labeled-graph (empty) → 1.0.0.0
raw patch · 4 files changed
+554/−0 lines, 4 filesdep +basedep +labeled-treesetup-changed
Dependencies added: base, labeled-tree
Files
- Data/LabeledGraph.hs +511/−0
- LICENSE +24/−0
- Setup.hs +2/−0
- labeled-graph.cabal +17/−0
+ Data/LabeledGraph.hs view
@@ -0,0 +1,511 @@+{-# LANGUAGE ScopedTypeVariables #-}+-----------------------------------------------------------------------------+-- |+-- Module : Data.LabeledGraph+-- Copyright : (c) The University of Glasgow 2002, Jean-Philippe Bernardy 2012+-- License : BSD-style+--+-- Maintainer : JP Bernardy+-- Stability : experimental+-- Portability : GHC+--+-- A version of the graph algorithms described in:+--+-- /Structuring Depth-First Search Algorithms in Haskell/,+-- by David King and John Launchbury.+--+-- Adapted to labeled graphs by JP Bernardy.+--+-----------------------------------------------------------------------------++module Data.Graph{-(++ -- * External interface++ -- At present the only one with a "nice" external interface+ stronglyConnComp, stronglyConnCompR, SCC(..), flattenSCC, flattenSCCs,++ -- * Graphs++ Graph, Table, Bounds, Edge, Vertex,++ -- ** Building graphs++ graphFromEdges, graphFromEdges', buildG, transposeG,+ -- reverseE,++ -- ** Graph properties++ vertices, edges,+ outdegree, indegree,++ -- * Algorithms++ dfs, dff,+ topSort,+ components,+ scc,+ bcc,+ -- tree, back, cross, forward,+ reachable, path,++ module Data.LabeledTree++ ) -} where++import Control.Monad.ST+import Data.Array.ST (STArray, newArray, readArray, writeArray)+import Data.LabeledTree (Tree(Node), Forest, (::>)((::>)) )++import Data.STRef++import Control.DeepSeq (NFData(rnf))+import Data.Maybe+import Data.Array+import Data.List+import qualified Data.Map as M+++-------------------------------------------------------------------------+-- -+-- External interface+-- -+-------------------------------------------------------------------------+{-+-- | Strongly connected component.+data SCC vertex = AcyclicSCC vertex -- ^ A single vertex that is not+ -- in any cycle.+ | CyclicSCC [vertex] -- ^ A maximal set of mutually+ -- reachable vertices.++instance NFData a => NFData (SCC a) where+ rnf (AcyclicSCC v) = rnf v+ rnf (CyclicSCC vs) = rnf vs++-- | The vertices of a list of strongly connected components.+flattenSCCs :: [SCC a] -> [a]+flattenSCCs = concatMap flattenSCC++-- | The vertices of a strongly connected component.+flattenSCC :: SCC vertex -> [vertex]+flattenSCC (AcyclicSCC v) = [v]+flattenSCC (CyclicSCC vs) = vs++-- | The strongly connected components of a directed graph, topologically+-- sorted.+stronglyConnComp+ :: Ord key+ => [(node, key, [key])]+ -- ^ The graph: a list of nodes uniquely identified by keys,+ -- with a list of keys of nodes this node has edges to.+ -- The out-list may contain keys that don't correspond to+ -- nodes of the graph; such edges are ignored.+ -> [SCC node]++stronglyConnComp edges0+ = map get_node (stronglyConnCompR edges0)+ where+ get_node (AcyclicSCC (n, _, _)) = AcyclicSCC n+ get_node (CyclicSCC triples) = CyclicSCC [n | (n,_,_) <- triples]++-- | The strongly connected components of a directed graph, topologically+-- sorted. The function is the same as 'stronglyConnComp', except that+-- all the information about each node retained.+-- This interface is used when you expect to apply 'SCC' to+-- (some of) the result of 'SCC', so you don't want to lose the+-- dependency information.