Print All the Subsets of a Given Set (Power Set)
Objective: Given a set of numbers, print all the posssible subsets of it including empty set.
Power Set: In mathematics, PowerSet of any given set S, PS(S) is set of all subsets of S including empty set.
Example:
S ={1,2,3}
PS(S): {{ᵩ}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}.
Approach:
Solution to this problem is similar to – Print All Combinations of subset of size K from Given Array
- Create an binary array of the same size as the given array.
- Now for every integer we have two options, whether to select it or ignore it.
- Now if we select it, we will put 1 in the boolean array at the corresponding index or if we ignore it, put 0 at that index.
- Say you have a variable called x, which represents the current index at the given array.
- Make x = 0 ( ignoring xth index) and x = 1( selecting xth index) and make recursive
Code:
Output:
{Empty} {3} {2} {23} {1} {13} {12} {123}