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-rw-r--r--2023/23-A_Long_Walk/second.hs148
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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