: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 :term:`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 :term:`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():
              ...

      it is 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 iterator object which will iterate over nodes in a topological
      order. When using this method, :meth:`~TopologicalSorter.prepare` and
      :meth:`~TopologicalSorter.done` should not be called. 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.