+stronglyConnCompR+ :: Ord key+ => [(node, key, [key])]+ -- ^ The graph: a list of nodes uniquely identified by keys,+ -- with a list of keys of nodes this node has edges to.+ -- The out-list may contain keys that don't correspond to+ -- nodes of the graph; such edges are ignored.+ -> [SCC (node, key, [key])] -- ^ Topologically sorted++stronglyConnCompR [] = [] -- added to avoid creating empty array in graphFromEdges -- SOF+stronglyConnCompR edges0+ = map decode forest+ where+ (graph, vertex_fn,_) = graphFromEdges edges0+ forest = scc graph+ decode (Node v []) | mentions_itself v = CyclicSCC [vertex_fn v]+ | otherwise = AcyclicSCC (vertex_fn v)+ decode other = CyclicSCC (dec other [])+ where+ dec (Node v ts) vs = vertex_fn v : foldr dec vs ts+ mentions_itself v = v `elem` (graph ! v)+-}+-------------------------------------------------------------------------+-- -+-- Graphs+-- -+-------------------------------------------------------------------------++-- | Abstract representation of vertices.+type Vertex = Int+-- | Table indexed by a contiguous set of vertices.+type Table a = Array Vertex a+-- | Adjacency list representation of a graph, mapping each vertex to its+-- list of successors.+type Graph e = Table [(e,Vertex)]+-- | The bounds of a 'Table'.+type Bounds = (Vertex, Vertex)+-- | An edge from the first vertex to the second.+type Edge e = (Vertex,e,Vertex)+++-- | Graph structure + colour on the vertices+data ColouredGraph c e = ColouredGraph (Graph e) (Colouring c)+type Colouring a = Vertex -> a+++showWithColor gr color = concat $ map showNode $ range $ bounds gr+ where showNode n = show n ++ ": " ++ show (color n) ++ " -> " ++ show (gr!n) ++ "\n"++showDotFile gr = + "digraph name {\n" +++ "rankdir=LR;\n" +++ (concatMap showEdge $ edges gr) +++ "}\n"+ where showEdge (from, t, to) = show from ++ " -> " ++ show to +++ " [label = \"" ++ show t ++ "\"];\n"+++instance (Show c, Show e) => Show (ColouredGraph c e) where+ show (ColouredGraph gr col) = showWithColor gr col+++-- | All vertices of a graph.+vertices :: Graph l -> [Vertex]+vertices = indices++-- | All edges of a graph.+edges :: Graph e -> [Edge e]+edges g = [ (v,l,w) | v <- vertices g, (l,w) <- g!v ]+++mapT :: (Vertex -> a -> b) -> Table a -> Table b+mapT f t = array (bounds t) [ (,) v (f v (t!v)) | v <- indices t ]++-- | Build a graph from a list of edges.+buildG :: Bounds -> [Edge e] -> Graph e+buildG bounds0 edges0 = accumArray (flip (:)) [] bounds0 [(v, (l,w)) | (v,l,w) <- edges0]++-- | The graph obtained by reversing all edges.+transposeG :: Graph e -> Graph e+transposeG g = buildG (bounds g) (reverseE g)++reverseE :: Graph e -> [Edge e]+reverseE g = [ (w, l, v) | (v, l, w) <- edges g ]++-- | Reverse all the edges of a graph+reverseG :: Graph e -> Graph e+reverseG g = buildG (bounds g) (reverseE g)+++-- | A table of the count of edges from each node.+outdegree :: Graph e -> Table Int+outdegree = mapT numEdges+ where numEdges _ ws = length ws++-- | A table of the count of edges into each node.+indegree :: Graph e -> Table Int+indegree = outdegree . transposeG++-- | Identical to 'graphFromEdges', except that the return value+-- does not include the function which maps keys to vertices. This+-- version of 'graphFromEdges' is for backwards compatibility.+graphFromEdges'+ :: Ord key+ => [(node, key, [(e,key)])]+ -> (Graph e, Vertex -> (node, key, [(e,key)]))+graphFromEdges' x = (a,b) where+ (a,b,_) = graphFromEdges x++-- | Build a graph from a list of nodes uniquely identified by keys,+-- with a list of keys of nodes this node should have edges to.