The numbers that can be arranged to form a rectangle are called Rectangular Numbers (also known as Pronic numbers). The first few rectangular numbers are:
0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462 . . . . . .
Given a number n, find n-th rectangular number.
Examples:
Input : 1 Output : 2 Input : 4 Output : 20 Input : 5 Output : 30
The number 2 is a rectangular number because it is 1 row by 2 columns. The number 6 is a rectangular number because it is 2 rows by 3 columns, and the number 12 is a rectangular number because it is 3 rows by 4 columns.
If we observe these numbers carefully, we can notice that n-th rectangular number is n(n+1).
// CPP Program to find n-th rectangular number #include <bits/stdc++.h> using namespace std;
// Returns n-th rectangular number int findRectNum( int n)
{ return n * (n + 1);
} // Driver code int main()
{ int n = 6;
cout << findRectNum(n);
return 0;
} |
// Java Program to find n-th rectangular number import java.io.*;
class GFG {
// Returns n-th rectangular number
static int findRectNum( int n)
{
return n * (n + 1 );
}
// Driver code
public static void main(String[] args)
{
int n = 6 ;
System.out.println(findRectNum(n));
}
} // This code is contributed by vt_m. |
// C# Program to find n-th rectangular number using System;
class GFG {
// Returns n-th rectangular number
static int findRectNum( int n)
{
return n * (n + 1);
}
// Driver code
public static void Main()
{
int n = 6;
Console.Write(findRectNum(n));
}
} // This code is contributed by vt_m. |
# Python3 Program to find n-th rectangular number # Returns n-th rectangular number def findRectNum(n):
return n * (n + 1 )
# Driver code n = 6
print (findRectNum(n))
# This code is contributed by Shreyanshi Arun. |
<?php // PHP Program to find n-th // rectangular number // Returns n-th rectangular // number function findRectNum( $n )
{ return $n * ( $n + 1);
} // Driver Code
$n = 6;
echo findRectNum( $n );
// This code is contributed by ajit ?> |
<script> // Javascript Program to find n-th rectangular number // Returns n-th rectangular number function findRectNum(n)
{ return n * (n + 1);
} // Driver code var n = 6;
document.write(findRectNum(n)); // This code is contributed by noob2000. </script> |
Output:
42
Time complexity: O(1) since performing constant operations
Space complexity: O(1) since using constant space for variables
Check if a given number is Pronic | Efficient Approach