Generate Random Point in a Circle — LeetCode 478 Python Solution

The problem

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).

Example

Input

["Solution", "randPoint", "randPoint", "randPoint"]

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);

Python solution

class Solution:
    def __init__(self, radius: float, x_center: float, y_center: float):
        self.radius = radius
        self.x_center = x_center
        self.y_center = y_center

    def randPoint(self) -> List[float]:
        length = math.sqrt(random.uniform(0, self.radius**2))
        degree = random.uniform(0, 1) * 2 * math.pi
        x = self.x_center + length * math.cos(degree)
        y = self.y_center + length * math.sin(degree)
        return [x, y]

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 478. Generate Random Point in a Circle is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Geometry.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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