148 lines
7.1 KiB
Haskell
148 lines
7.1 KiB
Haskell
-- requires cabal install --lib megaparsec parser-combinators heap vector
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module Main (main) where
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import Control.Applicative.Permutations
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import Control.Monad (void, when)
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import qualified Data.Char as C
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import Data.Either
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import Data.Functor
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import qualified Data.Heap as H
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import qualified Data.List as L
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import qualified Data.Map as M
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import Data.Maybe
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import qualified Data.Set as S
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import qualified Data.Vector as V
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import qualified Data.Vector.Unboxed as VU
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import Data.Void (Void)
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import Text.Megaparsec
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import Text.Megaparsec.Char
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import Debug.Trace
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exampleExpectedOutput = Just 154
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data Direction = N | S | E | W deriving (Eq, Show)
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data Tile = Floor | Wall | Slope Direction deriving (Eq, Show)
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type Line = V.Vector Tile
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type Input = V.Vector Line
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type Parser = Parsec Void String
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parseDirection :: Parser Direction
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parseDirection = char '^' $> N
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<|> char 'v' $> S
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<|> char '>' $> E
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<|> char '<' $> W
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parseTile :: Parser Tile
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parseTile = char '#' $> Wall
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<|> char '.' $> Floor
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<|> Slope <$> parseDirection
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parseLine :: Parser Line
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parseLine = do
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line <- some parseTile <* eol
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return $ V.generate (length line) (line !!)
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parseInput' :: Parser Input
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parseInput' = do
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line <- some parseLine <* eof
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return $ V.generate (length line) (line !!)
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parseInput :: String -> IO Input
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parseInput filename = do
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input <- readFile filename
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case runParser parseInput' filename input of
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Left bundle -> error $ errorBundlePretty bundle
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Right input' -> return input'
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newtype Cost = Cost Int deriving (Eq, Num, Ord, Show)
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newtype NodeId = NodeId Int deriving (Eq, Num, Ord, Show)
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newtype X = X Int deriving (Eq, Num, Ord, Show)
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newtype Y = Y Int deriving (Eq, Num, Ord, Show)
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type Adjacencies = M.Map NodeId [(NodeId, Cost)] -- keys are nodeIds and values are a list of (NodeId, cost)
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type Nodes = M.Map (X, Y) NodeId -- keys are (x, y) and values are nodeIds
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type Visited = M.Map (X, Y) ()
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compute :: Input -> Maybe Cost
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compute input = longuestPath adjacencies (let Just (a:[]) = M.lookup 0 adjacencies in a)
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where
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longuestPath :: Adjacencies -> (NodeId, Cost) -> Maybe Cost
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longuestPath adj (n, c) | n == 1 = Just $ c + 1
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| l' == [] = Nothing
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| otherwise = Just $ c + maximum l'
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where
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Just l = M.lookup n adj
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l' = catMaybes $ L.map (longuestPath adj') l
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adj' = M.delete n $ M.map (L.filter (\(i, _) -> n /= i)) adj
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(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
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explore :: NodeId -> Adjacencies -> Nodes -> Visited -> X -> Y -> Direction -> (Adjacencies, Nodes, Visited)
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explore node adjacencies nodes visited x y d = L.foldl' explore' (adjacencies, nodes, visited) $ nextSteps x y d
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where
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explore' :: (Adjacencies, Nodes, Visited) -> (X, Y, Direction, Bool) -> (Adjacencies, Nodes, Visited)
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explore' acc@(adjacencies, nodes, visited) (x, y, d, u) | isNothing destination = acc
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| otherwise = case M.lookup (x', y') nodes of
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Nothing -> explore node' adjacencies'' nodes' visited' x' y' d
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Just id -> (adjacencies'', nodes', visited')
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where
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destination = let s = goDownAPath visited False x y 1 d in s
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Just (visited', x', y', cost, u') = destination
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adjacencies'' = M.adjust (\l -> (node', cost):l) node $ M.adjust (\l -> if u || u' then l else (node, cost):l) node' adjacencies'
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nodes' = M.insert (x', y') node' nodes
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(node', adjacencies') = case M.lookup (x', y') nodes of
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Nothing -> let s = NodeId (M.size nodes) in (s, M.insert s [] adjacencies)
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Just node' -> (node', adjacencies)
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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
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goDownAPath visited u x y c d | M.member (x, y) nodes = Just (visited, x, y, c, u) -- we reached an already known intersection
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| M.member (x, y) visited = Nothing -- this tile has already been visited
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| isImpossibleSlope = Nothing
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| ns == [] = Nothing -- we hit a deadend
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| L.length ns > 1 = Just (visited', x, y, c, u'') -- we hit a crossroads
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| otherwise = goDownAPath visited' u'' x' y' (c+1) d'
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where
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(x', y', d', u') = head ns
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u'' = u || u'
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ns = nextSteps x y d
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visited' = M.insert (x, y) () visited
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isImpossibleSlope = case getTile (x, y) of
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Slope s -> s /= d
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otherwise -> False
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getTile :: (X, Y) -> Tile
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getTile (X x, Y y) = input V.! y V.! x
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nextSteps :: X -> Y -> Direction -> [(X, Y, Direction, Bool)] -- get the list of possible next steps at a point, given where we came from
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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)]
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where
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augmentWithUnidirectionality :: (X, Y, Direction) -> (X, Y, Direction, Bool)
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augmentWithUnidirectionality (x, y, d) = (x, y, d, isSlope $ getTile (x, y))
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isSlope :: Tile -> Bool
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--isSlope (Slope _) = True
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isSlope _ = False
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possible :: (X, Y, Direction) -> Bool
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possible (x', y', d') | t == Wall = False
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| d == opposite d' = False -- no going back
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-- | t == Floor = True
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| otherwise = True -- o == d' -- our direction must match the slope <- NO, this prevents us from properly finding intersections
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where
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t = getTile (x', y')
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Slope o = t
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Just start = V.findIndex (== Floor) $ input V.! 0
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startx = X start
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Just finish = V.findIndex (== Floor) $ input V.! finishyy
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finishx = X finish
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finishyy = V.length input - 1
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finishy = Y finishyy
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xydToxy :: (a, b, c) -> (a, b)
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xydToxy (x, y, _) = (x, y)
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opposite :: Direction -> Direction
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opposite N = S
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opposite S = N
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opposite E = W
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opposite W = E
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main :: IO ()
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main = do
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example <- parseInput "example"
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let exampleOutput = compute example
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when (exampleOutput /= exampleExpectedOutput) (error $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput)
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input <- parseInput "input"
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print $ compute input
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