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478. Generate Random Point in a Circle

Description

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].

 

Example 1:

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]

 

Constraints:

  • 0 < radius <= 108
  • -107 <= x_center, y_center <= 107
  • At most 3 * 104 calls will be made to randPoint.

Solutions

  • 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]

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