Making combinations in python

Question

I have four values

age = 23
gender = "M"
city ="Delhi"
religion = "Muslim"

I need these arranged by every combination with empty values like -

23 * * *
23 M * *
23 M Delhi *
23 M Delhi Muslim
* M * *
* M Delhi *
* M Delhi Muslim
* * Delhi *
* * Delhi Muslim
* * * Muslim
* * * *

I need this arranged by the number of dimensions in ascending order in a list. So combinations with one value should be on top. I have some 30+ attributes, so i need an automated way to do this in Python

Any ideas ?

Answer 1

NPE's answer solves the problem by constructing the full list of subsets in memory and then sorting it. This requires O(2ⁿ) space and O(n² 2ⁿ) time. If this is unacceptable, then here's a way to generate the subsets in O(n) space and O(n 2ⁿ) time.

from itertools import combinations

def subsets(s, placeholder = None):
    """
    Generate the subsets of `s` in order of size.
    Use `placeholder` for missing elements (default: None).
    """
    s = list(s)
    n = len(s)
    r = range(n)
    for i in range(n + 1):
        for c in combinations(r, i):
            result = [placeholder] * n
            for j in c:
                result[j] = s[j]
            yield result

>>> from pprint import pprint
>>> pprint(list(subsets([23, 'M', 'Delhi', 'Muslim'])))
[[None, None, None, None],
 [23, None, None, None],
 [None, 'M', None, None],
 [None, None, 'Delhi', None],
 [None, None, None, 'Muslim'],
 [23, 'M', None, None],
 [23, None, 'Delhi', None],
 [23, None, None, 'Muslim'],
 [None, 'M', 'Delhi', None],
 [None, 'M', None, 'Muslim'],
 [None, None, 'Delhi', 'Muslim'],
 [23, 'M', 'Delhi', None],
 [23, 'M', None, 'Muslim'],
 [23, None, 'Delhi', 'Muslim'],
 [None, 'M', 'Delhi', 'Muslim'],
 [23, 'M', 'Delhi', 'Muslim']]

Answer 2

How about the following:

In [21]: attrib = (23, "M", "Delhi", "Muslim")

In [25]: comb = list(itertools.product(*((a, None) for a in attrib)))

In [26]: comb
Out[26]: 
[(23, 'M', 'Delhi', 'Muslim'),
 (23, 'M', 'Delhi', None),
 (23, 'M', None, 'Muslim'),
 (23, 'M', None, None),
 (23, None, 'Delhi', 'Muslim'),
 (23, None, 'Delhi', None),
 (23, None, None, 'Muslim'),
 (23, None, None, None),
 (None, 'M', 'Delhi', 'Muslim'),
 (None, 'M', 'Delhi', None),
 (None, 'M', None, 'Muslim'),
 (None, 'M', None, None),
 (None, None, 'Delhi', 'Muslim'),
 (None, None, 'Delhi', None),
 (None, None, None, 'Muslim'),
 (None, None, None, None)]

Now, if I understood your sorting requirements correctly, the following should do it:

In [27]: sorted(comb, key=lambda x:sum(v is not None for v in x))
Out[27]: 
[(None, None, None, None),
 (23, None, None, None),
 (None, 'M', None, None),
 (None, None, 'Delhi', None),
 (None, None, None, 'Muslim'),
 (23, 'M', None, None),
 (23, None, 'Delhi', None),
 (23, None, None, 'Muslim'),
 (None, 'M', 'Delhi', None),
 (None, 'M', None, 'Muslim'),
 (None, None, 'Delhi', 'Muslim'),
 (23, 'M', 'Delhi', None),
 (23, 'M', None, 'Muslim'),
 (23, None, 'Delhi', 'Muslim'),
 (None, 'M', 'Delhi', 'Muslim'),
 (23, 'M', 'Delhi', 'Muslim')]

I've used None where you used *, but it's trivial to use the latter.

Of course with 30 attributes you're looking at ~1 billion combinations, so the flattening of the list with subsequent sorting probably won't work. However, what can you usefully do with 1 billion entries anyway?

Answer 3

Look at itertools, it has a method for combinations