2021 Day 12 Complete!

2021-12-12 09:17:41 -06:00
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+# Advent of Code
+
+--- Day 12: Passage Pathing ---
+
+   With your submarine's subterranean subsystems subsisting suboptimally, the only way you're getting out of this cave anytime soon is by finding a
+   path yourself. Not just a path - the only way to know if you've found the best path is to find all of them.
+
+   Fortunately, the sensors are still mostly working, and so you build a rough map of the remaining caves (your puzzle input). For example:
+
+ start-A
+ start-b
+ A-c
+ A-b
+ b-d
+ A-end
+ b-end
+
+   This is a list of how all of the caves are connected. You start in the cave named start, and your destination is the cave named end. An entry
+   like b-d means that cave b is connected to cave d - that is, you can move between them.
+
+   So, the above cave system looks roughly like this:
+
+     start
+     /   \
+ c--A-----b--d
+     \   /
+      end
+
+   Your goal is to find the number of distinct paths that start at start, end at end, and don't visit small caves more than once. There are two
+   types of caves: big caves (written in uppercase, like A) and small caves (written in lowercase, like b). It would be a waste of time to visit any
+   small cave more than once, but big caves are large enough that it might be worth visiting them multiple times. So, all paths you find should
+   visit small caves at most once, and can visit big caves any number of times.
+
+   Given these rules, there are 10 paths through this example cave system:
+
+ start,A,b,A,c,A,end
+ start,A,b,A,end
+ start,A,b,end
+ start,A,c,A,b,A,end
+ start,A,c,A,b,end
+ start,A,c,A,end
+ start,A,end
+ start,b,A,c,A,end
+ start,b,A,end
+ start,b,end
+
+   (Each line in the above list corresponds to a single path; the caves visited by that path are listed in the order they are visited and separated
+   by commas.)
+
+   Note that in this cave system, cave d is never visited by any path: to do so, cave b would need to be visited twice (once on the way to cave d
+   and a second time when returning from cave d), and since cave b is small, this is not allowed.
+
+   Here is a slightly larger example:
+
+ dc-end
+ HN-start
+ start-kj
+ dc-start
+ dc-HN
+ LN-dc
+ HN-end
+ kj-sa
+ kj-HN
+ kj-dc
+
+   The 19 paths through it are as follows:
+
+ start,HN,dc,HN,end
+ start,HN,dc,HN,kj,HN,end
+ start,HN,dc,end
+ start,HN,dc,kj,HN,end
+ start,HN,end
+ start,HN,kj,HN,dc,HN,end
+ start,HN,kj,HN,dc,end
+ start,HN,kj,HN,end
+ start,HN,kj,dc,HN,end
+ start,HN,kj,dc,end
+ start,dc,HN,end
+ start,dc,HN,kj,HN,end
+ start,dc,end
+ start,dc,kj,HN,end
+ start,kj,HN,dc,HN,end
+ start,kj,HN,dc,end
+ start,kj,HN,end
+ start,kj,dc,HN,end
+ start,kj,dc,end
+
+   Finally, this even larger example has 226 paths through it:
+
+ fs-end
+ he-DX
+ fs-he
+ start-DX
+ pj-DX
+ end-zg
+ zg-sl
+ zg-pj
+ pj-he
+ RW-he
+ fs-DX
+ pj-RW
+ zg-RW
+ start-pj
+ he-WI
+ zg-he
+ pj-fs
+ start-RW
+
+   How many paths through this cave system are there that visit small caves at most once?
+
+   Your puzzle answer was 4413.
+
+--- Part Two ---
+
+   After reviewing the available paths, you realize you might have time to visit a single small cave twice. Specifically, big caves can be visited
+   any number of times, a single small cave can be visited at most twice, and the remaining small caves can be visited at most once. However, the
+   caves named start and end can only be visited exactly once each: once you leave the start cave, you may not return to it, and once you reach the
+   end cave, the path must end immediately.
+
+   Now, the 36 possible paths through the first example above are:
+
+ start,A,b,A,b,A,c,A,end
+ start,A,b,A,b,A,end
+ start,A,b,A,b,end
+ start,A,b,A,c,A,b,A,end
+ start,A,b,A,c,A,b,end
+ start,A,b,A,c,A,c,A,end
+ start,A,b,A,c,A,end
+ start,A,b,A,end
+ start,A,b,d,b,A,c,A,end
+ start,A,b,d,b,A,end
+ start,A,b,d,b,end
+ start,A,b,end
+ start,A,c,A,b,A,b,A,end
+ start,A,c,A,b,A,b,end
+ start,A,c,A,b,A,c,A,end
+ start,A,c,A,b,A,end
+ start,A,c,A,b,d,b,A,end
+ start,A,c,A,b,d,b,end
+ start,A,c,A,b,end
+ start,A,c,A,c,A,b,A,end
+ start,A,c,A,c,A,b,end
+ start,A,c,A,c,A,end
+ start,A,c,A,end
+ start,A,end
+ start,b,A,b,A,c,A,end
+ start,b,A,b,A,end
+ start,b,A,b,end
+ start,b,A,c,A,b,A,end
+ start,b,A,c,A,b,end
+ start,b,A,c,A,c,A,end
+ start,b,A,c,A,end
+ start,b,A,end
+ start,b,d,b,A,c,A,end
+ start,b,d,b,A,end
+ start,b,d,b,end
+ start,b,end
+
+   The slightly larger example above now has 103 paths through it, and the even larger example now has 3509 paths through it.
+
+   Given these new rules, how many paths through this cave system are there?
+
+   Your puzzle answer was 118803.
+
+   Both parts of this puzzle are complete! They provide two gold stars: **
+
+   At this point, you should return to your Advent calendar and try another puzzle.
+
+   If you still want to see it, you can get your puzzle input.
+
+References
+
+   Visible links
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+   . https://adventofcode.com/2021/day/12/input