How to get all subsets of a set? (powerset)

Question

Given a set

{0, 1, 2, 3}

How can I produce the subsets:

[set(),
 {0},
 {1},
 {2},
 {3},
 {0, 1},
 {0, 2},
 {0, 3},
 {1, 2}         


        

Answer 1

Here is more code for a powerset. This is written from scratch:

>>> def powerset(s):
...     x = len(s)
...     for i in range(1 << x):
...         print [s[j] for j in range(x) if (i & (1 << j))]
...
>>> powerset([4,5,6])
[]
[4]
[5]
[4, 5]
[6]
[4, 6]
[5, 6]
[4, 5, 6]

Mark Rushakoff's comment is applicable here: "If you don't like that empty tuple at the beginning, on."you can just change the range statement to range(1, len(s)+1) to avoid a 0-length combination", except in my case you change for i in range(1 << x) to for i in range(1, 1 << x).

---

Returning to this years later, I'd now write it like this:

def powerset(s):
    x = len(s)
    masks = [1 << i for i in range(x)]
    for i in range(1 << x):
        yield [ss for mask, ss in zip(masks, s) if i & mask]

And then the test code would look like this, say:

print(list(powerset([4, 5, 6])))

Using yield means that you do not need to calculate all results in a single piece of memory. Precalculating the masks outside the main loop is assumed to be a worthwhile optimization.