Given an integer N, the task is to check if N is a Centered Decagonal Number or not. If the number N is a Centered Decagonal Number then print “Yes” else print “No”.
Centered Decagonal Number is centered figurative number that represents a decagon with dot in center and all other dot surrounding it in successive Decagonal Number form. The first few Centered decagonal numbers are 1, 11, 31, 61, 101, 151 …
Examples:
Input: N = 11
Output: Yes
Explanation:
Second Centered decagonal number is 11.
Input: N = 30
Output: No
Approach:
1. The Kth term of the Centered Decagonal Number is given as
2. As we have to check that the given number can be expressed as a Centered Decagonal Number or not. This can be checked as follows:
=>
=>
3. If the value of K calculated using the above formula is an integer, then N is a Centered Decagonal Number.
4. Else the number N is not a Centered Decagonal 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 decagonal number bool isCentereddecagonal( int N)
{ float n
= (5 + sqrt (20 * N + 5))
/ 10;
// Condition to check if N
// is Centered Decagonal Number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ int N = 11;
// Function call
if (isCentereddecagonal(N)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
} |
// Java implementation to check that a number // is a centered decagonal number or not import java.lang.Math;
class GFG{
// Function to check that the number // is a centered decagonal number public static boolean isCentereddecagonal( int N)
{ double n = ( 5 + Math.sqrt( 20 * N + 5 )) / 10 ;
// Condition to check if the number
// is a centered decagonal number
return (n - ( int )n) == 0 ;
} // Driver Code public static void main(String[] args)
{ int n = 11 ;
// Function call
if (isCentereddecagonal(n))
{
System.out.println( "Yes" );
}
else
{
System.out.println( "No" );
}
} } // This code is contributed by ShubhamCoder |
# Python3 program for the above approach import numpy as np
# Function to check if the number N # is a centered decagonal number def isCentereddecagonal(N):
n = ( 5 + np.sqrt( 20 * N + 5 )) / 10
# Condition to check if N
# is centered decagonal number
return (n - int (n)) = = 0
# Driver Code N = 11
# Function call if (isCentereddecagonal(N)):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed by PratikBasu |
// C# implementation to check that a number // is a centered decagonal number or not using System;
class GFG{
// Function to check that the number // is a centered decagonal number static bool isCentereddecagonal( int N)
{ double n = (5 + Math.Sqrt(20 * N + 5)) / 10;
// Condition to check if the number
// is a centered decagonal number
return (n - ( int )n) == 0;
} // Driver Code static public void Main ()
{ int n = 11;
// Function call
if (isCentereddecagonal(n))
{
Console.Write( "Yes" );
}
else
{
Console.Write( "No" );
}
} } // This code is contributed by ShubhamCoder |
<script> // Javascript program for the above approach // Function to check if number N // is a Centered decagonal number function isCentereddecagonal(N)
{ let n
= (5 + Math.sqrt(20 * N + 5))
/ 10;
// Condition to check if N
// is Centered Decagonal Number
return (n - parseInt(n)) == 0;
} // Driver Code let N = 11; // Function call if (isCentereddecagonal(N)) {
document.write( "Yes" );
} else {
document.write( "No" );
} </script> |
Output:
Yes
Time Complexity: O(logn)
Auxiliary Space: O(1)