### [issue17005] Add a topological sort algorithm

```

<1598493715.04.0.06462575371.issue17...@roundup.psfhosted.org>.

I missed a dependency in cutting down a larger example. Sorry.

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### [issue17005] Add a topological sort algorithm

```

I've been playing with Python 3.9.0rc1 and was looking at a particular graph to
see when it released tasks for processing.
I ran the following code:

from functools import reduce
from pprint import pprint as pp
from collections import defaultdict
from graphlib import TopologicalSorter
from heapq import heapify, heappush, heappop, heappushpop

print("""
###
###

A -> B -> C
↓↓↓
D -> E -> F
""")
graph3 = {"A": {"B", "D"},
"B": {"C", "E"},
"C": {"F"},
"D": {"E"},
"E": {"F"},
}

print("\n## NEW SIMULATION")
t = 0
heap = []
heapify(heap)
print(f"  {node}: {tm}")

print("\n# OUTPUT. (:> for task start times, <: for stop times).\n")
ts = TopologicalSorter(graph)
ts.prepare()
while ts.is_active():
heappush(heap, (finish, node))
print(f"{'  ' * t}{node}:> @{t}")
t, node = heappop(heap)
print(f"{'  ' * t}{node}<: @{t}")
ts.done(node)

I got the following output:

###
###

A -> B -> C
↓↓↓
D -> E -> F

## NEW SIMULATION

A: 2
B: 2
C: 2
D: 2
E: 2
F: 2

# OUTPUT. (:> for task start times, <: for stop times).

F:> @0
F<: @2
C:> @2
E:> @2
C<: @4
E<: @4
B:> @4
D:> @4
B<: @6
D<: @6
A:> @6
A<: @8

## NEW SIMULATION

A: 2
B: 2
C: 1
D: 2
E: 2
F: 2

# OUTPUT. (:> for task start times, <: for stop times).

F:> @0
F<: @2
C:> @2
E:> @2
C<: @3
E<: @4
B:> @4
D:> @4
B<: @6
D<: @6
A:> @6
A<: @8
>>>

Note that in the second simulation, C finish, but B isn't then immediately
started. I have my own code that also works like this but it isn't optimal.

Thanks guys.

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### [issue17005] Add a topological sort algorithm

```

New changeset 0a674638a3de14dc86b5294a5db067e0c2177a51 by Miss Islington (bot)
in branch '3.9':
bpo-17005: Move topological sort functionality to its own module (GH-20558)
https://github.com/python/cpython/commit/0a674638a3de14dc86b5294a5db067e0c2177a51

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### [issue17005] Add a topological sort algorithm

```

New changeset 2f172d8f1525defe9bba4d49e967fdfc69151731 by Pablo Galindo in
branch 'master':
bpo-17005: Move topological sort functionality to its own module (GH-20558)
https://github.com/python/cpython/commit/2f172d8f1525defe9bba4d49e967fdfc69151731

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### [issue17005] Add a topological sort algorithm

```

Change by miss-islington :

--
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### [issue17005] Add a topological sort algorithm

```

Opened https://github.com/python/cpython/pull/20558. I have *initially*
proposed "graphlib" as it feels more in-line with other stdlib module names and
as Jim pointed it does not collide with anything major. Also, I have proposed
this initial name to not keep the scope too short in case we want to add new
things in the future (although we can always say "no" and just keep this
functionality).

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### [issue17005] Add a topological sort algorithm

```

Change by Pablo Galindo Salgado :

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### [issue17005] Add a topological sort algorithm

```

Another option, `graphlib`[1], does exist on PyPI but is not maintained and
currently read-only by the author. Other flavors[2][3] of the same name also
don't seem to have much adoption so they shouldn't confuse if a name like
`graphlib` was chosen.

[1] https://github.com/bruth/graphlib/
[2] https://github.com/MengLiuPurdue/graph_lib
[3] https://github.com/EmileTrotignon/GraphLib

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### [issue17005] Add a topological sort algorithm

```

Eric V. Smith  added the comment:

I'd prefer a new module just for this. As for names, I like toposort over
topsort.

I already have a library on PyPI named toposort. Personally, I don't have a
problem with the stdlib taking over that name, and I'd just deprecate mine at
3.9, or whatever. I'm not sure if there are any ramifications of doing that,
however.

Or, pick another unused name, like toposortlib or something.

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### [issue17005] Add a topological sort algorithm

```

I checked and from the list of proposed names with "graph" prefixes, only
"graphutils" is not colliding with something on Pypi.

For the record "cslib" and "misclib" are also available but the scope of those
feel much much bigger.

I am going to open a PR to move this to "graphutils" for now. We can discuss
better in the PR for better names given that seems that there is an agreement
on moving this out of functools.

