Check if a Number is Triacontakaidigon

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

Triacontakaidigon number is class of figurate number. It has 32 – sided polygon called Triacontakaidigon. The N-th triacontakaidigon number count’s the 32 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few triacontakaidigonol numbers are 1, 32, 93, 184 ….

Examples:

Input: N = 32
Output: Yes
Explanation:
Second triacontakaidigon number is 32.

Input: 35
Output: No

Approach:
The K^th term of the triacontakaidigon number is given as K^{th} Term = (30*K^{2} – 28*K)/2
As we have to check that the given number can be expressed as a triacontakaidigon number or not. This can be checked as follows –

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

Below is the implementation of the above approach:

// C++ implementation to check whether
// a number is a triacontakaidigon number or not

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

// Function to check whether the
// number is a triacontakaidigon number
bool is_triacontakaidigon(int N)
{
    float n = (28 + sqrt(240 * N + 784)) / 60;

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

// Driver Code
int main()
{
    int i = 32;

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

    return 0;
}

Output:

Yes