For Advent of Code 2021 day 12 it took me a while to get going though for reasons unrelated to coding, Norovirus is not pleasant! So when I finally did the puzzle, I didn’t find it as difficult as I thought it would be based on some of the messages on the #adventofcode channel. The puzzle started with

With your submarine’s subterranean subsystems subsisting suboptimally

This deserves a medal in itself. In contrast the link to my previous efforts today is a bit lacking, so here’s Day 11.

The problem this time was all about charting a way through a complex cave system. The caves are specified using the following kind of input:

start-A
start-b
A-c
A-b
b-d
A-end
b-end

There are two types of caves - big caves are noted in uppercase, small caves in lowercase. The aim was to find out how many different paths could be taken through the cave system from start to end. The only wrinkle was that small caves could only be visited once.

First task

My first reaction here was to just create a map of caves and every cave that it can visit. Then I’d be able to recursively call a function until I found the end. Ok, so let’s build that map of lists. Initially, I thought I’d just use a standard Haskell Map with the key the name of the cave, and the elements lists of cave names, I’d just have to write a bit of code to convert a simple pair structure into lists. But then I found MultiMap which does the job for me:

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parseline :: String -> (String, String)
parseline s = (\[a, b] -> (a, b)) $ split '-' s

First, I’m turning the input strings into tuples of (from, to) - I found tuples to be more intuitive than arrays which my split returns. I borrowed split from Day 6.

Now, I had a list of tuples, I could turn it into a multimap:

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type NodeMap = M.MultiMap String String

makeMap :: [(String, String)] -> NodeMap
makeMap xs = M.fromList $ filter onlyendto 
                        $ filter onlystartfrom 
                        $ xs ++ map swap xs

This does the following:

• create a list of tuples and the tuples in reverse (so I could have (from, to) and (to, from)) and
• I filtered out tuples where "start" is a destination or "end" is an origin, both are invalid moves.

Now I had my MultiMap, I could use it to find all the paths recursively:

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findPaths :: NodeMap -> [String] -> String -> Int
findPaths _ _ "end" = 1
findPaths nm prev from 
  | isSmallCave from && 
    any (from==) prev   = 0
  | otherwise           = 
    sum $ map (findPaths nm (from:prev)) 
        $ M.lookup from nm

isSmallCave :: String -> Bool
isSmallCave (x:xs) = isLower x

To unpack this:

• the function is called with the Map, a list of previously visited caves and the current cave
• the function returns the number of paths it can take to the “end”
• if we call this with the “end” cave, the return values is 1.
• if we call this with a small cave that was previously visited, then we return 0, as it is an invalid route
• otherwise (i.e. it’s a large cave or a small cave we hadn’t previously visited) we lookup the list of caves we can connect to, and recursively call findPaths on it and then just sum up the return values.

To get the number of differents routes, we just have to call:

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findPaths nm [] "start"

(when I first tried this I got a stack overflow as I had my logic backwards and isSmallCave was checking for uppercase)

Second part

For the second part, it was the same problem, but a single small cave can be visited twice. Initially, I misread this and thought it said that all small caves can be visited twice, and I thought that’s easy. Instead of checking whether a small cave is in the list of previously visited caves, I just count how often it occurs and if it’s more than once, I return 0.

But as that did not give me the right output on the example input, I went back, re-read the requirements and then came up with this:

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findPaths :: NodeMap -> [String] -> String -> Int
findPaths _ _ "end" = 1
findPaths nm prev from 
  | isSmallCave from && 
    visitedCave prev from > 1 - countDuplicateSmallCaves prev = 0
  | otherwise = sum $ map (findPaths nm (from:prev)) 
                    $ M.lookup from nm

visitedCave :: [String] -> String -> Int
visitedCave prev cave = length $ filter (cave==) prev

countDuplicateSmallCaves :: [String] -> Int
countDuplicateSmallCaves prev = length $ filter (>1) 
                                       $ map length 
                                       $ group 
                                       $ sort 
                                       $ filter isSmallCave prev

To unpack that:

• I created a function to get the number of times a cave was previously visited
• I also created a function to count if there are duplicate small caves in the list of previously visited caves.
• Then I could just check if the number of visited caves is greater than 1 - dupes and there for it would only be possible to visit a single small cave once.
• As the code recursively visits each cave, it would automatically pick out all routes.

Rest of the solution on GitHub

Conclusion

In this puzzle, I used the MultiMap for the first time. That doesn’t come out of the box, but it just needed stack install multimap to make it available. I also wasn’t terribly happy with the part 2 solution, with the counting of the duplicate caves every time, that turned out to need 14 seconds to run. I have a suspicion that there’s some maths that would make this a bit more performant, but it was too late at night to worry about it.

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