Find All Subsets

Posted: 23 Jul, 2021
Difficulty: Easy

PROBLEM STATEMENT

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You are given an array ‘arr’ of ‘N’ distinct integers. Your task is to find all the non-empty subsets of the array.

Note: You can return the subsets in any order, you don’t have to specifically sort them.

 

Input Format :
The first line contains a single integer ‘T’ denoting the number of test cases, then each test case follows

The first line of each test case contains a single integers ‘N’ denoting the length of the array.

The second line of each test case contains ‘N’ integers denoting the array elements.
Output Format :
For each test case print each subset in a separate line.

Output for each test case will be printed in a separate line.
Note :
You are not required to print anything; it has already been taken care of. Just implement the function.
Constraints :
1 <= T <= 10      
1 <= N <= 10
10^-9 <= arr[i] <= 10^9

Time limit: 1 sec
Approach 1

 

One of the standard and useful method of finding the power set is through bit-masking.

Consider a number with N-bits in its binary representation, if we consider that the state of ith bit depicts whether the ith array element is included in the current subset or not, then we can uniquely identify one of the subsets (as each number has a different binary representation).

Now we can simply iterate from 1 to 2n-1, each number in this iteration will define a subset uniquely. To generate the subset just check for the bits that are ON in binary representation on the number, and for each ON bit, we will simply include an array element corresponding to its position.

Remember to not include an empty subset in the final answer.

 

The steps are as follows :

  1. Declare a 2-D container ans to store all the subsets
  2. Run a for loop for num from 1 to 2^N -1
  3. Run inner for loop for i from 0 to N-1
  4. If the ith bit in num has value equal to 1 then include ith element of the array in the current subset.
  5. Push each subset generated into ans
  6. Finally, return ans
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