How to Efficiently Generate the Powerset of a Set in Java?

Finding Powersets in Java: An Efficient Approach

The powerset of a set encompasses all possible subsets of the original set. For a set of size n, the powerset contains 2^n elements. In Java, it's common to handle the creation of powersets using efficient algorithms.

Consider the example:

Set mySet = new HashSet<>();
mySet.add(1);
mySet.add(2);
mySet.add(3);
Set> powerSet = getPowerset(mySet);

With this setup, the task is to design the getPowerset function that generates the powerset of mySet with optimal time complexity.

Optimal Time Complexity: O(2^n)

As mentioned, the powerset contains 2^n elements. Therefore, generating all these elements will inherently require O(2^n) time complexity.

Implementation

The following code offers a generic and efficient implementation:

public static Set> powerSet(Set originalSet) {

Set<Set<T>> sets = new HashSet<>();
if (originalSet.isEmpty()) {
    sets.add(new HashSet<>());
    return sets;
}
List<T> list = new ArrayList<>(originalSet);
T head = list.get(0);
Set<T> rest = new HashSet<>(list.subList(1, list.size()));
for (Set<T> set : powerSet(rest)) {
    Set<T> newSet = new HashSet<>();
    newSet.add(head);
    newSet.addAll(set);
    sets.add(newSet);
    sets.add(set);
}
return sets;

}

Example

Utilizing the example provided earlier:

Set mySet = new HashSet<>();
mySet.add(1);
mySet.add(2);
mySet.add(3);
for (Set s : powerSet(mySet)) {

System.out.println(s);

}

The output will be:

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

This demonstrates the creation of the powerset of the specified set with O(2^n) time complexity.

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