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 where
- AcyclicSCC vertex
- NECyclicSCC !(NonEmpty vertex)
- pattern CyclicSCC :: [vertex] -> SCC 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 #
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
(IsNode a, Binary a, Show (Key a)) => Binary (Graph a) Source #
Instance details Defined in Distribution.Compat.Graph Methods put :: Graph a -> Put Source # get :: Get (Graph a) Source # putList :: [Graph a] -> Put Source #
(NFData a, NFData (Key a)) => NFData (Graph a) Source #
Instance details Defined in Distribution.Compat.Graph Methods rnf :: Graph a -> () Source #
(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 #
(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 #

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
Instance details Defined in Distribution.Types.InstalledPackageInfo type Key InstalledPackageInfo = UnitId

Methods

nodeKey :: InstalledPackageInfo -> Key InstalledPackageInfo Source #

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

Ord k => IsNode (Node k a) Source #

Instance details

Defined in Distribution.Compat.Graph

Associated Types

type Key (Node k a)
Instance details Defined in Distribution.Compat.Graph type Key (Node k a) = k

Methods

nodeKey :: Node k a -> Key (Node k a) Source #

nodeNeighbors :: Node k a -> [Key (Node k a)] 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)
Instance details Defined in Distribution.Compat.Graph type Key (Either a b) = Key a

Methods

nodeKey :: Either a b -> Key (Either a b) Source #

nodeNeighbors :: Either a b -> [Key (Either a b)] 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 Source #

Strongly connected component.

Constructors

AcyclicSCC vertex

A single vertex that is not in any cycle.

NECyclicSCC !(NonEmpty vertex)

A maximal set of mutually reachable vertices.

Since: containers-0.7.0

Bundled Patterns

pattern CyclicSCC :: [vertex] -> SCC vertex

Partial pattern synonym for backward compatibility with containers < 0.7.

Instances

Instances details

Foldable1 SCC

Since: containers-0.7.0

Instance details

Defined in Data.Graph

Methods

fold1 :: Semigroup m => SCC m -> m Source #

foldMap1 :: Semigroup m => (a -> m) -> SCC a -> m Source #

foldMap1' :: Semigroup m => (a -> m) -> SCC a -> m Source #

toNonEmpty :: SCC a -> NonEmpty a Source #

maximum :: Ord a => SCC a -> a Source #

minimum :: Ord a => SCC a -> a Source #

head :: SCC a -> a Source #

last :: SCC a -> a Source #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> SCC a -> b Source #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> SCC a -> b Source #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> SCC a -> b Source #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> SCC a -> b Source #

Eq1 SCC

Since: containers-0.5.9

Instance details

Defined in Data.Graph

Methods

liftEq :: (a -> b -> Bool) -> SCC a -> SCC b -> Bool Source #

Read1 SCC

Since: containers-0.5.9

Instance details

Defined in Data.Graph

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (SCC a) Source #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [SCC a] Source #

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (SCC a) Source #

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [SCC a] Source #

Show1 SCC

Since: containers-0.5.9

Instance details

Defined in Data.Graph

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> SCC a -> ShowS Source #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [SCC a] -> ShowS Source #

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) #

Generic1 SCC

Instance details

Defined in Data.Graph

Associated Types

type Rep1 SCC

Since: containers-0.5.9

Instance details

Defined in Data.Graph

type Rep1 SCC = D1 ('MetaData "SCC" "Data.Graph" "containers-0.7-c801" 'False) (C1 ('MetaCons "AcyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "NECyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'SourceUnpack 'SourceStrict 'DecidedUnpack) (Rec1 NonEmpty)))

Methods

from1 :: SCC a -> Rep1 SCC a #

to1 :: Rep1 SCC a -> SCC a #

Lift vertex => Lift (SCC vertex :: Type)

Since: containers-0.6.6

Instance details

Defined in Data.Graph

Methods

lift :: Quote m => SCC vertex -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => SCC vertex -> Code m (SCC vertex)

NFData a => NFData (SCC a)

Instance details

Defined in Data.Graph

Methods

rnf :: SCC a -> () Source #

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) #

Generic (SCC vertex)

Instance details

Defined in Data.Graph

Associated Types

type Rep (SCC vertex)

Since: containers-0.5.9

Instance details

Defined in Data.Graph

type Rep (SCC vertex) = D1 ('MetaData "SCC" "Data.Graph" "containers-0.7-c801" 'False) (C1 ('MetaCons "AcyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 vertex)) :+: C1 ('MetaCons "NECyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'SourceUnpack 'SourceStrict 'DecidedUnpack) (Rec0 (NonEmpty vertex))))

Methods

from :: SCC vertex -> Rep (SCC vertex) x #

to :: Rep (SCC vertex) x -> 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 #

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 #

type Rep1 SCC

Since: containers-0.5.9

Instance details

Defined in Data.Graph

type Rep1 SCC = D1 ('MetaData "SCC" "Data.Graph" "containers-0.7-c801" 'False) (C1 ('MetaCons "AcyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "NECyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'SourceUnpack 'SourceStrict 'DecidedUnpack) (Rec1 NonEmpty)))

type Rep (SCC vertex)

Since: containers-0.5.9

Instance details

Defined in Data.Graph

type Rep (SCC vertex) = D1 ('MetaData "SCC" "Data.Graph" "containers-0.7-c801" 'False) (C1 ('MetaCons "AcyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 vertex)) :+: C1 ('MetaCons "NECyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'SourceUnpack 'SourceStrict 'DecidedUnpack) (Rec0 (NonEmpty vertex))))

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).