TL;DR

On with Advent of Code puzzle 18 from 2021: using a grammar for a side reason.

This dayâ€™s puzzle was an interesting one because it allowed me to discover a bit about myself.

Letâ€™s move on in order, anyway.

In a nutshell, weâ€™re given a string describing a binary tree like this:

``````[[[[1,3],[5,3]],[[1,3],[8,7]]],[[[4,9],[6,9]],[8,2]]]
``````

which corresponds to this:

``````-+-+-+-+- 1
| | | |
| | | +- 3
| | |
| | +-+- 5
| |   |
| |   +- 3
| |
| +-+-+- 1
|   | |
|   | +- 3
|   |
|   +-+- 8
|     |
|     +- 7
|
+-+-+-+- 4
| | |
| | +- 9
| |
| +-+- 6
|   |
|   +- 9
|
+-+- 8
|
+- 2
``````

Only leave nodes have numbers and non-leaf nodes always have exactly two branches.

The puzzle instructions provide instructions for transforming these structures as they become too big. In particular, these snailfish data structures canâ€™t go past the fourth level of nesting; when two of them are combined and this rule is broken, some transformations are applied to go back within the bounds.

My initial approach was to parse the data structure into a proper tree in memory, then apply the transformations onto the tree. Fact is that there might be some interaction between branches that are possibly quite apart from each other, which requires some book-keeping that reminded me of Red-Black trees.

While I think that Red-Black trees are amazing, my brain immediately went in fight or flight mode, trying to see if there would be some other (better?) way of doing this.

And flight it was.

I eventually landed on a different solution that is somehow easier to manage due to the specific requirements of the transformations. I mean, as user isaaccp implicitly pointed out, working with the binary tree was definitely doable, but for me it would have required much more effort and I flew.

In particular, the explode move allows reducing the depth of the tree or at least move towards reducing it, but itâ€™s not local to a specific section of the tree. In fact this explosion involves the closest leaves on the left and right of the textual representation of the tree; for this reason, itâ€™s easier to work either on the textual representation itself, or in a linear list of elements. I settled on isolating square brackets, numbers and commas for ease of reconstruction.

Example of this representation:

``````# '[[13,2123],[1232,11]]' would be divided in a list as follows:

[  [  13  ,  2123  ]  ,  [  1232  ,   5   ]   ]
# elements -->  ^  ^  ^^  ^  ^^^^  ^  ^  ^  ^^^^  ^   ^   ^   ^
#               0  1  2   3   4    5  6  7   8    9   10  11  12
``````

The example above is not a valid snailfish but it illustrates the concept.

The other operation (split) might potentially increase the overall depth of the tree but itâ€™s easier and it can be handed quickly in both the hierarchical tree and in the plain list representations. I decided to go for the latter for consistency with the explode part though.

These two operations are applied in a certain order until the resulting structure is within the bounds (i.e. no more tha level 4 and each leave no more than 9).

``````method !_reduce () {
@!array = \$!string.comb: / ( '[' | \d+ | ',' | ']' ) / unless @!array.elems;
while self!explode || self!split {}
\$!string = Nil;
}
``````

The fun thing was that the code initially meant for parsing the input into a tree structure for all operations was not a waste of time. While the explode (and split, for proximity) operations are better handled with the linear representation, calculating the magnitude of a snailfish is better approached with the tree representation (although itâ€™s definitely approachable with the linear approach). Hence I took the Grammar and Actions back, adapted them a bit and had my magnitude calculation code in little time (by my standards, that is):

``````grammar Grammar {
rule  TOP      { ^ <compound> \$ }
rule  compound { '[' <left> ',' <right> ']' }
rule  left     { <elem> }
rule  right    { <elem> }
rule  elem     { <compound> | <value> }
token value    { \d+ }
}

class Actions {
method TOP (\$/) { \$/.make: \$<compound>.made }
method compound (\$/) {
}
method left (\$/) { \$/.make: \$<elem>.made }
method right (\$/) { \$/.make: \$<elem>.made }
method elem (\$/) {
}
method value (\$/) { \$/.make: \$/.Int }
}

method !calc-magnitude () {
}
``````

To be totally fair, though, this is overkill and I used it only because I already had the grammar and most of the actions. Otherwise, this iterative string transformation would have been sufficient and much more compact:

``````method !calc-magnitude () {
my \$s = self.Str;
with \$s { s{\[ (\d+) ',' (\d+) \]} = \$0 * 3 + \$1 * 2 while /\D/ }
return 0+\$s;
}
``````

The joys of reuse, I guess.

Stay safe everybody!

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