# Advent of Code - 2021

This is a solution to Day 22 of Advent of Code 2021.

## Day 22 - Reactor Reboot

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:`10,10,10 10,10,11 10,10,12 10,11,10 10,11,11 10,11,12 10,12,10 10,12,11 10,12,12 11,10,10 11,10,11 11,10,12 11,11,10 11,11,11 11,11,12 11,12,10 11,12,11 11,12,12 12,10,10 12,10,11 12,10,12 12,11,10 12,11,11 12,11,12 12,12,10 12,12,11 12,12,12`

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:`11,11,13 11,12,13 11,13,11 11,13,12 11,13,13 12,11,13 12,12,13 12,13,11 12,13,12 12,13,13 13,11,11 13,11,12 13,11,13 13,12,11 13,12,12 13,12,13 13,13,11 13,13,12 13,13,13`

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:`10,10,10 10,10,11 10,11,10 10,11,11 11,10,10 11,10,11 11,11,10 11,11,11`

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?

### Read input

Today I'm using regular expression's **named groups** feature for the first time here. By prefixing a group with `?P<name>`

, after running `re.match`

, you can refer to individual groups by their `name`

.

It makes the regex often very much harder to read but I wanted to try it here.

Without named groups, I actually think this code would have looked better:

```
pattern = r'(on|off) x=(-?\d+..-?\d+),y=(-?\d+..-?\d+),z=(-?\d+..-?\d+)'
groups = re.match(pattern, line)
action = groups[0]
y_range = groups[1]
x_range = groups[2]
z_range = groups[3]
```

The thing with regex is that it can get complicated to read and understand real quick. I try to use it only for very simple patterns to make sure it can be understood by a glimpse. Anything more complicated than that, I prefer doing over multiple steps for clarity.

```
import re
from collections import namedtuple
from utils import read_input
Point = namedtuple('Point', ['x', 'y', 'z'])
Instruction = namedtuple('Instruction', ['action', 'start', 'end'])
def transformer(line):
pattern = r'(?P
```on|off) x=(?P-?\d+..-?\d+),y=(?P-?\d+..-?\d+),z=(?P-?\d+..-?\d+)'
m = re.match(pattern, line)
action = m.group('action')
x_range = m.group('x')
y_range = m.group('y')
z_range = m.group('z')
x1, x2 = x_range.split('..')
y1, y2 = y_range.split('..')
z1, z2 = z_range.split('..')
start = Point(x=int(x1), y=int(y1), z=int(z1))
end = Point(x=int(x2), y=int(y2), z=int(z2))
return Instruction(action, start, end)
instructions = read_input(22, transformer)

### Part 1

To start, we need to create all the cuboids in each of these ranges.

Since we're limiting our functionality to points between `[-50, 50]`

, we have a bit of bookkeeping in the start and then a triple for-loop for each of the axis.

```
def get_cuboids_in_range(start, end):
cuboids = []
if start.x < -50 and end.x < -50 or start.x > 50 and end.x > 50:
return []
if start.y < -50 and end.y < -50 or start.y > 50 and end.y > 50:
return []
if start.z < -50 and end.z < - 50 or start.z > 50 and end.z > 50:
return []
min_x = max(-50, min(50, start.x))
max_x = min(50, max(-50, end.x))
min_y = max(-50, min(50, start.y))
max_y = min(50, max(-50, end.y))
min_z = max(-50, min(50, start.z))
max_z = min(50, max(-50, end.z))
for x in range(min_x, max_x + 1):
for y in range(min_y, max_y + 1):
for z in range(min_z, max_z + 1):
cuboids.append(Point(x,y,z))
return cuboids
```

I keep track of lit cuboids and for each point in the given range, we either add it to the set (`on`

) or take it off (`off`

). Finally, we're left with a set of lit cuboids.

I learned today that `set`

has two methods for removing items: `discard`

and `remove`

. I've been using `remove`

with an `if`

guard all these years but there's a nice difference:

discard(...) method of builtins.set instance

Remove an element from a set if it is a member.If the element is not a member, do nothing.

remove(...) method of builtins.set instance

Remove an element from a set; it must be a member.If the element is not a member, raise a KeyError.

So whenever you need to remove items that might not exist in a set, `discard`

is a good option.

```
def activate_cuboids(instructions):
lit = set()
for instruction in instructions:
for point in get_cuboids_in_range(instruction.start, instruction.end):
match instruction.action:
case 'on':
lit.add(point)
case 'off':
lit.discard(point)
return lit
```

Afterward, considering only cubes in the region x=-50..50,y=-50..50,z=-50..50, how many cubes are on?

Let's count our lit cuboids!

```
result = len(activate_cuboids(instructions))
print(f'Solution: {result}')
assert result == 648681
```

Solution: 648681

### 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?

The size of the 3D grid grows so big (in my case, roughly 200k^3 points) that we can't rely on looping over every single point on every single range.

We need to do math! And to make that easier to manage, we'll make objects too!

`Area`

class is like a cuboid but without all of its bits.

Like a cuboid from the previous part, it knows its `start`

and `end`

points but also keeps track of points that are `off`

from it.

To calculate `Area`

's volume, we take each of the x/y/z axis, subtract start value from end (and add 1 to make these ranges inclusive on both ends; a (1,1) -> (3,3) has 3 points each way, not 2) and multiply those together. We then remove the volume of any area that's bit off from it to get the actual volume.

To `subtract`

one `Area`

from another, we calculate its intersection (using math I found from the Interwebs), then subtract that intersection from all our off'd areas and finally add the intersection to our own off area.

```
class Area:
def __init__(self, start, end):
self.start = start
self.end = end
self.off = []
def volume(self):
full_volume = (self.end.x - self.start.x + 1) * (self.end.y - self.start.y + 1) * (self.end.z - self.start.z + 1)
off_volume = sum(area.volume() for area in self.off)
return full_volume - off_volume
def subtract(self, other):
intersection = self.intersection(other)
if intersection.is_empty():
return
for other in self.off:
other.subtract(intersection)
self.off.append(intersection)
def intersection(self, another):
new = {
'start': [],
'end': []
}
for axis in ['x', 'y', 'z']:
one_start = getattr(self.start, axis)
one_end = getattr(self.end, axis)
another_start = getattr(another.start, axis)
another_end = getattr(another.end, axis)
max_start = max(one_start, another_start)
min_end = min(one_end, another_end)
if max_start < min_end + 1:
new_start = max_start
new_end = min_end
else:
new_start = 0
new_end = 0
new['start'].append(new_start)
new['end'].append(new_end)
start = Point(*new['start'])
end = Point(*new['end'])
return Area(start, end)
def is_empty(self):
xs = (self.start.x, self.end.x)
ys = (self.start.y, self.end.y)
zs = (self.start.z, self.end.z)
return xs == (0, 0) or ys == (0, 0) or zs == (0, 0)
def __repr__(self):
return f': {self.start}, {self.end}'
```

```
areas = []
for instruction in instructions:
area = Area(instruction.start, instruction.end)
for other in areas:
other.subtract(area)
if instruction.action == 'on':
areas.append(area)
result = sum(area.volume() for area in areas)
print(f'Solution: {result}')
assert result == 1302784472088899
```

Solution: 1302784472088899