Copyright	(c) Edward Z. Yang 2016
License	BSD3
Maintainer	cabal-dev@haskell.org
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Distribution.Compat.Graph

Contents

Graph type
Query
Construction
Combine
Graph algorithms
Conversions
Node type

Description

A data type representing directed graphs, backed by Data.Graph. It is strict in the node type.

This is an alternative interface to Data.Graph. In this interface, nodes (identified by the IsNode type class) are associated with a key and record the keys of their neighbors. This interface is more convenient than Graph, which requires vertices to be explicitly handled by integer indexes.

The current implementation has somewhat peculiar performance characteristics. The asymptotics of all map-like operations mirror their counterparts in Data.Map. However, to perform a graph operation, we first must build the Data.Graph representation, an operation that takes O(V + E log V). However, this operation can be amortized across all queries on that particular graph.

Some nodes may be broken, i.e., refer to neighbors which are not stored in the graph. In our graph algorithms, we transparently ignore such edges; however, you can easily query for the broken vertices of a graph using broken (and should, e.g., to ensure that a closure of a graph is well-formed.) It's possible to take a closed subset of a broken graph and get a well-formed graph.

Synopsis

data Graph a
class Ord (Key a) => IsNode a where
- type Key a
- nodeKey :: a -> Key a
- nodeNeighbors :: a -> [Key a]
null :: Graph a -> Bool
size :: Graph a -> Int
member :: IsNode a => Key a -> Graph a -> Bool
lookup :: IsNode a => Key a -> Graph a -> Maybe a
empty :: IsNode a => Graph a
insert :: IsNode a => a -> Graph a -> Graph a
deleteKey :: IsNode a => Key a -> Graph a -> Graph a
deleteLookup :: IsNode a => Key a -> Graph a -> (Maybe a, Graph a)
unionLeft :: IsNode a => Graph a -> Graph a -> Graph a
unionRight :: IsNode a => Graph a -> Graph a -> Graph a
stronglyConnComp :: Graph a -> [SCC a]
data SCC vertex
- = AcyclicSCC vertex
- | CyclicSCC [vertex]
cycles :: Graph a -> [[a]]
broken :: Graph a -> [(a, [Key a])]
neighbors :: Graph a -> Key a -> Maybe [a]
revNeighbors :: Graph a -> Key a -> Maybe [a]
closure :: Graph a -> [Key a] -> Maybe [a]
revClosure :: Graph a -> [Key a] -> Maybe [a]
topSort :: Graph a -> [a]
revTopSort :: Graph a -> [a]
toMap :: Graph a -> Map (Key a) a
fromDistinctList :: (IsNode a, Show (Key a)) => [a] -> Graph a
toList :: Graph a -> [a]
keys :: Graph a -> [Key a]
keysSet :: Graph a -> Set (Key a)
toGraph :: Graph a -> (Graph, Vertex -> a, Key a -> Maybe Vertex)
data Node k a = N a k [k]
nodeValue :: Node k a -> a

Graph type

data Graph a Source #

A graph of nodes a. The nodes are expected to have instance of class IsNode.

Instances

Instances details

Foldable Graph Source #
Instance details Defined in Distribution.Compat.Graph Methods fold :: Monoid m => Graph m -> m # foldMap :: Monoid m => (a -> m) -> Graph a -> m # foldMap' :: Monoid m => (a -> m) -> Graph a -> m # foldr :: (a -> b -> b) -> b -> Graph a -> b # foldr' :: (a -> b -> b) -> b -> Graph a -> b # foldl :: (b -> a -> b) -> b -> Graph a -> b # foldl' :: (b -> a -> b) -> b -> Graph a -> b # foldr1 :: (a -> a -> a) -> Graph a -> a # foldl1 :: (a -> a -> a) -> Graph a -> a # toList :: Graph a -> [a] # null :: Graph a -> Bool # length :: Graph a -> Int # elem :: Eq a => a -> Graph a -> Bool # maximum :: Ord a => Graph a -> a # minimum :: Ord a => Graph a -> a # sum :: Num a => Graph a -> a # product :: Num a => Graph a -> a #
(Eq (Key a), Eq a) => Eq (Graph a) Source #
Instance details Defined in Distribution.Compat.Graph Methods (==) :: Graph a -> Graph a -> Bool # (/=) :: Graph a -> Graph a -> Bool #
(IsNode a, Read a, Show (Key a)) => Read (Graph a) Source #
Instance details Defined in Distribution.Compat.Graph Methods readsPrec :: Int -> ReadS (Graph a) # readList :: ReadS [Graph a] # readPrec :: ReadPrec (Graph a) # readListPrec :: ReadPrec [Graph a] #
Show a => Show (Graph a) Source #
Instance details Defined in Distribution.Compat.Graph Methods showsPrec :: Int -> Graph a -> ShowS # show :: Graph a -> String # showList :: [Graph a] -> ShowS #
(IsNode a, Binary a, Show (Key a)) => Binary (Graph a) Source #
Instance details Defined in Distribution.Compat.Graph Methods put :: Graph a -> Put # get :: Get (Graph a) # putList :: [Graph a] -> Put #
(NFData a, NFData (Key a)) => NFData (Graph a) Source #
Instance details Defined in Distribution.Compat.Graph Methods rnf :: Graph a -> () #
Structured a => Structured (Graph a) Source #
Instance details Defined in Distribution.Compat.Graph Methods structure :: Proxy (Graph a) -> Structure Source # structureHash' :: Tagged (Graph a) MD5

