Program to check if N is a Centered Pentadecagonal Number
Given a number N, the task is to check whether N is a Centered pentadecagonal number or not. If the number N is a Centered Pentadecagonal Number then print “Yes” else print “No”.
Centered Pentadecagonal Number represents a dot in the centre and other dots surrounding it in successive Pentadecagonal(15-sided polygon) layers. The first few Centered pentadecagonal numbers are 1, 16, 46 …
Examples:
Input: N = 16
Output: Yes
Explanation:
Second Centered pentadecagonal number is 16.
Input: N = 20
Output: No
Approach:
1. The Kth term of the Centered pentadecagonal number is given as:
2. As we have to check that the given number can be expressed as a Centered Pentadecagonal 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 Pentadecagonal Number.
4. Else the number N is not a Centered Pentadecagonal 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 number N is a // Centered Pentadecagonal Number bool isCenteredpentadecagonal( int N) { float n = (16 + sqrt (120 * N + 105)) / 30; // Condition to check if N is a // Centered Pentadecagonal Number return (n - ( int )n) == 0; } // Driver Code int main() { // Given Number int N = 16; // Function call if (isCenteredpentadecagonal(N)) { cout << "Yes" ; } else { cout << "No" ; } return 0; } |
Java
// Java program for the above approach class GFG{ // Function to check if number N is a // Centered Pentadecagonal Number static boolean isCenteredpentadecagonal( int N) { float n = ( float )( 16 + Math.sqrt( 120 * N + 105 )) / 30 ; // Condition to check if N is a // Centered Pentadecagonal Number return (n - ( int )n) == 0 ; } // Driver Code public static void main(String[] args) { // Given Number int N = 16 ; // Function call if (isCenteredpentadecagonal(N)) { System.out.println( "Yes" ); } else { System.out.println( "No" ); } } } // This code is contributed by rutvik_56 |
Python3
# Python3 program for the above approach import math # Function to check if number N is a # centered pentadecagonal number def isCenteredpentadecagonal(N): n = ( 16 + math.sqrt( 120 * N + 105 )) / 30 # Condition to check if N is a # centered pentadecagonal number return (n - int (n)) = = 0 # Driver Code N = 16 # Function call if isCenteredpentadecagonal(N): print ( "Yes" ) else : print ( "No" ) # This code is contributed by ishayadav181 |
C#
// C# program for the above approach using System; class GFG{ // Function to check if number N is a // centered pentadecagonal number public static bool isCenteredpentadecagonal( int N) { double n = (16 + Math.Sqrt(120 * N + 105)) / 30; // Condition to check if N is a // centered pentadecagonal number return (n - ( int )n) == 0; } // Driver code public static void Main() { // Given number int N = 16; // Function call if (isCenteredpentadecagonal(N)) { Console.WriteLine( "Yes" ); } else { Console.WriteLine( "No" ); } } } // This code is contributed by divyeshrabadiya07 |
Javascript
<script> // Javascript program for the above approach // Function to check if number N is a // Centered Pentadecagonal Number function isCenteredpentadecagonal(N) { var n = (16 + Math.sqrt(120 * N + 105)) / 30; // Condition to check if N is a // Centered Pentadecagonal Number return (n - (parseInt(n))) == 0; } // Driver Code // Given Number var N = 16; // Function call if (isCenteredpentadecagonal(N)) { document.write( "Yes" ); } else { document.write( "No" ); } // This code is contributed by Kirti </script> |
Output:
No
Time Complexity: O(logN) since inbuilt sqrt function has been used
Auxiliary Space: O(1)