# Find N random points within a Circle

Given four integers N, R, X, and Y such that it represents a circle of radius R with [X, Y] as coordinates of the center. The task is to find N random points inside or on the circle.
Examples:

Input: R = 12, X = 3, Y = 3, N = 5
Output: (7.05, -3.36) (5.21, -7.49) (7.53, 0.19) (-2.37, 12.05) (1.45, 11.80)

Input: R = 5, X = 1, Y = 1, N = 3
Output: (4.75, 1.03) (2.57, 5.21) (-1.98, -0.76)

Approach: To find a random point in or on a circle we need two components, an angle(theta) and distance(D) from the center. After that Now, the point (xi, yi) can be expressed as:

```xi = X + D * cos(theta)
yi = Y + D * sin(theta)
```

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach ` `#include ` `using` `namespace` `std; ` `#define PI 3.141592653589 ` ` `  `// Return a random double between 0 & 1 ` `double` `uniform() ` `{ ` `    ``return` `(``double``)``rand``() / RAND_MAX; ` `} ` ` `  `// Function to find the N random points on ` `// the given circle ` `vector > randPoint( ` `    ``int` `r, ``int` `x, ``int` `y, ``int` `n) ` `{ ` `    ``// Result vector ` `    ``vector > res; ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// Get Angle in radians ` `        ``double` `theta = 2 * PI * uniform(); ` ` `  `        ``// Get length from center ` `        ``double` `len = ``sqrt``(uniform()) * r; ` ` `  `        ``// Add point to results. ` `        ``res.push_back({ x + len * ``cos``(theta), ` `                        ``y + len * ``sin``(theta) }); ` `    ``} ` ` `  `    ``// Return the N points ` `    ``return` `res; ` `} ` ` `  `// Function to display the content of ` `// the vector A ` `void` `printVector( ` `    ``vector > A) ` `{ ` ` `  `    ``// Iterate over A ` `    ``for` `(pair<``double``, ``double``> P : A) { ` ` `  `        ``// Print the N random points stored ` `        ``printf``(``"(%.2lf, %.2lf)\n"``, ` `               ``P.first, P.second); ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Given dimensions ` `    ``int` `R = 12; ` `    ``int` `X = 3; ` `    ``int` `Y = 3; ` `    ``int` `N = 5; ` ` `  `    ``// Function Call ` `    ``printVector(randPoint(R, X, Y, N)); ` `    ``return` `0; ` `} `

## Java

 `// Java program for the above approach ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `     `  `static` `final` `double` `PI = ``3.141592653589``; ` `static` `class` `pair  ` `{ ` `    ``double` `first, second; ` ` `  `    ``public` `pair(``double` `first, ` `                ``double` `second) ` `    ``{ ` `        ``super``(); ` `        ``this``.first = first; ` `        ``this``.second = second; ` `    ``} ` `} ` ` `  `// Return a random double between 0 & 1 ` `static` `double` `uniform(){``return` `Math.random();} ` ` `  `// Function to find the N random points on ` `// the given circle ` `static` `Vector randPoint(``int` `r, ``int` `x,  ` `                              ``int` `y, ``int` `n) ` `{ ` `     `  `    ``// Result vector ` `    ``Vector res = ``new` `Vector(); ` ` `  `    ``for``(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `         `  `        ``// Get Angle in radians ` `        ``double` `theta = ``2` `* PI * uniform(); ` ` `  `        ``// Get length from center ` `        ``double` `len = Math.sqrt(uniform()) * r; ` ` `  `        ``// Add point to results. ` `        ``res.add(``new` `pair(x + len * Math.cos(theta), ` `                         ``y + len * Math.sin(theta))); ` `    ``} ` `     `  `    ``// Return the N points ` `    ``return` `res; ` `} ` ` `  `// Function to display the content of ` `// the vector A ` `static` `void` `printVector(Vector A) ` `{ ` ` `  `    ``// Iterate over A ` `    ``for``(pair P : A) ` `    ``{ ` `         `  `        ``// Print the N random points stored ` `        ``System.out.printf(``"(%.2f, %.2f)\n"``,  ` `                          ``P.first, P.second); ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `     `  `    ``// Given dimensions ` `    ``int` `R = ``12``; ` `    ``int` `X = ``3``; ` `    ``int` `Y = ``3``; ` `    ``int` `N = ``5``; ` ` `  `    ``// Function call ` `    ``printVector(randPoint(R, X, Y, N)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```(7.05, -3.36)
(5.21, -7.49)
(7.53, 0.19)
(-2.37, 12.05)
(1.45, 11.80)
```

Time Complexity: O(N)
Space Complexity: O(N)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : Rajput-Ji

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.