Given an integer N, the task is to check if N is a Centered Dodecagonal Number or not. If the number N is a Centered Dodecagonal Number then print “Yes” else print “No”.
Centered Dodecagonal Number represents a dot in the center and other dots surrounding it in successive Dodecagonal Number(12 sided polygon) layers. The first few Centered Dodecagonal Numbers are 1, 13, 37, 73 …
Examples:
Input: N = 13
Output: Yes
Explanation:
Second Centered dodecagonal number is 13.
Input: N = 30
Output: No
Approach:
1 The Kth term of the Centered Dodecagonal Number is given as:
2. As we have to check that the given number can be expressed as a Centered Dodecagonal 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 Dodecagonal Number.
4. Else the number N is not a Centered Dodecagonal 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 dodecagonal number bool isCentereddodecagonal( int N)
{ float n
= (6 + sqrt (24 * N + 12))
/ 12;
// Condition to check if N
// is a Centered Dodecagonal Number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ // Given Number
int N = 13;
// Function call
if (isCentereddodecagonal(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 dodecagonal number static boolean isCentereddodecagonal( int N)
{ float n = ( float ) (( 6 + Math.sqrt( 24 * N +
12 )) / 12 );
// Condition to check if N is a
// centered dodecagonal number
return (n - ( int )n) == 0 ;
} // Driver Code public static void main(String[] args)
{ // Given Number
int N = 13 ;
// Function call
if (isCentereddodecagonal(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 the number N # is a centered dodecagonal number def isCentereddodecagonal(N):
n = ( 6 + np.sqrt( 24 * N + 12 )) / 12
# Condition to check if N
# is a centered dodecagonal number
return (n - int (n)) = = 0
# Driver Code N = 13
# Function call if (isCentereddodecagonal(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 dodecagonal number static bool isCentereddodecagonal( int N)
{ float n = ( float ) ((6 + Math.Sqrt(24 * N +
12)) / 12);
// Condition to check if N is a
// centered dodecagonal number
return (n - ( int )n) == 0;
} // Driver Code public static void Main( string [] args)
{ // Given Number
int N = 13;
// Function call
if (isCentereddodecagonal(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 dodecagonal number function isCentereddodecagonal(N)
{ let n
= (6 + Math.sqrt(24 * N + 12))
/ 12;
// Condition to check if N
// is a Centered Dodecagonal Number
return (n - parseInt(n)) == 0;
} // Driver Code // Given Number let N = 13; // Function call if (isCentereddodecagonal(N)) {
document.write( "Yes" );
} else {
document.write( "No" );
} // This code is contributed by subham348. </script> |
Output:
Yes
Time Complexity: O(logN) because it is using inbuilt sqrt function
Auxiliary Space: O(1)