gistfile1.js

/*
 * Return an array with the power set of a given string.
 * Definition of power set: The set of all possible subsets including the empty set.
 *
 * Example:
 *
 * powerSet("abc")
 * -> [ '' , 'a', 'b', 'c', 'ab', 'ac', 'bc', 'abc' ]
 *
 * Note:
 *  1. All characters in a subset should be sorted.
 *  2. Sets of the same characters are considered duplicates regardless of order and count only once, e.g. 'ab' and 'ba' are the same.
 *
 * Example 2 :
 *
 * powerSet("jump")
 * -> ["", "j", "ju", "jm", "jp", "jmu", "jmp", "jpu", "jmpu", "u", "m", "p", "mu", "mp", "pu", "mpu"]
 */

var powerSet = function(str){
  var result = {};
  var options = str.split("");

  var recurse = function(options, current) {
    for (var i = 0; i < options.length; i++) {
      if (current.indexOf(options[i]) === -1) {
        var newString = current + options[i];
        recurse(options, newString);
      } else {
        var s = current.split("")
        var sorted = s.sort();
        s = sorted.join("");
        result[s] = s;
      }
    }
  }

  recurse(options, "");

  return Object.keys(result);
}

var result = powerSet('jump');
console.log(result);

[ 'j',
'ju',
'jmu',
'jmpu',
'jpu',
'jm',
'jmp',
'jp',
'u',
'mu',
'mpu',
'pu',
'm',
'mp',
'p' ]

correct answer?

results for balloon

[ 'b',
'ab',
'abl',
'ablo',
'ablno',
'abln',
'abo',
'abno',
'abn',
'bl',
'blo',
'blno',
'bln',
'bo',
'bno',
'bn',
'a',
'al',
'alo',
'alno',
'aln',
'ao',
'ano',
'an',
'l',
'lo',
'lno',
'ln',
'o',
'no',
'n' ]