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After reading the rules more carefully, I see we can only build one
robot per round! (Not just one robot per material type, one robot!) Doh!
This reduces the combinatorial explosion a lot. The exhaustive search
has become a lot more feasible, with Blueprint 2 of the test input able
to cover 22 rounds in a minute and a half. I shouldn't only need to find
some small wins from here to get the 24-round runtime to something
sensible.
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As expected, the explosion in permutations makes this prohibitive.
With this stragegy, on Blueprint 2 of the test input, for:
10 rounds it takes 0.018s/59,979 iterations
11 rounds it takes 0.070s/1,257,483 iterations
12 rounds it takes 1.292s/59,156,010 iterations
13 rounds it takes 3m2.770s/8,395,942,157 iterations
Getting to 24 rounds just isn't feasible with that growth.
And I can't figure out how to cull unwanted permutations easily.
Going to have to try something else.
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It produces *a* result for each blueprint, but not the best result.
I feel like that's a hard problem. The number of decisions about what to
build when over 24 iterations explodes so much that you can't
brute-force the optimal geode count.
Either there's a way of pruning possibilities that I've not thought of,
or there's a pretty good heuristic you can get from the blueprint about
the proportions of how many of each type of material you want to be
producing, that you can pick what to build and get a geode count that
doesn't deviate from optimal in only 24 iterations.
One other possibility is transforming this puzzle into a SAT format and
letting a SAT solver attack it, with its ability to prune decision trees
effectively. But I don't have any actual experience with those, and I'm
not sure I have time to figure that out for AoC.
https://en.wikipedia.org/wiki/SAT_solver
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