Question

The powerset of {1, 2, 3} is:

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

Let’s say I 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 do I write the function getPowerset, with the best possible order of complexity?
(I think it might be O(2^n).)

Answer 1

Yes, it is O(2^n) indeed, since you need to generate, well, 2^n possible combinations. Here’s a working implementation, 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;
}  

And a test, given your example input:

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