Given a circle with a radius \(R\) centered at the origin \( (0,0) \) , generate a uniformly random point \( (x,y) \) inside the circle. The point should be evenly distributed over the entire area of the circle, rather than clustering near the center.

• A single positive number \( R \), representing the radius of the circle.

• A tuple \( (x,y) \) representing the coordinates of a randomly generated point inside the circle.

Solution

import random
import math
class Solution:
    def sample_point_in_circle(self, R:int):
        """Sample (x, y) points."""
        theta = random.uniform(0, 2 * math.pi)  # Random angle
        r = R * math.sqrt(random.uniform(0, 1))  # Random radius
        x = r * math.cos(theta)
        y = r * math.sin(theta)
        return (x, y)