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diff --git a/2023/17-Clumsy_Crucible/second.hs b/2023/17-Clumsy_Crucible/second.hs
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+-- requires cabal install --lib megaparsec parser-combinators heap vector
+module Main (main) where
+
+import           Control.Applicative.Permutations
+import           Control.Monad                    (void, when)
+import qualified Data.Char                        as C
+import           Data.Either
+import           Data.Functor
+import qualified Data.Heap                        as H
+import qualified Data.List                        as L
+import qualified Data.Map                         as M
+import           Data.Maybe
+import qualified Data.Set                         as S
+import qualified Data.Vector                      as V
+import qualified Data.Vector.Unboxed              as VU
+import           Data.Void                        (Void)
+import           Text.Megaparsec
+import           Text.Megaparsec.Char
+
+import           Debug.Trace
+
+exampleExpectedOutput = 94
+
+type Line = VU.Vector Int
+type Input = V.Vector Line
+
+type Parser = Parsec Void String
+
+parseLine :: Parser Line
+parseLine = do
+  line <- some (C.digitToInt <$> digitChar) <* eol
+  return $ VU.generate (length line) (line !!)
+
+parseInput' :: Parser Input
+parseInput' = do
+  line <- some parseLine <* eof
+  return $ V.generate (length line) (line !!)
+
+parseInput :: String -> IO Input
+parseInput filename = do
+  input <- readFile filename
+  case runParser parseInput' filename input of
+    Left bundle  -> error $ errorBundlePretty bundle
+    Right input' -> return input'
+
+data Heading = NS | EW deriving (Eq, Show)
+data Position = Position Int Int Int Heading deriving (Show) -- cost x y heading
+instance Ord Position where
+  compare (Position c1 _ _ _) (Position c2 _ _ _) = c1 `compare` c2
+instance Eq Position where
+  (Position c1 _ _ _) == (Position c2 _ _ _) = c1 == c2
+type Candidates = H.MinHeap Position
+type CostsState = M.Map (Int,Int) (Int, Int) -- (x, y) (NSCost, EWCost)
+
+step :: Input -> CostsState -> Position -> [Position]
+step input costs (Position cost x y h) = L.concat [next 1 1 0, next (-1) (-1) 0]
+  where
+    next :: Int -> Int -> Int -> [Position] -- diff increment costchange
+    next 11 _ _ = []
+    next (-11) _ _ = []
+    next d i costChange = case heatLoss of
+      Just hl -> if improvement hl then (Position (cost + costChange + hl) x' y' h') : next (d+i) i (costChange + hl)
+                                   else next (d+i) i (costChange + hl)
+      Nothing -> []
+      where
+        h' | h == NS = EW
+           | otherwise = NS
+        x' | h' == NS = x
+           | otherwise = x + d
+        y' | h' == NS = y + d
+           | otherwise = y
+        improvement :: Int -> Bool
+        improvement hl | d < 4 && d > -4 = False
+                       | otherwise = case M.lookup (x', y') costs of
+          Just (h1, h2) -> case h' of
+            NS -> cost + hl < h1
+            EW -> cost + hl < h2
+          Nothing -> undefined -- should not happen, we catch out of bound when looking for heatLoss
+        heatLoss :: Maybe Int
+        heatLoss = case input V.!? y' of
+          Just line -> line VU.!? x'
+          Nothing   -> Nothing
+
+compute :: Input -> Int
+compute input = compute' startingCosts startingCandidates
+  where
+    compute' :: CostsState -> Candidates -> Int
+    compute' costs candidates | x == size - 1 && y == size - 1 = cost
+                              | improvement = compute' costs' (H.union candidates' (H.fromList $ step input costs position))
+                              | otherwise = compute' costs candidates'
+      where
+        candidates' = H.drop 1 candidates
+        costs' = M.insert (x, y) (if h == NS then (cost, snd state) else (fst state, cost)) costs
+        improvement | h == NS = cost < fst state
+                    | otherwise = cost < snd state
+        position@(Position cost x y h) = head $ H.take 1 candidates
+        state = costs M.! (x, y)
+    infinity = maxBound :: Int
+    startingCandidates = H.fromList [Position 0 0 0 h|h <- [NS, EW]] :: Candidates
+    startingCosts = M.fromList [((x, y), (infinity, infinity))|x<-[0..size], y<-[0..size]]
+    size = V.length input
+
+main :: IO ()
+main = do
+  example <- parseInput "example"
+  let exampleOutput = compute example
+  when  (exampleOutput /= exampleExpectedOutput)  (error $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput)
+  input <- parseInput "input"
+  print $ compute input