# Program to check if N is a Dodecagonal Number

• Last Updated : 01 Apr, 2021

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

dodecagonal number represent Dodecagonal(12 sides polygon).The first few dodecagonal numbers are 1, 12, 33, 64, 105, 156, 217…

Examples:

Input: N = 12
Output: Yes
Explanation:
Second dodecagonal number is 12.

Input: N = 30
Output: No

Approach:

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

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

4. Else the number N is not a Dodecagonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach#include using namespace std; // Function to check if number N// is a dodecagonal number or notbool isdodecagonal(int N){    float n        = (4 + sqrt(20 * N + 16))          / 10;     // Condition to check if the    // N is a dodecagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 12;     // Function call    if (isdodecagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.util.*; class GFG{ // Function to check if number N// is a dodecagonal number or notstatic boolean isdodecagonal(int N){    float n = (float) ((4 + Math.sqrt(20 * N +                                      16)) / 10);     // Condition to check if the    // N is a dodecagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void main(String[] args){         // Given Number    int N = 12;     // Function call    if (isdodecagonal(N))    {        System.out.print("Yes");    }    else    {        System.out.print("No");    }}} // This code is contributed by sapnasingh4991

## Python3

 # Python3 program for the above approachimport numpy as np # Function to check if number N# is a dodecagonal number or notdef isdodecagonal(N):     n = (4 + np.sqrt(20 * N + 16)) / 10     # Condition to check if the    # N is a dodecagonal number    return (n - int(n)) == 0 # Driver CodeN = 12 # Function callif (isdodecagonal(N)):    print("Yes")else:    print("No") # This code is contributed by PratikBasu

## C#

 // C# program for the above approachusing System; class GFG{ // Function to check if number N// is a dodecagonal number or notstatic bool isdodecagonal(int N){         float n = (float) ((4 + Math.Sqrt(20 * N +                                      16)) / 10);     // Condition to check if the    // N is a dodecagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void Main(string[] args){         // Given number    int N = 12;     // Function call    if (isdodecagonal(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)

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