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