Given a number N, the task is to check if N is a Centered Pentagonal Number or not. If the number N is a Centered Pentagonal Number then print “Yes” else print “No”.
Centered Pentagonal Number is a centered figurate number that represents a pentagon with a dot in the center and other dots surrounding it in pentagonal layers successively. The first few Centered Pentagonal Number are 1, 6, 16, 31, 51, 76, 106 …
Examples:
Input: N = 6
Output: Yes
Explanation:
Second Centered pentagonal number is 6.
Input: N = 20
Output: No
Approach:
1. The Kth term of the Centered Pentagonal Number is given as
2. As we have to check that the given number can be expressed as a Centered Pentagonal 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 Pentagonal Number.
4. Else the number N is not a Centered Pentagonal 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 pentagonal number bool isCenteredpentagonal( int N)
{ float n
= (5 + sqrt (40 * N - 15))
/ 10;
// Condition to check if N is a
// Centered pentagonal number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ // Given Number
int N = 6;
// Function call
if (isCenteredpentagonal(N)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
} |
// Java program for the above approach import java.util.*;
class GFG{
// Function to check if number N // is a centered pentagonal number static boolean isCenteredpentagonal( int N)
{ float n = ( float ) (( 5 + Math.sqrt( 40 * N -
15 )) / 10 );
// Condition to check if N is a
// centered pentagonal number
return (n - ( int )n) == 0 ;
} // Driver Code public static void main(String[] args)
{ // Given Number
int N = 6 ;
// Function call
if (isCenteredpentagonal(N))
{
System.out.print( "Yes" );
}
else
{
System.out.print( "No" );
}
} } // This code is contributed by sapnasingh4991 |
# Python3 program for the above approach import numpy as np
# Function to check if number N # is a centered pentagonal number def isCenteredpentagonal(N):
n = ( 5 + np.sqrt( 40 * N - 15 )) / 10
# Condition to check if N is a
# centered pentagonal number
return (n - int (n)) = = 0
# Driver Code N = 6
# Function call if (isCenteredpentagonal(N)):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed by PratikBasu |
// C# program for the above approach using System;
class GFG{
// Function to check if number N // is a centered pentagonal number static bool isCenteredpentagonal( int N)
{ float n = ( float ) ((5 + Math.Sqrt(40 * N -
15)) / 10);
// Condition to check if N is a
// centered pentagonal number
return (n - ( int )n) == 0;
} // Driver Code public static void Main( string [] args)
{ // Given number
int N = 6;
// Function call
if (isCenteredpentagonal(N))
{
Console.Write( "Yes" );
}
else
{
Console.Write( "No" );
}
} } // This code is contributed by rutvik_56 |
<script> // javascript program for the above approach // Function to check if number N // is a centered pentagonal number function isCenteredpentagonal(N)
{ var n = ((5 + Math.sqrt(40 * N -
15)) / 10);
// Condition to check if N is a
// centered pentagonal number
return (n - parseInt(n) == 0);
} // Driver Code //Given Number var N = 6;
// Function call if (isCenteredpentagonal(N))
{ document.write( "Yes" );
} else { document.write( "No" );
} // This code is contributed by Amit Katiyar </script> |
Output:
Yes
Time Complexity: O(logN) because it is using inbuilt sqrt function
Auxiliary Space: O(1)