[Python-checkins] bpo-17005: Add a class to perform topological sorting to the standard library (GH-11583)

Pablo Galindo webhook-mailer at python.org
Thu Jan 23 10:30:04 EST 2020


https://github.com/python/cpython/commit/99e6c260d60655f3d2885af545cbc220b808d492
commit: 99e6c260d60655f3d2885af545cbc220b808d492
branch: master
author: Pablo Galindo <Pablogsal at gmail.com>
committer: GitHub <noreply at github.com>
date: 2020-01-23T15:29:52Z
summary:

bpo-17005: Add a class to perform topological sorting to the standard library (GH-11583)

Co-Authored-By: Tim Peters <tim.peters at gmail.com>

files:
A Doc/myfile.bz2
A Misc/NEWS.d/next/Core and Builtins/2020-01-17-00-00-58.bpo-17005.nTSxsy.rst
M Doc/library/functools.rst
M Doc/whatsnew/3.9.rst
M Lib/functools.py
M Lib/test/test_functools.py

diff --git a/Doc/library/functools.rst b/Doc/library/functools.rst
index bb7aac42daca7..8c408923b70a7 100644
--- a/Doc/library/functools.rst
+++ b/Doc/library/functools.rst
@@ -8,10 +8,16 @@
 .. moduleauthor:: Raymond Hettinger <python at rcn.com>
 .. moduleauthor:: Nick Coghlan <ncoghlan at gmail.com>
 .. moduleauthor:: Łukasz Langa <lukasz at langa.pl>
+.. moduleauthor:: Pablo Galindo <pablogsal at gmail.com>
 .. sectionauthor:: Peter Harris <scav at blueyonder.co.uk>
 
 **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.
diff --git a/Doc/myfile.bz2 b/Doc/myfile.bz2
new file mode 100644
index 0000000000000..7ada20f60926b
Binary files /dev/null and b/Doc/myfile.bz2 differ
diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
index d9c545adc43d6..a6e938faa991e 100644
--- a/Doc/whatsnew/3.9.rst
+++ b/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
 --
 
diff --git a/Lib/functools.py b/Lib/functools.py
index 2c01b2e59524b..050bec8605117 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -10,8 +10,9 @@
 # See C source code for _functools credits/copyright
 
 __all__ = ['update_wrapper', 'wraps', 'WRAPPER_ASSIGNMENTS', 'WRAPPER_UPDATES',
-           'total_ordering', 'cmp_to_key', 'lru_cache', 'reduce', 'partial',
-           'partialmethod', 'singledispatch', 'singledispatchmethod']
+           'total_ordering', 'cmp_to_key', 'lru_cache', 'reduce',
+           'TopologicalSorter', 'CycleError',
+           'partial', 'partialmethod', 'singledispatch', 'singledispatchmethod']
 
 from abc import get_cache_token
 from collections import namedtuple
@@ -192,6 +193,250 @@ def total_ordering(cls):
             setattr(cls, opname, opfunc)
     return cls
 
