Description

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:

  1. input and output values are in floating-point.
  2. radius and x-y position of the center of the circle is passed into the class constructor.
  3. a point on the circumference of the circle is considered to be in the circle.
  4. 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.

分析

题目的意思是：这道题给定一个圆，随机返回圆内的一个点。我最开始用random.random测了一下，发现并没有完全ac。看来问题并不简单。我参考了一下别人的思路，其中x1的random区间为[-1,1],y1的random区间为[-1,1]，那最终的坐标就可以算为：

[self.x_center+x1*self.radius,self.y_center+y1*self.radius]

x1和y1乘以半径，然后加上中心坐标就行了。

代码

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]:
        while(True):
            x1=(random.random()-0.5)*2
            y1=(random.random()-0.5)*2
            if(x1**2+y1**2<=1):
                return [self.x_center+x1*self.radius,self.y_center+y1*self.radius]
        


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

参考文献

​​Simple Python solution with minimum library use (92% Faster)​​