Generating all the elements of a power set - algorithm

Question

Power set is just set of all subsets for given set.
It includes all subsets (with empty set).
It's well-known that there are 2^N elements in this set, where N is count of elements in original set.
To build power set, following thing can be used:
Create a loop, which iterates all integers from 0 till 2^N-1
Proceed to binary representation for each integer
Each binary representation is a set of N bits (for lesser numbers, add leading zeros).
Each bit corresponds, if the certain set member is included in current subset.
import java.util.NoSuchElementException;
import java.util.BitSet;
import java.util.Iterator;
import java.util.Set;
import java.util.TreeSet;
public class PowerSet<E> implements Iterator<Set<E>>, Iterable<Set<E>> {
private final E[] ary;
private final int subsets;
private int i;
public PowerSet(Set<E> set) {
ary = (E[])set.toArray();
subsets = (int)Math.pow(2, ary.length) - 1;
}
public Iterator<Set<E>> iterator() {
return this;
}
#Override
public void remove() {
throw new UnsupportedOperationException("Cannot remove()!");
}
#Override
public boolean hasNext() {
return i++ < subsets;
}
#Override
public Set<E> next() {
if (!hasNext()) {
throw new NoSuchElementException();
}
Set<E> subset = new TreeSet<E>();
BitSet bitSet = BitSet.valueOf(new long[] { i });
if (bitSet.cardinality() == 0) {
return subset;
}
for (int e = bitSet.nextSetBit(0); e != -1; e = bitSet.nextSetBit(e + 1)) {
subset.add(ary[e]);
}
return subset;
}
// Unit Test
public static void main(String[] args) {
Set<Integer> numbers = new TreeSet<Integer>();
for (int i = 1; i < 4; i++) {
numbers.add(i);
}
PowerSet<Integer> pSet = new PowerSet<Integer>(numbers);
for (Set<Integer> subset : pSet) {
System.out.println(subset);
}
}
}
The output I am getting is:
[2]
[3]
[2, 3]
java.util.NoSuchElementException
at PowerSet.next(PowerSet.java:47)
at PowerSet.next(PowerSet.java:20)
at PowerSet.main(PowerSet.java:67)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:606)
at edu.rice.cs.drjava.model.compiler.JavacCompiler.runCommand(JavacCompiler.java:272)
So, the problems are:
I am got getting all the elements(debugging shows me next is called only for even i's).
The exception should not have been thrown.

Answer 1

The problem is in your hasNext. You have i++ < subsets there. What happens is that since hasNext is called once from next() and once more during the iteration for (Set<Integer> subset : pSet) you increment i by 2 each time. You can see this since
for (Set<Integer> subset : pSet) {
}
is actually equivalent to:
Iterator<PowerSet> it = pSet.iterator();
while (it.hasNext()) {
Set<Integer> subset = it.next();
}
Also note that
if (bitSet.cardinality() == 0) {
return subset;
}
is redundant. Try instead:
#Override
public boolean hasNext() {
return i <= subsets;
}
#Override
public Set<E> next() {
if (!hasNext()) {
throw new NoSuchElementException();
}
Set<E> subset = new TreeSet<E>();
BitSet bitSet = BitSet.valueOf(new long[] { i });
for (int e = bitSet.nextSetBit(0); e != -1; e = bitSet.nextSetBit(e + 1)) {
subset.add(ary[e]);
}
i++;
return subset;
}