+################################################################################
+### topological sort
+################################################################################
+
+_NODE_OUT = -1
+_NODE_DONE = -2
+
+
+class _NodeInfo:
+    __slots__ = 'node', 'npredecessors', 'successors'
+
+    def __init__(self, node):
+        # The node this class is augmenting.
+        self.node = node
+
+        # Number of predecessors, generally >= 0. When this value falls to 0,
+        # and is returned by get_ready(), this is set to _NODE_OUT and when the
+        # node is marked done by a call to done(), set to _NODE_DONE.
+        self.npredecessors = 0
+
+        # List of successor nodes. The list can contain duplicated elements as
+        # long as they're all reflected in the successor's npredecessors attribute).
+        self.successors = []
+
+
+class CycleError(ValueError):
+    """Subclass of ValueError raised by TopologicalSorterif cycles exist in the 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.
+    """
+    pass
+
+
+class TopologicalSorter:
+    """Provides functionality to topologically sort a graph of hashable nodes"""
+
+    def __init__(self, graph=None):
+        self._node2info = {}
+        self._ready_nodes = None
+        self._npassedout = 0
+        self._nfinished = 0
+
+        if graph is not None:
+            for node, predecessors in graph.items():
+                self.add(node, *predecessors)
+
+    def _get_nodeinfo(self, node):
+        if (result := self._node2info.get(node)) is None:
+            self._node2info[node] = result = _NodeInfo(node)
+        return result
+
+    def add(self, 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)
+        as well as 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".
+        """
+        if self._ready_nodes is not None:
+            raise ValueError("Nodes cannot be added after a call to prepare()")
+
+        # Create the node -> predecessor edges
+        nodeinfo = self._get_nodeinfo(node)
+        nodeinfo.npredecessors += len(predecessors)
+
+        # Create the predecessor -> node edges
+        for pred in predecessors:
+            pred_info = self._get_nodeinfo(pred)
+            pred_info.successors.append(node)
+
+    def prepare(self):
+        """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".
+        """
+        if self._ready_nodes is not None:
+            raise ValueError("cannot prepare() more than once")
+
+        self._ready_nodes = [i.node for i in self._node2info.values()
+                             if i.npredecessors == 0]
+        # ready_nodes is set before we look for cycles on purpose:
+        # if the user wants to catch the CycleError, that's fine,
+        # they can continue using the instance to grab as many
+        # nodes as possible before cycles block more progress
+        cycle = self._find_cycle()
+        if cycle:
+            raise CycleError(f"nodes are in a cycle", cycle)
+
+    def get_ready(self):
+        """Return a tuple of all the nodes that are ready.
+
+        Initially it returns all nodes with no predecessors; once those are marked
+        as processed by calling "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.
+        """
+        if self._ready_nodes is None:
+            raise ValueError("prepare() must be called first")
+
+        # Get the nodes that are ready and mark them
+        result = tuple(self._ready_nodes)
+        n2i = self._node2info
+        for node in result:
+            n2i[node].npredecessors = _NODE_OUT
+
+        # Clean the list of nodes that are ready and update
+        # the counter of nodes that we have returned.
+        self._ready_nodes.clear()
+        self._npassedout += len(result)
+
+        return result
+
+    def is_active(self):
+        """Return 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 "get_ready" or the
+        number of nodes marked "done" is less than the number that have been returned
+        by "get_ready".
+
+        Raises ValueError if called without calling "prepare" previously.
+        """
+        if self._ready_nodes is None:
+            raise ValueError("prepare() must be called first")
+        return self._nfinished < self._npassedout or bool(self._ready_nodes)
+
+    def __bool__(self):
+        return self.is_active()
+
+    def done(self, *nodes):
+        """Marks a set of nodes returned by "get_ready" as processed.
+
+        This method unblocks any successor of each node in *nodes* for being returned
+        in the future by a a call to "get_ready"
+
+        Raises :exec:`ValueError` if any node in *nodes* has already been marked as
+        processed by a previous call to this method, if a node was not added to the
+        graph by using "add" or if called without calling "prepare" previously or if
+        node has not yet been returned by "get_ready".
+        """
+
+        if self._ready_nodes is None:
+            raise ValueError("prepare() must be called first")
+
+        n2i = self._node2info
+
+        for node in nodes:
+
+            # Check if we know about this node (it was added previously using add()
+            if (nodeinfo := n2i.get(node)) is None:
+                raise ValueError(f"node {node!r} was not added using add()")
+
+            # If the node has not being returned (marked as ready) previously, inform the user.
+            stat = nodeinfo.npredecessors
+            if stat != _NODE_OUT:
+                if stat >= 0:
+                    raise ValueError(f"node {node!r} was not passed out (still not ready)")
+                elif stat == _NODE_DONE:
+                    raise ValueError(f"node {node!r} was already marked done")
+                else:
+                    assert False, f"node {node!r}: unknown status {stat}"
+
+            # Mark the node as processed
+            nodeinfo.npredecessors = _NODE_DONE
+
+            # Go to all the successors and reduce the number of predecessors, collecting all the ones
+            # that are ready to be returned in the next get_ready() call.
+            for successor in nodeinfo.successors:
+                successor_info = n2i[successor]
+                successor_info.npredecessors -= 1
+                if successor_info.npredecessors == 0:
+                    self._ready_nodes.append(successor)
+            self._nfinished += 1
+
+    def _find_cycle(self):
+        n2i = self._node2info
+        stack = []
+        itstack = []
+        seen = set()
+        node2stacki = {}
+
+        for node in n2i:
+            if node in seen:
+                continue
+
+            while True:
+                if node in seen:
+                    # If we have seen already the node and is in the
+                    # current stack we have found a cycle.
+                    if node in node2stacki:
+                        return stack[node2stacki[node]:] + [node]
+                    # else go on to get next successor
+                else:
+                    seen.add(node)
+                    itstack.append(iter(n2i[node].successors).__next__)
+                    node2stacki[node] = len(stack)
+                    stack.append(node)
+
+                # Backtrack to the topmost stack entry with
+                # at least another successor.
+                while stack:
+                    try:
+                        node = itstack[-1]()
+                        break
+                    except StopIteration:
+                        del node2stacki[stack.pop()]
+                        itstack.pop()
+                else:
+                    break
+        return None
+
+    def static_order(self):
+        """Returns an iterable of nodes in a topological order.
+
+        The particular order that is returned may depend on the specific
+        order in which the items were inserted in the graph.
+
+        Using this method does not require to call "prepare" or "done". If any
+        cycle is detected, :exc:`CycleError` will be raised.
+        """
+        self.prepare()
+        while self.is_active():
+            node_group = self.get_ready()
+            yield from node_group
+            self.done(*node_group)
+
 
