Generate random point in a circle

Math Geometry Rejection Sampling Randomized

42.5% acceptance

Jan 13, 2026

480

783

Given the radius and the position of the center of a circle, implement the function randPoint which generates a uniform random point inside the circle. Implement the Solution class: Solution(double radius, double x_center, double y_center) initializes the object with the radius of the circle radius and the position of the center (x_center, y_center). randPoint() returns a random point inside the circle. A point on the circumference of the circle is considered to be in the circle. The answer is returned as an array [x, y].

Solution

Rust

Time O(n)

Space O(n)

LeetCode

solution.rs

use rand::Rng;

struct Solution {
  radius: f64,
  x_center: f64,
  y_center: f64,
}

impl Solution {

  fn new(radius: f64, x_center: f64, y_center: f64) -> Self {
    Solution {
      radius,
      x_center,
      y_center,
    }
  }

  fn rand_point(&self) -> Vec<f64> {
    let mut rng = rand::rng();
    loop {
      let x = rng.random_range(-self.radius..=self.radius);
      let y = rng.random_range(-self.radius..=self.radius);
      if x * x + y * y <= self.radius * self.radius {
        return vec![self.x_center + x, self.y_center + y];
      }
    }
  }
}