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### [issue17005] Add a topological sort algorithm

```

I vote for it being in its own module (like difflib).  That would also be a
good place to put my proposed tsort() function with its simpler API.

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### [issue17005] Add a topological sort algorithm

```

`functools` is clearly a poor place for this. `imath` would also be.
`graph_stuff_probably_limited_to_a_topsort` is the only accurate name ;-)
Off-the-wall possibilities include `misclib` (stuff that just doesn't fit
anywhere else - yet) and `cslib` (Computer Science-y stuff).

Whichever name wins, we should probably look to ensure the name isn't also of a

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### [issue17005] Add a topological sort algorithm

```

dependencytools?

But I don't think it qualifies yet for the plural...

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### [issue17005] Add a topological sort algorithm

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I would like to hear Raymond and Tim advise on what the best name for the new
module should be :)

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### [issue17005] Add a topological sort algorithm

```

> The downside I see with any graph prefixed names is the fact that it implies
> a larger collection of graph operations.

I don't see that an issue. In the general term is better to have a general name
and discuss further improvements than just name the module "topological_sort"
and now being cornered if we ever want to add new graph-related stuff.

We can always say "no" to new functionality but changing the name of the module
is not possible once is released.

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### [issue17005] Add a topological sort algorithm

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The downside I see with any graph prefixed names is the fact that it implies a
larger collection of graph operations.

Add that to the fact that people might be more tempted to propose many  graph
related algorithms/utilities to a module with the same name.

A more localized name solves that.

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### [issue17005] Add a topological sort algorithm

```

I like graphutils for what it's worth.

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### [issue17005] Add a topological sort algorithm

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If we move it, I would prefer a new module that somehow makes clear the scope,
something like graphutils or graphtheory or graph (although this las one will
probably collide with many existing things).

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### [issue17005] Add a topological sort algorithm

```

It does seem out of place in functools, intensified by it's odd interjection
among the other functools objects.

Considering heapq and bisect exist as standalone modules, the idea that
topological sorting could go in its own module wouldn't be without precedent.

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### [issue17005] Add a topological sort algorithm

```

Could it make sense to have this in the often proposed imath module?

It's integers per se but Both number theory and graph theory are part of
discrete mathematics so it may feel more at home there?

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### [issue17005] Add a topological sort algorithm

```

Any suggestions for the new module? I assume we can move this to a new
topsort/topological_sort or similar...

What do people think?

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### [issue17005] Add a topological sort algorithm

```

It's great to have this feature in the standard library, but it really seems to
clutter the functools documentation. Everything else in functools applies
directly to functions and methods. Suddenly reading graph theory terminology
was disorienting for me. (Due to context, I expected "node" to mean some new
type of Python function.) It makes the documentation significantly longer, and
IMHO abstruse. Would it be sensible to move this to a separate module?

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### [issue17005] Add a topological sort algorithm

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How about I post a PR so we can talk about something concrete.  Then you two
can either fight it to its death or you can join me in making it is good as
possible, hopefully the latter :-)

I am not happy with the current API but do accept that both of you are in
satisfied with it.

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### [issue17005] Add a topological sort algorithm

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Change by Raymond Hettinger :

--
Removed message: https://bugs.python.org/msg365640

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### [issue17005] Add a topological sort algorithm

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How about I post a PR so we can talk about something concrete.  Then you two
can either fight it to its death or you can join me in making it is good as
possible, hopefully the latter :-)

I am not happy with the current API but do accept that both of you are in love
with it.

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### [issue17005] Add a topological sort algorithm

```

Is also notable to mention that you can also provide the graph as a dictionary
to the constructor:

>>> graph = {D: {B, C}, C: {A}, B: {A}, A:{object}}
>>> ts = TopologicalSorter(graph)

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### [issue17005] Add a topological sort algorithm

```

Possibly, sure.  But I believe it's hard to beat

for usability as a way to build the dependency graph.  For example, a list of
pairs is a comparative PITA for most use cases I've had.  Whether it's
following a recipe to bake a cake, or tracing a maze of C include files, it
seems _most_ natural to get input in the form "this thing depends on these
other things".  Not the other way around, and neither a sequence of pairs.

_If_ you buy that, then .add() is screamingly natural, and trying to squash a
pile of .add()s into a single sequence-of-sequences argument seems strained.

Typically I don't get input in one big, single gulp.  It's instead discovered
one item at a time.  Fine - .add() it and then move on to the next item.  It's
certainly possible to append the item and its predecessors to a persistent
(across items) list, and call a function once at the end with that list.

But what does that buy?  I'm building the list solely to meet the function's
input requirement - the list serves no other purpose.  Instead of calling
.add() N times, I call .append() N times.  "add" is 3 letters shorter ;-)

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### [issue17005] Add a topological sort algorithm

```

> We may need two versions then, a full-featured TopologicalSorter() class and
> a simple tsort() function that doesn't aspire to be all things to all people.

