2023-16 part 2 in haskell

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diff --git a/2023/16-The_Floor_Will_Be_Lava/second.hs b/2023/16-The_Floor_Will_Be_Lava/second.hs
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+-- requires cabal install --lib megaparsec parser-combinators
+module Main (main) where
+
+import Control.Applicative.Permutations
+import Control.Monad (void, when)
+import Data.Char qualified as C
+import Data.Either
+import Data.Functor
+import Data.List qualified as L
+import Data.Map qualified as M
+import Data.Maybe
+import Data.Set qualified as S
+import Data.Vector qualified as V
+import qualified Data.Vector.Unboxed as VU
+import Data.Void (Void)
+import Text.Megaparsec
+import Text.Megaparsec.Char
+
+import Debug.Trace
+
+exampleExpectedOutput = 51
+
+data Tile = Backslash | Empty | Horizontal | Slash | Vertical deriving Eq
+instance Show Tile where
+  show Backslash = "\\"
+  show Empty = "."
+  show Horizontal = "-"
+  show Slash = "/"
+  show Vertical = "|"
+type Line = V.Vector Tile
+type Input = V.Vector Line
+
+type Parser = Parsec Void String
+
+parseTile :: Parser Tile
+parseTile = char '\\' $> Backslash
+        <|> char '.' $> Empty
+        <|> char '-' $> Horizontal
+        <|> char '/' $> Slash
+        <|> char '|' $> Vertical
+
+parseLine :: Parser Line
+parseLine = do
+  line <- some parseTile <* eol
+  return $ V.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'
+
+type LineOutput = VU.Vector Bool
+type Output = V.Vector LineOutput
+data Heading = N | S | E | W deriving (Eq, Ord, Show)
+data Cursor = Cursor Int Int Heading deriving (Eq, Ord, Show)
+
+type Visited = M.Map Cursor ()
+
+next :: Cursor -> Cursor
+next (Cursor x y N) = Cursor x (y-1) N
+next (Cursor x y S) = Cursor x (y+1) S
+next (Cursor x y W) = Cursor (x-1) y W
+next (Cursor x y E) = Cursor (x+1) y E
+
+compute' :: Input -> Cursor -> Int
+compute' input startingCursor = V.foldl' count 0 . fst $ walk startingOutput M.empty startingCursor
+  where
+    count :: Int -> LineOutput -> Int
+    count i l = i + VU.length (VU.filter id l)
+    startingOutput = V.replicate size $ VU.replicate size False
+    size = V.length input
+    walk :: Output -> Visited -> Cursor -> (Output, Visited)
+    walk output v c | isNothing nextTile = (output, v)
+                    | justNextTile == Empty = walk output' v c'
+                    | visited = (output, v)
+                    | justNextTile == Horizontal = if h == W || h == E then walk output' v c'
+                                                                       else let (output'', v'') = walk output' v' (Cursor x y E) in walk output'' v'' $ Cursor x y W
+                    | justNextTile == Vertical = if h == N || h == S then walk output' v c'
+                                                                     else let (output'', v'') = walk output' v' (Cursor x y N) in walk output'' v'' $ Cursor x y S
+                    | justNextTile == Backslash = case h of
+                        N -> walk output' v' $ Cursor x y W
+                        S -> walk output' v' $ Cursor x y E
+                        W -> walk output' v' $ Cursor x y N
+                        E -> walk output' v' $ Cursor x y S
+                    | justNextTile == Slash = case h of
+                        N -> walk output' v' $ Cursor x y E
+                        S -> walk output' v' $ Cursor x y W
+                        W -> walk output' v' $ Cursor x y S
+                        E -> walk output' v' $ Cursor x y N
+      where
+        c'@(Cursor x y h) = next c
+        nextTile = case input V.!? y of
+          Just l -> l V.!? x
+          Nothing -> Nothing
+        justNextTile = fromJust nextTile
+        line = output V.! y
+        visited = M.member c' v
+        v' = M.insert c' () v
+        output' = if visited then output
+                             else output V.// [(y, line VU.// [(x, True)])]
+
+compute :: Input -> Int
+compute input = maximum $ map (compute' input) cursors
+  where
+    cursors = [Cursor (-1) y E | y <- [0..l]]
+           ++ [Cursor l y W | y <- [0..l]]
+           ++ [Cursor x (-1) S | x <- [0..l]]
+           ++ [Cursor x l N | x <- [0..l]]
+    l = 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