Generate Random Point in a Circle

lcpy gen -n 478   # by problem number
lcpy gen -s generate_random_point_in_a_circle   # by problem name

Input
["Solution", "randPoint", "randPoint", "randPoint"]
[[1.0, 0.0, 0.0], [], [], []]
Output
[null, [-0.02493, -0.38077], [0.82314, 0.38945], [0.36572, 0.17248]]

Explanation
Solution solution = new Solution(1.0, 0.0, 0.0);
solution.randPoint(); // return [-0.02493, -0.38077]
solution.randPoint(); // return [0.82314, 0.38945]
solution.randPoint(); // return [0.36572, 0.17248]

import math
import random


class Solution:
    # Time: O(1) per rand_point call, O(1) init
    # Space: O(1)

    def __init__(self, radius: float, x_center: float, y_center: float) -> None:
        self.radius = radius
        self.x_center = x_center
        self.y_center = y_center

    def rand_point(self) -> list[float]:
        # Sampling radius as sqrt(u) * R makes the point density uniform per
        # unit area: a uniform angle sweeps equal area only at equal radii, so
        # the radial CDF r^2/R^2 must be inverted with sqrt(u).
        length = math.sqrt(random.random()) * self.radius
        angle = random.uniform(0, 2 * math.pi)
        return [
            self.x_center + length * math.cos(angle),
            self.y_center + length * math.sin(angle),
        ]