# Find the number of rectangles of size 2*1 which can be placed inside a rectangle of size n*m

• Last Updated : 22 Apr, 2021

Given two integers  . Find the number of rectangles of size 2*1 that can be placed inside a rectangle of size n*m.
Note:

1. No two small rectangles overlap.
2. Each small rectangle lies entirely inside the large rectangle. It is allowed to touch the edges of the large rectangle. Examples

```Input : n = 3, m =3
Output : 4

Input : n = 2, m = 4
Output : 4```

Approach:

1. If N is even, then place M rows of N/2 small rectangles and cover the whole large rectangle.
2. If M is even, then place N rows of M/2 small rectangles and cover the whole large rectangle.
3. If both are odd then cover N – 1 row of the board with small rectangles and put floor(M/2) small rectangles to the last row. In the worst case (N and M are odd) one cell remains uncovered.

Below is the implementation of the above approach:

## C++

 `// CPP program to Find the number of``// rectangles of size 2*1 can be placed``// inside a rectangle of size n*m``#include ``using` `namespace` `std;` `// function to Find the number of``// rectangles of size 2*1 can be placed``// inside a rectangle of size n*m``int` `NumberOfRectangles(``int` `n, ``int` `m)``{``    ``// if n is even``    ``if` `(n % 2 == 0)``        ``return` `(n / 2) * m;` `    ``// if m is even``    ``else` `if` `(m % 2 == 0)``        ``return` `(m / 2) * n;` `    ``// if both are odd``    ``return` `(n * m - 1) / 2;``}` `// Driver code``int` `main()``{``    ``int` `n = 3, m = 3;` `    ``// function call``    ``cout << NumberOfRectangles(n, m);` `    ``return` `0;``}`

## Java

 `// Java program to Find the number of``// rectangles of size 2*1 can be placed``// inside a rectangle of size n*m` `public` `class` `GFG {``    ` `    ``// function to Find the number of``    ``// rectangles of size 2*1 can be placed``    ``// inside a rectangle of size n*m``    ``static` `int` `NumberOfRectangles(``int` `n, ``int` `m)``    ``{``        ``// if n is even``        ``if` `(n % ``2` `== ``0``)``            ``return` `(n / ``2``) * m;``      ` `        ``// if m is even``        ``else` `if` `(m % ``2` `== ``0``)``            ``return` `(m / ``2``) * n;``      ` `        ``// if both are odd``        ``return` `(n * m - ``1``) / ``2``;``    ``}``    ``public` `static` `void` `main(String args[])``    ``{``         ``int` `n = ``3``, m = ``3``;``          ` `            ``// function call``            ``System.out.println(NumberOfRectangles(n, m));``          ` `    ``}``    ``// This Code is contributed by ANKITRAI1``}`

## Python3

 `# Python 3 program to Find the``# number of rectangles of size``# 2*1 can be placed inside a``# rectangle of size n*m` `# function to Find the number``# of rectangles of size 2*1``# can be placed inside a``# rectangle of size n*m``def` `NumberOfRectangles(n, m):` `    ``# if n is even``    ``if` `(n ``%` `2` `=``=` `0``):``        ``return` `(n ``/` `2``) ``*` `m` `    ``# if m is even``    ``elif` `(m ``%` `2` `=``=` `0``):``        ``return` `(m ``/``/` `2``) ``*` `n` `    ``# if both are odd``    ``return` `(n ``*` `m ``-` `1``) ``/``/` `2` `# Driver code``if` `__name__ ``=``=` `"__main__"``:``    ``n ``=` `3``    ``m ``=` `3` `    ``# function call``    ``print``(NumberOfRectangles(n, m))` `# This code is contributed``# by ChitraNayal`

## C#

 `// C# program to Find the number of``// rectangles of size 2*1 can be placed``// inside a rectangle of size n*m``using` `System;` `class` `GFG``{``    ` `// function to Find the number of``// rectangles of size 2*1 can be placed``// inside a rectangle of size n*m``static` `int` `NumberOfRectangles(``int` `n, ``int` `m)``{``    ``// if n is even``    ``if` `(n % 2 == 0)``        ``return` `(n / 2) * m;` `    ``// if m is even``    ``else` `if` `(m % 2 == 0)``        ``return` `(m / 2) * n;` `    ``// if both are odd``    ``return` `(n * m - 1) / 2;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `n = 3, m = 3;` `    ``// function call``    ``Console.WriteLine(NumberOfRectangles(n, m));``    ` `}``// This code is contributed``// by Akanksha Rai(Abby_akku)``}`

## PHP

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## Javascript

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Output:
`4`

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