cube in list(cubes):
if cube.intersects(new_cube):
cubes.remove(cube)
split(cubes, cube, new_cube)
if instr == "on":
cubes.add(new_cube)
total = sum([cube.volume() for cube in cubes])
print("Number of cubes lit: {}".format(total))
I am not going to go over it to deeply, but you need to be careful when splitting the cube to make sure the split regions do not overlap. This split function can split the original cube anywhere from 1 smaller cube (if the comparison cube covers a whole face of the original with some intersecting depth) to 6 smaller cubes (if the comparison cube is fully contained within the original cube). Once I split the cube once, I adjust the start position for the respective axis to make sure this overlap does not happen with the remaining splits, if any.
Once the splitting functionality works, it's just a matter of iterating through the instructions and using each volume as a comparison cube to the ones that have already been processed. If any two cubes intersect, remove the original from the set and split it x ways based on the type of intersection. Add the new splits to the set. Only add the comparison cube to the set if the instruction is "on." If it's "off," then just continue to the next instruction.
❯ time python3 solution22.py input22
Number of cubes lit: 1134088247046731
python3 solution22.py input22 0.23s user 0.01s system 99% cpu 0.243 total