2023-23 part 2 in haskell

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diff --git a/2023/23-A_Long_Walk/second.hs b/2023/23-A_Long_Walk/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 = Just 154
+
+data Direction = N | S | E | W deriving (Eq, Show)
+data Tile = Floor | Wall | Slope Direction deriving (Eq, Show)
+type Line = V.Vector Tile
+type Input = V.Vector Line
+
+type Parser = Parsec Void String
+
+parseDirection :: Parser Direction
+parseDirection = char '^' $> N
+             <|> char 'v' $> S
+             <|> char '>' $> E
+             <|> char '<' $> W
+
+parseTile :: Parser Tile
+parseTile = char '#' $> Wall
+        <|> char '.' $> Floor
+        <|> Slope <$> parseDirection
+
+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'
+
+newtype Cost = Cost Int deriving (Eq, Num, Ord, Show)
+newtype NodeId = NodeId Int deriving (Eq, Num, Ord, Show)
+newtype X = X Int deriving (Eq, Num, Ord, Show)
+newtype Y = Y Int deriving (Eq, Num, Ord, Show)
+type Adjacencies = M.Map NodeId [(NodeId, Cost)] -- keys are nodeIds and values are a list of (NodeId, cost)
+type Nodes = M.Map (X, Y) NodeId -- keys are (x, y) and values are nodeIds
+type Visited = M.Map (X, Y) ()
+
+compute :: Input -> Maybe Cost
+compute input = longuestPath adjacencies (let Just (a:[]) = M.lookup 0 adjacencies in a)
+  where
+    longuestPath :: Adjacencies -> (NodeId, Cost) -> Maybe Cost
+    longuestPath adj (n, c) | n == 1 = Just $ c + 1
+                            | l' == [] = Nothing
+                            | otherwise = Just $ c + maximum l'
+      where
+        Just l = M.lookup n adj
+        l' =  catMaybes $ L.map (longuestPath  adj') l
+        adj' = M.delete n $ M.map (L.filter (\(i, _) -> n /= i)) adj
+    (adjacencies, nodes, _) = explore 0 (M.fromList [(0, []), (1, [])]) (M.fromList [((startx, 0), 0), ((finishx, finishy), 1)]) (M.fromList [((startx, 0), ()), ((finishx, finishy), ())]) startx 1 S
+    explore :: NodeId -> Adjacencies -> Nodes -> Visited -> X -> Y -> Direction -> (Adjacencies, Nodes, Visited)
+    explore node adjacencies nodes visited x y d = L.foldl' explore' (adjacencies, nodes, visited) $ nextSteps x y d
+      where
+        explore' :: (Adjacencies, Nodes, Visited) -> (X, Y, Direction, Bool) -> (Adjacencies, Nodes, Visited)
+        explore' acc@(adjacencies, nodes, visited) (x, y, d, u) | isNothing destination = acc
+                                                                | otherwise = case M.lookup (x', y') nodes of
+                                                                    Nothing -> explore node' adjacencies'' nodes' visited' x' y' d
+                                                                    Just id -> (adjacencies'', nodes', visited')
+          where
+            destination = let s = goDownAPath visited False x y 1 d in s
+            Just (visited', x', y', cost, u') = destination
+            adjacencies'' = M.adjust (\l -> (node', cost):l) node $ M.adjust (\l -> if u || u' then l else (node, cost):l) node' adjacencies'
+            nodes' = M.insert (x', y') node' nodes
+            (node', adjacencies') = case M.lookup (x', y') nodes of
+              Nothing    -> let s = NodeId (M.size nodes) in (s, M.insert s [] adjacencies)
+              Just node' -> (node', adjacencies)
+            goDownAPath :: Visited -> Bool -> X -> Y -> Cost -> Direction -> Maybe (Visited, X, Y, Cost, Bool) -- returns the next intersection's coordinates and cost, and if it is unidirectional
+            goDownAPath visited u x y c d | M.member (x, y) nodes = Just (visited, x, y, c, u) -- we reached an already known intersection
+                                          | M.member (x, y) visited = Nothing -- this tile has already been visited
+                                          | isImpossibleSlope = Nothing
+                                          | ns == [] = Nothing -- we hit a deadend
+                                          | L.length ns > 1 = Just (visited', x, y, c, u'') -- we hit a crossroads
+                                          | otherwise = goDownAPath visited' u'' x' y' (c+1) d'
+              where
+                (x', y', d', u') = head ns
+                u'' = u || u'
+                ns = nextSteps x y d
+                visited' = M.insert (x, y) () visited
+                isImpossibleSlope = case getTile (x, y) of
+                  Slope s   -> s /= d
+                  otherwise -> False
+    getTile :: (X, Y) -> Tile
+    getTile (X x, Y y) = input V.! y V.! x
+    nextSteps :: X -> Y -> Direction -> [(X, Y, Direction, Bool)] -- get the list of possible next steps at a point, given where we came from
+    nextSteps x y d = L.map augmentWithUnidirectionality $ L.filter possible [(x-1, y, W), (x+1, y, E), (x, y-1, N), (x, y+1, S)]
+      where
+        augmentWithUnidirectionality :: (X, Y, Direction) -> (X, Y, Direction, Bool)
+        augmentWithUnidirectionality (x, y, d) = (x, y, d, isSlope $ getTile (x, y))
+        isSlope :: Tile -> Bool
+        --isSlope (Slope _) = True
+        isSlope _         = False
+        possible :: (X, Y, Direction) -> Bool
+        possible (x', y', d') | t == Wall = False
+                              | d == opposite d' = False -- no going back
+                              -- | t == Floor = True
+                              | otherwise = True -- o == d' -- our direction must match the slope <- NO, this prevents us from properly finding intersections
+          where
+            t = getTile (x', y')
+            Slope o = t
+    Just start = V.findIndex (== Floor) $ input V.! 0
+    startx = X start
+    Just finish = V.findIndex (== Floor) $ input V.! finishyy
+    finishx = X finish
+    finishyy = V.length input - 1
+    finishy = Y finishyy
+    xydToxy :: (a, b, c) -> (a, b)
+    xydToxy (x, y, _) = (x, y)
+    opposite :: Direction -> Direction
+    opposite N = S
+    opposite S = N
+    opposite E = W
+    opposite W = E
+
+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