bpo-17005: Add a topological sort algorithm

Doc/library/functools.rst

@@ -8,10 +8,16 @@
 .. moduleauthor:: Raymond Hettinger <[email protected]>
 .. moduleauthor:: Nick Coghlan <[email protected]>
 .. moduleauthor:: Łukasz Langa <[email protected]>
+.. moduleauthor:: Pablo Galindo <[email protected]>
 .. sectionauthor:: Peter Harris <[email protected]>
 
 **Source code:** :source:`Lib/functools.py`
 
+.. testsetup:: default
+
+   import functools
+   from functools import *
+
 --------------
 
 The :mod:`functools` module is for higher-order functions: functions that act on
@@ -512,6 +518,192 @@ The :mod:`functools` module defines the following functions:
    .. versionadded:: 3.8
 
 
+.. 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. For example, this method can be used to implement a simple
+   version of the C3 linearization algorithm used by Python to calculate the Method
+   Resolution Order (MRO) of a derived class:
+
+   .. doctest::
+
+       >>> class A: pass
+       >>> class B(A): pass
+       >>> class C(A): pass
+       >>> class D(B, C): pass
+
+       >>> D.__mro__
+       (<class 'D'>, <class 'B'>, <class 'C'>, <class 'A'>, <class 'object'>)
+
+       >>> graph = {D: {B, C}, C: {A}, B: {A}, A:{object}}
+       >>> ts = TopologicalSorter(graph)
+       >>> topological_order = tuple(ts.static_order())
+       >>> tuple(reversed(topological_order))
+       (<class 'D'>, <class 'B'>, <class 'C'>, <class 'A'>, <class 'object'>)
+
+   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.
+      made.
+
+      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
+
+
 .. function:: update_wrapper(wrapper, wrapped, assigned=WRAPPER_ASSIGNMENTS, updated=WRAPPER_UPDATES)
 
    Update a *wrapper* function to look like the *wrapped* function. The optional
@@ -621,3 +813,19 @@ differences.  For instance, the :attr:`~definition.__name__` and :attr:`__doc__`
 are not created automatically.  Also, :class:`partial` objects defined in
 classes behave like static methods and do not transform into bound methods
 during instance attribute look-up.
+
+
+Exceptions
+----------
+The :mod:`functools` 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.

Doc/whatsnew/3.9.rst

@@ -166,6 +166,13 @@ ftplib
 if the given timeout for their constructor is zero to prevent the creation of
 a non-blocking socket. (Contributed by Dong-hee Na in :issue:`39259`.)
 
+functools
+---------
+
+Add the :class:`functools.TopologicalSorter` class to offer functionality to perform
+topological sorting of graphs. (Contributed by Pablo Galindo, Tim Peters and Larry
+Hastings in :issue:`17005`.)
+
 gc
 --