# 478. Generate Random Point in a Circle

### Description

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.

**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.

### Constraints

### Approach

### Links

* GeeksforGeeks
* [Leetcode](https://leetcode.com/problems/generate-random-point-in-a-circle/)
* ProgramCreek
* YouTube

### **Examples**

{% tabs %}
{% tab title="Example 1" %}
**Input:**

\["Solution", "randPoint", "randPoint", "randPoint"]

\[\[1, 0, 0], \[], \[], \[]]

**Output:** \[null, \[-0.72939, -0.65505], \[-0.78502, -0.28626], \[-0.83119, -0.19803]]
{% endtab %}

{% tab title="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]]
{% endtab %}
{% endtabs %}

### **Solutions**

{% tabs %}
{% tab title="Solution 1" %}

```java
/**
 * Time complexity : 
 * Space complexity : 
 */

class Solution {
    
    private static final Random random = new Random();
    private double radius;
    private double x_center;
    private double 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 r = Math.sqrt(random.nextDouble()) * radius;
        double theta = random.nextDouble() * 2 * Math.PI;
        return new double[]{
            x_center + r * Math.cos(theta),
            y_center + r * Math.sin(theta)
        };
    }
}

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

{% endtab %}
{% endtabs %}

### **Follow up**

*


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