# 478. Generate Random Point in a Circle 在圆内随机生成点

## # 题目描述：

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.

## # 解题方法

``````class Solution:

"""
:type x_center: float
:type y_center: float
"""
self.x = x_center
self.y = y_center

def randPoint(self):
"""
:rtype: List[float]
"""
nr = math.sqrt(random.random()) * self.r
alpha = random.random() * 2 * 3.141592653
newx = self.x + nr * math.cos(alpha)
newy = self.y + nr * math.sin(alpha)
return [newx, newy]

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

C++代码如下：

``````class Solution {
public:
Solution(double radius, double x_center, double y_center) {
x = x_center;
y = y_center;
}

vector<double> randPoint() {
const double PI = 3.141592653;
double nr = sqrt(rand() / double(RAND_MAX)) * rad;
double alpha = rand() / double(RAND_MAX) * 2 * PI;
double nx = x + nr * cos(alpha);
double ny = y + nr * sin(alpha);
return {nx, ny};
}
private:
double x, y;
};

/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(radius, x_center, y_center);
* vector<double> param_1 = obj.randPoint();
*/
``````

https://zhanghuimeng.github.io/post/leetcode-478-generate-random-point-in-a-circle/

## # 日期

2018 年 10 月 14 日 —— 周赛做出来3个题，开心 2019 年 2 月 1 日 —— 2019已经过去了一个月