Python Program to get all possible differences between set elements

Given a set, the task is to write a Python program to get all possible differences between its elements.

Input : test_set = {1, 5, 2, 7, 3, 4, 10, 14}
Output : {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
Explanation : All possible differences are computed.

Input : test_set = {1, 5, 2, 7}
Output : {1, 2, 3, 4, 5, 6}
Explanation : All possible differences are computed.

Method #1 : Using combinations() + abs() + loop

In this, all the possible pairs are extracted using combinations(). Then loop is used to traverse and abs() is used to get difference. 

Output:

The original set is : {1, 2, 3, 4, 5, 7, 10, 14}

All possible differences : {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

Method #2 : Using set comprehension + combinations() + abs()

In this, we perform task of getting and setting all elements using set comprehension as one liner approach to solve the problem. 

Output:

The original set is : {1, 2, 3, 4, 5, 7, 10, 14}

All possible differences : {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

Method #3: Using nested loops

Using nested loops to iterate over all possible pairs of elements in the set. We compute the absolute difference between each pair and add it to a set. Finally, we return the set of differences.

Algorithm:

1. Create an empty set to store the differences.
2. Use nested loops to iterate over all possible pairs of elements in the set.
3. Compute the absolute difference between each pair of elements.
4. Add the difference to the set of differences.
5. Return the set of differences.

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

Time complexity: O(n^2), where n is the size of the set.The remove() function is a constant time operation and does not affect the time complexity.
Auxiliary Space: O(n), where n is the size of the set

Method #5: Using numpy array and broadcasting

• Convert the set test_set into a numpy array using numpy.array().
• Calculate the absolute difference between the array and its transpose using numpy broadcasting.
• Flatten the resulting array using numpy.ravel() and convert it into a set to remove duplicates.
• Print the resulting set of differences.

OUTPUT : 
All possible differences : {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

Time complexity: O(n^2), where n is the length of the test_set. 
Auxiliary space: O(n^2), for the intermediate array.