Program to check if N is a Star Number
Last Updated :
20 Sep, 2022
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++
#include <bits/stdc++.h>
using namespace std;
bool isStar( int N)
{
float n
= (6 + sqrt (24 * N + 12))
/ 6;
return (n - ( int )n) == 0;
}
int main()
{
int i = 13;
if (isStar(i)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
}
|
Java
import java.io.*;
import java.util.*;
class GFG{
static boolean isStar( int N)
{
double n = ( 6 + Math.sqrt( 24 * N + 12 )) / 6 ;
return (n - ( int )n) == 0 ;
}
public static void main(String[] args)
{
int i = 13 ;
if (isStar(i))
{
System.out.println( "Yes" );
}
else
{
System.out.println( "No" );
}
}
}
|
Python3
import math
def isStar(N):
n = (math.sqrt( 24 * N + 12 ) + 6 ) / 6
return (n - int (n)) = = 0
i = 13
if isStar(i):
print ( "Yes" )
else :
print ( "No" )
|
C#
using System;
class GFG{
static bool isStar( int N)
{
double n = (6 + Math.Sqrt(24 * N + 12)) / 6;
return (n - ( int )n) == 0;
}
public static void Main()
{
int i = 13;
if (isStar(i))
{
Console.WriteLine( "Yes" );
}
else
{
Console.WriteLine( "No" );
}
}
}
|
Javascript
<script>
function isStar(N)
{
let n
= (6 + Math.sqrt(24 * N + 12))
/ 6;
return (n - parseInt(n)) == 0;
}
let i = 13;
if (isStar(i)) {
document.write( "Yes" );
}
else {
document.write( "No" );
}
</script>
|
Time Complexity: O(logN) because inbuilt sqrt function has been used, which has time complexity O(logN)
Auxiliary Space: O(1)
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