// idea: do not ever sort
// simply keep looping from left to right and back to left
// whenever a smaller number is found,
// subtract as many multiples of that number from the rest of the array

const subtractMultiples = (a: number, b: number): number => {
  // subtract a from b as many times as possible
  const mod = b % a;
  if (mod === 0) {
    // figure out how many times a can be subtracted from b
    const div = b / a - 1;
    return b - a * div;
  } else {
    return mod;
  }
}

const operate = (arr: number[]): boolean => {

  let step = 1;
  let i = 0;
  let done = false;
  let hasChangedDuringLoop = false;
  while (!done) {
    if (i + step >= arr.length || i + step < 0) {
      // reverse direction
      step = -step;
      if (!hasChangedDuringLoop) {
        done = true;
      }
      hasChangedDuringLoop = false;
    }

    const first = arr[i];
    const next = arr[i + step];

    if (first > next) {
      arr[i] = subtractMultiples(next, first);
      hasChangedDuringLoop = true;
    } else if (first < next) {
      arr[i + step] = subtractMultiples(first, next);
      hasChangedDuringLoop = true;
    }

    i += step;
  }

  return true;
}

export function solution(numbers: number[]): number {
  let done = false;
  while (!done) {
    done = operate(numbers);
  }

  // sum the numbers
  return numbers.reduce((acc, num) => acc + num, 0);
}