How this other version would differ from using .add() + .static_order() as Tim
mentions? Originally we designed static_order() so it will satisfy the simpler
use cases so I would suggest aspiring to simplify that interface if needed

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### [issue17005] Add a topological sort algorithm

```

> If your alternative isn't equally easy to use in a parallelized
> context, I'll be at best +0.

We may need two versions then, a full-featured TopologicalSorter() class and a
simple tsort() function that doesn't aspire to be all things to all people.

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### [issue17005] Add a topological sort algorithm

```

Change by STINNER Victor :

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### [issue17005] Add a topological sort algorithm

```

I just want to echo what Tim mentioned with the extra data point that some of
the maintainers of some popular and wide-used open-source libraries that indeed
have to deal with this problem or the parallel version of the problem (like
gaborbernat in this thread, the maintainer of "tox" and "virtualenv") do indeed
find the current API desirable.

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### [issue17005] Add a topological sort algorithm

```

Raymond, what application do you have that wouldn't be completely addressed by
sticking to just .add() (to record dependencies) and .static_order() (to
retrieve a linear order)?

Larry Hastings and I originally worked out the fancier bits of the interface to
deal with problems he actually had, and for which no existing Python topsort
implementation we could find was of any use:  extract maximal parallelism.  If
you don't want that, fine, stick to the two simple bits.

The bits to support parallelism are very easy to use to write correct
parallelized code, but of course can seem baffling if you don't give a rip
about parallelism.  But in that case you have no need to learn about them
either.

If your alternative isn't equally easy to use in a parallelized context, I'll
be at best +0.

About "fast", this is linear time, in the sum of the number of items and
dependencies.  Including the part checking for a cycle, which is by far the
"hardest" part.  So it's asymptotically optimal, although I've never seen a
real context in which topsort speed made a lick of difference.

In the real world, in a parallelized context it can be important to check for a
cycle _before_ running a topsort:  actions are performed ASAP based on
order-deduced-so-far, and it can be no good to find out "oh! I can't finish
this" at the end.  There's actually nothing gratuitous here.  If it seems
;-)

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### [issue17005] Add a topological sort algorithm

```

At some point in the next two or three weeks, I'll have a chance to work on
this more and to offer a competing patch.  IMO, the current checkin is
over-engineered, both in its API and implementation.  This could have been a
simple, fast tool written as one or two short Python functions.

Also, I would like to try to out the API alternatives on some groups of
engineers to get some user feedback.

For me, as the API currently stands, I would have to write a wrapper to make it
usable for my applications.

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### [issue17005] Add a topological sort algorithm

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Change by wim glenn :

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### [issue17005] Add a topological sort algorithm

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New changeset 65ecc390c1fa5acdd6348ae3f9843bbdcd8870d1 by Pablo Galindo in
branch 'master':
bpo-17005: Minor improvements to the documentation of TopologicalSorter
(GH-18155)
https://github.com/python/cpython/commit/65ecc390c1fa5acdd6348ae3f9843bbdcd8870d1

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### [issue17005] Add a topological sort algorithm

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Change by Pablo Galindo Salgado :

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### [issue17005] Add a topological sort algorithm

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New changeset 99e6c260d60655f3d2885af545cbc220b808d492 by Pablo Galindo in
branch 'master':
bpo-17005: Add a class to perform topological sorting to the standard library
(GH-11583)
https://github.com/python/cpython/commit/99e6c260d60655f3d2885af545cbc220b808d492

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### [issue17005] Add a topological sort algorithm

```

I would like to suggest a `dependency_resolver` API that I have been using that
goes in line with what Tim Peters proposes in
https://bugs.python.org/issue17005#msg359702

A DAG would be an object that can be iterated in topological order with
__iter__ (for simple sequential usage) or have a way of managing all the tasks
that can be run in parallel. The later is done with a generator function:

```
def dependency_resolver(self):
"""Yield the set of nodes that have all dependencies satisfied (which
could be an empty set). Send the next
```

which is used with something like:

```
deps = dag.dependency_resolver()
#Graph empty
return
#Note this is a can be done in parallel/async
while True:
try:
except StopIteration:
#Exit when we have sent in all the nodes in the graph
break
else:

```

An implementation I have used for some time is here:

https://github.com/NNPDF/reportengine/blob/master/src/reportengine/dag.py

although I'd make simpler now. In practice I have found that the function I use
most of the time to build the graph is:

outputs={set of existing nodes}).

which adds the node to the graph if it was not there and maps updates the
dependencies to add inputs and outputs, which in my experience matches the way
one discovers dependencies for things like packages.

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### [issue17005] Add a topological sort algorithm

```

I think the new interface feeds better for usage in both sequential or parallel
workflows, which means we can use a single UI for both, so  from myself

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### [issue17005] Add a topological sort algorithm

```

I have been playing with the API for a while and I have to say that I have
fallen in love with it: I tried to reimplement many snippets of parallel and
non-parallel topological-order processing of a graph with this and it always
fits very nicely.

