advent-of-code/2023/23-A_Long_Walk/second.hs

148 lines
7.1 KiB
Haskell

-- 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