229 lines
9.1 KiB
Haskell
229 lines
9.1 KiB
Haskell
{-# LANGUAGE NamedFieldPuns #-}
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module Lib where
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import Control.Monad (join)
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import Flow
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import qualified Data.Map.Strict as Map
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import Data.Maybe (listToMaybe, maybeToList)
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import qualified Data.Set as Set
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import Text.ParserCombinators.ReadP
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type IntType = Int
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data Vec2 = Vec2 IntType IntType
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deriving (Eq, Ord, Show)
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vAdd :: Vec2 -> Vec2 -> Vec2
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vAdd (Vec2 aX aY) (Vec2 bX bY) = Vec2 (aX+bX) (aY+bY)
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data Direction = North | East | South | West
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deriving (Eq, Ord, Show)
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dOpposite :: Direction -> Direction
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dOpposite North = South
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dOpposite East = West
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dOpposite South = North
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dOpposite West = East
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dVec :: Direction -> Vec2
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dVec North = Vec2 0 (-1)
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dVec East = Vec2 1 0
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dVec South = Vec2 0 1
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dVec West = Vec2 (-1) 0
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data Tile = Path | Start | End | Wall
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deriving (Eq, Ord, Show)
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type WorldMap = Map.Map Vec2 Tile
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data Edge = Edge { eDirFrom :: Direction, eFrom :: Vec2, eDirTo :: Direction, eTo :: Vec2, ePrice :: Int }
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deriving (Show)
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type WorldGraphEdges = Map.Map Vec2 [Edge]
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data WorldGraph = WorldGraph { wStart :: Vec2, wEnd :: Vec2, wEdges :: WorldGraphEdges }
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deriving (Show)
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task1 :: String -> IO IntType
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task1 input =
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let worldMap = parseFile input
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rawGraph = mapToGraph worldMap
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in do
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worldGraph <- simplifyGraph rawGraph
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worldGraph |> wEdges |> Map.elems |> join |> showEdgesSimple |> putStrLn
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(bestPath, _) <- dijkstra worldGraph Map.empty (Map.singleton (wStart worldGraph, East) (0, []))
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return bestPath
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task2 :: String -> IO IntType
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task2 input =
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let worldMap = parseFile input
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rawGraph = mapToGraph worldMap
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in do
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(bestCost, bestPaths) <- dijkstra rawGraph Map.empty (Map.singleton (wStart rawGraph, East) (0, []))
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[wEnd rawGraph] : bestPaths |> join |> Set.fromList |> length |> return
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showEdgesSimple :: [Edge] -> String
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showEdgesSimple [] = ""
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showEdgesSimple (edge:edges) = (show $ eFrom edge) ++ " -> " ++ (show $ eTo edge) ++ ": " ++ (show $ ePrice edge) ++ "\n" ++ (showEdgesSimple edges)
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type WasBestePreis = (Int, [(Vec2, Direction)])
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dijkstra :: WorldGraph -> Map.Map (Vec2, Direction) WasBestePreis -> Map.Map (Vec2, Direction) WasBestePreis -> IO (Int, [[Vec2]])
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dijkstra world@WorldGraph { wEdges, wEnd, wStart } done unvisited
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| null unvisited =
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let bestePreis = [North, East, South, West] |> map (\d -> done Map.!? (wEnd, d) |> maybeToList) |> join |> foldr combineBestePreis (maxBound :: IntType, [])
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in bestePreis |> \(p, os) -> (p, map (reconstructPath done) os |> join) |> return
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| otherwise =
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let ((pos, dir), (cost, _)) = findNext
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nextDone = Map.insert (pos, dir) (unvisited Map.! (pos, dir)) done
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outgoing = Map.findWithDefault [] pos wEdges
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unvisitedOutgoing = outgoing |> filter (\Edge { eTo, eDirTo } -> Map.notMember (eTo, eDirTo) done)
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unvisitedOutgoingWithPrice = unvisitedOutgoing |> map (\e@Edge { eDirFrom, ePrice } -> (e, if dir == dOpposite eDirFrom then cost + ePrice else cost + ePrice + 1000)) :: [(Edge, IntType)]
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unvisitedWithoutCurrent = Map.delete (pos, dir) unvisited