I have shown this API also to some library maintainers that have to deal with
topological sorting (like the tox maintainer) and they are very enthusiastic

Tim, I have updated PR 11583 to use the proposed API with test and docs. Could
you make a review when you have some time so we can polish it for the 3.9
release?

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### [issue17005] Add a topological sort algorithm

```

Oh, it's fine!  Kahn's algorithm is what I meant when I wrote the "bog-standard
implementation" before.

I don't believe I've ever seen a context in real life where topsort speed made
a lick of real difference, so I expect any linear-time (in the sum of the
number of nodes and edges) would be fine.  Nevertheless, for recording a node's
successors ("children" in your code), I've always used a list rather than a
set.  Lists run faster and require less memory than sets, and - unlike sets -
in Python inherently preserve insertion order.  Iteration order can become
visible (e.g., if B, C, and D depend on A, what's "the" topsort order?  it
depends on the order A's children appear when iterating over them - predictable
with a list, "it depends" with a set).

Note:  "but we have to guard against redundant edges!" would be a red herring.
Kahn's algorithm couldn't care less, provided that predecessor counts
accurately reflect the number of edges (redundant or not) entering a node.

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### [issue17005] Add a topological sort algorithm

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Disregarding the API, what do you think about the approach of
https://github.com/python/cpython/pull/11583 for the implementation? Under my
benchmarks (check previous comments) it seems to perform very good with regards
to memory and time.

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### [issue17005] Add a topological sort algorithm

```

I'll add ts.py, which was a work-in-progress that implements a minor variation
of most everything I typed about.  If nothing else, its _find_cycle is useful
as a non-recursive linear-time cycle finder (recursion is deadly here because
recursive depth-first search can easily "blow the stack" on larger graphs).

There's also "if 1:"/"else:" blocks that set up parallel cases, using threads
or processes, and two ways of managing the parallelism (the one I showed
before, and a more elaborate one that puts an upper bound on how large the
queues can grow - which is sometimes "a problem" for multiprocessing.queue).

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### [issue17005] Add a topological sort algorithm

```

Fair enough, I will read this carefully again and try to sketch a prototype
soon :)

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### [issue17005] Add a topological sort algorithm

```

> I am slightly confused about what .prepare() should do. Why
> is this step necessary?

To say "I'm done adding edges".  Any call to add() after prepare() should raise
an exception.  Likewise, e.g., any call to get_ready() before prepare() should
raise an exception.  In a bog-standard topsort implementation, saving for each
node a sequence of successors and a count of predecessors, this is also the
time to collect all the nodes that have no predecessors (the first batch

Much the same could be done without prepare() by get_ready() making a special
case out of the first time it's called.  That's more magical, though.  "I'm
done adding edges" is utterly non-magical.

> - Why we need the .done() method here? Why not instead make get_ready()
> simply a generator so you can just write
>

The point of done() is to enable maximum exploitation of parallelism.  As
already sketched, if a user doesn't care about that, fine, a different method
(like static_order()) can generate all the nodes in _some_ static topsort
order, with no need for done().

But suppose a user does care about parallelism.  Consider graph

A -> B
A -> C
A -> D
B -> D

Output A B C D is a topsort, but useless unless the user is content to "do" one
node at a time.

Instead get_ready() first returns [A] (or a tuple, or a generator, or a set ...
something iterable).  A is handed out to worker processes/threads, but
get_ready() will return an empty iterable until done(A) is called.  Indeed, if
"doing" A fails, it's NOT the case that anything else can ever be started.

If/when "doing A" succeeds, then done(A) is called, and the next get_ready()
returns [B, C].  Those can be done in parallel, but D can't be started until
done(B) is called.  done(B) may or may not be called before done(C) is called -
the topsort itself has no way to know in advance, nor _should_ it impose its
own view of that.  Note that D does not depend on C, so there's no need to wait
for _both_ in [B, C] to finish.  It's necessary and sufficient that B be marked
done() for D to be ready to go.

> It seems that the .done() is very tight to use this API as a "task
> scheduler" but maybe I am doing something here in my understanding
> of the API.

done() says nothing about how the user "should" schedule work items, but
instead allows get_ready() to return all the work items whose predecessors have
That's the maximum set of nodes that _can_ be worked on at the time.  The
topsort class itself has no policy about how or when they "should" be worked
on, get_ready() is just identifying all the possibilities that exist.  Which is
impossible to know unless the class is also told which nodes it already passed
out have finished - the purpose of done().

is_active() eventually returns False when all the nodes passed out by
get_ready() have been marked done(), _and_ there are no more nodes ready to
pass out.  At that point, there's a cycle in the input relations if and only if
there's some node get_ready() never passed out.

