freeCodeCamp Challenge Guide: Problem 85: Counting rectangles

Guide
#1

Problem 85: Counting rectangles

Solutions

Solution 1 (Click to Show/Hide) 
function countingRectangles(n) {
  function numberOfRectangles(h, w) {
    return (h * (h + 1) * w * (w + 1)) / 4;
  }

  function rectangleArea(h, w) {
    return h * w;
  }

  let rectanglesCount = 1;
  let maxSide = 1;
  while (rectanglesCount < n) {
    maxSide++;
    rectanglesCount = numberOfRectangles(maxSide, 1);
  }

  let bestDiff = Math.abs(rectanglesCount - n);
  let bestSize = [maxSide, 1];

  let curHeight = maxSide - 1;
  let curWidth = 1;

  for (curWidth; curWidth < curHeight; curWidth++) {
    for (curHeight; curHeight > curWidth; curHeight--) {
      rectanglesCount = numberOfRectangles(curHeight, curWidth);
      const curDiff = Math.abs(rectanglesCount - n);
      if (curDiff < bestDiff) {
        bestDiff = curDiff;
        bestSize = [curHeight, curWidth];
      }

      if (rectanglesCount < n) {
        break;
      }
    }
  }
  return rectangleArea(...bestSize);
}