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I had several strategy switches from brute-force to pathfinding (when doing part1 input instead of example) because It simply wouldn't finish.
My solution only found the first path to the design, which is why I rewrote to only count how many towels there are for each prefix I have already built. Do that until there is either only one entry with the total combinations count or no entry and it's impossible to build the design.
I like the final solution, its small (unlike my other solutions) and runs fast.
π
import Control.Arrow
import Data.Map (Map)
import qualified Data.List as List
import qualified Data.Map as Map
parse :: String -> ([String], [String])
parse = lines . init
>>> (map (takeWhile (/= ',')) . words . head &&& drop 2)
countDesignPaths :: [String] -> String -> Map Int Int -> Int
countDesignPaths ts d es
| Map.null es = 0
| ml == length d = mc
| otherwise = countDesignPaths ts d es''
where
((ml, mc), es') = Map.deleteFindMin es
ns = List.filter (flip List.isPrefixOf (List.drop ml d))
>>> List.map length
>>> List.map (ml +)
$ ts
es'' = List.foldl (\ m l' -> Map.insertWith (+) l' mc m) es'
$ ns
solve (ts, ds) = List.map (flip (countDesignPaths ts) (Map.singleton 0 1))
>>> (List.length . List.filter (/= 0) &&& List.sum)
$ ds
main = getContents
>>= print
. solve
. parse