In my prototype implementation, that's another thing prepare() does:  checks
for a cycle, and raises CycleError if there is one.  The user can catch &
ignore that if they like, and continue calling get_ready() and done() until no
more progress can be made.  I think it's more likely, though, that the user
would stare at the cycle attached to the CycleError instance, do whatever it
takes to break the cycle, and start over again.

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### [issue17005] Add a topological sort algorithm

```

> Am I seriously suggesting this for Python?  Sure.  It's fun to advance the
> practical state of the art :-)

I think this API looks very interesting! I have some questions before start
implementing it to play a bit with it:

- I am slightly confused about what .prepare() should do. Why is this step
necessary?

- Why we need the .done() method here? Why not instead make get_ready() simply
a generator so you can just write

It seems that the .done() is very tight to use this API as a "task scheduler"
but maybe I am doing something here in
my understanding of the API.

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### [issue17005] Add a topological sort algorithm

```

Change by Senthil Kumaran :

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### [issue17005] Add a topological sort algorithm

```

Let's stir this up a bit ;-)  I recently had occasion to exchange ideas with
Larry Hastings about topsorts for use in a package manager he's writing.  I
thought his API for adding edges was ... perfect:

So, e.g., add(A, B, C) says A depends on B, and on C, but says nothing else
about B and C.  This is almost always the way topsorts show up in real life:
you know what a thing depends *on* directly, but have scant idea how things may
be in the opposite direction.  For example, you know that baking a cake
requires (among other things) flour, but have no real idea of the universe of
other things that require flour.  Likewise Larry knows which packages each
package requires, but not the reverse.  Etc.

If you're building input to a topsort from a graph, also trivial:

for n, p in node2predecessors.items():

and it doesn't matter whether the predecessors in the original graph were
stored in a list, set, tuple, or any other iterable container.  Nothing special
about an empty collection of predecessors either.

The other big thing that came up is that most topsort programs were useless for
time, and there's huge opportunity for exploiting parallelism.  But a flat
sequence in topsort order gives no clue about what _can_ be done in parallel.
Instead you really want several methods, like

prepare()

to say that you're done building the graph; and,

to get all nodes ready to go, which haven't already been returned by
get_ready() calls (initially, this is the collection of nodes with no
predecessors, which prepare() can know); and,

done(node)

to say that `node` (returned by a previous call to get_ready()) is finished
now, so that the next call to get_ready() can return all (if any) nodes for
which `node` was the last non-done predecessor; and,

is_active()

to say whether the topsort can make more progress (is_active() returns True iff
there are still nodes ready to go that haven't yet been passed out by
get_ready(), or if the number of nodes marked done() is less than the number
that have been passed out by get_ready()).

These are all easy to code, and allow the user to extract all the opportunities
for parallelism that theoretically exist.  There is no static order that can do
so, since the opportunities that exist at any time depend on the times and
order in which nodes are marked done() in real life - and that may vary from
one run to the next.

Of course a deterministic static order can be derived from those, like, e.g.,

def static_order(self):
self.prepare()
while self.is_active():
yield node
self.done(node)

For parallel use, e.g.,

self.prepare()
while instance.is_active():
inq.put(node)
node = outq.get()
instance.done(node)

where worker threads or processes take nodes to work on off of queue `inq`,
then, when the work for a node is done, put the node on queue `outq`.

Am I seriously suggesting this for Python?  Sure.  It's fun to advance the
practical state of the art :-)

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### [issue17005] Add a topological sort algorithm

```

I'd like to push back on the idea that graphs with isolated vertices are
"unusual cases" as suggested by Raymond.

A very common use case (possibly the most common) for topological sorting is
job scheduling. In this use case you have a collection of jobs, some of which
have dependencies on other jobs, and you want to output a schedule according to
which the jobs can be executed so that each job is executed after all its
dependencies.

In this use case, any job that has no dependencies, and is not itself a
dependency of any other job, is an isolated vertex in the dependency graph.
This means that the proposed interface (that is, the interface taking only
pairs of vertices) will not be suitable for this use case. Any any programmer
who tries to use it for this use case will be setting themselves up for failure.

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### [issue17005] Add a topological sort algorithm

```

Unless Łukasz gives us a nod to work out this API for the second beta, we'll
need to defer this to 3.9.   IMO, the API in the patch is not user friendly.
It started on the right path but became contorted (for both inputs and outputs)
to serve unusual cases.

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### [issue17005] Add a topological sort algorithm

```

> * allow input as ordered pairs like the Unix tsort command
> * allow more convenient input as dependency sequences (like graphviz):

This is how my first proposal started (and I still like it a bit more than the
dictionary input), but there are some concerns (check other comments) regarding
this API, like representing isolated nodes or disjoint graphs.

