advent-of-code/2021/day11

https://adventofcode.com/2021/day/11

--- Day 11: Dumbo Octopus ---

You enter a large cavern full of rare bioluminescent dumbo octopuses! They seem to not like the Christmas lights on your submarine, so you turn them off for now.

There are 100 octopuses arranged neatly in a 10 by 10 grid. Each octopus slowly gains energy over time and flashes brightly for a moment when its energy is full. Although your lights are off, maybe you could navigate through the cave without disturbing the octopuses if you could predict when the flashes of light will happen.

Each octopus has an energy level - your submarine can remotely measure the energy level of each octopus (your puzzle input). For example:

[code]

5483143223
2745854711
5264556173
6141336146
6357385478
4167524645
2176841721
6882881134
4846848554
5283751526

[/code]

The energy level of each octopus is a value between 0 and 9. Here, the top-left octopus has an energy level of 5, the bottom-right one has an energy level of 6, and so on.

You can model the energy levels and flashes of light in steps. During a single step, the following occurs:

• First, the energy level of each octopus increases by 1.
• Then, any octopus with an energy level greater than 9 flashes. This increases the energy level of all adjacent octopuses by 1, including octopuses that are diagonally adjacent. If this causes an octopus to have an energy level greater than 9, it also flashes. This process continues as long as new octopuses keep having their energy level increased beyond 9. (An octopus can only flash at most once per step.)
• Finally, any octopus that flashed during this step has its energy level set to 0, as it used all of its energy to flash.

Adjacent flashes can cause an octopus to flash on a step even if it begins that step with very little energy. Consider the middle octopus with 1 energy in this situation:

[code]

Before any steps:
11111
19991
19191
19991
11111

After step 1:
34543
4 _000_ 4
5 _000_ 5
4 _000_ 4
34543

After step 2:
45654
51115
61116
51115
45654

[/code]

An octopus is highlighted when it flashed during the given step.

Here is how the larger example above progresses:

[code]

Before any steps:
5483143223
2745854711
5264556173
6141336146
6357385478
4167524645
2176841721
6882881134
4846848554
5283751526

After step 1:
6594254334
3856965822
6375667284
7252447257
7468496589
5278635756
3287952832
7993992245
5957959665
6394862637

After step 2:
88 _0_ 7476555
5 _0_ 89 _0_ 87 _0_ 54
85978896 _0_ 8
84857696 _00_
87 _00_ 9 _0_ 88 _00_
66 _000_ 88989
68 _0000_ 5943
_000000_ 7456
9 _000000_ 876
87 _0000_ 6848

After step 3:
_00_ 5 _0_ 9 _00_ 866
85 _00_ 8 _00_ 575
99 _000000_ 39
97 _000000_ 41
9935 _0_ 8 _00_ 63
77123 _00000_
791125 _000_ 9
221113 _0000_
_0_ 421125 _000_
_00_ 21119 _000_

After step 4:
2263 _0_ 31977
_0_ 923 _0_ 31697
_00_ 3222115 _0_
_00_ 41111163
_00_ 76191174
_00_ 53411122
_00_ 4236112 _0_
5532241122
1532247211
113223 _0_ 211

After step 5:
4484144 _000_
2 _0_ 44144 _000_
2253333493
1152333274
11873 _0_ 3285
1164633233
1153472231
6643352233
2643358322
2243341322

After step 6:
5595255111
3155255222
33644446 _0_ 5
2263444496
2298414396
2275744344
2264583342
7754463344
3754469433
3354452433

After step 7:
67 _0_ 7366222
4377366333
4475555827
34966557 _0_ 9
35 _00_ 6256 _0_ 9
35 _0_ 9955566
3486694453
8865585555
486558 _0_ 644
4465574644

After step 8:
7818477333
5488477444
5697666949
46 _0_ 876683 _0_
473494673 _0_
474 _00_ 97688
69 _0000_ 7564
_000000_ 9666
8 _00000_ 4755
68 _0000_ 7755

After step 9:
9 _0_ 6 _0000_ 644
78 _00000_ 976
69 _000000_ 8 _0_
584 _00000_ 82
5858 _0000_ 93
69624 _00000_
8 _0_ 2125 _000_ 9
222113 _000_ 9
9111128 _0_ 97
7911119976

After step 10:
_0_ 481112976
_00_ 31112 _00_ 9
_00_ 411125 _0_ 4
_00_ 811114 _0_ 6
_00_ 991113 _0_ 6
_00_ 93511233
_0_ 44236113 _0_
553225235 _0_
_0_ 53225 _0_ 6 _00_
_00_ 3224 _0000_

[/code]

After step 10, there have been a total of 204 flashes. Fast forwarding, here is the same configuration every 10 steps:

[code]

After step 20:
3936556452
56865568 _0_ 6
449655569 _0_
444865558 _0_
445686557 _0_
568 _00_ 86577
7 _00000_ 9896
_0000000_ 344
6 _000000_ 364
46 _0000_ 9543

After step 30:
_0_ 643334118
4253334611
3374333458
2225333337
2229333338
2276733333
2754574565
5544458511
9444447111
7944446119

After step 40:
6211111981
_0_ 421111119
_00_ 42111115
_000_ 3111115
_000_ 3111116
_00_ 65611111
_0_ 532351111
3322234597
2222222976
2222222762

After step 50:
9655556447
48655568 _0_ 5
448655569 _0_
445865558 _0_
457486557 _0_
57 _000_ 86566
6 _00000_ 9887
8 _000000_ 533
68 _00000_ 633
568 _0000_ 538

After step 60:
25333342 _00_
274333464 _0_
2264333458
2225333337
2225333338
2287833333
3854573455
1854458611
1175447111
1115446111

After step 70:
8211111164
_0_ 421111166
_00_ 42111114
_000_ 4211115
_0000_ 211116
_00_ 65611111
_0_ 532351111
7322235117
5722223475
4572222754

After step 80:
1755555697
59655556 _0_ 9
448655568 _0_
445865558 _0_
457 _0_ 86557 _0_
57 _000_ 86566
7 _00000_ 8666
_0000000_ 99 _0_
_0000000_ 8 _00_
_0000000000_

After step 90:
7433333522
2643333522
2264333458
2226433337
2222433338
2287833333
2854573333
4854458333
3387779333
3333333333

After step 100:
_0_ 397666866
_0_ 749766918
_00_ 53976933
_000_ 4297822
_000_ 4229892
_00_ 53222877
_0_ 532222966
9322228966
7922286866
6789998766

[/code]

After 100 steps, there have been a total of _1656_ flashes.

Given the starting energy levels of the dumbo octopuses in your cavern, simulate 100 steps. How many total flashes are there after 100 steps?