[Python-ideas] Include partitioning in itertools

[Serhiy Storchaka]

On 01.11.15 13:08, Albert ten Oever wrote:
> I really hope this isn't proposed before - I couldn't find anything in
> the archives.
>
> I want to propose to include a 'partition' (mathematically more correct:
> a set partition) function in itertools. To my knowledge, partitioning of
> a set (iterable) is quite a common thing to do and a logic extension of
> the combinatoric generators in itertools.
>
> It is implemented as a Python recipe
> (http://code.activestate.com/recipes/576795-partitioning-a-sequence/). I
> found that implementing a partition generator of an iterable isn't very
> straightforward, which, in my opinion, strengthens the case for
> implementing it as a separate function.

The implementation can be simpler and don't require itertools:

def partition(seq):
     if seq:
         yield [seq]
     for i in range(1, len(seq)):
         s = seq[i:]
         for p in partition(seq[:i]):
             p.append(s)
             yield p

 >>> from pprint import pprint
 >>> pprint(sorted(partition('abcde'), key=len))
[['abcde'],
  ['a', 'bcde'],
  ['ab', 'cde'],
  ['abc', 'de'],
  ['abcd', 'e'],
  ['a', 'b', 'cde'],
  ['a', 'bc', 'de'],
  ['ab', 'c', 'de'],
  ['a', 'bcd', 'e'],
  ['ab', 'cd', 'e'],
  ['abc', 'd', 'e'],
  ['a', 'b', 'c', 'de'],
  ['a', 'b', 'cd', 'e'],
  ['a', 'bc', 'd', 'e'],
  ['ab', 'c', 'd', 'e'],
  ['a', 'b', 'c', 'd', 'e']]