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147 lines
3.1 KiB
Markdown
147 lines
3.1 KiB
Markdown
https://adventofcode.com/2021/day/12
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## \--- Day 12: Passage Pathing ---
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With your submarine's subterranean subsystems subsisting suboptimally, the
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only way you're getting out of this cave anytime soon is by finding a path
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yourself. Not just _a_ path - the only way to know if you've found the _best_
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path is to find _all_ of them.
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Fortunately, the sensors are still mostly working, and so you build a rough
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map of the remaining caves (your puzzle input). For example:
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[code]
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start-A
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start-b
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A-c
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A-b
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b-d
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A-end
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b-end
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[/code]
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This is a list of how all of the caves are connected. You start in the cave
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named `start`, and your destination is the cave named `end`. An entry like
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`b-d` means that cave `b` is connected to cave `d` \- that is, you can move
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between them.
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So, the above cave system looks roughly like this:
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[code]
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start
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/ \
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c--A-----b--d
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\ /
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end
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[/code]
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Your goal is to find the number of distinct _paths_ that start at `start`, end
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at `end`, and don't visit small caves more than once. There are two types of
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caves: _big_ caves (written in uppercase, like `A`) and _small_ caves (written
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in lowercase, like `b`). It would be a waste of time to visit any small cave
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more than once, but big caves are large enough that it might be worth visiting
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them multiple times. So, all paths you find should _visit small caves at most
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once_ , and can _visit big caves any number of times_.
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Given these rules, there are `_10_` paths through this example cave system:
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[code]
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start,A,b,A,c,A,end
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start,A,b,A,end
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start,A,b,end
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start,A,c,A,b,A,end
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start,A,c,A,b,end
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start,A,c,A,end
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start,A,end
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start,b,A,c,A,end
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start,b,A,end
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start,b,end
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[/code]
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(Each line in the above list corresponds to a single path; the caves visited
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by that path are listed in the order they are visited and separated by
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commas.)
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Note that in this cave system, cave `d` is never visited by any path: to do
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so, cave `b` would need to be visited twice (once on the way to cave `d` and a
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second time when returning from cave `d`), and since cave `b` is small, this
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is not allowed.
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Here is a slightly larger example:
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[code]
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dc-end
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HN-start
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start-kj
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dc-start
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dc-HN
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LN-dc
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HN-end
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kj-sa
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kj-HN
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kj-dc
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[/code]
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The `19` paths through it are as follows:
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[code]
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start,HN,dc,HN,end
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start,HN,dc,HN,kj,HN,end
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start,HN,dc,end
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start,HN,dc,kj,HN,end
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start,HN,end
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start,HN,kj,HN,dc,HN,end
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start,HN,kj,HN,dc,end
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start,HN,kj,HN,end
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start,HN,kj,dc,HN,end
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start,HN,kj,dc,end
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start,dc,HN,end
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start,dc,HN,kj,HN,end
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start,dc,end
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start,dc,kj,HN,end
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start,kj,HN,dc,HN,end
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start,kj,HN,dc,end
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start,kj,HN,end
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start,kj,dc,HN,end
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start,kj,dc,end
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[/code]
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Finally, this even larger example has `226` paths through it:
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[code]
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fs-end
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he-DX
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fs-he
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start-DX
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pj-DX
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end-zg
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zg-sl
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zg-pj
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pj-he
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RW-he
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fs-DX
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pj-RW
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zg-RW
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start-pj
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he-WI
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zg-he
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pj-fs
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start-RW
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[/code]
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_How many paths through this cave system are there that visit small caves at
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most once?_
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