Program to check if N is a Heptadecagonal Number
Given an integer N, the task is to check if it is a Heptadecagonal Number or not. If the number N is an Heptadecagonal Number then print “Yes” else print “No”.
Heptadecagonal Number is class of figurate number. It has 17-sided polygon called heptadecagon. The N-th heptadecagonal number counts the seventeen number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few heptadecagonal numbers are 1, 17, 48, 94, 155, 231…
Examples:
Input: N = 17
Output: Yes
Explanation:
Second heptadecagonal number is 17.
Input: N = 30
Output: No
Approach:
1. The Kth term of the heptadecagonal number is given as
2. As we have to check that the given number can be expressed as a heptadecagonal number or not. This can be checked as follows –
=>
=>
3. If the value of K calculated using the above formula is an integer, then N is a Heptadecagonal Number.
4. Else N is not a Heptadecagonal Number.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
bool isheptadecagonal( int N)
{
float n
= (13 + sqrt (120 * N + 169))
/ 30;
return (n - ( int )n) == 0;
}
int main()
{
int N = 17;
if (isheptadecagonal(N)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
}
|
Java
import java.util.*;
class GFG{
static boolean isheptadecagonal( int N)
{
float n = ( float ) (( 13 + Math.sqrt( 120 * N +
169 )) / 30 );
return (n - ( int )n) == 0 ;
}
public static void main(String[] args)
{
int N = 17 ;
if (isheptadecagonal(N))
{
System.out.print( "Yes" );
}
else
{
System.out.print( "No" );
}
}
}
|
Python3
import numpy as np
def isheptadecagonal(N):
n = ( 13 + np.sqrt( 120 * N + 169 )) / 30
return (n - int (n)) = = 0
N = 17
if (isheptadecagonal(N)):
print ( "Yes" )
else :
print ( "No" )
|
C#
using System;
class GFG{
static bool isheptadecagonal( int N)
{
float n = ( float ) ((13 + Math.Sqrt(120 * N +
169)) / 30);
return (n - ( int )n) == 0;
}
public static void Main( string [] args)
{
int N = 17;
if (isheptadecagonal(N))
{
Console.Write( "Yes" );
}
else
{
Console.Write( "No" );
}
}
}
|
Javascript
<script>
function isheptadecagonal(N)
{
let n
= (13 + Math.sqrt(120 * N + 169))
/ 30;
return (n - parseInt(n)) == 0;
}
let N = 17;
if (isheptadecagonal(N)) {
document.write( "Yes" );
}
else {
document.write( "No" );
}
</script>
|
Time Complexity: O(logN) because inbuilt sqrt function has been used
Auxiliary Space: O(1)
Last Updated :
20 Sep, 2022
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