Saturday, January 28, 2017

Power Set Algorithm - Iterative

The power set of a set S is the set of all subsets of S including the empty set and S itself. For example, the power set of {1, 2, 3} is {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}.

Previously, I wrote about how you can generate the power set using a recursive algorithm. This time I'll show you how to use iteration.

Recall, that when we are generating a set for the power set, each element can either be in the set or out of the set. In other words, each set can be represented in binary form, where 1 means that the element is in the set and 0 means that it is not. For example, given a set {a, b, c}, the binary string 101 would represent {a, c}.

Generating the power set just comes down to generating all numbers from 0 to 2^n (since there are 2^n possible subsets) and converting the binary representation of the number into the set!

Here is the algorithm:

public static <E> List<List<E>> powerSet(final List<E> list) {
  final List<List<E>> result = new ArrayList<>();
  final int numSubSets = 1 << list.size(); // 2^n
  for (int i = 0; i < numSubSets; i++) {
    final List<E> subSet = new ArrayList<>();
    int index = 0;
    for (int j = i; j > 0; j >>= 1) { // keep shifting right
      if ((j & 1) == 1) { // check last bit
        subSet.add(list.get(index));
      }
      index++;
    }
    result.add(subSet);
  }
  return result;
}

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