Javascript implementation(s) of a Power Set function

powerset.iterative.js

/* Calculates the power set, P(s) := { s' : s' is a subset of s } 
 * Assumes an implementation of a Set that has the following methods:
 * add, equals, forEach, clone
 */
var powerSet = function(set) {
  var prevSet = new Set();                  // prevSet := {}
  var currSet = new Set().add(new Set());   // currSet := { {} }

  // Main loop will continually add elements to currSet until no
  // new elements are added
  while (!currSet.equals(prevSet)) {
    prevSet = currSet.clone();

    // for c <- currSet:
    currSet.forEach(function(currSetElem) {
      // for e <- s:
      set.forEach(function(setElem) {
        // currSet := currSet U { c U {e} }
        currSet.add(currSetElem.clone().add(setElem));
      });
    });
  }

  return currSet;
};

/* Some complexity analysis:
 * The while loop is O(n), as it loops to compute the singletons, the doubles, the triples, ..., the n-tuples
 * The currSet loop is O(2^n), as the largest it will be is 2^n
 * The set loop is O(n^2), as the set loop is O(n) and the currSetElem.clone() call is O(n), so O(n*n)
 * Thus the total complexity is O(n * n^2 * 2^n) = O(n^3 * 2^n)
 */

powerset.recursive.js

/* Recursive implementation
 */
var powerSet = function(set) {
  var loop = function(prev, curr) {
    if (!prev.equals(curr)) {
      // Need to compute more elements of the power set
      prev = curr.clone();
  
      // for c <- currSet:
      curr.forEach(function(currSetElem) {
        // for e <- s:
        set.forEach(function(setElem) {
          // currSet := currSet U { c U {e} }
          curr.add(currSetElem.clone().add(setElem));
        });
      });

      return loop(prev, curr);
    } else {
      // All elements computed!
      return curr;
    }
  };

  // prev := {}, curr := { {} }
  return loop(new Set(), new Set().add(new Set()));
};