 ################################################################################
 ### cmp_to_key() function converter
diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index a97ca398e77a3..9503f4086b1cb 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -3,7 +3,7 @@
 import collections
 import collections.abc
 import copy
-from itertools import permutations
+from itertools import permutations, chain
 import pickle
 from random import choice
 import sys
@@ -13,9 +13,12 @@
 import typing
 import unittest
 import unittest.mock
+import os
 from weakref import proxy
 import contextlib
 
+from test.support.script_helper import assert_python_ok
+
 import functools
 
 py_functools = support.import_fresh_module('functools', blocked=['_functools'])
@@ -1158,6 +1161,275 @@ def __eq__(self, other):
         return self.value == other.value
 
 
+class TestTopologicalSort(unittest.TestCase):
+
+    def _test_graph(self, graph, expected):
+
+        def static_order_with_groups(ts):
+            ts.prepare()
+            while ts.is_active():
+                nodes = ts.get_ready()
+                for node in nodes:
+                    ts.done(node)
+                yield nodes
+
+        ts = functools.TopologicalSorter(graph)
+        self.assertEqual(list(static_order_with_groups(ts)), list(expected))
+
+        ts = functools.TopologicalSorter(graph)
+        self.assertEqual(list(ts.static_order()), list(chain(*expected)))
+
+    def _assert_cycle(self, graph, cycle):
+        ts = functools.TopologicalSorter()
+        for node, dependson in graph.items():
+            ts.add(node, *dependson)
+        try:
+            ts.prepare()
+        except functools.CycleError as e:
+            msg, seq = e.args
+            self.assertIn(' '.join(map(str, cycle)),
+                          ' '.join(map(str, seq * 2)))
+        else:
+            raise
+
+    def test_simple_cases(self):
+        self._test_graph(
+            {2: {11},
+             9: {11, 8},
+             10: {11, 3},
+             11: {7, 5},
+             8: {7, 3}},
+            [(3, 5, 7), (11, 8), (2, 10, 9)]
+        )
+
+        self._test_graph({1: {}}, [(1,)])
+
+        self._test_graph({x: {x+1} for x in range(10)},
+                         [(x,) for x in range(10, -1, -1)])
+
+        self._test_graph({2: {3}, 3: {4}, 4: {5}, 5: {1},
+                          11: {12}, 12: {13}, 13: {14}, 14: {15}},
+                         [(1, 15), (5, 14), (4, 13), (3, 12), (2, 11)])
+
+        self._test_graph({
+                0: [1, 2],
+                1: [3],
+                2: [5, 6],
+                3: [4],
+                4: [9],
+                5: [3],
+                6: [7],
+                7: [8],
+                8: [4],
+                9: []
+            },
+            [(9,), (4,), (3, 8), (1, 5, 7), (6,), (2,), (0,)]
+        )
+
+        self._test_graph({
+                0: [1, 2],
+                1: [],
+                2: [3],
+                3: []
+            },
+            [(1, 3), (2,), (0,)]
+        )
+
+        self._test_graph({
+                0: [1, 2],
+                1: [],
+                2: [3],
+                3: [],
+                4: [5],
+                5: [6],
+                6: []
+            },
+            [(1, 3, 6), (2, 5), (0, 4)]
+        )
+
+    def test_no_dependencies(self):
+        self._test_graph(
+            {1: {2},
+             3: {4},
