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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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