+-- The out-list may contain keys that don't correspond to+-- nodes of the graph; they are ignored.+graphFromEdges+ :: forall key e node. + Ord key+ => [(node, key, [(e,key)])]+ -> (Graph e, Vertex -> (node, key, [(e,key)]), key -> Maybe Vertex)+graphFromEdges edges0+ = (graph, \v -> vertex_map ! v, key_vertex)+ where+ max_v = length edges0 - 1+ bounds0 = (0,max_v) :: (Vertex, Vertex)+ sorted_edges = sortBy lt edges0+ edges1 = zipWith (,) [0..] sorted_edges++ graph :: Graph e+ graph = array bounds0 [(,) v [(e,v') | (e,k) <- ks, let Just v' = key_vertex k] + | (,) v (_, _, ks) <- edges1]+ key_map = array bounds0 [(,) v k | (,) v (_, k, _ ) <- edges1]+ vertex_map = array bounds0 edges1++ (_,k1,_) `lt` (_,k2,_) = k1 `compare` k2++ key_vertex :: key -> Maybe Vertex+ -- returns Nothing for non-interesting vertices+ key_vertex k = findVertex 0 max_v+ where+ findVertex a b | a > b+ = Nothing+ findVertex a b = case compare k (key_map ! mid) of+ LT -> findVertex a (mid-1)+ EQ -> Just mid+ GT -> findVertex (mid+1) b+ where+ mid = (a + b) `div` 2+ +-------------------------------------------------------------------------+-- -+-- Depth first search+-- -+-------------------------------------------------------------------------++-- | A spanning forest of the graph, obtained from a depth-first search of+-- the graph starting from each vertex in an unspecified order.+dff :: Graph e -> [Tree e Vertex]+dff g = dfs g (vertices g)++-- | A spanning forest of the part of the graph reachable from the listed+-- vertices, obtained from a depth-first search of the graph starting at+-- each of the listed vertices in order.+dfs :: Graph e -> [Vertex] -> [Tree e Vertex]+dfs g vs = map dropLabel $ prune (bounds g) (map (\v -> error "dfs: no top-level label" ::> generate g v) vs)++dropLabel ~(_ ::> t) = t+++generate :: Graph e -> Vertex -> Tree e Vertex+generate g v = Node v [e ::> generate g v' | (e,v') <- g!v]++prune :: Bounds -> Forest e Vertex -> Forest e Vertex+prune bnds ts = run bnds (chop ts)++chop :: Forest e Vertex -> SetM s (Forest e Vertex)+chop [] = return []+chop ((e ::> Node v ts) : us)+ = do+ visited <- contains v+ if visited then+ chop us+ else do+ include v+ as <- chop ts+ bs <- chop us+ return ((e ::> Node v as) : bs)++-- A monad holding a set of vertices visited so far.+-- Use the ST for constant-time primitives.++newtype SetM s a = SetM { runSetM :: STArray s Vertex Bool -> ST s a }++instance Monad (SetM s) where+ return x = SetM $ const (return x)+ SetM v >>= f = SetM $ \ s -> do { x <- v s; runSetM (f x) s }++run :: Bounds -> (forall s. SetM s a) -> a+run bnds act = runST (newArray bnds False >>= runSetM act)++contains :: Vertex -> SetM s Bool+contains v = SetM $ \ m -> readArray m v++include :: Vertex -> SetM s ()+include v = SetM $ \ m -> writeArray m v True+++-------------------------------------------------------------------------+-- -+-- Algorithms+-- -+-------------------------------------------------------------------------++------------------------------------------------------------+-- Algorithm 1: depth first search numbering+------------------------------------------------------------++type DList a = a -> a++dconcat :: [DList a] -> DList a+dconcat = foldr (.) id ++preorder' :: [e] -> Tree e a -> DList [(a,[e])]+preorder' es (Node a ts) = ((a,es) :) . preorderF' es ts++preorderF' :: [e] -> Forest e a -> DList [(a,[e])] +preorderF' es ts = dconcat [ preorder' (e : es) t | (e ::> t) <- ts]++second f (a,b) = (a,f b)++preorderF :: [Tree e a] -> [(a,[e])]+preorderF ts = dconcat [ preorder' [] t | t <- ts] []++tabulate :: Bounds -> [Vertex] -> Table Int+tabulate bnds vs = array bnds (zipWith (,) vs [1..])