Data.Graph.Inductive.Query.DFS

Depth-first search algorithms.

Names consist of:

1. An optional direction parameter, specifying which nodes to visit next.

u

undirectional: ignore edge direction

r

reversed: walk edges in reverse

x

user defined: speciy which paths to follow

1. "df" for depth-first

2. A structure parameter, specifying the type of the result.

   s

   Flat list of results

   f

   Structured Tree of results

3. An optional "With", which instead of putting the found nodes directly into the result, adds the result of a computation on them into it.
4. An optional prime character, in which case all nodes of the graph will be visited, instead of a user-given subset.

Documentation

type CFun a b c = Context a b -> c

Standard

dfs :: Graph gr => [Node] -> gr a b -> [Node]

Depth-first search.

dfs' :: Graph gr => gr a b -> [Node]

dff :: Graph gr => [Node] -> gr a b -> [Tree Node]

Directed depth-first forest.

dff' :: Graph gr => gr a b -> [Tree Node]

dfsWith :: Graph gr => CFun a b c -> [Node] -> gr a b -> [c]

dfsWith' :: Graph gr => CFun a b c -> gr a b -> [c]

dffWith :: Graph gr => CFun a b c -> [Node] -> gr a b -> [Tree c]

dffWith' :: Graph gr => CFun a b c -> gr a b -> [Tree c]

xdfsWith

Arguments

:: Graph gr

=> CFun a b [Node]

Mapping from a node to its neighbours to be visited as well. suc' for example makes xdfsWith traverse the graph following the edge directions, while pre' means reversed directions.

-> CFun a b c

Mapping from the Context of a node to a result value.

-> [Node]

Nodes to be visited.

-> gr a b

-> [c]

Most general DFS algorithm to create a list of results. The other list-returning functions such as dfs are all defined in terms of this one.

xdfsWith d f vs = preorderF . xdffWith d f vs

xdfWith :: Graph gr => CFun a b [Node] -> CFun a b c -> [Node] -> gr a b -> ([Tree c], gr a b)

Most general DFS algorithm to create a forest of results, otherwise very similar to xdfsWith. The other forest-returning functions such as dff are all defined in terms of this one.

xdffWith :: Graph gr => CFun a b [Node] -> CFun a b c -> [Node] -> gr a b -> [Tree c]

Discard the graph part of the result of xdfWith.

xdffWith d f vs g = fst (xdfWith d f vs g)

Undirected

udfs :: Graph gr => [Node] -> gr a b -> [Node]

Undirected depth-first search, obtained by following edges regardless of their direction.

udfs' :: Graph gr => gr a b -> [Node]

udff :: Graph gr => [Node] -> gr a b -> [Tree Node]

Undirected depth-first forest, obtained by following edges regardless of their direction.

udff' :: Graph gr => gr a b -> [Tree Node]

udffWith :: Graph gr => CFun a b c -> [Node] -> gr a b -> [Tree c]

udffWith' :: Graph gr => CFun a b c -> gr a b -> [Tree c]

Reversed

rdff :: Graph gr => [Node] -> gr a b -> [Tree Node]

Reverse depth-first forest, obtained by following predecessors.

rdff' :: Graph gr => gr a b -> [Tree Node]

rdfs :: Graph gr => [Node] -> gr a b -> [Node]

Reverse depth-first search, obtained by following predecessors.

rdfs' :: Graph gr => gr a b -> [Node]

rdffWith :: Graph gr => CFun a b c -> [Node] -> gr a b -> [Tree c]

rdffWith' :: Graph gr => CFun a b c -> gr a b -> [Tree c]

Applications of depth first search/forest

topsort :: Graph gr => gr a b -> [Node]

Topological sorting, i.e. a list of Nodes so that if there's an edge between a source and a target node, the source appears earlier in the result.

topsort' :: Graph gr => gr a b -> [a]

topsort, returning only the labels of the nodes.

scc :: Graph gr => gr a b -> [[Node]]

Collection of strongly connected components

reachable :: Graph gr => Node -> gr a b -> [Node]

Collection of nodes reachable from a starting point.

Applications of undirected depth first search/forest

components :: Graph gr => gr a b -> [[Node]]

Collection of connected components

noComponents :: Graph gr => gr a b -> Int

Number of connected components

isConnected :: Graph gr => gr a b -> Bool

Is the graph connected?

condensation :: Graph gr => gr a b -> gr [Node] ()

The condensation of the given graph, i.e., the graph of its strongly connected components.