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

Generating the Powerset of a Set in Java

The powerset of a set is the set of all subsets of that set. For example, the powerset of {1, 2, 3} is:

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

Suppose we have a Set in Java:

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

How can we write the getPowerset function with the optimal time complexity?

Solution

The time complexity of the powerset function is O(2^n), where n is the number of elements in the set. This is because the powerset of a set with n elements contains 2^n subsets.

Here's a working implementation of the getPowerset function using generics and sets:

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

Test

Let's test the getPowerset function with the given example input:

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

This will print the following output:

[]
[1]
[2]
[1, 2]
[3]
[1, 3]
[2, 3]
[1, 2, 3]

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