> return both the sorted sequence and cycles

Regarding the output, I like returning a collection of sets, where every set
represents all possible elements of the same order in the result. This also
helps if the user has some expectation regarding the ordering. For example, in:

['ABDGI', 'BEG', 'CEH', 'KCFHJ']

the results starting with

['A', 'B', 'D'

and

['A', 'B', 'K'

are both valid.

With the current implementation, this is the equivalent of C3 linearization:

from itertools import tee
from collections import defaultdict
def c3_linearization(inheritance_seqs):
graph = defaultdict(set)
for seq in inheritance_seqs:
a, b = tee(seq)
next(b, None)
for child, parent in zip(a,b):
retun ((list(group) for group in functools.toposort(graph)), [])
return tuple(reversed(order))

>>> class A: pass
>>> class B(A): pass
>>> class C(A): pass
>>> class D(B, C): pass

>> D.__mro__
(__main__.D, __main__.B, __main__.C, __main__.A, object)

>> c3_linearization([(D, B, A, object), (D, C, A, object)])
[{__main__.D}, {__main__.B, __main__.C}, {__main__.A}, {object}]

What do you think?

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### [issue17005] Add a topological sort algorithm

```

Change by Raymond Hettinger :

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### [issue17005] Add a topological sort algorithm

```

Attaching some of my 2013 work on this.  Here are some API notes:

* spell-out the name topological_sort()

* allow input as ordered pairs like the Unix tsort command
https://en.wikipedia.org/wiki/Tsort#Examples

* allow more convenient input as dependency sequences (like graphviz):
[['a', 'b', 'c', 'x], ['b', 'd', 'e', 'y']]
is short for and equivalent to:
[(a,b), (b,c), (c,x), (b,d), (d, e), (e, y)]

* return both the sorted sequence and cycles
(both are individually useful and the latter
is helpful in debugging in only the former is wanted)

* desire to match the C3 MRO computation

* would like the ordering to be stable and deterministic
(this precludes picking arbitrary elements from sets).

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### [issue17005] Add a topological sort algorithm

```

(A, B, C, D, E, F) would not be correct as B is order 2 and "C" and "A" is
order 1. The correct orders are the inner-group permutations of:

[{'A', 'F'}, {'B', 'D', 'E'}, {'C'}]

(Assuming that the lower diagram goes from top to bottom)

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### [issue17005] Add a topological sort algorithm

```

> 2) Topological sorting usually is well-defined on totally connected graphs,
> so I do not know what exactly it means to topologically sort two disjoint
> graphs. This was one of the main drawbacks of the tuple-based approach, but I
> think it may be a good property.

To give a use-case, I'm currently using topological sort to order a list of
tasks does not share a dependency with another group any relative order between
those two groups is correct:

A -> B

C
/ \
D   E
\ /
F

The order (A, B, C, D, E, F) would be correct in this example as would (C, A,
E, B, D, F).

I think the general topological sort in Python should be able to handle such
inputs.

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### [issue17005] Add a topological sort algorithm

```

Although I think the API with the dictionary may be cleaner, I still do not
like it completely.

1) One of the reasons is that implementing C3 directly with the topological
sort is not straightforward as the different nodes that are at the same level
are unordered and therefore any permutation of all these is a valid topological
sort, while C3 comes from a stable sort. The version with pairs is stable on
the other hand.

2) Topological sorting usually is well-defined on totally connected graphs, so
I do not know what exactly it means to topologically sort two disjoint graphs.
This was one of the main drawbacks of the tuple-based approach, but I think it
may be a good property.

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### [issue17005] Add a topological sort algorithm

```

I have updated the PR to receive a dictionary of sets as in Eric V. Smith's
package. I have maintained the guts of the current algorithm as it scales much
better:

>>> test_data = {x:{x+n for n in range(100)} for x in range(1000)}

>>> %timeit list(toposort.toposort(test_data)) # The one in PyPi
910 ms ± 2.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

>>> %timeit list(functools.toposort(test_data)) # In this PR

69.3 ms ± 280 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

>>> list(functools.toposort(l)) == list(toposort.toposort(l))
True

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### [issue17005] Add a topological sort algorithm

```

I have updated the PR to receive a dictionary of sets as in Eric V. Smith's
package. I have maintained the guts of the current algorithm as it scales much
better:

>>> test_data = {x:{x+n for n in range(100)} for x in range(1000)}

>>> %timeit list(toposort.toposort(l)) # The one in PyPi
910 ms ± 2.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

>>> %timeit list(functools.toposort(l)) # In this PR

69.3 ms ± 280 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

>>> list(functools.toposort(l)) == list(toposort.toposort(l))
True

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### [issue17005] Add a topological sort algorithm

```

Eric V. Smith  added the comment:

This is why I prefer the API exposed by https://pypi.org/project/toposort/

list(toposort({2: {11},
9: {11, 8, 10},
10: {11, 3},
11: {7, 5},
8: {7, 3},
}))

returns [{3, 5, 7}, {8, 11}, {2, 10}, {9}]

For an node with no edges, use an empty set:

list(toposort({100: set(),
2: {11},
9: {11, 8, 10},
10: {11, 3},
11: {7, 5},
8: {7, 3},
}))
[{3, 100, 5, 7}, {8, 11}, {2, 10}, {9}]

I also don't think we should provide multiple APIs. Let's just provide one, and
recipes for any helpers, if needed. For example, to flatten the result into a
list. Or to take a list of edges as the input.

