478. Generate Random Point in a Circle

Given the radius and x-y positions of the center of a circle, write a function randPoint which generates a uniform random point in the circle.

Note:
input and output values are in floating-point.
radius and x-y position of the center of the circle is passed into the class constructor.
a point on the circumference of the circle is considered to be in the circle.
randPoint returns a size 2 array containing x-position and y-position of the random point, in that order.

Example 1:
Input:
[“Solution”,”randPoint”,”randPoint”,”randPoint”]
[[1,0,0],[],[],[]]
Output: [null,[-0.72939,-0.65505],[-0.78502,-0.28626],[-0.83119,-0.19803]]

Example 2:
Input:
[“Solution”,”randPoint”,”randPoint”,”randPoint”]
[[10,5,-7.5],[],[],[]]
Output: [null,[11.52438,-8.33273],[2.46992,-16.21705],[11.13430,-12.42337]]
Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution’s constructor has three arguments, the radius, x-position of the center, and y-position of the center of the circle. randPoint has no arguments. Arguments are always wrapped with a list, even if there aren’t any.

Solution:
math logical - x^2 + y^2 = r^2

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import math
import random
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
        self.x_min = x_center - radius
        self.x_max = x_center + radius
        self.y_min = y_center - radius
        self.y_max = y_center + radius

    def randPoint(self) -> List[float]:
        while True:
            x, y = random.uniform(self.x_min, self.x_max), random.uniform(self.y_min, self.y_max)
            if math.pow((x-self.x_center), 2) + math.pow((y-self.y_center), 2) <= math.pow(self.radius, 2):
                return [x, y]


# Your Solution object will be instantiated and called as such:
# obj = Solution(radius, x_center, y_center)
# param_1 = obj.randPoint()

references

• https://leetcode.com/problems/generate-random-point-in-a-circle/