GraphSCC-1.0.4/0000755000000000000000000000000012173322426011276 5ustar0000000000000000GraphSCC-1.0.4/LICENSE0000644000000000000000000000204512173322426012304 0ustar0000000000000000Copyright (c) 2008 Iavor S. Diatchki Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. GraphSCC-1.0.4/Setup.hs0000644000000000000000000000005712173322426012734 0ustar0000000000000000import Distribution.Simple main = defaultMain GraphSCC-1.0.4/GraphSCC.cabal0000644000000000000000000000165012173322426013656 0ustar0000000000000000Name: GraphSCC Version: 1.0.4 License: BSD3 License-file: LICENSE Author: Iavor S. Diatchki Maintainer: diatchki@galois.com Category: Algorithms Synopsis: Tarjan's algorithm for computing the strongly connected components of a graph. Description: Tarjan's algorithm for computing the strongly connected components of a graph. Build-type: Simple Cabal-Version: >= 1.6 flag use-maps default: False description: Use IntMap instead of mutable arrays. library Build-Depends: base < 10, array, containers Exposed-modules: Data.Graph.SCC Extensions: CPP GHC-options: -O2 -Wall if flag(use-maps) Other-modules: Data.Graph.MapSCC cpp-options: -DUSE_MAPS else Extensions: Rank2Types Other-modules: Data.Graph.ArraySCC source-repository head type: git location: git://github.com/yav/GraphSCC.git GraphSCC-1.0.4/Data/0000755000000000000000000000000012173322426012147 5ustar0000000000000000GraphSCC-1.0.4/Data/Graph/0000755000000000000000000000000012173322426013210 5ustar0000000000000000GraphSCC-1.0.4/Data/Graph/MapSCC.hs0000644000000000000000000000760012173322426014615 0ustar0000000000000000-- | Implements Tarjan's algorithm for computing the strongly connected -- components of a graph. For more details see: -- . -- -- This implementation uses 'IntMap' instead of mutable arrays in the algorithm. -- The benefit is that the implementation conforms to the Haskell 98 standard, -- however, the algorithm is a bit slower on large graphs. {-# LANGUAGE Safe #-} module Data.Graph.MapSCC(scc) where import Data.Graph(Graph,Vertex) import qualified Data.IntMap as Map import Data.Array import Control.Monad(ap) import Data.List(foldl') -- | Computes the strongly connected components (SCCs) in the graph in O(???) -- time. The resulting tuple contains: -- * A (reversed) topologically sorted list of SCCs. -- Each SCCs is assigned a unique identifier of type 'Int'. -- * An O(log(V)) mapping from vertices in the original graph to -- the identifier of their SCC. This mapping will raise an exception -- if it is applied to integers that do not correspond to -- vertices in the input graph. -- -- This function assumes that the adjacency lists in the original graph -- mention only nodes that are in the graph. Violating this assumption -- will result in an exception. scc :: Graph -> ([(Int,[Vertex])], Vertex -> Int) scc g = let s = roots g (S Map.empty Map.empty [] 1 [] 1) (indices g) sccm = ixes s in (sccs s, \i -> Map.findWithDefault (err i) i sccm) where err i = error $ show i ++ " is not a vertex in the graph" data S = S { ixes :: !(Map.IntMap Int) -- ^ Index in DFS traversal, or SCC for vertex. -- Legend for the index array: -- -ve: Node is on the stack with the given number -- +ve: Node belongs to the SCC with the given number , lows :: !