TL;DR

In AoC 2022/16 - Pressured shame, I left with this:

So yeah, I still have to go some way before I have a general solution program.

Then, in follow-up post AoC 2022/16 - Paying a debt, I left with this:

The code above is not exceptionally fast, taking about 10 minutes to complete the search over my input. Anyway, this is an acceptable time by my standards, so I call it a win.

Then, after writing that post, of course I found a better way, in the form of this Rust code. Which made it possible to enhance the computation from 10 minutes toâ€¦ about 20 seconds (in Raku, of course). Yup, you read it right - a 30x improvement!

Itâ€™s at the same timeâ€¦

• â€¦ fantastic, thereâ€™s always something to learn!
• â€¦ humbling, I was so wrong in my gut feelings about which way to go!
• â€¦ frustrating, because at the end of the day itâ€™s basically A* and I should know much, much better!

Anyway, I re-implemented the Rust code in Raku and itâ€™s available here. Itâ€™s fully commented, so I will not repeat the full explanation here, but just add a few notes:

• as before, we consider an overlay graph where only the start valve and the valves with some positive rate are included, in a sort of full-mesh where we evaluate the shortest distance between any two valves.
• Distances between nodes are incremented by one unit because it does not make sense to â€śvisitâ€ť a valve if we have no intention to open it, at least considering the â€śoverlayâ€ť. Opening requires a minute, hence the + 1 added to the distance.
• The heuristic is based on the upper bound possible for the score starting from a given state. This is, in turn, calculated based on the best possible score increment that we might possibly obtain, based on the following observations:
• each â€śresidualâ€ť valve is considered in decreasing order of possible gain, based on the residual time;
• the contribution is calculated based on reaching the node (considering the minimum distance from any node) and calculating its contribution.
• the neighbors of each valve are sorted based on the possible additional gain, in descending order. This makes sure to try and expand the most promising nodes before other ones, in the hope to prune search branches thanks to the heuristic.

This heuristic part guarantees us that we never underestimate the upper limit, which in turn guarantees that the solution will be optimal (because we will never cut an optimal solution search subtree because of an underestimation). This is where A* comes from, together with using a priority queue to expand states that are more promising before the other ones.

Not coming up with the right heuristic is the main error that I did in this challenge, I think. At the end of the day, it only required a fresh mind and determination. Iâ€™ll keep it in mind next time!

Overall, this has probably been the most interesting puzzle this year, with the possible exception of puzzle 19, which is the next puzzle I want to read more about aroundâ€¦

In the meantime, stay safe folks!

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