+             5: {6}},
+            [(2, 4, 6), (1, 3, 5)]
+        )
+
+        self._test_graph(
+            {1: set(),
+             3: set(),
+             5: set()},
+            [(1, 3, 5)]
+        )
+
+    def test_the_node_multiple_times(self):
+        # Test same node multiple times in dependencies
+        self._test_graph({1: {2}, 3: {4}, 0: [2, 4, 4, 4, 4, 4]},
+                         [(2, 4), (1, 3, 0)])
+
+        # Test adding the same dependency multiple times
+        ts = functools.TopologicalSorter()
+        ts.add(1, 2)
+        ts.add(1, 2)
+        ts.add(1, 2)
+        self.assertEqual([*ts.static_order()], [2, 1])
+
+    def test_graph_with_iterables(self):
+        dependson = (2*x + 1 for x in range(5))
+        ts = functools.TopologicalSorter({0: dependson})
+        self.assertEqual(list(ts.static_order()), [1, 3, 5, 7, 9, 0])
+
+    def test_add_dependencies_for_same_node_incrementally(self):
+        # Test same node multiple times
+        ts = functools.TopologicalSorter()
+        ts.add(1, 2)
+        ts.add(1, 3)
+        ts.add(1, 4)
+        ts.add(1, 5)
+
+        ts2 = functools.TopologicalSorter({1: {2, 3, 4, 5}})
+        self.assertEqual([*ts.static_order()], [*ts2.static_order()])
+
+    def test_empty(self):
+        self._test_graph({}, [])
+
+    def test_cycle(self):
+        # Self cycle
+        self._assert_cycle({1: {1}}, [1, 1])
+        # Simple cycle
+        self._assert_cycle({1: {2}, 2: {1}}, [1, 2, 1])
+        # Indirect cycle
+        self._assert_cycle({1: {2}, 2: {3}, 3: {1}}, [1, 3, 2, 1])
+        # not all elements involved in a cycle
+        self._assert_cycle({1: {2}, 2: {3}, 3: {1}, 5: {4}, 4: {6}}, [1, 3, 2, 1])
+        # Multiple cycles
+        self._assert_cycle({1: {2}, 2: {1}, 3: {4}, 4: {5}, 6: {7}, 7: {6}},
+                           [1, 2, 1])
+        # Cycle in the middle of the graph
+        self._assert_cycle({1: {2}, 2: {3}, 3: {2, 4}, 4: {5}}, [3, 2])
+
+    def test_calls_before_prepare(self):
+        ts = functools.TopologicalSorter()
+
+        with self.assertRaisesRegex(ValueError, r"prepare\(\) must be called first"):
+            ts.get_ready()
+        with self.assertRaisesRegex(ValueError, r"prepare\(\) must be called first"):
+            ts.done(3)
+        with self.assertRaisesRegex(ValueError, r"prepare\(\) must be called first"):
+            ts.is_active()
+
+    def test_prepare_multiple_times(self):
+        ts = functools.TopologicalSorter()
+        ts.prepare()
+        with self.assertRaisesRegex(ValueError, r"cannot prepare\(\) more than once"):
+            ts.prepare()
+
+    def test_invalid_nodes_in_done(self):
+        ts = functools.TopologicalSorter()
+        ts.add(1, 2, 3, 4)
+        ts.add(2, 3, 4)
+        ts.prepare()
+        ts.get_ready()
+
+        with self.assertRaisesRegex(ValueError, "node 2 was not passed out"):
+            ts.done(2)
+        with self.assertRaisesRegex(ValueError, r"node 24 was not added using add\(\)"):
+            ts.done(24)
+
+    def test_done(self):
+        ts = functools.TopologicalSorter()
+        ts.add(1, 2, 3, 4)
+        ts.add(2, 3)
+        ts.prepare()
+
+        self.assertEqual(ts.get_ready(), (3, 4))
+        # If we don't mark anything as done, get_ready() returns nothing
+        self.assertEqual(ts.get_ready(), ())
+        ts.done(3)
+        # Now 2 becomes available as 3 is done
