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-- requires cabal install --lib megaparsec parser-combinators heap vector fgl
-- very slow with runghc, use ghc -O3 -o first first.hs
module Main (main) where
import Control.Applicative.Permutations
import Control.Monad (void, when)
import qualified Data.Char as C
import Data.Either
import Data.Function
import Data.Functor
import Data.Graph.Inductive
import qualified Data.Heap as H
import qualified Data.List as L
import qualified Data.Map as M
import Data.Maybe
import Data.Ratio
import qualified Data.Set as S
import Data.Tuple
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 = 54
type Input = M.Map String (S.Set String)
type Parser = Parsec Void String
parseLabel :: Parser String
parseLabel = some letterChar <* optional (char ':') <* optional hspace
parseLine :: Parser (String, S.Set String)
parseLine = (,) <$> parseLabel
<*> (S.fromList <$> some parseLabel)
parseInput' :: Parser Input
parseInput' = M.fromList <$> (some (parseLine <* eol) <* 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'
compute :: Input -> Int
compute input = size1 * (order g - size1)
where
n = L.nub $ M.keys input ++ (S.elems . S.unions $ M.elems input)
e = [(from, to) | (from, tos) <- M.assocs input, to <- S.elems tos]
n' = zip n [1..]
e' = map (\(from, to) -> (fromJust $ L.lookup from n', fromJust $ L.lookup to n', from ++ "-" ++ to)) e
g :: Gr String String
g = undir $ mkGraph (map swap n') e'
size1 = length group1
group1 = compute' (nodes g)
-- Karger's algorithm to compute a minimum cut
-- implementation from https://github.com/jrp2014/AoC2023/blob/main/Day25/Day25.hs#L60
compute' :: [Node] -> [Node]
compute' s | sum (map count s) == 3 = s
| otherwise = compute' (L.delete (L.maximumBy (compare `on` count) s) s)
where
count :: Node -> Int
count ns = length $ suc g ns L.\\ s
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
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