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### [issue17005] Add a topological sort algorithm

```

Terry J. Reedy  added the comment:

I think 'toposort' is a good name for a function that implements 'topological
sorting'.
https://en.wikipedia.org/wiki/Topological_sorting

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### [issue17005] Add a topological sort algorithm

```

Just to elaborate on what I mean by "bug magnet". (I'm sure Pablo understands
this, but there may be other readers who would like to see it spelled out.)

Suppose that you have a directed graph represented as a mapping from a vertex
to an iterable of its out-neighbours. Then the "obvious" way to get a total
order on the vertices in the graph would be to generate the edges and pass them
to topsort:

def edges(graph):
return ((v, w) for v, ww in graph.items() for w in ww)
order = topsort(edges(graph))

This will appear to work fine if it is never tested with a graph that has
isolated vertices (which would be an all too easy omission).

To handle isolated vertices you have to remember to write something like this:

reversed_graph = {v: [] for v in graph}
for v, ww in graph.items():
for w in ww:
reversed_graph[w].append(v)
order = topsort(edges(graph)) + [
v for v, ww in graph.items() if not ww and not reversed_graph[v]]

I think it likely that beginner programmers will forget to do this and be
surprised later on when their total order is missing some of the vertices.

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### [issue17005] Add a topological sort algorithm

```

> 1. The name "topsort" is most naturally parsed as "top sort" which could be
> misinterpreted (as a sort that puts items on top in some way). If the name
> must be abbreviated then "toposort" would be better.

I totally agree that `topsort` is a bad name, I used it more or less as a dummy
for starting the discussion about the implementation.

> 2. "Topological sort" is a terrible name: the analogy with topological graph
> theory is (i) unlikely to be helpful to anyone; and (ii) not quite right. I
> know that the name is widely used in computing, but a name incorporating
> "linearize" or "linear order" or "total order" would be much clearer.

Topological sort (not as the function name) but as an operation is a very well
known concept and is well defined. If you are referring to not use "Topological
Sort" in the docstrings or the documentation, I strongly oppose.

Regarding the interface, I am more happy to change it once there is an
agreement. I am still awaiting Raymond's comments regarding this so we can
start discussing.

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### [issue17005] Add a topological sort algorithm

```

I approve in general with the principle of including a topological sort
algorithm in the standard library. However, I have three problems with the
approach in PR 11583:

1. The name "topsort" is most naturally parsed as "top sort" which could be
misinterpreted (as a sort that puts items on top in some way). If the name must
be abbreviated then "toposort" would be better.

2. "Topological sort" is a terrible name: the analogy with topological graph
theory is (i) unlikely to be helpful to anyone; and (ii) not quite right. I
know that the name is widely used in computing, but a name incorporating
"linearize" or "linear order" or "total order" would be much clearer.

3. The proposed interface is not suitable for all cases! The function topsort
takes a list of directed edges and returns a linear order on the vertices in
those edges (if any linear order exists). But this means that if there are any
isolated vertices (that is, vertices with no edges) in the dependency graph,
then there is no way of passing those vertices to the function. This means that
(i) it is inconvenient to use the proposed interface because you have to find
the isolated vertices in your graph and add them to the linear order after
calling the function; (ii) it is a bug magnet because many programmers will
omit this step, meaning that their code will unexpectedly fail when their graph
has an isolated vertex. The interface needs to be redesigned to take the graph
in some other representation.

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### [issue17005] Add a topological sort algorithm

```

As the name been already discussed ?

I fear that topsort might only be clear to people already knowing what it does.
topoligical_sort would be more discoverable and explicit and one can always do

from functools import topological_sort as tsort

if he wants to save some typing later.

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### [issue17005] Add a topological sort algorithm

```

The one in PR 11583 is twice as fast:

>timeit for ->
>topsort([(2,11),(9,11),(9,8),(9,10),(10,11),(10,3),(11,7),(11,5),(8,7),(8,3)])
12.4 µs ± 59.1 ns per loop (mean ± std. dev. of 7 runs, 10 loops each)

>timeit for ->
>tsort([(2,11),(9,11),(9,8),(9,10),(10,11),(10,3),(11,7),(11,5),(8,7),(8,3)])
29.1 µs ± 147 ns per loop (mean ± std. dev. of 7 runs, 1 loops each)

