Approximate Pi from Random Points

You are given an array pts of points in the unit square. Each point is represented as an array of two numbers [x, y], where 0 <= x <= 1 and 0 <= y <= 1.

A point lies inside the quarter circle of radius 1 if x*x + y*y <= 1.

Write a function approx(pts) that returns an approximation of pi using the fraction of points that fall inside the quarter circle.

Assume:

• pts is never null
• pts contains at least one point
• every point has exactly two numeric coordinates

Example function signature:

function approx(pts) {
  return 0;
}

Approximate Pi from Random Points

You are given an array pts of points in the unit square [0, 1] x [0, 1]. Each point is represented as [x, y]. A point lies inside the quarter circle of radius 1 centered at the origin if x*x + y*y <= 1.

Use the fraction of points that fall inside the quarter circle to approximate pi. Since the area of the quarter circle is pi / 4 and the area of the unit square is 1, the approximation is:

pi ≈ 4 * (number of points inside the quarter circle) / (total number of points)

Write a function that returns this approximation as a floating-point number.

Constraints

• 1 <= len(pts) <= 100000
• Each point has exactly two numeric coordinates
• 0 <= x <= 1 and 0 <= y <= 1 for every point

Hints

1. First count how many points satisfy x*x + y*y <= 1.
2. The ratio inside / total estimates the area of the quarter circle, which is pi / 4.