Day 12: Hot Springs

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  • Leo Uino@lemmy.sdf.org
    4·
    1 year ago

    Haskell

    Phew! I struggled with this one. A lot of the code here is from my original approach, which cuts down the search space to plausible positions for each group. Unfortunately, that was still way too slow…

    It took an embarrassingly long time to try memoizing the search (which made precomputing valid points far less important). Anyway, here it is!

    Solution 
    {-# LANGUAGE LambdaCase #-}

import Control.Monad
import Control.Monad.State
import Data.List
import Data.List.Split
import Data.Map (Map)
import qualified Data.Map as Map
import Data.Maybe

readInput :: String -> ([Maybe Bool], [Int])
readInput s =
  let [a, b] = words s
   in ( map (\case '#' -> Just True; '.' -> Just False; '?' -> Nothing) a,
        map read $ splitOn "," b
      )

arrangements :: ([Maybe Bool], [Int]) -> Int
arrangements (pat, gs) = evalState (searchMemo 0 groups) Map.empty
  where
    len = length pat
    groups = zipWith startPoints gs $ zip minStarts maxStarts
      where
        minStarts = scanl (\a g -> a + g + 1) 0 $ init gs
        maxStarts = map (len -) $ scanr1 (\g a -> a + g + 1) gs
        startPoints g (a, b) =
          let ps = do
                (i, pat') <- zip [a .. b] $ tails $ drop a pat
                guard $
                  all (\(p, x) -> maybe True (== x) p) $
                    zip pat' $
                      replicate g True ++ [False]
                return i
           in (g, ps)
    clearableFrom i =
      fmap snd $
        listToMaybe $
          takeWhile ((<= i) . fst) $
            dropWhile ((< i) . snd) clearableRegions
      where
        clearableRegions =
          let go i [] = []
              go i pat =
                let (a, a') = span (/= Just True) pat
                    (b, c) = span (== Just True) a'
                 in (i, i + length a - 1) : go (i + length a + length b) c
           in go 0 pat
    searchMemo :: Int -> [(Int, [Int])] -> State (Map (Int, Int) Int) Int
    searchMemo i gs = do
      let k = (i, length gs)
      cached <- gets (Map.!? k)
      case cached of
        Just x -> return x
        Nothing -> do
          x <- search i gs
          modify (Map.insert k x)
          return x
    search i gs | i >= len = return $ if null gs then 1 else 0
    search i [] = return $
      case clearableFrom i of
        Just b | b == len - 1 -> 1
        _ -> 0
    search i ((g, ps) : gs) = do
      let maxP = maybe i (1 +) $ clearableFrom i
          ps' = takeWhile (<= maxP) $ dropWhile (< i) ps
      sum <$> mapM (\p -> let i' = p + g + 1 in searchMemo i' gs) ps'

expand (pat, gs) =
  (intercalate [Nothing] $ replicate 5 pat, concat $ replicate 5 gs)

main = do
  input <- map readInput . lines <$> readFile "input12"
  print $ sum $ map arrangements input
  print $ sum $ map (arrangements . expand) input