Program to check if N is a Octadecagon number

Last Updated : 22 Dec, 2022

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

Octadecagon Number is a 18-sided polygon. The first few Octadecagon Numbers are 1, 18, 51, 100, 165, 246, 343, ...

Examples:

Input: N = 18
Output: Yes
Explanation:
Second Octadecagon number is 18.

Input: N = 30
Output: No

Approach:

1. The K^th term of the Octadecagon number is given as
K^{th} Term = \frac{16*K^{2} - 14*K}{2}
2. As we have to check whether the given number can be expressed as an Octadecagon Number or not. This can be checked as:

=> N = \frac{16*K^{2} - 14*K}{2}
=> K = \frac{14 + \sqrt{128*N + 196}}{32}

3. If the value of K calculated using the above formula is an integer, then N is an Octadecagon Number.
4. Else N is not an Octadecagon 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
// Octadecagon Number
bool isOctadecagon(int N)
{
    float n
        = (14 + sqrt(128 * N + 196))
          / 32;

    // Condition to check if the
    // number is a Octadecagon number
    return (n - (int)n) == 0;
}

// Driver Code
int main()
{
    // Given Number
    int N = 18;

    // Function call
    if (isOctadecagon(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 
// octadecagon Number 
public static boolean isOctadecagon(int N) 
{ 
    double n = (14 + Math.sqrt(128 * N + 
                               196)) / 32; 
    
    // Condition to check if the 
    // number is a octadecagon number 
    return (n - (int)n) == 0; 
} 

// Driver Code    
public static void main(String[] args) 
{
        
    // Given Number 
    int N = 18; 
    
    // Function call 
    if (isOctadecagon(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
# octadecagon number
def isOctadecagon(N):

    n = (14 + math.sqrt(128 * N + 196)) // 32
    
    # Condition to check if the
    # number is a octadecagon number
    return ((n - int(n)) == 0)

# Driver code 
if __name__=='__main__':
    
    # Given number
    N = 18
    
    # Function Call
    if isOctadecagon(N):
        print('Yes')
    else:
        print('No')

# This code is contributed by rutvik_56

// C# program for the above approach 
using System;
class GFG{
    
// Function to check if N is a 
// octadecagon Number 
public static bool isOctadecagon(int N) 
{ 
    double n = (14 + Math.Sqrt(128 * N + 
                               196)) / 32; 
    
    // Condition to check if the 
    // number is a octadecagon number 
    return (n - (int)n) == 0; 
} 

// Driver Code 
public static void Main(String[] args) 
{
        
    // Given Number 
    int N = 18; 
    
    // Function call 
    if (isOctadecagon(N))
    { 
        Console.WriteLine("Yes");
    } 
    else
    { 
        Console.WriteLine("No");
    } 
}
}

// This code is contributed by 29AjayKumar

JavaScript

<script>

// javascript program for the above approach


/// Function to check if N is a
// Octadecagon Number
function isOctadecagon( N)
{
    let n
        = (14 + Math.sqrt(128 * N + 196))
          / 32;

    // Condition to check if the
    // number is a Octadecagon number
    return (n - parseInt(n)) == 0;
}


// Driver Code

    // Given Number
    let N = 18;

    // Function Call
    if (isOctadecagon(N)) {
        document.write( "Yes");
    }
    else {
        document.write( "No");
    }

// This code contributed by gauravrajput1 

</script>