(Map.IntMap Int) -- ^ Least reachable node , stack :: ![Vertex] -- ^ Traversal stack , num :: !Int -- ^ Next node number , sccs :: ![(Int,[Vertex])] -- ^ Finished SCCs , next_scc :: !Int -- ^ Next SCC number } roots :: Graph -> S -> [Vertex] -> S roots g st (v:vs) = case Map.lookup v (ixes st) of Just {} -> roots g st vs Nothing -> roots g (from_root g st v) vs roots _ s [] = s from_root :: Graph -> S -> Vertex -> S from_root g s v = let me = num s newS = check_adj g s { ixes = Map.insert v (negate me) (ixes s) , lows = Map.insert v me (lows s) , stack = v : stack s, num = me + 1 } v (g ! v) in case Map.lookup v (lows newS) of Just x | x < me -> newS | otherwise -> case span (/= v) (stack newS) of (as,b:bs) -> let this = b : as n = next_scc newS ixes' = foldl' (\m i -> Map.insert i n m) (ixes newS) this in S { ixes = ixes' , lows = lows newS , stack = bs , num = num newS , sccs = (n,this) : sccs newS , next_scc = n + 1 } _ -> error ("bug in scc---vertex not on the stack: " ++ show v) Nothing -> error ("bug in scc--vertex disappeared from lows: " ++ show v) check_adj :: Graph -> S -> Vertex -> [Vertex] -> S check_adj g st v (v':vs) = case Map.lookup v' (ixes st) of Nothing -> let newS = from_root g st v' Just new_low = min `fmap` Map.lookup v (lows newS) `ap` Map.lookup v' (lows newS) lows' = Map.insert v new_low (lows newS) in check_adj g newS { lows = lows' } v vs Just i | i < 0 -> let lows' = Map.adjust (min (negate i)) v (lows st) in check_adj g st { lows = lows' } v vs | otherwise -> check_adj g st v vs check_adj _ st _ [] = st GraphSCC-1.0.4/Data/Graph/SCC.hs0000644000000000000000000000602612173322426014160 0ustar0000000000000000{-# LANGUAGE CPP, Safe #-} module Data.Graph.SCC ( scc , sccList , sccListR , sccGraph , stronglyConnComp , stronglyConnCompR ) where #ifdef USE_MAPS import Data.Graph.MapSCC #else import Data.Graph.ArraySCC #endif import Data.Graph(SCC(..),Graph,Vertex,graphFromEdges') import Data.Array as A import Data.List(nub) -- | Compute the list of strongly connected components of a graph. -- The components are topologically sorted: -- if v1 in C1 points to v2 in C2, then C2 will come before C1 in the list. sccList :: Graph -> [SCC Vertex] sccList g = reverse $ map (to_scc g lkp) cs where (cs,lkp) = scc g -- | Compute the list of strongly connected components of a graph. -- Each component contains the adjecency information from the original graph. -- The components are topologically sorted: -- if v1 in C1 points to v2 in C2, then C2 will come before C1 in the list. sccListR :: Graph -> [SCC (Vertex,[Vertex])] sccListR g = reverse $ map cvt cs where (cs,lkp) = scc g cvt (n,[v]) = let adj = g ! v in if n `elem` map lkp adj then CyclicSCC [(v,adj)] else AcyclicSCC (v,adj) cvt (_,vs) = CyclicSCC [ (v, g ! v) | v <- vs ] -- | Quotient a graph with the relation that relates vertices that -- belong to the same SCC. The vertices in the new graph are the -- SCCs of the old graph, and there is an edge between two components, -- if there is an edge between any of their vertices. -- The entries in the resulting list are in reversed-topologically sorted: -- if v1 in C1 points to v2 in C2, then C1 will come before C2 in the list. sccGraph :: Graph -> [(SCC Int, Int, [Int])] sccGraph g = map to_node cs where (cs,lkp) = scc g to_node x@(n,this) = ( to_scc g lkp x , n , nub $ concatMap (map lkp . (g !)) this ) stronglyConnComp :: Ord key => [(node, key, [key])] -> [SCC node] stronglyConnComp es = reverse $ map cvt cs where (g,back) = graphFromEdges' es (cs,lkp) = scc g cvt (n,[v]) = let (node,_,_) = back v in if n `elem` map lkp (g ! v) then CyclicSCC [node] else AcyclicSCC node cvt (_,vs) = CyclicSCC [ node | (node,_,_) <- map back vs ] stronglyConnCompR :: Ord key => [(node, key, [key])] -> [SCC (node, key, [key])] stronglyConnCompR es = reverse $ map cvt cs where (g,back) = graphFromEdges' es (cs,lkp) = scc g cvt (n,[v]) = if n `elem` map