Copyright | (c) Edward Z. Yang 2016 |
---|---|
License | BSD3 |
Maintainer | cabal-dev@haskell.org |
Stability | experimental |
Portability | portable |
Safe Haskell | Safe-Inferred |
Language | Haskell2010 |
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
A graph of nodes a
. The nodes are expected to have instance
of class IsNode
.
Instances
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
; given a node we can determine its key (Key
anodeKey
)
and the keys of its neighbors (nodeNeighbors
).
Query
lookup :: IsNode a => Key a -> Graph a -> Maybe a Source #
O(log V). Lookup the node at a key in the graph.
Construction
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.
Graph algorithms
stronglyConnComp :: Graph a -> [SCC a] Source #
Ω(V + E). Compute the strongly connected components of a graph. Requires amortized construction of graph.
Strongly connected component.
AcyclicSCC vertex | A single vertex that is not in any cycle. |
CyclicSCC [vertex] | A maximal set of mutually reachable vertices. |
Instances
Foldable SCC | Since: containers-0.5.9 |
Defined in Data.Graph fold :: Monoid m => SCC m -> m Source # foldMap :: Monoid m => (a -> m) -> SCC a -> m Source # foldMap' :: Monoid m => (a -> m) -> SCC a -> m Source # foldr :: (a -> b -> b) -> b -> SCC a -> b Source # foldr' :: (a -> b -> b) -> b -> SCC a -> b Source # foldl :: (b -> a -> b) -> b -> SCC a -> b Source # foldl' :: (b -> a -> b) -> b -> SCC a -> b Source # foldr1 :: (a -> a -> a) -> SCC a -> a Source # foldl1 :: (a -> a -> a) -> SCC a -> a Source # toList :: SCC a -> [a] Source # null :: SCC a -> Bool Source # length :: SCC a -> Int Source # elem :: Eq a => a -> SCC a -> Bool Source # maximum :: Ord a => SCC a -> a Source # minimum :: Ord a => SCC a -> a Source # | |
Eq1 SCC | Since: containers-0.5.9 |
Read1 SCC | Since: containers-0.5.9 |
Defined in Data.Graph | |
Show1 SCC | Since: containers-0.5.9 |
Traversable SCC | Since: containers-0.5.9 |
Functor SCC | Since: containers-0.5.4 |
Generic1 SCC | |
Lift vertex => Lift (SCC vertex :: Type) | Since: containers-0.6.6 |
Data vertex => Data (SCC vertex) | Since: containers-0.5.9 |
Defined in Data.Graph gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> SCC vertex -> c (SCC vertex) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (SCC vertex) Source # toConstr :: SCC vertex -> Constr Source # dataTypeOf :: SCC vertex -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (SCC vertex)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (SCC vertex)) Source # gmapT :: (forall b. Data b => b -> b) -> SCC vertex -> SCC vertex Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> SCC vertex -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> SCC vertex -> r Source # gmapQ :: (forall d. Data d => d -> u) -> SCC vertex -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> SCC vertex -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) Source # | |
Generic (SCC vertex) | |
Read vertex => Read (SCC vertex) | Since: containers-0.5.9 |
Show vertex => Show (SCC vertex) | Since: containers-0.5.9 |
NFData a => NFData (SCC a) | |
Defined in Data.Graph | |
Eq vertex => Eq (SCC vertex) | Since: containers-0.5.9 |
type Rep1 SCC | Since: containers-0.5.9 |
Defined in Data.Graph type Rep1 SCC = D1 ('MetaData "SCC" "Data.Graph" "containers-0.6.7" '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 List))) | |
type Rep (SCC vertex) | Since: containers-0.5.9 |
Defined in Data.Graph type Rep (SCC vertex) = D1 ('MetaData "SCC" "Data.Graph" "containers-0.6.7" '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]))) |
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
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.
Sets
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.