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# 478     Generate Random Point in a Circle

## 478. [Generate Random Point in a Circle](https://leetcode.com/problems/generate-random-point-in-a-circle/description/)

## 1. Question

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](https://www.webopedia.com/TERM/F/floating_point_number.html).
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.

## 2. Implementation

(1) 用极坐标表示

思路:

```java
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;
        int degree = (int)(Math.random() * 360);
        double x = x_center + len * Math.cos(degree);
        double y = y_center + len * Math.sin(degree);
        return new double[] {x, y};
    }
}

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

## 3. Time & Space Complexity

时间复杂度O(1), 空间复杂度O(1)