lkp (g ! v) then CyclicSCC [back v] else AcyclicSCC (back v) cvt (_,vs) = CyclicSCC (map back vs) -------------------------------------------------------------------------------- to_scc :: Graph -> (Vertex -> Int) -> (Int,[Vertex]) -> SCC Vertex to_scc g lkp (n,[v]) = if n `elem` map lkp (g ! v) then CyclicSCC [v] else AcyclicSCC v to_scc _ _ (_,vs) = CyclicSCC vs GraphSCC-1.0.4/Data/Graph/ArraySCC.hs0000644000000000000000000000740212173322426015156 0ustar0000000000000000-- | Implements Tarjan's algorithm for computing the strongly connected -- components of a graph. For more details see: -- {-# LANGUAGE Rank2Types, Trustworthy #-} module Data.Graph.ArraySCC(scc) where import Data.Graph(Graph,Vertex) import Data.Array.ST(STUArray, newArray, readArray, writeArray) import Data.Array as A import Data.Array.Unsafe(unsafeFreeze) import Control.Monad.ST import Control.Monad(ap) -- | Computes the strongly connected components (SCCs) of the graph in -- O(#edges + #vertices) time. The resulting tuple contains: -- -- * A (reversed) topologically sorted list of SCCs. -- Each SCCs is assigned a unique identifier of type 'Int'. -- -- * An O(1) mapping from vertices in the original graph to the identifier -- of their SCC. This mapping will raise an \"out of bounds\" -- exception if it is applied to integers that do not correspond to -- vertices in the input graph. -- -- This function assumes that the adjacency lists in the original graph -- mention only nodes that are in the graph. Violating this assumption -- will result in \"out of bounds\" array exception. scc :: Graph -> ([(Int,[Vertex])], Vertex -> Int) scc g = runST ( do ixes <- newArray (bounds g) 0 lows <- newArray (bounds g) 0 s <- roots g ixes lows (S [] 1 [] 1) (indices g) sccm <- unsafeFreeze ixes return (sccs s, \i -> sccm ! i) ) type Func s a = Graph -- The original graph -> STUArray s Vertex Int -- Index in DFS traversal, or SCC for vertex. -- Legend for the index array: -- 0: Node not visited -- -ve: Node is on the stack with the given number -- +ve: Node belongs to the SCC with the given number -> STUArray s Vertex Int -- Least reachable node -> S -- State -> a data S = S { stack :: ![Vertex] -- ^ Traversal stack , num :: !Int -- ^ Next node number , sccs :: ![(Int,[Vertex])] -- ^ Finished SCCs , next_scc :: !Int -- ^ Next SCC number } roots :: Func s ([Vertex] -> ST s S) roots g ixes lows st (v:vs) = do i <- readArray ixes v if i == 0 then do s1 <- from_root g ixes lows st v roots g ixes lows s1 vs else roots g ixes lows st vs roots _ _ _ s [] = return s from_root :: Func s (Vertex -> ST s S) from_root g ixes lows s v = do let me = num s writeArray ixes v (negate me) writeArray lows v me newS <- check_adj g ixes lows s { stack = v : stack s, num = me + 1 } v (g ! v) x <- readArray lows v if x < me then return newS else case span (/= v) (stack newS) of (as,b:bs) -> do let this = b : as n = next_scc newS mapM_ (\i -> writeArray ixes i n) this return S { stack = bs , num = num newS , sccs = (n,this) : sccs newS , next_scc = n + 1 } _ -> error ("bug in scc---vertex not on the stack: " ++ show v) check_adj :: Func s (Vertex -> [Vertex] -> ST s S) check_adj g ixes lows st v (v':vs) = do i <- readArray ixes v' case () of _ | i == 0 -> do newS <- from_root g ixes lows st v' new_low <- min `fmap` readArray lows v `ap` readArray lows v' writeArray lows v new_low check_adj g ixes lows newS v vs | i < 0 -> do j <- readArray lows v writeArray lows v (min j (negate i)) check_adj g ixes lows st v vs | otherwise -> check_adj g ixes lows st v vs check_adj _ _ _ st _ [] = return st