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++
// C++ implementation to check that // a number is a Tridecagon number or not #include <bits/stdc++.h> using namespace std;
// Function to check that the // number is a Tridecagon number bool isTridecagon( int N)
{ float n
= (9 + sqrt (88 * N + 81))
/ 22;
// Condition to check if the
// number is a Tridecagon number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ int i = 13;
// Function call
if (isTridecagon(i)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
} |
Java
// Java implementation to check that a // number is a tridecagon number or not class GFG{
// Function to check that the // number is a tridecagon number static boolean isTridecagon( int N)
{ float n = ( float ) (( 9 + Math.sqrt( 88 * N +
81 )) / 22 );
// Condition to check if the
// number is a tridecagon number
return (n - ( int )n) == 0 ;
} // Driver Code public static void main(String[] args)
{ int i = 13 ;
// Function call
if (isTridecagon(i))
{
System.out.print( "Yes" );
}
else
{
System.out.print( "No" );
}
} } // This code is contributed by 29AjayKumar |
Python3
# Python3 implementation to check that # a number is a tridecagon number or not import math
# Function to check that the # number is a tridecagon number def isTridecagon(N):
n = ( 9 + math.sqrt( 88 * N + 81 )) / 22
# Condition to check if the
# number is a tridecagon number
return (n - int (n)) = = 0
# Driver Code i = 13
# Function call if (isTridecagon(i)):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed by divyamohan123 |
C#
// C# implementation to check that a // number is a tridecagon number or not using System;
class GFG{
// Function to check that the // number is a tridecagon number static bool isTridecagon( int N)
{ float n = ( float )((9 + Math.Sqrt(88 * N +
81)) / 22);
// Condition to check if the
// number is a tridecagon number
return (n - ( int )n) == 0;
} // Driver Code public static void Main()
{ int i = 13;
// Function call
if (isTridecagon(i))
{
Console.Write( "Yes" );
}
else
{
Console.Write( "No" );
}
} } // This code is contributed by Code_Mech |
Javascript
<script> // JavaScript implementation to check that // a number is a Tridecagon number or not // Function to check that the // number is a Tridecagon number function isTridecagon(N)
{ var n
= (9 + Math.sqrt(88 * N + 81))
/ 22;
// Condition to check if the
// number is a Tridecagon number
return (n - parseInt(n)) == 0;
} // Driver Code var i = 13;
// Function call if (isTridecagon(i)) {
document.write( "Yes" );
} else {
document.write( "No" );
} </script> |
Output:
Yes
Time Complexity: O(logN) because inbuilt sqrt function is being used
Auxiliary Space: O(1)