Demonstrates an algorithm for calculating power sets

power_sets.js

function pretty_print(set) {
  set.forEach(item => {
    console.log(JSON.stringify(item));
  })
}

// where set is something of the form [item, item, item]
function get_power_set(set) {
  // our result will itself be a set
  let result = [];
  const set_length = set.length;

  // now for our algorithm.
  let add_length = set_length;
  let iterate_length = 1;
  while (add_length > 0) {
    // we now go through the array as many times as
    // iterate_length, which will be 1 at the start,
    // 2 next, etc, up to set_length-1;
    for (let i = 0; i < iterate_length; i++) {
      // add a subset of the original set to our result
      result = [...result, set.slice(i, iterate_length)]
    }

    // decrement add_length and increment iterate_length
    iterate_length++;
    add_length -= 1;
  }

  // finally push the empty set
  result = [...result, []];

  // order by size for readability
  result.sort((a, b) => a.length > b.length);

  return result;
}

// simple power set
const power_set = get_power_set(['a', 'b', 'c']);

// we can continue to get more abstract
const power_set_of_power_set = get_power_set(power_set);

// show some demonstrations
console.log('---POWER SET---' + `Cardinality: ${power_set.length}`);
pretty_print(power_set);
console.log('---NEXT ORDER POWER SET---' + `Cardinality: ${power_set_of_power_set.length}`);
pretty_print(power_set_of_power_set);

Try it out here: https://codepen.io/helvetici/full/RMOady/