This SRFI has complex authorship. The original specification and corresponding implementation were written by Shiro Kawai for Gauche. This SRFI was written by John Cowan, but its design is based on the Gauche specification. The implementation was written principally by Arvydas Silanskas based on the Gauche implementation, and then modified further by John Cowan to match this SRFI.
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Topological sorting is an algorithm that takes a graph consisting of nodes and other nodes that depend on them, forming a partial order, and returns a list representing a total ordering of the graph. If the graph is cyclic, the topological sort will fail, and an error will be signaled.
None at present.
Consider the following graph representing steps to be performed:
This graph means that (among other things) steps 5 and 7 must be performed before step 11, and step 11 must be performed before steps 2, 9, and 10. By topologically sorting this graph, we get one possible total ordering of the steps that satisfies the partial order.
(topological-sort graph =
Topologically sorts graph,
which is a list of connections. Each connection is a list of the form
(node dependency dependency ...
meaning that dependencies are dependent on node.
The optional argument = specifies the identity relation
between nodes; it defaults to
It is an error if the same node (in the sense of =) appears in more than one connection.
If graph is circular, an error satisfying
circular-graph? is signaled.
The graph shown above can be represented as
((5 11) (7 11 8) (3 8 10) (11 2 9 10) (8 9)).
One possible result of applying `topological-sort` to this graph
is the list
(3 7 5 11 2 8 10 9), meaning that
performing steps 3, 7, 5, ..., 10, 9 in that order will satisfy
the partial ordering of the graph.
The sample implementation is available in the SRFI 234 repository repository.
Credit is due to the members of the SRFI 234 mailing list.
The graph is in the public domain and is available at https://upload.wikimedia.org/wikipedia/commons/0/03/Directed_acyclic_graph_2.svg.
© 2022 John Cowan, Arvydas Silanskas, Shiro Kawai.
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