Given a number N, the task is to check if N is a Centered Tridecagonal Number or not. If the number N is a Centered Tridecagonal Number then print “Yes” else print “No”.
Centered tridecagonal number represents a dot at the center and other dots surrounding the center dot in the successive tridecagonal(13 sided polygon) layer. The first few Centered tridecagonal numbers are 1, 14, 40, 79 …
Examples:
Input: N = 14
Output: Yes
Explanation:
Second Centered tridecagonal number is 14.
Input: N = 30
Output: No
Approach:
1. The Kth term of the Centered Tridecagonal Number is given as
2. As we have to check that the given number can be expressed as a Centered Tridecagonal 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 Tridecagonal Number.
4. Else the number N is not a Centered Tridecagonal 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 tridecagonal number bool isCenteredtridecagonal( int N)
{ float n
= (13 + sqrt (104 * N + 65))
/ 26;
// Condition to check if the N
// is a Centered tridecagonal number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ // Given Number
int N = 14;
// Function call
if (isCenteredtridecagonal(N)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
} |
// Java program for the above approach class GFG{
// Function to check if the number N // is a centered tridecagonal number static boolean isCenteredtridecagonal( int N)
{ float n = ( float ) (( 13 + Math.sqrt( 104 * N +
65 )) / 26 );
// Condition to check if the N
// is a centered tridecagonal number
return (n - ( int )n) == 0 ;
} // Driver Code public static void main(String[] args)
{ // Given Number
int N = 14 ;
// Function call
if (isCenteredtridecagonal(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 tridecagonal number def isCenteredtridecagonal(N):
n = ( 13 + np.sqrt( 104 * N + 65 )) / 26
# Condition to check if N
# is centered tridecagonal number
return (n - int (n)) = = 0
# Driver Code N = 14
# Function call if (isCenteredtridecagonal(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 tridecagonal number static bool isCenteredtridecagonal( int N)
{ float n = ( float ) ((13 + Math.Sqrt(104 * N +
65)) / 26);
// Condition to check if the N
// is a centered tridecagonal number
return (n - ( int )n) == 0;
} // Driver Code public static void Main( string [] args)
{ // Given Number
int N = 14;
// Function call
if (isCenteredtridecagonal(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 tridecagonal number function isCenteredtridecagonal(N)
{ let n
= (13 + Math.sqrt(104 * N + 65))
/ 26;
// Condition to check if the N
// is a Centered tridecagonal number
return (n - parseInt(n)) == 0;
} // Driver Code // Given Number let N = 14; // Function call if (isCenteredtridecagonal(N)) {
document.write( "Yes" );
} else {
document.write( "No" );
} // This code is contributed by subham348. </script> |
Output:
Yes
Time Complexity: O(logN) since inbuilt sqrt function is being used
Auxiliary Space: O(1)