Python - How To Find Powerset in Python

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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, 2], [3], [1, 3], [2, 3], [1, 2, 3], [4], [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 

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