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++ 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 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 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# 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 |
<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)