# Find Powerset in Python

Hemank Mehtani Oct 10, 2023

In mathematics, a power set of any set is a set that contains all the possible subsets of a given set along with an empty set. In other words, all subsets of a set is also known as a powerset. There can be a power set of lists, sets, strings, etc., in Python.

In this tutorial, we will find the power set of a given set in Python.

## Use the Iterative Approach to Get a Powerset in Python

Though we can use both recursive approach and iterative approach to find a powerset, the iterative approach is preferred over recursive as it a faster process.

We use a nested `for` loop to create such a powerset.

For example,

``````def powerset(fullset):
listsub = list(fullset)
subsets = []
for i in range(2 ** len(listsub)):
subset = []
for k in range(len(listsub)):
if i & 1 << k:
subset.append(listsub[k])
subsets.append(subset)
return subsets

subsets = powerset(set([1, 2, 3, 4]))
print(subsets)
print(len(subsets))
``````

Output:

``````[[], , , [1, 2], , [1, 3], [2, 3], [1, 2, 3], , [1, 4], [2, 4], [1, 2, 4], [3, 4], [1, 3, 4], [2, 3, 4], [1, 2, 3, 4]]
16
``````

## Use the `itertools.combinations` Function to Find a Powerset in Python

`itertools` is a module in Python used to iterate over data structures. These data structures are also known as iterables. They can be stepped over by using for-loop.

The `combinations` function from this module can create combinations of a set to create a powerset.

See the code below.

``````from itertools import combinations

def powerset(string):
n = len(string)
for i in range(0, n + 1):
for element in combinations(string, i):
print("".join(element))

string = ["x", "y", "z"]
powerset(string)
``````

Output:

``````x
y
z
xy
xz
yz
xyz
``````

## Use the List Comprehension Method to Find a Powerset in Python

List Comprehension is a way to create new lists based on the existing list. It offers a shorter syntax being more compact and faster than the other functions and loops used for creating a list.

We use a nested `for` loop in this method also.

For example,

``````def get_subsets(fullset):
listrep = list(fullset)
n = len(listrep)
return [[listrep[k] for k in range(n) if i & 1 << k] for i in range(2 ** n)]

string = ["x", "y", "z"]
print(get_subsets(string))
``````

Output:

``````[[], ['x'], ['y'], ['x', 'y'], ['z'], ['x', 'z'], ['y', 'z'], ['x', 'y', 'z']]
``````

## Use the Recursive Method to Find a Powerset in Python

The recursive method is a method where a function keeps on invoking itself with different arguments. We can create a recursive function to find the powerset of a set.

For example,

``````def powerSet(string, index, c):
if index == len(string):
print(c)
return
powerSet(string, index + 1, c + string[index])
powerSet(string, index + 1, c)

s1 = ["a", "b", "c"]
index = 0
c = ""
powerSet(s1, index, c)
``````

Output:

``````abc
ab
ac
a
bc
b
c
``````