Program to check if N is a Centered heptagonal number

Given an integer N, the task is to check if it is a Centered heptagonal number or not.

Centered heptagonal number is centered figure number that represents a heptagon with dot in center and all other dot surrounding in heptagonal form..The first few Centered heptagonal number are 1, 8, 22, 43, 71, 106, 148, …

Examples:

Input: N = 8
Output: Yes
Explanation:
8 is the Second Centered heptagonal number.

Input: 20
Output: No
Explanation:
20 is not a Centered heptagonal number.



Approach:

To solve the problem mentioned above we have to know that the Kth term of the Centered heptagonal number is given as: K^{th} Term = \frac {7*N^{2} - 7*N + 2}{2}

As we have to check that the given number can be expressed as a Centered heptagonal number or not. This can be checked by generalizing the equation as:

=> N =  \frac {7*k^{2} - 7*k + 2}{2}

=> K = \frac{7 + \sqrt{56*N + 7}}{14}

Finally, check the value of computation using this formula if it is an integer, if yes then it means that N is a Centered heptagonal number.

Below is the implementation of the above approach:

C++

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// C++ implementation to check that
// a number is a Centered
// heptagonal number or not
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to check that the
// number is a Centered
// heptagonal number
bool isCenteredheptagonal(int N)
{
    float n = (7 + sqrt(56 * N - 7)) / 14;
  
    // Condition to check if the
    // number is a Centered heptagonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
int main()
{
    int n = 8;
  
    // Function call
    if (isCenteredheptagonal(n)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

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Java

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// Java implementation to check that 
// a number is a Centered 
// heptagonal number or not 
import java.lang.Math;
  
class GFG
{
      
// Function to check that the 
// number is a Centered 
// heptagonal number 
public static boolean isCenteredheptagonal(int N) 
    double n = (7 + Math.sqrt(56 * N - 7)) / 14
  
    // Condition to check if the 
    // number is a Centered heptagonal number 
    return (n - (int)n) == 0
  
// Driver Code
public static void main(String[] args) 
{
    int n = 8
  
    // Function call 
    if (isCenteredheptagonal(n)) 
    
        System.out.println("Yes");
    
    else 
    
        System.out.println("No");
    
}
}
  
// This code is contributed by divyeshrabadiya07

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Python3

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# Python3 implementation to check 
# that a number is a centered
# heptagonal number or not
import math
  
# Function to check that the
# number is a centered
# heptagonal number
def isCenteredheptagonal(N):
      
    n = (7 + math.sqrt(56 * N - 7)) / 14
      
    # Condition to check if the number
    # is a centered heptagonal number
    return (n - int(n)) == 0
      
# Driver Code
n = 8
  
# Function call
if (isCenteredheptagonal(n)):
    print("Yes")
else:
    print("No")
      
# This code is contributed by ShubhamCoder

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C#

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// C# implementation to check that
// a number is a centered
// heptagonal number or not
using System;
  
class GFG{
  
// Function to check that the
// number is a centered
// heptagonal number
static bool isCenteredheptagonal(int N)
{
    double n = (7 + Math.Sqrt(56 * N - 7)) / 14;
      
    // Condition to check if the number
    // is a centered heptagonal number
    return (n - (int)n) == 0;
}
      
// Driver Code
static public void Main ()
{
    int n = 8;
      
    // Function call
    if (isCenteredheptagonal(n))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
  
// This code is contributed by ShubhamCoder

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Output:

Yes

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