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### [issue17005] Add a topological sort algorithm

```

The one in PR 11583 is twice as faster:

>timeit for ->
>topsort([(2,11),(9,11),(9,8),(9,10),(10,11),(10,3),(11,7),(11,5),(8,7),(8,3)])
12.4 µs ± 59.1 ns per loop (mean ± std. dev. of 7 runs, 10 loops each)

>timeit for ->
>tsort([(2,11),(9,11),(9,8),(9,10),(10,11),(10,3),(11,7),(11,5),(8,7),(8,3)])
29.1 µs ± 147 ns per loop (mean ± std. dev. of 7 runs, 1 loops each)

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### [issue17005] Add a topological sort algorithm

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Thanks. I have some API nits to work to make this more broadly useful.  I'll
all those on the PR comments soonish :-)

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### [issue17005] Add a topological sort algorithm

```

Change by Pablo Galindo Salgado :

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### [issue17005] Add a topological sort algorithm

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Change by Pablo Galindo Salgado :

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### [issue17005] Add a topological sort algorithm

```

Here is an implementation that I've used for years. It is somewhat shorter than
the one in PR 11583:

class CycleError(LogicalError, ValueError):
"""dependencies cycle detected

"""

def tsort(pairs):
"""topological sort

Just like unix tsort(1)

>>> tsort([(1, 2), (7, 8), (8, 10), (7, 4), (2, 3), (4, 10)])
[1, 7, 2, 8, 4, 3, 10]
>>> try:
... tsort([(1,2), (2,1)])
... except CycleError as e:
... print(e)
([], Counter({1: 1, 2: 1}), {1: [2], 2: [1]})
"""
# inspired by
http://mail.python.org/pipermail/python-list/1999-July/002831.html
successors = {}
predecessor_counts = collections.Counter()
for x, y in pairs:
successors.setdefault(x, []).append(y)
predecessor_counts.setdefault(x, 0)
predecessor_counts[y] += 1
ordered = [x for x in predecessor_counts
if predecessor_counts[x] == 0]
for x in ordered:
del predecessor_counts[x]
for y in successors.get(x, ()):
predecessor_counts[y] -= 1
if predecessor_counts[y] == 0:
ordered.append(y)
if predecessor_counts:
raise CycleError(ordered, predecessor_counts, successors)
return ordered

--

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### [issue17005] Add a topological sort algorithm

```

Change by Pablo Galindo Salgado :

--
keywords: +patch, patch
pull_requests: +11266, 11267
stage:  -> patch review

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### [issue17005] Add a topological sort algorithm

```

Change by Pablo Galindo Salgado :

--
keywords: +patch, patch, patch
pull_requests: +11266, 11267, 11268
stage:  -> patch review

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### [issue17005] Add a topological sort algorithm

```

Change by Pablo Galindo Salgado :

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pull_requests: +11266
stage:  -> patch review

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### [issue17005] Add a topological sort algorithm

```

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### [issue17005] Add a topological sort algorithm

```

+1

I had tsort in my own utilities library for so long that I thought it was in
stdlib already.  I found this issue after unsuccessfully searching
docs.python.org. :-)

I think functools will be a fine place for it.  It is somewhat related to total
ordering and solves the problem which is common when implementing functional
mini-languages.

Another possibility is shutil given that tsort is a standard POSIX command,
http://pubs.opengroup.org/onlinepubs/009695299/utilities/tsort.html, but I
think this will be too obscure.

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### [issue17005] Add a topological sort algorithm

```
Changes by Tshepang Lekhonkhobe tshep...@gmail.com:

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### [issue17005] Add a topological sort algorithm

```
Changes by Terry J. Reedy tjre...@udel.edu:

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### [issue17005] Add a topological sort algorithm

```
New submission from Raymond Hettinger:

I suggest adding a topological sort algorithm to the standard library.

In addition to being a fundamental algorithm, it is immediately useful in
demonstrating how the MRO computation works and for pure Python implementations
of MRO logic.   IIRC, the pgen code was also expressed in pure Python for the
same reason.

I've attached a first-draft of the algorithm and an alternative that only
implements a topological merge.  This is just an early draft and there are a
number of open points:

* which module to put it in
* a better implementation may be possible (perhaps using fewer dictionaries and
sets).

--
files: mro_merge.py
messages: 180319
nosy: rhettinger
priority: low
severity: normal
status: open
title: Add a topological sort algorithm
type: enhancement
versions: Python 3.4

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### [issue17005] Add a topological sort algorithm

```

Good idea!

I'm using http://pypi.python.org/pypi/topsort/0.9 for a couple of years. The
initial code was written by Tim Peters.

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### [issue17005] Add a topological sort algorithm

```
Changes by Raymond Hettinger raymond.hettin...@gmail.com:

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### [issue17005] Add a topological sort algorithm

```
Eric V. Smith added the comment:

+1

I'll note (by inspection only) your example code doesn't work under Python 3.x!
:)

(print as a statement)

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```