Copyright | (c) Edward Z. Yang 2016 |
---|---|

License | BSD3 |

Maintainer | cabal-dev@haskell.org |

Stability | experimental |

Portability | portable |

Safe Haskell | None |

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`

a`nodeKey`

)
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 |
| ||||

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 |
| ||||

Read1 SCC |
| ||||

Defined in Data.Graph | |||||

Show1 SCC |
| ||||

Traversable SCC |
| ||||

Functor SCC |
| ||||

Generic1 SCC | |||||

Defined in Data.Graph
| |||||

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

Data vertex => Data (SCC vertex) |
| ||||

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) | |||||

Defined in Data.Graph
| |||||

Read vertex => Read (SCC vertex) |
| ||||

Show vertex => Show (SCC vertex) |
| ||||

NFData a => NFData (SCC a) | |||||

Defined in Data.Graph | |||||

Eq vertex => Eq (SCC vertex) |
| ||||

type Rep1 SCC |
| ||||

Defined in Data.Graph type Rep1 SCC = D1 ('MetaData "SCC" "Data.Graph" "containers-0.6.8-7764" '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 []))) | |||||

type Rep (SCC vertex) |
| ||||

Defined in Data.Graph type Rep (SCC vertex) = D1 ('MetaData "SCC" "Data.Graph" "containers-0.6.8-7764" '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.