Subsets / Powerset

Introduction

In this lesson, 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.

Problem Statement

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

Input: [100]

Output: [[], [100]]

Explanation: The subsets of any given input are equal to its power set.

if, input n = 3, then, powerset => $2^{n}$ = $2^{3}$ = 8.

Assume input has a length greater than or equals to 1.

Hint: Use left-shift operator to achieve this.

Solution

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 $2^{n}$ 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 counter input.