class Ord (Key a) => IsNode a where Source #

The IsNode class is used for datatypes which represent directed graph nodes. A node of type a is associated with some unique key of type Key a; given a node we can determine its key (nodeKey) and the keys of its neighbors (nodeNeighbors).

Associated Types

type Key a Source #

Methods

nodeKey :: a -> Key a Source #

nodeNeighbors :: a -> [Key a] Source #

Instances

Instances details

IsNode InstalledPackageInfo Source #
Instance details Defined in Distribution.Types.InstalledPackageInfo Associated Types type Key InstalledPackageInfo Source # Methods nodeKey :: InstalledPackageInfo -> Key InstalledPackageInfo Source # nodeNeighbors :: InstalledPackageInfo -> [Key InstalledPackageInfo] Source #
(IsNode a, IsNode b, Key a ~ Key b) => IsNode (Either a b) Source #
Instance details Defined in Distribution.Compat.Graph Associated Types type Key (Either a b) Source # Methods nodeKey :: Either a b -> Key (Either a b) Source # nodeNeighbors :: Either a b -> [Key (Either a b)] Source #
Ord k => IsNode (Node k a) Source #
Instance details Defined in Distribution.Compat.Graph Associated Types type Key (Node k a) Source # Methods nodeKey :: Node k a -> Key (Node k a) Source # nodeNeighbors :: Node k a -> [Key (Node k a)] Source #

Query

null :: Graph a -> Bool Source #

O(1). Is the graph empty?

size :: Graph a -> Int Source #

O(1). The number of nodes in the graph.

member :: IsNode a => Key a -> Graph a -> Bool Source #

O(log V). Check if the key is in the graph.

lookup :: IsNode a => Key a -> Graph a -> Maybe a Source #

O(log V). Lookup the node at a key in the graph.

Construction

empty :: IsNode a => Graph a Source #

O(1). The empty graph.

insert :: IsNode a => a -> Graph a -> Graph a Source #

O(log V). Insert a node into a graph.

deleteKey :: IsNode a => Key a -> Graph a -> Graph a Source #

O(log V). Delete the node at a key from the graph.

deleteLookup :: IsNode a => Key a -> Graph a -> (Maybe a, Graph a) Source #

O(log V). Lookup and delete. This function returns the deleted value if it existed.

Combine

unionLeft :: IsNode a => Graph a -> Graph a -> Graph a Source #

O(V + V'). Left-biased union, preferring entries from the first map when conflicts occur.

unionRight :: IsNode a => Graph a -> Graph a -> Graph a Source #

O(V + V'). Right-biased union, preferring entries from the second map when conflicts occur. nodeKey x = nodeKey (f x).

Graph algorithms

stronglyConnComp :: Graph a -> [SCC a] Source #

Ω(V + E). Compute the strongly connected components of a graph. Requires amortized construction of graph.

data SCC vertex #

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

Instances details

Functor SCC	Since: containers-0.5.4
Instance details Defined in Data.Graph Methods fmap :: (a -> b) -> SCC a -> SCC b # (<$) :: a -> SCC b -> SCC a #
Foldable SCC	Since: containers-0.5.9
Instance details Defined in Data.Graph Methods fold :: Monoid m => SCC m -> m # foldMap :: Monoid m => (a -> m) -> SCC a -> 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	Since: containers-0.5.9
Instance details Defined in Data.Graph 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) #
Eq1 SCC	Since: containers-0.5.9
Instance details Defined in Data.Graph Methods liftEq :: (a -> b -> Bool) -> SCC a -> SCC b -> Bool #
Read1 SCC	Since: containers-0.5.9
Instance details Defined in Data.Graph Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (SCC a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [SCC a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (SCC a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [SCC a] #
Show1 SCC	Since: containers-0.5.9
Instance details Defined in Data.Graph 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)	Since: containers-0.5.9
Instance details Defined in Data.Graph Methods (==) :: SCC vertex -> SCC vertex -> Bool # (/=) :: SCC vertex -> SCC vertex -> Bool #
Data vertex => Data (SCC vertex)	Since: containers-0.5.9
Instance details Defined in Data.Graph 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 :: forall r r'. (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)	Since: containers-0.5.9
Instance details Defined in Data.Graph Methods readsPrec :: Int -> ReadS (SCC vertex) # readList :: ReadS [SCC vertex] # readPrec :: ReadPrec (SCC vertex) # readListPrec :: ReadPrec [SCC vertex] #
Show vertex => Show (SCC vertex)	Since: containers-0.5.9
Instance details Defined in Data.Graph Methods showsPrec :: Int -> SCC vertex -> ShowS # show :: SCC vertex -> String # showList :: [SCC vertex] -> ShowS #
Generic (SCC vertex)	Since: containers-0.5.9
Instance details Defined in Data.Graph Associated Types type Rep (SCC vertex) :: Type -> Type # Methods from :: SCC vertex -> Rep (SCC vertex) x # to :: Rep (SCC vertex) x -> SCC vertex #
NFData a => NFData (SCC a)
Instance details Defined in Data.Graph Methods rnf :: SCC a -> () #
Generic1 SCC	Since: containers-0.5.9
Instance details Defined in Data.Graph Associated Types type Rep1 SCC :: k -> Type # Methods from1 :: forall (a :: k). SCC a -> Rep1 SCC a # to1 :: forall (a :: k). Rep1 SCC a -> SCC a #
type Rep (SCC vertex)
Instance details Defined in Data.Graph type Rep (SCC vertex) = D1 ('MetaData "SCC" "Data.Graph" "containers-0.6.2.1" 'False) (C1 ('MetaCons "AcyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 vertex)) :+: C1 ('MetaCons "CyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [vertex])))
type Rep1 SCC
Instance details Defined in Data.Graph type Rep1 SCC = D1 ('MetaData "SCC" "Data.Graph" "containers-0.6.2.1" 'False) (C1 ('MetaCons "AcyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "CyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 [])))

