Sum of first N Star Numbers
Given a number N, the task is to find the sum of the first N star numbers.
The first few star numbers are 1, 13, 37, 73,..
Examples:
Input: N = 2
Output: 14
Explanation: 1, 13 are the first two star numbers.
Input: N = 3
Output: 51
Approach 1:
- Nth Star number is given as
- Run a loop from 1 to N, to find the first N star numbers.
- Add all the above-calculated star numbers.
- Return the sum.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int star_num( int n)
{
return (6 * n * n - 6 * n + 1);
}
int sum_star_num( int n)
{
int summ = 0;
for ( int i = 1; i < n + 1; i++)
{
summ += star_num(i);
}
return summ;
}
int main()
{
int n = 3;
cout << sum_star_num(n);
}
|
Java
class GFG{
static int star_num( int n)
{
return ( 6 * n * n - 6 * n + 1 );
}
static int sum_star_num( int n)
{
int summ = 0 ;
for ( int i = 1 ; i < n + 1 ; i++)
{
summ += star_num(i);
}
return summ;
}
public static void main(String[] args)
{
int n = 3 ;
System.out.println(sum_star_num(n));
}
}
|
Python3
def star_num(n):
return ( 6 * n * n - 6 * n + 1 )
def sum_star_num(n) :
summ = 0
for i in range ( 1 , n + 1 ):
summ + = star_num(i)
return summ
n = 3
print (sum_star_num(n))
|
C#
using System;
class GFG{
static int star_num( int n)
{
return (6 * n * n - 6 * n + 1);
}
static int sum_star_num( int n)
{
int summ = 0;
for ( int i = 1; i < n + 1; i++)
{
summ += star_num(i);
}
return summ;
}
public static void Main(String[] args)
{
int n = 3;
Console.WriteLine(sum_star_num(n));
}
}
|
Javascript
<script>
function star_num(n)
{
return (6 * n * n - 6 * n + 1);
}
function sum_star_num(n)
{
let summ = 0;
for (let i = 1; i < n + 1; i++)
{
summ += star_num(i);
}
return summ;
}
let n = 3;
document.write(sum_star_num(n));
</script>
|
Time complexity: O(N).
Auxiliary Space: O(1)
Efficient Approach:
- We already know , , and
- Nth star number is given as
- So, the sum of the first N Star Numbers is
Sum =
Sum =
Sum = - Calculate the sum and return.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int sum_star_num( int n)
{
int summ = 2 * n * (n + 1) * (n - 1) + n;
return summ;
}
int main()
{
int n = 3;
cout << sum_star_num(n);
return 0;
}
|
Java
class GFG{
static int sum_star_num( int n)
{
int summ = 2 * n * (n + 1 ) * (n - 1 ) + n;
return summ;
}
public static void main(String[] args)
{
int n = 3 ;
System.out.println(sum_star_num(n));
}
}
|
Python3
def sum_star_num(n) :
summ = 2 * n * (n + 1 ) * (n - 1 ) + n
return summ
n = 3
print (sum_star_num(n))
|
C#
using System;
class GFG{
static int sum_star_num( int n)
{
int summ = 2 * n * (n + 1) * (n - 1) + n;
return summ;
}
public static void Main(String[] args)
{
int n = 3;
Console.WriteLine(sum_star_num(n));
}
}
|
Javascript
<script>
function sum_star_num(n)
{
let summ = 2 * n * (n + 1) * (n - 1) + n;
return summ;
}
let n = 3;
document.write(sum_star_num(n));
</script>
|
Time complexity: O(1).
Auxiliary Space: O(1)
Last Updated :
25 Jul, 2022
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