Add partitions function

[rominf]

Add partitions function

Partitioning set or interval is a known thing in mathematics. This PR adds a function to do find all partitions of a collection. For more information what is considered a partition, see docstring.

Thanks, Tigran Saluev (http://saluev.com/) for the implementation.

UPD: the code was rewritten from scratch.

[bbayles]

Thanks for the PR.

A few comments:

• It looks like this relies on slicing. Could you make it such that a generic iterable could be used?
• flake8 is complaining about a long line (see Travis output)
• Could we get Tigran Saluev's blessing on including his implementation?

Thanks again.

[Saluev]

👍

[Saluev]

In my code though the first line was collection = list(collection), so the problem 1 did not exist.

[rominf]

It looks like this relies on slicing. Could you make it such that a generic iterable could be used?

It's possible, but then you will get a list of lists of strings with length 1 if the input is the string. To make them strings user will have to write a quite long and slow code. Also, making list(iterable) will implicitly consume generators which is a bad thing and consume memory. I think that if the user wants to pass a generator, he has to explicitly (explicit is better than implicit, as Python Zen states) call list, which is not hard at all:

partitions(list(generator))

[Saluev]

Just in case: I don't agree with that. I think consuming a generator passed to an iteration tool is totally fine. It always happens anyway. itertools.product and other alike functions HAVE to do that. And I don't think we should do strings-driven optimizations in an itertools library as well.

(Also I consider the reference to Zen to be pure demagogy.)

[rominf]

Now the iterables are supported, but collections are left as is, without converting them to lists.
@bbayles, is everything OK?

[rominf]

I rewrote the code from scratch. Now it's shorter and works 30% faster.

[rominf]

Now function converts all iterables to the lists.

@bbayles, @pylang is everything OK?

[bbayles]

Merged with some additional tests and docstring changes. This will be in the next release. Many thanks!

[rominf]

@bbayles, I think that the difference between partition and this function should be noted.

partition divides iterable into two, but those iterable are not contiguous in the original iterable (function takes some items from iterable, then skips some items, then takes, and so on). But partitions generates all contiguous itrerables.

I've tried to describe it in a formal way. You've removed that. OK, but then, insert, please, an informal note about this.