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Program to check if N is a Tetradecagonal Number

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  • Last Updated : 15 Jan, 2022
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Given an integer N, the task is to check if N is a Tetradecagonal Number or not. If the number N is a Tetradecagonal Number then print “Yes” else print “No”.

Tetradecagonal Number is 14-sided polygon called Tetrakaidecagon or Tetradecagon and belongs to the figurative number. The nth tetradecagonal number dotted with some dots and create a series of the pattern. They have a common sharing corner point and dotted with their spaces to each other. The dots continue with nth nested loop.The first few Tetradecagonal Numbers are 1, 14, 39, 76, 125, 186, … 
 

Examples:  

Input: N = 14 
Output: Yes 
Explanation: 
Second tetradecagonal number is 14.

Input: N = 40 
Output: No  

Approach:  

  • The Kth term of the tetradecagonal number is given as
    K^{th} Term = \frac{12*K^{2} - 10*K}{2}
  • As we have to check whether the given number can be expressed as a Tetradecagonal Number or not. This can be checked as: 

=> N = \frac{12*K^{2} - 10*K}{2}
=> K = \frac{10 + \sqrt{96*N + 100}}{24}
 

  • If the value of K calculated using the above formula is an integer, then N is a Tetradecagonal Number.
  • Else N is not a Tetradecagonal Number.

Below is the implementation of the above approach: 

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if N is a
// Tetradecagonal Number
bool istetradecagonal(int N)
{
    float n
        = (10 + sqrt(96 * N + 100))
          / 24;
 
    // Condition to check if the
    // number is a tetradecagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    // Given Number
    int N = 11;
 
    // Function call
    if (istetradecagonal(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java




// Java program for the above approach
import java.lang.Math;
 
class GFG{
     
// Function to check if N is a
// tetradecagonal number
public static boolean istetradecagonal(int N)
{
    double n = (10 + Math.sqrt(96 * N +
                               100)) / 24;
     
    // Condition to check if the number
    // is a tetradecagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code   
public static void main(String[] args)
{
         
    // Given number
    int N = 11;
     
    // Function call
    if (istetradecagonal(N))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by divyeshrabadiya07       

Python3




# Python3 program for the above approach
import math
 
# Function to check if N is a
# Tetradecagonal Number
def istetradecagonal(N):
     
    n = (10 + math.sqrt(96 * N + 100)) / 24
     
    # Condition to check if the
    # number is a tetradecagonal number
    if (n - int(n)) == 0:
        return True
         
    return False
 
# Driver Code
 
# Given Number
N = 11
 
# Function call
if (istetradecagonal(N)):
    print("Yes")
else:
    print("No")
 
# This code is contributed by shubhamsingh10

C#




// C# program for the above approach
using System;
 
class GFG{
     
// Function to check if N is a
// tetradecagonal number
public static bool istetradecagonal(int N)
{
    double n = (10 + Math.Sqrt(96 * N +
                               100)) / 24;
         
    // Condition to check if the number
    // is a tetradecagonal number
    return (n - (int)n) == 0;
}
     
// Driver Code
static public void Main ()
{
             
    // Given number
    int N = 11;
         
    // Function call
    if (istetradecagonal(N))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by shubhamsingh10

Javascript




<script>
 
// Javascript program for the above approach
 
// Function to check if N is a
// Tetradecagonal Number
function istetradecagonal(N)
{
    n = (10 + Math.sqrt(96 * N + 100))
          / 24;
 
    // Condition to check if the
    // number is a tetradecagonal number
    return (n - parseInt(n)) == 0;
}
 
// Driver Code
// Given Number
N = 11;
// Function call
if (istetradecagonal(N)) {
    document.write("Yes");
}
else {
    document.write("No");
}
      
</script>

Output: 

No

 

Time Complexity: O(1)

Auxiliary Space: O(1)


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