Check if given number is a Dodecahedral number

Given a number N, the task is to check if N is a dodecahedral Number –

Dodecahedral Number belongs to a figurate number and represents it dodecahedron. The first few dodecahedral numbers are 1, 20, 84, 220, 455, 816, 1330 …

Examples:

Input: N = 20
Output: Yes
Explanation: 20 is the second dodecahedral number

Input: N = 6
Output: No

Approach:

The nth term of dodecahedral number is given by \frac{n * (3 * n – 1) * (3 * n – 2)}{2}
Run a loop starting from 1, to find i^th dodecahedral number.
Check if ith term is equal to n or not. If equal return true
If ith term is greater than n then return false
else increment i and continue the loop

Below is the implementation of the above approach:

// C++ program for the above approach 
#include <bits/stdc++.h> 
using namespace std; 

// Function to check if the number N 
// is a dodecahedral number 
bool isDodecahedral(int N) 
{ 
    int i = 1;
    while(true)
    {
        // finding ith term
        int ith_term = i * (3 * i - 1) * (3 * i - 2) / 2; 
        // checking if the number N 
        // is a dodecahedral number 
        if(ith_term == N)
        {
            return true;
        }
        // if ith_term > N then
        // N is not a dodecahedral number
        if(ith_term > N)
        {
            return false;
        }
        // incrementing i
        i++;
    }
} 

// Driver Code 
int main() 
{ 
    // Given Number 
    int N = 20; 

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

Output:

Yes

Time complexity: O(N).