Program to check if N is a Centered nonadecagonal number

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

Centered nonadecagonal number represents a dot in the centre and other dots surrounding it in successive nonadecagon(19 sided polygon) layers.The first few Centered nonadecagonal numbers are 1, 20, 58, 115, 191, 286

Examples:

Input: N = 20 
Output: Yes 
Explanation:
20 is the Second Centered nonadecagonal number is 20.
Input: 38 
Output: No 
Explanation:
38 is not a Centered nonadecagonal number. 

Approach: To solve the problem mentioned above we have to know that the K^th term of the Centered nonadecagonal number is given as: 
As we have to check that the given number can be expressed as a Centered nonadecagonal number or not. This can be checked by generalizing the formula to:

=> 
=> 

Finally, check the value of computation using this formula if it is an integer, if yes then it means that N is a Centered nonadecagonal number.
Below is the implementation of the above approach:

C++

// C++ implementation to check that
// a number is a Centered
// nonadecagonal number or not

#include <bits/stdc++.h>
using namespace std;

// Function to check that the
// number is a Centered
// nonadecagonal number
bool isCenterednonadecagonal(int N)
{
    float n = (19
               + sqrt(152 * N + 209))
              / 38;

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

// Driver Code
int main()
{
    int n = 20;

    // Function call
    if (isCenterednonadecagonal(n)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java implementation to check that
// a number is a Centered
// nonadecagonal number or not
class GFG{

// Function to check that the
// number is a Centered
// nonadecagonal number
static boolean isCenterednonadecagonal(int N)
{
    float n = (float)((19 + Math.sqrt(152 * N +
                                      209)) / 38);

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

// Driver Code
public static void main(String[] args)
{
    int n = 20;

    // Function call
    if (isCenterednonadecagonal(n))
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}

// This code is contributed by sapnasingh4991

Python3

# Python3 implementation to check that
# a number is a Centered
# nonadecagonal number or not
import math

# Function to check that the
# number is a Centered
# nonadecagonal number
def isCenterednonadecagonal(N):

    n = (19 + math.sqrt(152 * N +
                        209)) / 38;

    # Condition to check if the
    # number is a Centered
    # nonadecagonal number
    return (n - int(n)) == 0;

# Driver Code
n = 20;

# Function call
if (isCenterednonadecagonal(n)):
    print("Yes");

else:
    print("No");

# This code is contributed by Code_Mech

C#

// C# implementation to check that
// a number is a Centered
// nonadecagonal number or not
using System;
class GFG{

// Function to check that the
// number is a Centered
// nonadecagonal number
static bool isCenterednonadecagonal(int N)
{
    float n = (float)((19 + Math.Sqrt(152 * N +
                                      209)) / 38);

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

// Driver Code
public static void Main()
{
    int n = 20;

    // Function call
    if (isCenterednonadecagonal(n))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}

// This code is contributed by Nidhi_biet

Javascript

<script>

// Javascript implementation to check that
// a number is a Centered
// nonadecagonal number or not

// Function to check that the
// number is a Centered
// nonadecagonal number
function isCenterednonadecagonal(N)
{
    var n = (19
               + Math.sqrt(152 * N + 209))
              / 38;

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

// Driver Code
var n = 20;

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


</script>

Output:

Yes

Time Complexity: O(logn) for given n, because it using inbuilt sqrt function
Auxiliary Space: O(1)