+++preArr :: Bounds -> [Tree e Vertex] -> Table Int+preArr bnds = tabulate bnds . map fst . preorderF++------------------------------------------------------------+-- Algorithm 2: topological sorting+------------------------------------------------------------++postorder :: Tree e a -> [a] -> [a]+postorder (Node a ts) = postorderF (map dropLabel ts) . (a :)++postorderF :: [Tree e a] -> [a] -> [a]+postorderF ts = foldr (.) id $ map postorder ts++postOrd :: Graph e -> [Vertex]+postOrd g = postorderF (dff g) []++-- | A topological sort of the graph.+-- The order is partially specified by the condition that a vertex /i/+-- precedes /j/ whenever /j/ is reachable from /i/ but not vice versa.+topSort :: Graph e -> [Vertex]+topSort = reverse . postOrd++------------------------------------------------------------+-- Algorithm 3: connected components+------------------------------------------------------------++-- | The connected components of a graph.+-- Two vertices are connected if there is a path between them, traversing+-- edges in either direction.+components :: Graph e -> [Tree e Vertex]+components = dff . undirected++undirected :: Graph e -> Graph e+undirected g = buildG (bounds g) (edges g ++ reverseE g)++------------------------------------------------------------+-- Algorithm 4: strongly connected components+------------------------------------------------------------++-- | The strongly connected components of a graph.+scc :: Graph e -> [Tree e Vertex]+scc g = dfs g (reverse (postOrd (transposeG g)))+++------------------------------------------------------------+-- Algorithm 6: Finding reachable vertices+------------------------------------------------------------++-- | A list of vertices reachable from a given vertex.+reachable :: Graph e -> Vertex -> [(Vertex,[e])]+reachable g v = preorderF (dfs g [v])+++-- | Is the second vertex reachable from the first?+path :: Graph e -> Vertex -> Vertex -> Bool+path g v w = w `elem` map fst (reachable g v)++------------------------------------------------------------+-- Algorithm 7: Biconnected components+------------------------------------------------------------+{-+-- | The biconnected components of a graph.+-- An undirected graph is biconnected if the deletion of any vertex+-- leaves it connected.+bcc :: Graph -> Forest [Vertex]+bcc g = (concat . map bicomps . map (do_label g dnum)) forest+ where forest = dff g+ dnum = preArr (bounds g) forest++do_label :: Graph e -> Table Int -> Tree e Vertex -> Tree e (Vertex,Int,Int)+do_label g dnum (Node v ts) = Node (v,dnum!v,lv) us+ where us = map (do_label g dnum) ts+ lv = minimum ([dnum!v] ++ [dnum!w | w <- g!v]+ ++ [lu | Node (_,_,lu) _ <- us])++bicomps :: Tree (Vertex,Int,Int) -> Forest [Vertex]+bicomps (Node (v,_,_) ts)+ = [ Node (v:vs) us | (_,Node vs us) <- map collect ts]++collect :: Tree e (Vertex,Int,Int) -> (Int, Tree e [Vertex])+collect (Node (v,dv,lv) ts) = (lv, Node (v:vs) cs)+ where collected = map collect ts+ vs = concat [ ws | (lw, Node ws _) <- collected, lw<dv]+ cs = concat [ if lw<dv then us else [Node (v:ws) us]+ | (lw, Node ws us) <- collected ]+ + +-}+-------------+-- * Cycamore stuff++put ref item = + do l <- readSTRef ref+ writeSTRef ref (item:l)++allocId uidRef = + do uid <- readSTRef uidRef+ writeSTRef uidRef (uid + 1)+ return uid++simpleGenerator f x = (x, f x)++unfoldManyST :: forall key edgeLabel colour stTag. (Ord key) => (key -> (colour, [(edgeLabel, key)]))+ -> [key] -> ST stTag ([Vertex], ColouredGraph colour edgeLabel)+unfoldManyST gen seeds =+ do mtab <- newSTRef M.empty+ allNodes <- newSTRef []+ uidRef <- newSTRef firstId+ let -- cyc :: a -> ST s Vertex+ cyc src = + do probe <- memTabFind mtab src+ case probe of+ Just result -> return result+ Nothing -> do+ v <- allocId uidRef+ memTabBind src v mtab + let (lab, deps) = gen src+ ws <- mapM (cyc . snd) deps+ let res = (v, lab, [(fst d, w) | d <- deps | w <- ws])+ put allNodes res+ return v+ mapM_ cyc seeds+ list <- readSTRef allNodes+ seedsResult <- (return . map fromJust) =<< mapM (memTabFind mtab) seeds+ lastId <- readSTRef uidRef+ let cycamore = array (firstId, lastId-1) [(i, k) | (i, a, k) <- list]+ let labels = array (firstId, lastId-1) [(i, a) | (i, a, k) <- list]+ return (seedsResult, ColouredGraph cycamore (labels!))+ where firstId = 0::Vertex+ memTabFind mt key = return . M.lookup key =<< readSTRef mt+ memTabBind key val mt = modifySTRef mt (M.insert key val)++unfold :: forall key edgeLabel colour stTag. (Ord key) => (key -> (colour, [(edgeLabel, key)]))+ -> key -> (Vertex, ColouredGraph colour edgeLabel)+unfold f r = (r', res)+ where ([r'], res) = unfoldMany f [r]++unfoldMany :: forall key edgeLabel colour stTag. (Ord key) => (key -> (colour, [(edgeLabel, key)]))+ -> [key] -> ([Vertex], ColouredGraph colour edgeLabel)+unfoldMany f roots = runST (unfoldManyST f roots)++fold' :: Eq c => c -> (Vertex -> [(b,c)] -> c) -> Graph b -> Vertex -> c+fold' z f gr v = scan' z f gr v++scan' :: Eq c => c -> (Vertex -> [(b,c)] -> c) -> Graph b -> Colouring c+scan' bot f gr = (finalTbl !)+ where finalTbl = fixedPoint updateTbl initialTbl+ initialTbl = listArray bnds (replicate (rangeSize bnds) bot)+ + fixedPoint f x = fp x+ where fp z = if z == z' then z else fp z'+ where z' = f z+ updateTbl tbl = listArray bnds $ map recompute $ vertices gr+ where recompute v = f v [(b, tbl!k) | (b, k) <- gr!v]+ bnds = bounds gr++scan :: Eq c => c -> (a -> [(e,c)] -> c) -> ColouredGraph a e -> ColouredGraph c e+scan bot f (ColouredGraph gr a) = ColouredGraph gr (scan' bot f' gr)+ where f' v kids = f (a v) kids+
+ LICENSE view
@@ -0,0 +1,24 @@+Copyright (c) <year>, <copyright holder>+All rights reserved.++Redistribution and use in source and binary forms, with or without+modification, are permitted provided that the following conditions are met:+ * Redistributions of source code must retain the above copyright+ notice, this list of conditions and the following disclaimer.+ * Redistributions in binary form must reproduce the above copyright+ notice, this list of conditions and the following disclaimer in the+ documentation and/or other materials provided with the distribution.+ * Neither the name of the <organization> nor the+ names of its contributors may be used to endorse or promote products+ derived from this software without specific prior written permission.++THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE+DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY+DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ labeled-graph.cabal view
@@ -0,0 +1,17 @@+name: labeled-graph+version: 1.0.0.0+license: BSD3+license-file: LICENSE+maintainer: jeanphilippe.bernardy@gmail.com+synopsis: Labeled graph structure+category: Data Structures+description:+ Labeled tree structure, on the model of the standard Data.Graph+build-type: Simple+cabal-version: >=1.6++Library + build-depends: base >= 1 && < 6+ build-depends: labeled-tree >= 1 && < 1000+ exposed-modules:+ Data.LabeledGraph