Rectangular (or Pronic) Numbers
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).
C++
// 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
// 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#
// 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. |
Python
# 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 // 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 ?> |
Javascript
<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