bpo-17005: Move topological sort functionality to its own module (GH-20558)

The topological sort functionality that was introduced initially in the
functools module has been moved to a new graphlib module to
better accommodate the new tools and keep the original scope of the
functools module. 

1 files changed, 209 insertions, 0 deletions

diff --git a/Doc/library/graphlib.rst b/Doc/library/graphlib.rst
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+:mod:`graphlib` --- Functionality to operate with graph-like structures
+=========================================================================
+
+.. module:: graphlib
+   :synopsis: Functionality to operate with graph-like structures
+
+
+**Source code:** :source:`Lib/graphlib.py`
+
+.. testsetup:: default
+
+   import graphlib
+   from graphlib import *
+
+--------------
+
+
+.. class:: TopologicalSorter(graph=None)
+
+   Provides functionality to topologically sort a graph of hashable nodes.
+
+   A topological order is a linear ordering of the vertices in a graph such that
+   for every directed edge u -> v from vertex u to vertex v, vertex u comes
+   before vertex v in the ordering. For instance, the vertices of the graph may
+   represent tasks to be performed, and the edges may represent constraints that
+   one task must be performed before another; in this example, a topological
+   ordering is just a valid sequence for the tasks. A complete topological
+   ordering is possible if and only if the graph has no directed cycles, that
+   is, if it is a directed acyclic graph.
+
+   If the optional *graph* argument is provided it must be a dictionary
+   representing a directed acyclic graph where the keys are nodes and the values
+   are iterables of all predecessors of that node in the graph (the nodes that
+   have edges that point to the value in the key). Additional nodes can be added
+   to the graph using the :meth:`~TopologicalSorter.add` method.
+
+   In the general case, the steps required to perform the sorting of a given
+   graph are as follows:
+
+         * Create an instance of the :class:`TopologicalSorter` with an optional
+           initial graph.
+         * Add additional nodes to the graph.
+         * Call :meth:`~TopologicalSorter.prepare` on the graph.
+         * While :meth:`~TopologicalSorter.is_active` is ``True``, iterate over
+           the nodes returned by :meth:`~TopologicalSorter.get_ready` and
+           process them. Call :meth:`~TopologicalSorter.done` on each node as it
+           finishes processing.
+
+   In case just an immediate sorting of the nodes in the graph is required and
+   no parallelism is involved, the convenience method
+   :meth:`TopologicalSorter.static_order` can be used directly:
+
+   .. doctest::
+
+       >>> graph = {"D": {"B", "C"}, "C": {"A"}, "B": {"A"}}
+       >>> ts = TopologicalSorter(graph)
+       >>> tuple(ts.static_order())
+       ('A', 'C', 'B', 'D')
+
+   The class is designed to easily support parallel processing of the nodes as
+   they become ready. For instance::
+
+       topological_sorter = TopologicalSorter()
+
+       # Add nodes to 'topological_sorter'...
+
+       topological_sorter.prepare()
+       while topological_sorter.is_active():
+           for node in topological_sorter.get_ready():
+               # Worker threads or processes take nodes to work on off the
+               # 'task_queue' queue.
+               task_queue.put(node)
+
+           # When the work for a node is done, workers put the node in
+           # 'finalized_tasks_queue' so we can get more nodes to work on.
+           # The definition of 'is_active()' guarantees that, at this point, at
+           # least one node has been placed on 'task_queue' that hasn't yet
+           # been passed to 'done()', so this blocking 'get()' must (eventually)
+           # succeed.  After calling 'done()', we loop back to call 'get_ready()'
+           # again, so put newly freed nodes on 'task_queue' as soon as
+           # logically possible.
+           node = finalized_tasks_queue.get()
+           topological_sorter.done(node)
+
+   .. method:: add(node, *predecessors)
+
+      Add a new node and its predecessors to the graph. Both the *node* and all
+      elements in *predecessors* must be hashable.
+
+      If called multiple times with the same node argument, the set of
+      dependencies will be the union of all dependencies passed in.
+
+      It is possible to add a node with no dependencies (*predecessors* is not
+      provided) or to provide a dependency twice. If a node that has not been
+      provided before is included among *predecessors* it will be automatically
+      added to the graph with no predecessors of its own.
