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 K^th 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++ 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;
}

// 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

# 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

// 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

<script>
// Javascript implementation to check that
// a number is a Centered
// heptagonal number or not

// Function to check that the
// number is a Centered
// heptagonal number
function isCenteredheptagonal(N)
{
    let n = (7 + Math.sqrt(56 * N - 7)) / 14;

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

// Driver Code
let n = 8;

// Function call
if (isCenteredheptagonal(n)) {
    document.write("Yes");
}
else {
    document.write("No");
}

// This code is contributed by rishavmahato348.
</script>

Yes

Time Complexity: O(logN)

Auxiliary Space: O(1)