Check if a number is an enneacontagon number

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

enneacontagon number: is class of figurate number. It has 90 – sided polygon called enneacontagon. The N-th enneacontagon number count’s the 90 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few enneacontagonol numbers are 1, 90, 267, 532 …

Examples :

Input : N = 90 
Output :  Yes 
Explanation :  
Second enneacontagon number is 90. 

Input :  35 
Output :  No

Approach :

1. The K^th term of the enneacontagon number is given as K^th Term = (88*K² – 86*K) / 2
2. As we have to check that the given number can be expressed as a enneacontagon number or not. This can be checked as follows –

N = (88*K2 - 86*K) / 2, so K = (86 + sqrt(704*N + 7396)) / 176

1. Finally, check the value of computed using this formulae is an integer, which means that N is a enneacontagon number.

Implementation :

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

#include <bits/stdc++.h>

using namespace std;

// Function to check that the
// number is a  enneacontagon number
bool isEnneacontagon(int N)
{
    float n
        = (86 + sqrt(704*N + 7396))
          / 176;

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

// Driver Code
int main()
{
    int i = 90;

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

Yes