Graph.hs

pop :: MaybeT (State BfsState) [Int]
pop = do
    (x :< xs) <- viewl <$> gets queue
    modify $ \y -> y { queue = xs }
    return x

push :: [Int] ->  MaybeT (State BfsState) ()
push x = do q <- gets queue
            modify $ \y -> y { queue = q |> x }

visit :: Int -> MaybeT (State BfsState) ()
visit x = do v <- gets visited
             modify $ \y -> y { visited = Set.insert x v }

bfs :: Int -> Int -> Graph -> Maybe [Int]
bfs start end g = evalState (runMaybeT loop') (BfsState (Seq.empty |> [start]) Set.empty) where
    loop' = do
        join $ guard . not . Seq.null <$> gets queue --If queue empty, treminate
        (c : path) <- pop
        isVis <- Set.member c <$> gets visited
        if c == end then return $ c : path
        else if isVis then loop'
        else do visit c
                forM_ (map (: c : path) (g ! c)) push
                loop'