Given an integer N, the task is to check if it is a Heptadecagonal Number or not. If the number N is an Heptadecagonal Number then print “Yes” else print “No”.
Heptadecagonal Number is class of figurate number. It has 17-sided polygon called heptadecagon. The N-th heptadecagonal number counts the seventeen number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few heptadecagonal numbers are 1, 17, 48, 94, 155, 231…
Examples:
Input: N = 17
Output: Yes
Explanation:
Second heptadecagonal number is 17.
Input: N = 30
Output: No
Approach:
1. The Kth term of the heptadecagonal number is given as
2. As we have to check that the given number can be expressed as a heptadecagonal 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 Heptadecagonal Number.
4. Else N is not a Heptadecagonal 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 heptadecagonal number bool isheptadecagonal( int N)
{ float n
= (13 + sqrt (120 * N + 169))
/ 30;
// Condition to check if number N
// is a heptadecagonal number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ // Given Number
int N = 17;
// Function call
if (isheptadecagonal(N)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
} |
// Java program for the above approach import java.util.*;
class GFG{
// Function to check if the number N // is a heptadecagonal number static boolean isheptadecagonal( int N)
{ float n = ( float ) (( 13 + Math.sqrt( 120 * N +
169 )) / 30 );
// Condition to check if number N
// is a heptadecagonal number
return (n - ( int )n) == 0 ;
} // Driver Code public static void main(String[] args)
{ // Given Number
int N = 17 ;
// Function call
if (isheptadecagonal(N))
{
System.out.print( "Yes" );
}
else
{
System.out.print( "No" );
}
} } // This code is contributed by Amit Katiyar |
# Python3 program for the above approach import numpy as np
# Function to check if the number N # is a heptadecagonal number def isheptadecagonal(N):
n = ( 13 + np.sqrt( 120 * N + 169 )) / 30
# Condition to check if number N
# is a heptadecagonal number
return (n - int (n)) = = 0
# Driver Code N = 17
# Function call if (isheptadecagonal(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 heptadecagonal number static bool isheptadecagonal( int N)
{ float n = ( float ) ((13 + Math.Sqrt(120 * N +
169)) / 30);
// Condition to check if number N
// is a heptadecagonal number
return (n - ( int )n) == 0;
} // Driver Code public static void Main( string [] args)
{ // Given Number
int N = 17;
// Function call
if (isheptadecagonal(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 heptadecagonal number function isheptadecagonal(N)
{ let n
= (13 + Math.sqrt(120 * N + 169))
/ 30;
// Condition to check if number N
// is a heptadecagonal number
return (n - parseInt(n)) == 0;
} // Driver Code // Given Number let N = 17; // Function call if (isheptadecagonal(N)) {
document.write( "Yes" );
} else {
document.write( "No" );
} // This code is contributed by subham348. </script> |
Output:
Yes
Time Complexity: O(logN) because inbuilt sqrt function has been used
Auxiliary Space: O(1)