478. Generate Random Point in a Circle

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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.

思路：naive的想法就是reject sample

import random

class Solution(object):

    def __init__(self, radius, x_center, y_center):
        """
        :type radius: float
        :type x_center: float
        :type y_center: float
        """
        self.radius=radius
        self.x_center=x_center
        self.y_center=y_center
        

    def randPoint(self):
        """
        :rtype: List[float]
        """
        while 1:
            x=random.uniform(self.x_center-self.radius, self.x_center+self.radius)
            y=random.uniform(self.y_center-self.radius, self.y_center+self.radius)
            if (x-self.x_center)**2+(y-self.y_center)**2<=self.radius**2: break
        return [x,y]


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

这样做不是很高效，一种思路是转换到极坐标系，角度随机选，但是半径不能均匀选，因为需要的是半径的平方是均分分布（就是CDF），所以半径就是均匀分布的开方

class Solution {
    double radius, x_center, y_center;
    public Solution(double radius, double x_center, double y_center) {
        this.radius=radius;
        this.x_center=x_center;
        this.y_center=y_center;
    }
    
    public double[] randPoint() {
        double len= Math.sqrt(Math.random())*radius;
        double deg= Math.random()*2*Math.PI;
        double x= x_center+len*Math.cos(deg);
        double y= y_center+len*Math.sin(deg);
        return new double[]{x,y};
    }
}