Program to check if N is a Centered Hexadecagonal Number
Given a number N, the task is to check if N is a Centered Hexadecagonal Number or not. If the number N is a Centered Hexadecagonal Number then print “Yes” else print “No”.
Centered Hexadecagonal Number represents a dot in the centre and other dots around it in successive Hexadecagonal(16 sided polygon) layers… The first few Centered Hexadecagonal Numbers are 1, 17, 49, 97, 161, 241 …
Examples:
Input: N = 17
Output: Yes
Explanation:
Second Centered hexadecagonal number is 17.
Input: N = 20
Output: No
Approach:
1. The Kth term of the Centered Hexadecagonal Number is given as
2. As we have to check that the given number can be expressed as a Centered Hexadecagonal 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 Hexadecagonal Number.
4. Else the number N is not a Centered Hexadecagonal 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 the number N // is a Centered hexadecagonal number bool isCenteredhexadecagonal( int N) { float n = (8 + sqrt (32 * N + 32)) / 16; // Condition to check if the N is a // Centered hexadecagonal number return (n - ( int )n) == 0; } // Driver Code int main() { // Given Number int N = 17; // Function call if (isCenteredhexadecagonal(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 the number N // is a centered hexadecagonal number static boolean isCenteredhexadecagonal( int N) { double n = ( 8 + Math.sqrt( 32 * N + 32 )) / 16 ; // Condition to check if the N is a // centered hexadecagonal number return (n - ( int )n) == 0 ; } // Driver code public static void main(String[] args) { // Given Number int N = 17 ; // Function call if (isCenteredhexadecagonal(N)) { System.out.println( "Yes" ); } else { System.out.println( "No" ); } } } // This code is contributed by coder001 |
Python3
# Python3 program for the above approach import numpy as np # Function to check if the number N # is a Centered hexadecagonal number def isCenteredhexadecagonal(N): n = ( 8 + np.sqrt( 32 * N + 32 )) / 16 # Condition to check if the N is a # Centered hexadecagonal number return (n - int (n)) = = 0 # Driver Code N = 17 # Function call if (isCenteredhexadecagonal(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 the number N // is a centered hexadecagonal number static bool isCenteredhexadecagonal( int N) { double n = (8 + Math.Sqrt(32 * N + 32)) / 16; // Condition to check if the N is a // centered hexadecagonal number return (n - ( int )n) == 0; } // Driver code public static void Main( string [] args) { // Given Number int N = 17; // Function call if (isCenteredhexadecagonal(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 the number N // is a Centered hexadecagonal number function isCenteredhexadecagonal( N) { let n = (8 + Math.sqrt(32 * N + 32)) / 16; // Condition to check if the N is a // Centered hexadecagonal number return (n - parseInt(n)) == 0; } // Driver Code // Given Number let N = 17; // Function Call if (isCenteredhexadecagonal(N)) { document.write( "Yes" ); } else { document.write( "No" ); } // This code contributed by Rajput-Ji </script> |
Output:
Yes
Time Complexity: O(logN), for using inbuilt sqrt function.
Auxiliary Space: O(1)