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++
// 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)