# Program to check if N is a Dodecagonal Number

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 whether 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 not bool 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 Code int main() {     // Given Number     int N = 12;       // Function call     if (isdodecagonal(N)) {         cout << "Yes";     }     else {         cout << "No";     }     return 0; }

## Java

 // Java program for the above approach import java.util.*;   class GFG{   // Function to check if number N // is a dodecagonal number or not static 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 Code public 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 approach  import numpy as np   # Function to check if number N  # is a dodecagonal number or not  def 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 Code  N = 12   # Function call  if (isdodecagonal(N)):     print("Yes")  else:     print("No")   # This code is contributed by PratikBasu

## C#

 // C# program for the above approach using System;   class GFG{   // Function to check if number N // is a dodecagonal number or not static 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 Code public 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(log N), since sqrt() function has been used
Auxiliary Space: O(1)

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