I though that's easy. I immediately spotted the recursion. I've done path finding and especially Dijkstra before. Instead of looking into details of Dijkstra I just started coding without taking some time to think. This was my problem today. I give up today after 1.5 hours without any good progress so I just have to stop myself.
Recursion, especially debugging, is just fucking my mind.
I see that I start a node and that it has neighbours. Each neighbour is a branching event.
start with two neighbours produces the first two branches.
I thought an abort condition cave = end plus the body of the recusion being the map on the neighbours does the trick but I somehow can't manage to build up the recursion mechanics. I always end up with my algorithm reaching the end only one time.
The problem: I have created a data structure of caves that store their state. Unfortunately I only realized after 2 hours of recursion debugging that I can't do this. I sohuld have known better. Because if b is visited a single time on any of the available branches it's burned even though there might be parallel worlds (aka branches) that might work for it. My recursion should carry around copies of the caves and not use the global.
It's too late for fixing my approach now and I have to give up.
--- 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?