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-- requires cabal install --lib megaparsec parser-combinators heap vector
module Main (main) where
import Control.Monad (void, when)
import Data.Functor
import qualified Data.Heap as H
import qualified Data.List as L
import qualified Data.Map as M
import qualified Data.Vector as V
import Data.Void (Void)
import Text.Megaparsec
import Text.Megaparsec.Char
exampleExpectedOutput = (6, 1)
type Coord = (Int, Int)
type Input = [Coord]
type Parser = Parsec Void String
parseNumber :: Parser Int
parseNumber = read <$> some digitChar
parseCoord :: Parser Coord
parseCoord = (,) <$> parseNumber <* char ','
<*> parseNumber <* eol
parseInput' :: Parser Input
parseInput' = some parseCoord <* eof
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 Cost = Int
data Position = Position Coord Cost deriving Show
instance Ord Position where
compare (Position _ c1) (Position _ c2) = c1 `compare` c2
instance Eq Position where
(Position p1 _ ) == (Position p2 _ ) = p1 == p2
type Visited = M.Map Coord Cost
type Maze = M.Map Coord ()
type Candidates = H.MinHeap Position
compute' :: Int -> Int -> Input -> Bool
compute' size cutoff input = walk (M.singleton (0, 0) 0) $ H.singleton (Position (0, 0) 0)
where
walk :: Visited -> Candidates -> Bool
walk v h | H.isEmpty h = False
| x == size && y == size = True
| otherwise = walk v' $ H.union h' $ H.fromList n
where
([pos@(Position p@(x, y) c)], h') = H.splitAt 1 h
n = nexts v pos
v' = L.foldl' (\acc (Position a b) -> M.insert a b acc) v n
nexts :: Visited -> Position -> [Position]
nexts v (Position p c) = L.filter (valid v) . map (\p' -> Position p' (c+1)) $ candidates p
valid :: Visited -> Position -> Bool
valid v (Position p@(x, y) c) = x >= 0 && x <= size && y >= 0 && y <= size && not (M.member p maze) && case M.lookup p v of
Just c' -> c < c'
Nothing -> True
candidates :: Coord -> [Coord]
candidates (x, y) = [ (x-1, y), (x+1, y), (x, y-1), (x, y+1) ]
maze = M.fromList $ zip (take cutoff input) (L.repeat ())
compute :: Int -> Int -> Int -> Input -> Coord
compute size n m input | mid == n = input L.!! n
| valid = compute size mid m input
| otherwise = compute size n mid input
where
mid = (n + (m - n) `div` 2)
valid = compute' size mid input
main :: IO ()
main = do
example <- parseInput "example"
let exampleOutput = compute 6 12 (length example) example
when (exampleOutput /= exampleExpectedOutput) (error $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput)
input <- parseInput "input"
print $ compute 70 1024 (length input) input
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