Given an integer N, the task is to check if it is a star number or not.
Star number is a centered figurate number that represents a centered hexagram (six-pointed star) similar to Chinese checker game. The first few Star numbers are 1, 13, 37, 73 …
Examples:
Input: N = 13
Output: Yes
Explanation:
Second star number is 13.
Input: 14
Output: No
Explanation:
Second star number is 13, where as 37 is third.
Therefore, 14 is not a star number.
Approach:
- The Kth term of the star number is given as
- As we have to check that the given number can be expressed as a star number or not. This can be checked as follows –
=>
=>
=>
-
- Finally, check the value of computed using this formulae is an integer, which means that N is a star number.
Below is the implementation of the above approach:
// C++ implementation to check that // a number is a star number or not #include <bits/stdc++.h> using namespace std;
// Function to check that the // number is a star number bool isStar( int N)
{ float n
= (6 + sqrt (24 * N + 12))
/ 6;
// Condition to check if the
// number is a star number
return (n - ( int )n) == 0;
} // Driver Code int main()
{ int i = 13;
// Function call
if (isStar(i)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
} |
// Java implementation to check that // a number is a star number or not import java.io.*;
import java.util.*;
class GFG{
// Function to check that the // number is a star number static boolean isStar( int N)
{ double n = ( 6 + Math.sqrt( 24 * N + 12 )) / 6 ;
// Condition to check if the
// number is a star number
return (n - ( int )n) == 0 ;
} // Driver code public static void main(String[] args)
{ int i = 13 ;
// Function call
if (isStar(i))
{
System.out.println( "Yes" );
}
else
{
System.out.println( "No" );
}
} } // This code is contributed by coder001 |
# Python3 implementation to check that # a number is a star number or not import math
# Function to check that the # number is a star number def isStar(N):
n = (math.sqrt( 24 * N + 12 ) + 6 ) / 6
# Condition to check if the
# number is a star number
return (n - int (n)) = = 0
# Driver Code i = 13
# Function call if isStar(i):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed by ishayadav181 |
// C# implementation to check that // a number is a star number or not using System;
class GFG{
// Function to check that the // number is a star number static bool isStar( int N)
{ double n = (6 + Math.Sqrt(24 * N + 12)) / 6;
// Condition to check if the
// number is a star number
return (n - ( int )n) == 0;
} // Driver code public static void Main()
{ int i = 13;
// Function call
if (isStar(i))
{
Console.WriteLine( "Yes" );
}
else
{
Console.WriteLine( "No" );
}
} } // This code is contributed by Code_Mech |
<script> // Javascript implementation to check that // a number is a star number or not // Function to check that the // number is a star number function isStar(N)
{ let n
= (6 + Math.sqrt(24 * N + 12))
/ 6;
// Condition to check if the
// number is a star number
return (n - parseInt(n)) == 0;
} // Driver Code let i = 13; // Function call if (isStar(i)) {
document.write( "Yes" );
} else {
document.write( "No" );
} // This code is contributed by rishavmahato348. </script> |
Output:
Yes
Time Complexity: O(logN) because inbuilt sqrt function has been used, which has time complexity O(logN)
Auxiliary Space: O(1)