Initially, I was thrown for a loop. It wasn’t apparent to me what data structure to use or the problem’s properties. My first (and correct) instinct was to interpret the data as a directed graph, but then what? Try to find some total ordering, if such a thing was possible?

As it turns out, that instinct was also correct. By drawing the sample data (or counting or printing it out), I noticed that every page number had a defined relation with every other page number. This meant that a total ordering (rather than a lattice) existed, meaning it was possible to construct a comparison function.

So, the algorithm for part 1 was to check if a list was sorted, and part 2 was to sort the list. There’s probably a 1-3 line solution for both parts a and b, but that’s for Mr. The Reader.

as discussed in a different part of the thread, I consider the input size for square inputs to be N, the “side length” of the square.

Context: I participated (and completed!) in AoC last year and pragmatically wrote my code as a set of utility modules for solving these pathological problems. So, I had about 80% of the boilerplate for this problem written, waiting for me to read and relearn.

Anyway, the analysis: P1. was pretty straightforward. Just walk along the map, turn right if you hit an obstacle, and stop when you leave the map. I guessed that there may be a case where one needs to turn in place more than once to escape an obstacle, but I never checked if that was true. Either way, I got the answer out. This is a worst-case O(n²) solution, which was fast for n = 130.

P2. I chose to brute force this, and it was fine. I iterated through the grid, placing a wall if possible, and checked if this produced a loop using an explored set. This is worst case O(n⁴), which, for n=130, takes a few seconds to spit out the answer. It’s parallelisable, though, so there’s that. If a faster solution existed, I’d love to know.