# leetcode478. Generate Random Point in a Circle

raledong

## 题目要求

``````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1：Rejection Sampling

``````    public double[] randPoint2() {
double x0 = x_center - radius;
double y0 = y_center - radius;
while(true) {
double xg = x0 + Math.random() * radius * 2;
double yg = y0 + Math.random() * radius * 2;
if (Math.pow((xg - x_center) , 2) + Math.pow((yg - y_center), 2) <= radius * radius)
return new double[]{xg, yg};
}
}``````

## 思路二：极坐标

``````    public double[] randPoint() {
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};
}``````

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