TL;DR

On with Advent of Code puzzle 11 from 2021: taking it with calm.

Dec. 11th, 2021 was a Saturday and I took it easy. Like sleeping a bit more, I mean.

Hence, when I got to solve the daily puzzle, I knew I was well behind my past selves from the days before, and that I could take it with calm.

The challenge is interesting and still puts you in that freezing spot where you have to decide whether to go all-in with brute force or design things a bit. The former is often the right way to go in a hurry as it’s simpler, but with calm comes time to do things and overengineer them.

I was not like producing successive frames of the thing because doing the whole iteration over the whole grid all over the time, just to increase a counter, seems overkill. Yes, I have a different mental category about overkill than anybody else.

So I decided to make time tick and calculate the right value of an octopus at a given time with some modular arithmetic. I mean, if an isolated cell starts at 5, it will be at 8 in the third step, right? It will flash at the fifth step and go back to 0, right? So, the value $v$ of that octopus at any future step $s$ will be:

\[v_s = (v_0 + s) \mod 10\]

Now, of course this does not save us from iterating over all octopuses at each step, because we need to know which cells fire at that step. So we’re back at octopus 1, right? Ehr, I mean square 1.

One thing that we can do, though, is to divide all octopuses into buckets depending on their value. All of them with a value of 0 will end up in bucket 0, and so on. With this initial categorization, we know exactly which octopuses will flash at step $s$, because we can calculate the corresponding flashing bucket $f_s$ like this:

\[f_s = -s \mod 10\]

Yes, it seems like going backwards in time, but this is just to counterbalance the fact that we are not actually increasing octopuses’ values as time ticks on.

Now, of course, we have to take into account that octopuses are connected in a grid, which means that they might change bucket as time passes, depending on their neighbors flashing. This means that we need:

  • to know the neighbors of each octopus, so that we can increase them when it flashes, and
  • to easily move an octopus from a bucket to another.

The first need can be addressed implicitly, by iterating the $3 \cdot 3$ grid around an octopus each time. Or we can do this at once at the beginning, and then use a Set to memorize the connections, because they don’t change over time.

The second pushed me to choose a Hash for tracking the contents of each bucket. This allows efficient insertion and deletion of any elements inside, depending on our needs, as well as keeping track of each octopus by its position (represented as a string of the type X,Y).

At each step, the right flashing bucket is selected and the keys of the associated hash are used as an initial list of flashing octopuses. This list is not iterated the usual way, though, because more octopuses might flash at that step, depending on the chain reaction effect; for this reason, the pattern of iteration is like this:

while @flashing.elems > 0 {
    my $octopus = @flashing.shift;
    ...

In this way it’s possible to push more flashing octopuses into @flashing and be sure that all of them will be considered.

The rules say that a flashing octopus does not flash twice in the same step, so this means that flashing octopuses never leave their bucket. All the other, though, can move across buckets, up until they flash of course.

So… enough talking, let’s get to the code. While coding I adopted a slightly different terminology, so you will not read “octopus” or “flashing” but “cell” (i.e. the octopus’s position) and “firing” instead. I was probably thinking about neural nets.

#!/usr/bin/env raku
use v6;

sub MAIN ($filename = $?FILE.subst(/\.raku$/, '.tmp')) {
   my $inputs = get-inputs($filename);
   my ($part1, $part2) = solve($inputs);

   my $highlight = "\e[1;97;45m";
   my $reset     = "\e[0m";
   put "part1 $highlight$part1$reset";
   put "part2 $highlight$part2$reset";
}

sub get-inputs ($filename) {
   my @grid = $filename.IO.words».comb(/\d/)».Array;
   my (%info-about, @dumbos-in);
   my ($mx, $my) = @grid[0].end, @grid.end;
   for 0 .. $my -> $y {
      for 0 .. $mx -> $x {
         my $key = "$x,$y";
         my %h = value => @grid[$y][$x];
         %info-about{$key} = @dumbos-in[%h<value>]{$key} = %h;
         %h<neighbors> = set gather {
            for [-1 .. 1] X [-1 .. 1] -> ($dx, $dy) {
               next unless $dx || $dy;
               my ($X, $Y) = ($x + $dx, $y + $dy);
               next unless 0 <= $X <= $mx && 0 <= $Y <= $my;
               take "$X,$Y";
            }
         };
      }
   }
   return [%info-about, @dumbos-in, @grid];
}

sub printable (%ia, $mx, $my) {
   return sub ($step, $msg is copy = Nil) {
      $msg //= "#$step";
      put "- $msg";
      (0 .. $mx).map(-> $x { (%ia{"$x,$_"}<value> + $step) % 10 }).join('').put
         for 0 .. $my;
      put '';
   };
}

sub solve ($inputs) {
   my ($info-about, $dumbos-in, $grid) = @$inputs;
   my $mx = $grid[0].end;
   my $my = $grid.end;
   my $number-of-cells = ($mx + 1) * ($my + 1);
   my &printout = printable($info-about, $mx, $my);
   &printout(0, 'start');
   my $overall-count = 0;
   my $sync-step;
   for 1 .. * -> $step {
      my $fire-value = (0 - $step) % 10;
      my @firing = $dumbos-in[$fire-value].keys;
      my $this-count = 0;
      while (@firing.elems) {
         my $cell = @firing.shift;
         ++$this-count;
         for $info-about{$cell}<neighbors>.keys -> $n-key {
            my $neighbor = $info-about{$n-key};
            my $n-value = $neighbor<value>;
            next if $n-value == $fire-value; # also firing in this step
            $neighbor<value> = my $next-n-value = ($n-value + 1) % 10;
            $dumbos-in[$next-n-value]{$n-key} = $neighbor;
            $dumbos-in[$n-value]{$n-key}:delete;
            @firing.push: $n-key if $next-n-value == $fire-value;
         }
      }
      $sync-step = $step if $this-count == $number-of-cells;
      $overall-count += $this-count if $step <= 100;
      &printout($step) if $step == 100;
      last if $step >= 100 && $sync-step;
   }
   &printout($sync-step);
   return ($overall-count, $sync-step);
}

The get-inputs function takes care to produce all the data structures to properly track the whole process. Then solve… solves the puzzle, collecting both outputs along the way.

For step 1 the condition is easy: stop incrementing the $overall-count at the 100th step.

For step 2 the condition is easy as well: get the step number when the count of all octopuses firing at that step is equal to… all of them, i.e. $number-of-cells.

We can’t be sure which of the two occurs first, so the last condition checks for both $step >= 100 (first part is happy) and $sync-step having a non-false value (second part is happy).

The printable function is a factory that returns a sub with which we can print the grid for a specific state/step number. It closes upon the data structure (because we evolve it) and takes the step number as input. Nothing particularly clean, I know.

Well I guess it’s enough with this toy! Stay safe folks!