"graphlib" --- Functionality to operate with graph-like structures
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**Source code:** Lib/graphlib.py

======================================================================

class graphlib.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
   "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 "TopologicalSorter" with an optional
     initial graph.

   * Add additional nodes to the graph.

   * Call "prepare()" on the graph.

   * While "is_active()" is "True", iterate over the nodes returned by
     "get_ready()" and process them. Call "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
   "TopologicalSorter.static_order()" can be used directly:

      >>> 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)

   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 "ValueError" if called after "prepare()".

   prepare()

      Mark the graph as finished and check for cycles in the graph. If
      any cycle is detected, "CycleError" will be raised, but
      "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 "add()".

   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 "TopologicalSorter.get_ready()" or the
      number of nodes marked "TopologicalSorter.done()" is less than
      the number that have been returned by
      "TopologicalSorter.get_ready()".

      The "__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 "ValueError" if called without calling "prepare()"
      previously.

   done(*nodes)

      Marks a set of nodes returned by "TopologicalSorter.get_ready()"
      as processed, unblocking any successor of each node in *nodes*
      for being returned in the future by a call to
      "TopologicalSorter.get_ready()".

      Raises "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
      "TopologicalSorter.add()", if called without calling "prepare()"
      or if node has not yet been returned by "get_ready()".

   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 "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 "ValueError" if called without calling "prepare()"
      previously.

   static_order()

      Returns an iterator object which will iterate over nodes in a
      topological order. When using this method, "prepare()" and
      "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:

         >>> 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
      "get_ready()") and the order between them is determined by the
      order of insertion.

      If any cycle is detected, "CycleError" will be raised.

   Added in version 3.9.


Exceptions
==========

The "graphlib" module defines the following exception classes:

exception graphlib.CycleError

   Subclass of "ValueError" raised by "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
   "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.
