In this coding problem, we need to find the power-set of given input without duplicates.
In this article, we discuss the subsets of a given input. This is one of the most popular questions asked in coding interviews.
Companies that have asked this in their coding interview are Apple, Microsoft, Amazon, Facebook, and many more.
We need to write a program that finds all possible subsets (the power set) of a given input. The solution set must not contain duplicate subsets.
Input: [1, 2, 3] Output: [,,,[1,2],,[1,3],[2,3],[1,2,3]]
Input:  Output: [, ]
- The subsets of any given input are equal to its power set.
- If input
n=3, the powerset will be
2n, which is
23 = 8.
- Assume input has a length greater than or equal to
In this program, we find the power set of a given input using bitwise operations. In general, if we have
n elements then the subsets are
2n subsets. So for every possible case of having at least two elements, we can see that an element is present and not present in the subsets. Think of a solution that is iterative, uses bitwise operators, and generates the powerset.
Here is how we generate each subset using the outer-loop variable
counter. Here is a table indicating how the value gets generated based on the
We need to consider a
counter variable that starts from
2n - 1.
For every value, we are considering the binary representation and here we use the set bits in the binary representation to generate corresponding subsets.
- If all set bits are
0, then the corresponding subset is empty
- If the last bit is
1, then we put
1in the subset as
We use two loops here, the outer loop starts from
2n - 1, and the inner loop continues to input array length
In the inner loop, we conditionally check
(counter & (1 << j )) != 0), if yes, then we print the corresponding element from an array.
O(n*2n) the time complexity is
ntimes the power set.
O(2n) we are storing
2n subset elements in an array. So the extra space is directly proportional to