cycles :: Graph a -> [[a]] Source #

Ω(V + E). Compute the cycles of a graph. Requires amortized construction of graph.

broken :: Graph a -> [(a, [Key a])] Source #

O(1). Return a list of nodes paired with their broken neighbors (i.e., neighbor keys which are not in the graph). Requires amortized construction of graph.

neighbors :: Graph a -> Key a -> Maybe [a] Source #

Lookup the immediate neighbors from a key in the graph. Requires amortized construction of graph.

revNeighbors :: Graph a -> Key a -> Maybe [a] Source #

Lookup the immediate reverse neighbors from a key in the graph. Requires amortized construction of graph.

closure :: Graph a -> [Key a] -> Maybe [a] Source #

Compute the subgraph which is the closure of some set of keys. Returns Nothing if one (or more) keys are not present in the graph. Requires amortized construction of graph.

revClosure :: Graph a -> [Key a] -> Maybe [a] Source #

Compute the reverse closure of a graph from some set of keys. Returns Nothing if one (or more) keys are not present in the graph. Requires amortized construction of graph.

topSort :: Graph a -> [a] Source #

Topologically sort the nodes of a graph. Requires amortized construction of graph.

revTopSort :: Graph a -> [a] Source #

Reverse topologically sort the nodes of a graph. Requires amortized construction of graph.

Conversions

Maps

toMap :: Graph a -> Map (Key a) a Source #

O(1). Convert a graph into a map from keys to nodes. The resulting map m is guaranteed to have the property that all ((k,n) -> k == nodeKey n) (toList m).

Lists

fromDistinctList :: (IsNode a, Show (Key a)) => [a] -> Graph a Source #

O(V log V). Convert a list of nodes (with distinct keys) into a graph.

toList :: Graph a -> [a] Source #

O(V). Convert a graph into a list of nodes.

keys :: Graph a -> [Key a] Source #

O(V). Convert a graph into a list of keys.

Sets

keysSet :: Graph a -> Set (Key a) Source #

O(V). Convert a graph into a set of keys.

Graphs

toGraph :: Graph a -> (Graph, Vertex -> a, Key a -> Maybe Vertex) Source #

O(1). Convert a graph into a Graph. Requires amortized construction of graph.

Node type

data Node k a Source #

A simple, trivial data type which admits an IsNode instance.

Constructors

N a k [k]

Instances

Instances details

Functor (Node k) Source #
Instance details Defined in Distribution.Compat.Graph Methods fmap :: (a -> b) -> Node k a -> Node k b # (<$) :: a -> Node k b -> Node k a #
(Eq a, Eq k) => Eq (Node k a) Source #
Instance details Defined in Distribution.Compat.Graph Methods (==) :: Node k a -> Node k a -> Bool # (/=) :: Node k a -> Node k a -> Bool #
(Show a, Show k) => Show (Node k a) Source #
Instance details Defined in Distribution.Compat.Graph Methods showsPrec :: Int -> Node k a -> ShowS # show :: Node k a -> String # showList :: [Node k a] -> ShowS #
Ord k => IsNode (Node k a) Source #
Instance details Defined in Distribution.Compat.Graph Associated Types type Key (Node k a) Source # Methods nodeKey :: Node k a -> Key (Node k a) Source # nodeNeighbors :: Node k a -> [Key (Node k a)] Source #
type Key (Node k a) Source #
Instance details Defined in Distribution.Compat.Graph type Key (Node k a) = k

nodeValue :: Node k a -> a Source #

Get the value from a Node.