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nextUnvisited = foldr (\(Edge { eTo, eDirTo }, price) -> Map.alter (pure . maybeCombineBestePreis (price, [(pos, dir)])) (eTo, eDirTo)) unvisitedWithoutCurrent unvisitedOutgoingWithPrice
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in dijkstra world nextDone nextUnvisited
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where
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findNext :: ((Vec2, Direction), WasBestePreis)
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findNext =
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let options = unvisited |> Map.assocs
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in foldr (\a@(_,(aC,_)) b@(_,(bC,_)) -> if aC < bC then a else b) (head options) (drop 1 options)
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maybeCombineBestePreis :: WasBestePreis -> Maybe WasBestePreis -> WasBestePreis
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maybeCombineBestePreis a Nothing = a
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maybeCombineBestePreis a (Just b) = combineBestePreis a b
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combineBestePreis :: WasBestePreis -> WasBestePreis -> WasBestePreis
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combineBestePreis (aP, aOs) (bP, bOs)
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| aP < bP = (aP, aOs)
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| aP == bP = (aP, aOs ++ bOs)
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| aP > bP = (bP, bOs)
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reconstructPath :: Map.Map (Vec2, Direction) WasBestePreis -> (Vec2, Direction) -> [[Vec2]]
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reconstructPath done cur@(curPos,_) =
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case done Map.!? cur of
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Nothing -> [[curPos]]
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Just (_,[]) -> [[curPos]]
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Just (_,os) -> map (reconstructPath done) os |> join |> map (\subPath -> curPos : subPath)
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showEntries :: Show a => Show b => [(a,b)] -> String
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showEntries [] = ""
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showEntries ((k,v):rest) = show k ++ ": " ++ show v ++ "\n" ++ showEntries rest
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findBestPath :: WorldGraph -> [(Vec2, Direction)] -> Maybe Int
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findBestPath _ [] = error "Must call findBestPath with an initial position"
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findBestPath world@WorldGraph { wEdges, wEnd } ((lastPos, lastDir):path) =
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let edgeOptions = wEdges Map.!? lastPos |> expectJust ("Position is missing in map " ++ show lastPos) |> filter (\Edge{eTo=optTo} -> not $ listContains optTo $ map (\(p,_) -> p) path)
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in case edgeOptions |> map (maybeToList . exploreOption) |> join of
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[] -> Nothing
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prices -> return $ minimum prices
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where
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exploreOption :: Edge -> Maybe Int
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exploreOption edge@Edge{ePrice, eDirFrom, eTo, eDirTo}
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| eTo == wEnd = Just hopPrize
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| otherwise = findBestPath world ((eTo, eDirTo):(lastPos, lastDir):path) |> fmap (\pr -> pr + hopPrize)
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where
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hopPrize :: Int
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hopPrize = if eDirFrom == dOpposite lastDir then ePrice else ePrice + 1000
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mapToGraph :: WorldMap -> WorldGraph
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mapToGraph worldMap =
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let start = Map.assocs worldMap |> filter (\(_, t) -> t == Start) |> listToMaybe |> expectJust "No start found" |> entryKey
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end = Map.assocs worldMap |> filter (\(_, t) -> t == End) |> listToMaybe |> expectJust "No end found" |> entryKey
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pathMap = worldMap |> Map.filter ((/=) Wall)
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edges = pathMap |> Map.keys |> map edgesFromPos |> join
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edgesByFrom = map (\e -> (eFrom e, [e])) edges |> Map.fromListWith (++)
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in WorldGraph { wStart = start, wEnd = end, wEdges = edgesByFrom }
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where
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edgesFromPos :: Vec2 -> [Edge]
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edgesFromPos pos =
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[North, East, South, West]
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|> map (\dir -> dVec dir |> vAdd pos |> \t -> if validTarget $ worldMap Map.!? t then [Edge { eDirTo = dir, eTo = t, eDirFrom = dOpposite dir, eFrom = pos, ePrice = 1 }] else [])
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|> join
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validTarget :: Maybe Tile -> Bool
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validTarget (Just Wall) = False
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validTarget (Just _) = True
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validTarget _ = False
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simplifyGraph :: WorldGraph -> IO WorldGraph
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simplifyGraph world@WorldGraph { wStart, wEnd, wEdges } =
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case Map.assocs wEdges |> filter (\(p, edges) -> p /= wStart && p /= wEnd && length edges <= 2) of
