Given a number N, the task is to check if N is a Pentadecagon Number or not. If the number N is an Pentadecagon Number then print “Yes” else print “No”.
Pentadecagon Number is a 15-sided polygon..The first few Pentadecagon numbers are 1, 15, 42, 82, 135, 201, …
Examples:
Input: N = 15
Output: Yes
Explanation:
Second Pentadecagon number is 15.
Input: N = 30
Output: No
Approach:
- The Kth term of the Pentadecagon number is given as
- As we have to check that the given number can be expressed as a Pentadecagon Number or not. This can be checked as:
=>
=>
- If the value of K calculated using the above formula is an integer, then N is a Pentadecagon Number.
- Else N is not a Pentadecagon Number.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to check if N is a // Pentadecagon number bool isPentadecagon( int N)
{ float n
= (11 + sqrt (104 * N + 121))
/ 26;
// Condition to check if the
// number is a Pentadecagon number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ // Given Number
int N = 15;
// Function call
if (isPentadecagon(N)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
} |
Java
// Java program for the above approach import java.io.*;
import java.util.*;
class GFG {
// Function to check if N is // a pentadecagon number public static boolean isPentadecagon( int N)
{ double n = ( 11 + Math.sqrt( 104 * N +
121 )) / 26 ;
// Condition to check if the number
// is a pentadecagon number
return (n - ( int )n) == 0 ;
} // Driver code public static void main(String[] args)
{ // Given Number
int N = 15 ;
// Function call
if (isPentadecagon(N))
{
System.out.println( "Yes" );
}
else
{
System.out.println( "No" );
}
} } // This code is contributed by coder001 |
Python3
# Python3 program for the above approach from math import sqrt
# Function to check if N is a # pentadecagon number def isPentadecagon(N):
n = ( 11 + sqrt( 104 * N + 121 )) / 26 ;
# Condition to check if the
# number is a pentadecagon number
return (n - int (n) = = 0 );
# Driver Code if __name__ = = "__main__" :
# Given number
N = 15 ;
# Function call
if (isPentadecagon(N)):
print ( "Yes" );
else :
print ( "No" );
# This code is contributed by AnkitRai01 |
C#
// C# program for the above approach using System;
class GFG {
// Function to check if N is // a pentadecagon number public static bool isPentadecagon( int N)
{ double n = (11 + Math.Sqrt(104 * N +
121)) / 26;
// Condition to check if the number
// is a pentadecagon number
return (n - ( int )n) == 0;
} // Driver code public static void Main(String[] args)
{ // Given Number
int N = 15;
// Function call
if (isPentadecagon(N))
{
Console.WriteLine( "Yes" );
}
else
{
Console.WriteLine( "No" );
}
} } // This code is contributed by Amit Katiyar |
Javascript
<script> // JavaScript program for the above approach // Function to check if N is a // Pentadecagon number function isPentadecagon(N)
{ var n = (11 + Math.sqrt(104 * N + 121))
/ 26;
// Condition to check if the
// number is a Pentadecagon number
return (n - parseInt(n)) == 0;
} // Given Number var N = 15;
// Function call if (isPentadecagon(N)) {
document.write( "Yes" );
} else {
document.write( "No" );
} </script> |
Output:
Yes
Time Complexity: O(logN) since inbuilt sqrt function has been used
Auxiliary Space: O(1)
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