combineSumSticks.js

const Heap = require('heap');

/**
 * Combine sticks, while adding the sums, to get the lowest combined sum possible
 * @param {[number]} sticks - array of lengths
 * @return {number}
 */
function combineSumSticks(sticks) {
  const heap = new Heap();
  var totalSum = 0;

  sticks.forEach(stick => heap.push(stick));
  var smStick, smallStick;

  while (heap.peek()) {
    smStick = heap.pop();
    smallStick = heap.pop();

    if (!smStick || !smallStick) {
      break;
    }

    var sumStick = smStick + smallStick;

    totalSum += sumStick;
    heap.push(sumStick);
  }

  return totalSum;
}

combineSumSticks([1, 2, 3, 4]); // 19
combineSumSticks([1, 2, 3, 4, 5]); // 33
combineSumSticks([1, 2, 3, 4, 5, 6]); // 51