New update is available. Click here to update.

Print All Subsets

PROBLEM STATEMENT

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

Note: elements inside each subset should be sorted in increasing order. But you can print 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.
The subsets can be print in any order.
Output for each test case will be printed in a separate line.

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 i^th bit depicts whether the i^tharray 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 :

Declare a 2-D container ans to store all the subsets
Run a for loop for num from 1 to 2^N -1
Run inner for loop for i from 0 to N-1
If the i^thbit in num has value equal to 1 then include i^th element of the array in the current subset.
Push each subset generated into ans
Finally, sort and print each container inside ans in a separate line

Try Problem

Approach 2

Each element has 2 choices, it can either be included or excluded.

Using backtracking we can create all the possible subsets, we can add the current element to the temporary array and make a recursive call for the next element, when the function call returns we remove the current element from the temporary array and again make a recursive call for the next element (standard backtracking approach).

Each time we reach the end of the array, we will add the temporary array to the answer.

The steps are as follows :

Initialize a 2D vector ans to store all the subsets
Initialize a vector temp to store the current subset
Create a recursive function SubsetFinder which takes the following parameters: idx to store current index, temp vector to store current subset, ans 2D vector to store all subsets, arr vector that is the input vector.
The initial call is made with idx equal to 0, empty temp vector, empty ans 2D vector, given arr input vector
In SubsetFinder we add the idx^th element to temp vector and recursively call SubsetFinder with idx+1
When a function call is returned, we remove the idx^thelement from temp, and again recursively call SubsetFinder with idx+1
If the value of idx is equal to size of the input array, add temp to ans
Finally, sort and print each container inside ans in a separate line