Program to check if N is a Tridecagonal Number or not
Given an integer N, the task is to check if it is a Tridecagonal number or not.
Tridecagon number is a thirteen-sided polygon. The first few Tridecagon numbers are 1, 13, 36, 70, 115, 171, …
Examples:
Input: N = 13
Output: Yes
Explanation:
Second Tridecagon number is 13.
Input: N = 30
Output: No
Approach:
- The Kth term of the Tridecagon number is given as
- As we have to check that the given number can be expressed as a Tridecagon 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 Tridecagon number.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
bool isTridecagon( int N)
{
float n
= (9 + sqrt (88 * N + 81))
/ 22;
return (n - ( int )n) == 0;
}
int main()
{
int i = 13;
if (isTridecagon(i)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
}
|
Java
class GFG{
static boolean isTridecagon( int N)
{
float n = ( float ) (( 9 + Math.sqrt( 88 * N +
81 )) / 22 );
return (n - ( int )n) == 0 ;
}
public static void main(String[] args)
{
int i = 13 ;
if (isTridecagon(i))
{
System.out.print( "Yes" );
}
else
{
System.out.print( "No" );
}
}
}
|
Python3
import math
def isTridecagon(N):
n = ( 9 + math.sqrt( 88 * N + 81 )) / 22
return (n - int (n)) = = 0
i = 13
if (isTridecagon(i)):
print ( "Yes" )
else :
print ( "No" )
|
C#
using System;
class GFG{
static bool isTridecagon( int N)
{
float n = ( float )((9 + Math.Sqrt(88 * N +
81)) / 22);
return (n - ( int )n) == 0;
}
public static void Main()
{
int i = 13;
if (isTridecagon(i))
{
Console.Write( "Yes" );
}
else
{
Console.Write( "No" );
}
}
}
|
Javascript
<script>
function isTridecagon(N)
{
var n
= (9 + Math.sqrt(88 * N + 81))
/ 22;
return (n - parseInt(n)) == 0;
}
var i = 13;
if (isTridecagon(i)) {
document.write( "Yes" );
}
else {
document.write( "No" );
}
</script>
|
Time Complexity: O(logN) because inbuilt sqrt function is being used
Auxiliary Space: O(1)
Last Updated :
19 Sep, 2022
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