# Check whether two convex regular polygon have same center or not

Given two positive integers N and M which denotes the sides of the convex regular polygon where N < M, the task is to check whether polygons have the same center or not if N-sided polygon was inscribed in an M-sided polygon.**Center of Polygon:** Point inside a polygon which is equidistant from each vertex of the polygon. **Examples:**

Input:N = 9, M = 3Output:YESExplanation:

Polygon of side 3 when inscribed in a polygon of side 9, then both polygons have same center.Input:N = 10, M = 3Output:NOExplanation:

Polygon of side 3 when inscribed in a polygon of side 10, then both polygons don’t have same center.

**Approach:** The key observation in this problem is that when **M % N == 0**, that means the sides of N-sided polygon equally covers the sides of M-sided polygon, which means both the polygons have same center.**Algorithm:**

- Check if M is divisible by N, If yes then both the polygons have same center.
- Otherwise both polygons have the different centers.

Below is the implementation of the above approach:

## C++

`// C++ implementation to check whether` `// two convex polygons have same center` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to check whether two convex` `// polygons have the same center or not` `int` `check(` `int` `n, ` `int` `m){` ` ` `if` `(m % n == 0){` ` ` `cout << ` `"YES"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"NO"` `;` ` ` `}` ` ` `return` `0;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 5;` ` ` `int` `m = 10;` ` ` ` ` `check(n, m);` ` ` `return` `0;` `}` |

## Java

`// Java implementation to check whether` `// two convex polygons have same center` `class` `GFG{` ` ` `// Function to check whether two convex` `// polygons have the same center or not` `static` `int` `check(` `int` `n, ` `int` `m){` ` ` `if` `(m % n == ` `0` `){` ` ` `System.out.print(` `"YES"` `);` ` ` `}` ` ` `else` `{` ` ` `System.out.print(` `"NO"` `);` ` ` `}` ` ` `return` `0` `;` `}` ` ` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `5` `;` ` ` `int` `m = ` `10` `;` ` ` ` ` `check(n, m);` `}` `}` `// This code is contributed by sapnasingh4991` |

## Python3

`# Python3 implementation to check whether` `# two convex polygons have same center` `# Function to check whether two convex` `# polygons have the same center or not` `def` `check(n, m):` ` ` `if` `(m ` `%` `n ` `=` `=` `0` `):` ` ` `print` `(` `"YES"` `)` ` ` `else` `:` ` ` `print` `(` `"NO"` `)` `# Driver Code` `n ` `=` `5` `m ` `=` `10` `check(n, m)` `# This code is contributed by mohit kumar 29` |

## C#

`// C# implementation to check whether` `// two convex polygons have same center` `using` `System;` `class` `GFG{` ` ` `// Function to check whether two convex` `// polygons have the same center or not` `static` `int` `check(` `int` `n, ` `int` `m){` ` ` `if` `(m % n == 0){` ` ` `Console.Write(` `"YES"` `);` ` ` `}` ` ` `else` `{` ` ` `Console.Write(` `"NO"` `);` ` ` `}` ` ` `return` `0;` `}` ` ` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `n = 5;` ` ` `int` `m = 10;` ` ` ` ` `check(n, m);` `}` `}` ` ` `// This code is contributed by Rajput-Ji` |

## Javascript

`<script>` `// Javascript implementation to check whether` `// two convex polygons have same center` `// Function to check whether two convex` `// polygons have the same center or not` `function` `check(n, m)` `{` ` ` `if` `(m % n == 0)` ` ` `{` ` ` `document.write(` `"YES"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `document.write(` `"NO"` `);` ` ` `}` ` ` `return` `0;` `}` `// Driver code` `var` `n = 5;` `var` `m = 10;` ` ` `check(n, m);` ` ` `// This code is contributed by Kirti` `</script>` |

**Output:**

YES

**Performance Analysis:**

**Time Complexity:**O(1).**Auxiliary Space:**O(1).