Copyright	(c) The University of Glasgow 2002
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell98

Data.Graph

Contents

External interface
Graphs
- Building graphs
- Graph properties
Algorithms

Description

A version of the graph algorithms described in:

Structuring Depth-First Search Algorithms in Haskell, by David King and John Launchbury.

Synopsis

External interface

stronglyConnComp Source #

Arguments

:: 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]

The strongly connected components of a directed graph, topologically sorted.

stronglyConnCompR Source #

Arguments

:: 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

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.

data SCC vertex Source #

Strongly connected component.

Constructors

AcyclicSCC vertex	A single vertex that is not in any cycle.
CyclicSCC [vertex]	A maximal set of mutually reachable vertices.

Instances

Functor SCC Source #	Since: 0.5.4
Methods fmap :: (a -> b) -> SCC a -> SCC b # (<$) :: a -> SCC b -> SCC a #
Foldable SCC Source #	Since: 0.5.9
Methods fold :: Monoid m => SCC m -> m # foldMap :: Monoid m => (a -> m) -> SCC a -> m # foldr :: (a -> b -> b) -> b -> SCC a -> b # foldr' :: (a -> b -> b) -> b -> SCC a -> b # foldl :: (b -> a -> b) -> b -> SCC a -> b # foldl' :: (b -> a -> b) -> b -> SCC a -> b # foldr1 :: (a -> a -> a) -> SCC a -> a # foldl1 :: (a -> a -> a) -> SCC a -> a # toList :: SCC a -> [a] # null :: SCC a -> Bool # length :: SCC a -> Int # elem :: Eq a => a -> SCC a -> Bool # maximum :: Ord a => SCC a -> a # minimum :: Ord a => SCC a -> a # sum :: Num a => SCC a -> a # product :: Num a => SCC a -> a #
Traversable SCC Source #	Since: 0.5.9
Methods traverse :: Applicative f => (a -> f b) -> SCC a -> f (SCC b) # sequenceA :: Applicative f => SCC (f a) -> f (SCC a) # mapM :: Monad m => (a -> m b) -> SCC a -> m (SCC b) # sequence :: Monad m => SCC (m a) -> m (SCC a) #
Generic1 SCC Source #
Associated Types type Rep1 (SCC :: * -> ) :: -> * # Methods from1 :: SCC a -> Rep1 SCC a # to1 :: Rep1 SCC a -> SCC a #
Eq1 SCC Source #	Since: 0.5.9
Methods liftEq :: (a -> b -> Bool) -> SCC a -> SCC b -> Bool #
Read1 SCC Source #	Since: 0.5.9
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (SCC a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [SCC a] #
Show1 SCC Source #	Since: 0.5.9
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> SCC a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [SCC a] -> ShowS #
Eq vertex => Eq (SCC vertex) Source #
Methods (==) :: SCC vertex -> SCC vertex -> Bool # (/=) :: SCC vertex -> SCC vertex -> Bool #
Data vertex => Data (SCC vertex) Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> SCC vertex -> c (SCC vertex) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (SCC vertex) # toConstr :: SCC vertex -> Constr # dataTypeOf :: SCC vertex -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (SCC vertex)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (SCC vertex)) # gmapT :: (forall b. Data b => b -> b) -> SCC vertex -> SCC vertex # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> SCC vertex -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> SCC vertex -> r # gmapQ :: (forall d. Data d => d -> u) -> SCC vertex -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> SCC vertex -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) #
Read vertex => Read (SCC vertex) Source #
Methods readsPrec :: Int -> ReadS (SCC vertex) # readList :: ReadS [SCC vertex] # readPrec :: ReadPrec (SCC vertex) # readListPrec :: ReadPrec [SCC vertex] #
Show vertex => Show (SCC vertex) Source #
Methods showsPrec :: Int -> SCC vertex -> ShowS # show :: SCC vertex -> String # showList :: [SCC vertex] -> ShowS #
Generic (SCC vertex) Source #
Associated Types type Rep (SCC vertex) :: * -> * # Methods from :: SCC vertex -> Rep (SCC vertex) x # to :: Rep (SCC vertex) x -> SCC vertex #
NFData a => NFData (SCC a) Source #
Methods rnf :: SCC a -> () #
type Rep1 SCC Source #
type Rep1 SCC = D1 (MetaData "SCC" "Data.Graph" "containers-0.5.11.0-2rqg2XomGs1D7TicQqCxiI" False) ((:+:) (C1 (MetaCons "AcyclicSCC" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) (C1 (MetaCons "CyclicSCC" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 []))))
type Rep (SCC vertex) Source #
type Rep (SCC vertex) = D1 (MetaData "SCC" "Data.Graph" "containers-0.5.11.0-2rqg2XomGs1D7TicQqCxiI" False) ((:+:) (C1 (MetaCons "AcyclicSCC" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 vertex))) (C1 (MetaCons "CyclicSCC" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [vertex]))))

flattenSCC :: SCC vertex -> [vertex] Source #

The vertices of a strongly connected component.

flattenSCCs :: [SCC a] -> [a] Source #

The vertices of a list of strongly connected components.

Graphs

type Graph = Table [Vertex] Source #

Adjacency list representation of a graph, mapping each vertex to its list of successors.

type Table a = Array Vertex a Source #

Table indexed by a contiguous set of vertices.

type Bounds = (Vertex, Vertex) Source #

The bounds of a Table.

type Edge = (Vertex, Vertex) Source #

An edge from the first vertex to the second.

type Vertex = Int Source #

Abstract representation of vertices.

Building graphs

graphFromEdges :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex) Source #

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' :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key])) Source #

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.

buildG :: Bounds -> [Edge] -> Graph Source #

Build a graph from a list of edges.

transposeG :: Graph -> Graph Source #

The graph obtained by reversing all edges.

Graph properties

vertices :: Graph -> [Vertex] Source #

All vertices of a graph.

edges :: Graph -> [Edge] Source #

All edges of a graph.

outdegree :: Graph -> Table Int Source #

A table of the count of edges from each node.

indegree :: Graph -> Table Int Source #

A table of the count of edges into each node.

Algorithms

dfs :: Graph -> [Vertex] -> Forest Vertex Source #

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.

dff :: Graph -> Forest Vertex Source #

A spanning forest of the graph, obtained from a depth-first search of the graph starting from each vertex in an unspecified order.

topSort :: Graph -> [Vertex] Source #

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.

components :: Graph -> Forest Vertex Source #

The connected components of a graph. Two vertices are connected if there is a path between them, traversing edges in either direction.

scc :: Graph -> Forest Vertex Source #

The strongly connected components of a graph.

bcc :: Graph -> Forest [Vertex] Source #

The biconnected components of a graph. An undirected graph is biconnected if the deletion of any vertex leaves it connected.

reachable :: Graph -> Vertex -> [Vertex] Source #

A list of vertices reachable from a given vertex.

path :: Graph -> Vertex -> Vertex -> Bool Source #

Is the second vertex reachable from the first?

module Data.Tree