+        self.assertEqual(ts.get_ready(), (2,))
+        self.assertEqual(ts.get_ready(), ())
+        ts.done(4)
+        ts.done(2)
+        # Only 1 is missing
+        self.assertEqual(ts.get_ready(), (1,))
+        self.assertEqual(ts.get_ready(), ())
+        ts.done(1)
+        self.assertEqual(ts.get_ready(), ())
+        self.assertFalse(ts.is_active())
+
+    def test_is_active(self):
+        ts = functools.TopologicalSorter()
+        ts.add(1, 2)
+        ts.prepare()
+
+        self.assertTrue(ts.is_active())
+        self.assertEqual(ts.get_ready(), (2,))
+        self.assertTrue(ts.is_active())
+        ts.done(2)
+        self.assertTrue(ts.is_active())
+        self.assertEqual(ts.get_ready(), (1,))
+        self.assertTrue(ts.is_active())
+        ts.done(1)
+        self.assertFalse(ts.is_active())
+
+    def test_not_hashable_nodes(self):
+        ts = functools.TopologicalSorter()
+        self.assertRaises(TypeError, ts.add, dict(), 1)
+        self.assertRaises(TypeError, ts.add, 1, dict())
+        self.assertRaises(TypeError, ts.add, dict(), dict())
+
+    def test_order_of_insertion_does_not_matter_between_groups(self):
+        def get_groups(ts):
+            ts.prepare()
+            while ts.is_active():
+                nodes = ts.get_ready()
+                ts.done(*nodes)
+                yield set(nodes)
+
+        ts = functools.TopologicalSorter()
+        ts.add(3, 2, 1)
+        ts.add(1, 0)
+        ts.add(4, 5)
+        ts.add(6, 7)
+        ts.add(4, 7)
+
+        ts2 = functools.TopologicalSorter()
+        ts2.add(1, 0)
+        ts2.add(3, 2, 1)
+        ts2.add(4, 7)
+        ts2.add(6, 7)
+        ts2.add(4, 5)
+
+        self.assertEqual(list(get_groups(ts)), list(get_groups(ts2)))
+
+    def test_static_order_does_not_change_with_the_hash_seed(self):
+        def check_order_with_hash_seed(seed):
+            code = """if 1:
+                import functools
+                ts = functools.TopologicalSorter()
+                ts.add('blech', 'bluch', 'hola')
+                ts.add('abcd', 'blech', 'bluch', 'a', 'b')
+                ts.add('a', 'a string', 'something', 'b')
+                ts.add('bluch', 'hola', 'abcde', 'a', 'b')
+                print(list(ts.static_order()))
+                """
+            env = os.environ.copy()
+            # signal to assert_python not to do a copy
+            # of os.environ on its own
+            env['__cleanenv'] = True
+            env['PYTHONHASHSEED'] = str(seed)
+            out = assert_python_ok('-c', code, **env)
+            return out
+
+        run1 = check_order_with_hash_seed(1234)
+        run2 = check_order_with_hash_seed(31415)
+
+        self.assertNotEqual(run1, "")
+        self.assertNotEqual(run2, "")
+        self.assertEqual(run1, run2)
+
+
 class TestLRU:
 
     def test_lru(self):
diff --git a/Misc/NEWS.d/next/Core and Builtins/2020-01-17-00-00-58.bpo-17005.nTSxsy.rst b/Misc/NEWS.d/next/Core and Builtins/2020-01-17-00-00-58.bpo-17005.nTSxsy.rst
new file mode 100644
index 0000000000000..e5336437754af
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2020-01-17-00-00-58.bpo-17005.nTSxsy.rst	
@@ -0,0 +1,3 @@
+Add :class:`functools.TopologicalSorter` to the :mod:`functools` module to
+offers functionality to perform topological sorting of graphs. Patch by
+Pablo Galindo, Tim Peters and Larry Hastings.



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