Find all subsets of set (power set) in java

If you want to practice data structure and algorithm programs, you can go through Java coding interview questions.

In this post, we will see how to find all subsets of set or power set in java.


Problem

Given a set of distinct integers, arr, return all possible subsets (the power set).

For example:

💻 Awesome Tech Resources:
  • Looking for ⚒️ tech jobs? Go to our job portal.
  • Looking for tech events? Go to tech events 🗓️ Calendar.️
Input: nums = [1,2,3] Output:
[
[3],
[1],
[2],
[1,2,3],
[1,3],
[2,3],
[1,2],
[] ]

We will use two approaches here.


Using recursion

You can find all subsets of set or power set using recursion. Here is the simple approach.

  • As each recursion call will represent subset here, we will add resultList(see recursion code below) to the list of subsets in each call.
  • Iterate over elements of a set.
  • In each iteration
    • Add elements to the list
    • explore(recursion) and make start = i+1 to go through remaining elements of the array.
    • Remove element from the list.

Here is java code for recursion.

Output

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

Let’s understand with the help of a diagram.

subset helper recursion

If you notice, each node(resultList) represent subset here.

Using bit manipulation

You can find all subsets of set or power set using iteration as well.

There will be 2^N subsets for a given set, where N is the number of elements in set.
For example, there will be 2^4 = 16 subsets for the set {1, 2, 3, 4}.

Each ‘1’ in the binary representation indicate an element in that position.
For example, the binary representation of number 6 is 0101 which in turn represents the subset {1, 3} of the set {1, 2, 3, 4}.

subset binary

How can we find out which bit is set for binary representation, so that we can include the element in the subset?

To check if 0th bit is set, you can do logical & with 1

To check if 1st bit is set, you can do logical & with 2

To check if 2nd bit is set, you can do logical & with 2^2

.

.

To check if nth bit is set, you can do logical & with 2^n.

Let’s say with the help of example:

For a set {1 ,2, 3}

0 1 1  &  0 0 1 = 1    –> 1 will be included in subset

0 1 1  &  0 1 0 = 1    –> 2 will be included in subset

0 1 1  &  1 0  0 =0   –> 3 will not be included in subset.

Here is java code for the bit approach.

Output

{ }
{ 1 }
{ 2 }
{ 1 2 }
{ 3 }
{ 1 3 }
{ 2 3 }
{ 1 2 3 }

Here is complete representation of bit manipulation approach.

Subset bit manipulation

That’s all about finding all subsets of set(power set).

Related Posts

  • Data structures in java
    16 April

    Data Structures in java

    In this post, we will see about various data structures in java. Data structure is a way of storing and organizing data. Data structure provide a way to process and store data efficiently. For example: 💻 Awesome Tech Resources: Looking for ⚒️ tech jobs? Go to our job portal. Looking for tech events? Go to […]

  • 29 November

    Top 100+ Java coding interview questions

    I have been posting data structure and coding interview questions on various topics such as Array, Queue, Stack, Binary tree, LinkedList, String, Number, ArrayList, etc. So I am consolidating a list of java coding interview questions to create an index post. I will keep adding links to this post whenever I will add new java […]

  • 18 April

    Minimum Number of Jumps to reach last Index

    If you want to practice data structure and algorithm programs, you can go through Java coding interview questions. In this post, we will see how to find Minimum Number of Jumps to reach last Index. Problem Given an array A of positive integers possibly zeroes, every index indicating the maximum length of a jump that can […]

  • 28 March

    Sort an array of 0s, 1s and 2s

    If you want to practice data structure and algorithm programs, you can go through Java coding interview questions. In this post, we will see how to sort an array of 0s, 1s and 2s.We have already seen a post on sort 0s and 1s in an array. Problem Given an array containing zeroes, ones and twos […]

  • 04 March

    Check if it is possible to reach end of given Array by Jumping

    If you want to practice data structure and algorithm programs, you can go through Java coding interview questions.   Problem Given an array with positive integers as elements indicating the maximum length of a jump which can be made from any position in the array. Check if it is possible to have a jumps combination […]

  • 17 February

    Check if Array Elements are Consecutive

    If you want to practice data structure and algorithm programs, you can go through 100+ data structure and algorithm programs. In this post, we will see how to check if array elements are consecutive. Problem Given an array, we need to check if array contains consecutive elements. For example: Input: array[] = {5, 3, 4, […]

Comments

  1. Hey,

    Amazing job and a great explanation. Keep up the good work. You are helping the community. I completely support you.

Leave a Reply

Your email address will not be published. Required fields are marked *

Subscribe to our newletter

Get quality tutorials to your inbox. Subscribe now.