Skip to content
Related Articles
Program to check if N is a Nonagonal Number
• Last Updated : 01 Apr, 2021

Given a number N, the task is to check if N is a Nonagonal Number or not. If the number N is an Nonagonal Number then print “Yes” else print “No”.

Nonagonal Number is a figurate number that extends the concept of triangular and square numbers to the Nonagon. Specifically, the nth Nonagonal Numbers count the number of dots in a pattern of n nested nonagons(9 sided polygon), all sharing a common corner, where the ith nonagon in the pattern has sides made of i dots spaced one unit apart from each other. The first few Nonagonal Numbers are 1, 9, 24, 46, 75, 111, 154, …

Examples:

Input: N = 9
Output: Yes
Explanation:
Second Nonagonal Number is 9.

Input: N = 20
Output: No

Approach:

1. The Kth term of the nonagonal number is given as 2. As we have to check that the given number can be expressed as a Nonagonal Number or not. This can be checked as:

=> => 3. If the value of K calculated using the above formula is an integer, then N is a Nonagonal Number.

4. Else N is not a Nonagonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach#include using namespace std; // Function to check if N is a// is a Nonagonal Numberbool isnonagonal(int N){    float n        = (5 + sqrt(56 * N + 25))          / 14;     // Condition to check if the    // number is a nonagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 9;     // Function call    if (isnonagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.lang.Math; class GFG{     // Function to check if N is a// nonagonal numberpublic static boolean isnonagonal(int N){    double n = (5 + Math.sqrt(56 * N + 25)) / 14;         // Condition to check if the    // number is a nonagonal number    return (n - (int)n) == 0;} // Driver code    public static void main(String[] args){             // Given number    int N = 9;         // Function call    if (isnonagonal(N))    {        System.out.println("Yes");    }    else    {        System.out.println("No");    }}} // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 program for the above approach # Function to check if N is a# nonagonal numberdef isnonagonal(N):    n = (5 + pow((56 * N + 25), 1 / 2)) / 14;     # Condition to check if the    # number is a nonagonal number    return (n - int(n)) == 0; # Driver codeif __name__ == '__main__':     # Given number    N = 9;     # Function call    if (isnonagonal(N)):        print("Yes");    else:        print("No"); # This code is contributed by Rajput-Ji

## C#

 // C# program for the above approachusing System; class GFG{     // Function to check if N is a// nonagonal numberpublic static bool isnonagonal(int N){    double n = (5 + Math.Sqrt(56 * N + 25)) / 14;         // Condition to check if the    // number is a nonagonal number    return (n - (int)n) == 0;} // Driver code    public static void Main(string[] args){             // Given number    int N = 9;         // Function call    if (isnonagonal(N))    {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}} // This code is contributed by rutvik_56

## Javascript

 
Output:
Yes

Time Complexity: O(1)

Auxiliary Space: O(1)

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.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live

My Personal Notes arrow_drop_up