+
+      Raises :exc:`ValueError` if called after :meth:`~TopologicalSorter.prepare`.
+
+   .. method:: prepare()
+
+      Mark the graph as finished and check for cycles in the graph. If any cycle
+      is detected, :exc:`CycleError` will be raised, but
+      :meth:`~TopologicalSorter.get_ready` can still be used to obtain as many
+      nodes as possible until cycles block more progress. After a call to this
+      function, the graph cannot be modified, and therefore no more nodes can be
+      added using :meth:`~TopologicalSorter.add`.
+
+   .. method:: is_active()
+
+      Returns ``True`` if more progress can be made and ``False`` otherwise.
+      Progress can be made if cycles do not block the resolution and either
+      there are still nodes ready that haven't yet been returned by
+      :meth:`TopologicalSorter.get_ready` or the number of nodes marked
+      :meth:`TopologicalSorter.done` is less than the number that have been
+      returned by :meth:`TopologicalSorter.get_ready`.
+
+      The :meth:`~TopologicalSorter.__bool__` method of this class defers to
+      this function, so instead of::
+
+          if ts.is_active():
+              ...
+
+      if possible to simply do::
+
+          if ts:
+              ...
+
+      Raises :exc:`ValueError` if called without calling
+      :meth:`~TopologicalSorter.prepare` previously.
+
+   .. method:: done(*nodes)
+
+      Marks a set of nodes returned by :meth:`TopologicalSorter.get_ready` as
+      processed, unblocking any successor of each node in *nodes* for being
+      returned in the future by a call to :meth:`TopologicalSorter.get_ready`.
+
+      Raises :exc:`ValueError` if any node in *nodes* has already been marked as
+      processed by a previous call to this method or if a node was not added to
+      the graph by using :meth:`TopologicalSorter.add`, if called without
+      calling :meth:`~TopologicalSorter.prepare` or if node has not yet been
+      returned by :meth:`~TopologicalSorter.get_ready`.
+
+   .. method:: get_ready()
+
+      Returns a ``tuple`` with all the nodes that are ready. Initially it
+      returns all nodes with no predecessors, and once those are marked as
+      processed by calling :meth:`TopologicalSorter.done`, further calls will
+      return all new nodes that have all their predecessors already processed.
+      Once no more progress can be made, empty tuples are returned.
+
+      Raises :exc:`ValueError` if called without calling
+      :meth:`~TopologicalSorter.prepare` previously.
+
+   .. method:: static_order()
+
+      Returns an iterable of nodes in a topological order. Using this method
+      does not require to call :meth:`TopologicalSorter.prepare` or
+      :meth:`TopologicalSorter.done`. This method is equivalent to::
+
+          def static_order(self):
+              self.prepare()
+              while self.is_active():
+                  node_group = self.get_ready()
+                  yield from node_group
+                  self.done(*node_group)
+
+      The particular order that is returned may depend on the specific order in
+      which the items were inserted in the graph. For example:
+
+      .. doctest::
+
+          >>> ts = TopologicalSorter()
+          >>> ts.add(3, 2, 1)
+          >>> ts.add(1, 0)
+          >>> print([*ts.static_order()])
+          [2, 0, 1, 3]
+
+          >>> ts2 = TopologicalSorter()
+          >>> ts2.add(1, 0)
+          >>> ts2.add(3, 2, 1)
+          >>> print([*ts2.static_order()])
+          [0, 2, 1, 3]
+
+      This is due to the fact that "0" and "2" are in the same level in the
+      graph (they would have been returned in the same call to
+      :meth:`~TopologicalSorter.get_ready`) and the order between them is
+      determined by the order of insertion.
+
+
+      If any cycle is detected, :exc:`CycleError` will be raised.
+
+   .. versionadded:: 3.9
+
+
+Exceptions
+----------
+The :mod:`graphlib` module defines the following exception classes:
+
+.. exception:: CycleError
+
+   Subclass of :exc:`ValueError` raised by :meth:`TopologicalSorter.prepare` if cycles exist
+   in the working graph. If multiple cycles exist, only one undefined choice among them will
+   be reported and included in the exception.
+
+   The detected cycle can be accessed via the second element in the :attr:`~CycleError.args`
+   attribute of the exception instance and consists in a list of nodes, such that each node is,
+   in the graph, an immediate predecessor of the next node in the list. In the reported list,
+   the first and the last node will be the same, to make it clear that it is cyclic.
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