CombSpace and Comb

CombSpace

class CombSpace(iterable_or_length, n_elements, *, slice_=None, perm_type=None)

A space of combinations.

This is a subclass of PermSpace; see its documentation for more details.

Each item in a CombSpace is a Comb, i.e. a combination. This is similar to itertools.combinations(), except it offers far, far more functionality. The combinations may be accessed by index number, the combinations can be of a custom type, the space may be sliced, etc.

Here is the simplest possible CombSpace:

>>> comb_space = CombSpace(4, 2)
<CombSpace: 0..3, n_elements=2>
>>> comb_space[2]
<Comb, n_elements=2: (0, 3)>
>>> tuple(comb_space)
(<Comb, n_elements=2: (0, 1)>, <Comb, n_elements=2: (0, 2)>,
 <Comb, n_elements=2: (0, 3)>, <Comb, n_elements=2: (1, 2)>,
 <Comb, n_elements=2: (1, 3)>, <Comb, n_elements=2: (2, 3)>)

The members are Comb objects, which are sequence-like objects that have extra functionality. (See documentation of Comb and its base class Perm for more info.)

Comb

class Comb(perm_sequence, perm_space=None)

A combination of items from a CombSpace.

In combinatorics, a combination is like a permutation except with no order. In the combi package, we implement that by making the items in Comb be in canonical order. (This has the same effect as having no order because each combination of items can only appear once, in the canonical order, rather than many different times in many different orders like with Perm.)

Example:

>>> comb_space = CombSpace('abcde', 3)
>>> comb = Comb('bcd', comb_space)
>>> comb
<Comb, n_elements=3: ('a', 'b', 'c')>
>>> comb_space.index(comb)
6