A series of 2SAT checker refactorings
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| {-# LANGUAGE LambdaCase #-} | |
| {-# LANGUAGE NamedFieldPuns #-} | |
| {-# LANGUAGE ScopedTypeVariables #-} | |
| import qualified Data.Graph as G | |
| import qualified Data.Array as A | |
| import qualified Prelude as P | |
| import Prelude hiding (lookup, read, replicate) | |
| import Control.Monad.ST | |
| import Data.STRef | |
| import Control.Monad (forM_) | |
| import Data.Vector.Mutable (STVector, read, replicate, write) | |
| data TarjanEnv s = TarjanEnv | |
| { index :: STRef s Int | |
| , stack :: STRef s [Int] | |
| , stackSet :: STVector s Bool | |
| , indices :: STVector s (Maybe Int) | |
| , lowlinks :: STVector s (Maybe Int) | |
| , output :: STRef s (Maybe [[Int]]) | |
| , possible :: STRef s Bool | |
| } | |
| whenM :: Monad m => m Bool -> m () -> m () | |
| whenM condM block = condM >>= \cond -> if cond then block else return () | |
| tarjan :: Int -> G.Graph -> Maybe [[Int]] | |
| tarjan n graph = runST $ do | |
| tarjanEnv <- TarjanEnv | |
| <$> newSTRef 0 | |
| <*> newSTRef [] | |
| <*> replicate size False | |
| <*> replicate size Nothing | |
| <*> replicate size Nothing | |
| <*> newSTRef (Just []) | |
| <*> newSTRef True | |
| forM_ (G.vertices graph) $ \v -> | |
| whenM ((&&) | |
| <$> ((==) Nothing <$> read (indices tarjanEnv) v) | |
| <*> readSTRef (possible tarjanEnv)) $ | |
| strongConnect n v graph tarjanEnv | |
| readSTRef (output tarjanEnv) | |
| where | |
| size = snd (A.bounds graph) + 1 | |
| strongConnect :: forall s. Int -> Int -> G.Graph -> TarjanEnv s -> ST s () | |
| strongConnect n v graph tarjanEnv@TarjanEnv{ index, stack, stackSet, indices, lowlinks, output, possible } = do | |
| i <- readSTRef index | |
| write indices v (Just i) | |
| write lowlinks v (Just i) | |
| modifySTRef' index (+1) | |
| push v | |
| forM_ (graph A.! v) $ \w -> read indices w >>= \case | |
| Nothing -> do | |
| strongConnect n w graph tarjanEnv | |
| write lowlinks v =<< (min <$> read lowlinks v <*> read lowlinks w) | |
| Just{} -> whenM (read stackSet w) $ | |
| write lowlinks v =<< (min <$> read lowlinks v <*> read indices w) | |
| whenM ((==) <$> read lowlinks v <*> read indices v) $ do | |
| scc <- addSCC n v [] | |
| modifySTRef' output $ \sccs -> (:) <$> scc <*> sccs | |
| where | |
| addSCC :: Int -> Int -> [Int] -> ST s (Maybe [Int]) | |
| addSCC n v scc = pop >>= \w -> if ((other n w) `elem` scc) | |
| then writeSTRef possible False >> return Nothing | |
| else | |
| let scc' = w:scc | |
| in if w == v then return (Just scc') else addSCC n v scc' | |
| push :: Int -> ST s () | |
| push e = do | |
| modifySTRef' stack (e:) | |
| write stackSet e True | |
| pop :: ST s Int | |
| pop = do | |
| e <- head <$> readSTRef stack | |
| modifySTRef' stack tail | |
| write stackSet e False | |
| return e | |
| denormalise = subtract | |
| normalise = (+) | |
| other n v = 2*n - v | |
| clauses n [u,v] = [(other n u, v), (other n v, u)] | |
| checkSat :: String -> IO Bool | |
| checkSat name = do | |
| p <- map (map P.read . words) . lines <$> readFile name | |
| let pNo = head $ head p | |
| pn = map (map (normalise pNo)) $ tail p | |
| pGraph = G.buildG (0,2*pNo) $ concatMap (clauses pNo) pn | |
| return $ (Nothing /=) $ tarjan pNo pGraph | |
| main = forM_ [1..6] $ \n -> print =<< (checkSat $ "2sat" ++ show n ++ ".txt") |
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