Program to check if N is a Centered Pentagonal Number or not
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++
// 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
// 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
# 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#
// 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 |
Javascript
<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)