查找可以放置在大小为n * m的矩形内的大小为2 * 1的矩形的数量

给定两个整数$n$ ， $m$ 。查找可以放置在大小为n * m的矩形内的大小为2 * 1的矩形的数量。
笔记：

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.

例子：

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

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

方法：

1. 如果N是偶数，则放置M行N / 2个小矩形，并覆盖整个大矩形。
2. 如果M为偶数，则放置N行M / 2个小矩形，并覆盖整个大矩形。
3. 如果两者都为奇数，则用小矩形覆盖N – 1行的木板，并将floor(M / 2)小矩形置于最后一行。在最坏的情况下(N和M为奇数)，一个单元仍未被发现。

下面是上述方法的实现：

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)
}

Javascript

 
// Javascript 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
function NumberOfRectangles(n, 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
var n = 3, m = 3;
           
// Function call
document.write(NumberOfRectangles(n, m));
 
// This code is contributed by Ankita saini
 

输出：

4

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