LeetCode 478. Generate Random Point in a Circle

This is the design problem.
we are given the radius and the xy position of the center of the curcle, we need to generates a uniform random point in the circle.

and we will be given a set of queries, like this:
Input:
[“Solution”,“randPoint”,“randPoint”,“randPoint”]
[[1,0,0],[],[],[]]
Output: [null,[-0.72939,-0.65505],[-0.78502,-0.28626],[-0.83119,-0.19803]]

class Solution {

    public Solution(double radius, double x_center, double y_center) {
        
    }
    
    public double[] randPoint() {
        
    }
}

首先如何uniformly generate?
参见本博主此篇博文：
Java 如何取随机数？

本题也非常简单
遵从了一个原则：一个大的随机均匀取点的区域，其中的任何一个子区域也都是均匀的。
所以我们就先在正方形里面取 然后直到取到圆形中的。
通俗一点讲 这叫Rejection Sampling。

代码如下：

class Solution {

    private double rad, dxc, dyc;
    public Solution(double radius, double x_center, double y_center) {
        rad = radius;
        dxc = x_center;
        dyc = y_center;
    }
    
    public double[] randPoint() {
        //we should choose the number with in the sqaure range, and then check it if in the circle, we only return who is within the circle.
        //we should choose the number in [dxc - rad, dxc + rad], and [dyx - rad, dyc - rad]
        double x = Math.random() * 2 * rad - rad + dxc;
        double y = Math.random() * 2 * rad - rad + dyc;
        while (Math.sqrt(Math.pow(x - dxc, 2) + Math.pow(y - dyc, 2)) >= rad) {
            x = Math.random() * 2 * rad - rad + dxc;
            y = Math.random() * 2 * rad - rad + dyc;
        }
        return new double[]{x, y};
    }
}