Given a number N, the task is to check whether N is a Centered pentadecagonal number or not. If the number N is a Centered Pentadecagonal Number then print “Yes” else print “No”.
Centered Pentadecagonal Number represents a dot in the centre and other dots surrounding it in successive Pentadecagonal(15-sided polygon) layers. The first few Centered pentadecagonal numbers are 1, 16, 46 …
Examples:
Input: N = 16
Output: Yes
Explanation:
Second Centered pentadecagonal number is 16.
Input: N = 20
Output: No
Approach:
1. The Kth term of the Centered pentadecagonal number is given as:
2. As we have to check that the given number can be expressed as a Centered Pentadecagonal Number or not. This can be checked as:
=>
=>
3. If the value of K calculated using the above formula is an integer, then N is a Centered Pentadecagonal Number.
4. Else the number N is not a Centered Pentadecagonal Number.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to check if number N is a // Centered Pentadecagonal Number bool isCenteredpentadecagonal( int N)
{ float n
= (16 + sqrt (120 * N + 105))
/ 30;
// Condition to check if N is a
// Centered Pentadecagonal Number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ // Given Number
int N = 16;
// Function call
if (isCenteredpentadecagonal(N)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
} |
// Java program for the above approach class GFG{
// Function to check if number N is a // Centered Pentadecagonal Number static boolean isCenteredpentadecagonal( int N)
{ float n = ( float )( 16 + Math.sqrt( 120 * N +
105 )) / 30 ;
// Condition to check if N is a
// Centered Pentadecagonal Number
return (n - ( int )n) == 0 ;
} // Driver Code public static void main(String[] args)
{ // Given Number
int N = 16 ;
// Function call
if (isCenteredpentadecagonal(N))
{
System.out.println( "Yes" );
}
else
{
System.out.println( "No" );
}
} } // This code is contributed by rutvik_56 |
# Python3 program for the above approach import math
# Function to check if number N is a # centered pentadecagonal number def isCenteredpentadecagonal(N):
n = ( 16 + math.sqrt( 120 * N + 105 )) / 30
# Condition to check if N is a
# centered pentadecagonal number
return (n - int (n)) = = 0
# Driver Code N = 16
# Function call if isCenteredpentadecagonal(N):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed by ishayadav181 |
// C# program for the above approach using System;
class GFG{
// Function to check if number N is a // centered pentadecagonal number public static bool isCenteredpentadecagonal( int N)
{ double n = (16 + Math.Sqrt(120 * N +
105)) / 30;
// Condition to check if N is a
// centered pentadecagonal number
return (n - ( int )n) == 0;
} // Driver code public static void Main()
{ // Given number
int N = 16;
// Function call
if (isCenteredpentadecagonal(N))
{
Console.WriteLine( "Yes" );
}
else
{
Console.WriteLine( "No" );
}
} } // This code is contributed by divyeshrabadiya07 |
<script> // Javascript program for the above approach // Function to check if number N is a // Centered Pentadecagonal Number function isCenteredpentadecagonal(N)
{ var n = (16 + Math.sqrt(120 * N +
105)) / 30;
// Condition to check if N is a
// Centered Pentadecagonal Number
return (n - (parseInt(n))) == 0;
} // Driver Code // Given Number var N = 16;
// Function call if (isCenteredpentadecagonal(N))
{ document.write( "Yes" );
} else { document.write( "No" );
} // This code is contributed by Kirti </script> |
Output:
No
Time Complexity: O(logN) since inbuilt sqrt function has been used
Auxiliary Space: O(1)