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[] -> return world
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((pos, []):_) -> simplifyGraph WorldGraph { wStart, wEnd, wEdges = Map.delete pos wEdges }
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((_, [e]):_) -> do
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--putStrLn $ "Removing " ++ (show e)
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simplifyGraph WorldGraph { wStart, wEnd, wEdges = removeEdge e wEdges }
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((_, [e1, e2]):_) ->
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let newEdges = wEdges |> combineEdges e1 e2
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in do
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--putStrLn $ "Combining " ++ (show e1) ++ " : " ++ (show e2)
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simplifyGraph WorldGraph { wStart, wEnd, wEdges = newEdges }
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_ -> error "Ureachable in simplifyGraph"
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where
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combineEdges :: Edge -> Edge -> WorldGraphEdges -> WorldGraphEdges
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combineEdges e1@Edge { eDirFrom = eDirFrom1, eTo = eTo1, eDirTo = eDirTo1, ePrice = ePrice1 } e2@Edge { eDirFrom = eDirFrom2, eTo = eTo2, eDirTo = eDirTo2, ePrice = ePrice2 } edges =
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let combinedPrice = ePrice1 + ePrice2 + if eDirFrom1 == dOpposite eDirFrom2 then 0 else 1000
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in edges |> removeEdge e1 |> removeEdge e2
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|> Map.adjust (\es -> Edge { eFrom = eTo1, eDirFrom = eDirTo1, eTo = eTo2, eDirTo = eDirTo2, ePrice = combinedPrice }:es) eTo1
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|> Map.adjust (\es -> Edge { eFrom = eTo2, eDirFrom = eDirTo2, eTo = eTo1, eDirTo = eDirTo1, ePrice = combinedPrice }:es) eTo2
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removeEdge :: Edge -> WorldGraphEdges -> WorldGraphEdges
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removeEdge Edge { eFrom, eTo } edgesMap =
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edgesMap
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|> Map.adjust (\edges -> edges |> filter (not . (isEdgeTo eTo))) eFrom
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|> Map.adjust (\edges -> edges |> filter (not . (isEdgeTo eFrom))) eTo
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isEdgeTo :: Vec2 -> Edge -> Bool
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isEdgeTo testTo Edge { eTo } = testTo == eTo
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parseFile :: String -> WorldMap
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parseFile input =
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case readP_to_S parse input of
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[] -> error "Failed to parse"
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((v,_):_) -> v
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where
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parse :: ReadP WorldMap
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parse = do
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worldMap <- parseWorld
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_ <- eof
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return worldMap
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parseWorld :: ReadP WorldMap
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parseWorld = do
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ls <- many1 parseLine
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zip [0..] ls |> map (\(y, line) -> zip [0..] line |> map (\(x, c) -> (Vec2 x y, toTile c))) |> join |> Map.fromList |> return
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where
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parseLine :: ReadP String
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parseLine = do
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content <- munch1 (not . isNewLine)
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_ <- char '\n'
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return content
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toTile :: Char -> Tile
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toTile '.' = Path
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toTile 'S' = Start
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toTile 'E' = End
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toTile '#' = Wall
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toTile c = error $ "Unknown tile: " ++ [c]
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isNewLine :: Char -> Bool
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isNewLine = (==) '\n'
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listContains :: Eq a => a -> [a] -> Bool
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listContains _ [] = False
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listContains a (e:es) = if a == e then True else listContains a es
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nothingIfEmpty :: Foldable t => t a -> Maybe (t a)
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nothingIfEmpty values
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| null values = Nothing
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| otherwise = Just values
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entryKey :: (a,b) -> a
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entryKey (k,_) = k
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entryValue :: (a,b) -> b
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entryValue (_,v) = v
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expectJust :: String -> Maybe a -> a
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expectJust message Nothing = error message
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expectJust _ (Just value) = value
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