bwPowerSet.js

/**
 * Find power-set of a set using BITWISE approach.
 *
 * @param {*[]} originalSet
 * @return {*[][]}
 */
export default function powerSet(originalSet) {
  const subSets = [];

  // We will have 2^n possible combinations (where n is a length of original set).
  // It is because for every element of original set we will decide whether to include
  // it or not (2 options for each set element).
  const numberOfCombinations = 2 ** originalSet.length;

  // Each number in binary representation in a range from 0 to 2^n does exactly what we need:
  // it shows by its bits (0 or 1) whether to include related element from the set or not.
  // For example, for the set {1, 2, 3} the binary number of 0b010 would mean that we need to
  // include only "2" to the current set.
  for (let combinationIndex = 0; combinationIndex < numberOfCombinations; combinationIndex += 1) {
    const subSet = [];

    for (let setElementIndex = 0; setElementIndex < originalSet.length; setElementIndex += 1) {
      // Decide whether we need to include current element into the subset or not.
      if (combinationIndex & (1 << setElementIndex)) {
        subSet.push(originalSet[setElementIndex]);
      }
    }

    // Add current subset to the list of all subsets.
    subSets.push(subSet);
  }

  return subSets;
}