可以放置在较大矩形内的较小矩形的数量

给定四个整数L，B，l和b ，其中L和B表示较大矩形的尺寸， l和b表示较小矩形的尺寸，任务是计算可以在内部绘制的较小矩形的数量一个更大的矩形。
注意：较小的矩形可以部分重叠。

例子：

Input: L = 5, B = 3, l = 4, b = 1
Output: 6
Explanation:
There are 6 rectangles of dimension 4 × 1 that can be drawn inside a bigger rectangle of dimension 5 × 3.

Input: L = 3, B = 2, l = 2, b = 1
Output: 3
Explanation:
There are 3 rectangles of dimension 3 × 2 can be drawn inside a bigger rectangle of dimension 2 × 1.

天真的方法：想法是遍历较大矩形的长度L和宽度B ，以计算可以在较大矩形范围内绘制的尺寸为lxb的较小矩形的数量。遍历后打印总数。
时间复杂度： O(L * B)
辅助空间： O(1)

高效的方法：上述问题可以使用置换和组合来解决。步骤如下：

1. 使用长度L的较小矩形l的长度的总可能值由(L – 1 + 1)给出。
2. 使用长度B的较小矩形b的宽度的总可能值由(B – b + 1)给出。
3. 因此，可以形成的可能矩形的总数由下式给出：

 
 

(L – l + 1) * (B – b + 1)

 

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function to count smaller rectangles
// within the larger rectangle
int No_of_rectangles(int L, int B,
                    int l, int b)
{
    // If the dimension of the smaller
    // rectangle is greater than the
    // bigger one
    if ((l > L) || (b > B)) {
        return -1;
    }
 
    else {
 
        // Return the number of smaller
        // rectangles possible
        return (L - l + 1) * (B - b + 1);
    }
}
 
// Driver Code
int main()
{
    // Dimension of bigger rectangle
    int L = 5, B = 3;
 
    // Dimension of smaller rectangle
    int l = 4, b = 1;
 
    // Function call
    cout << No_of_rectangles(L, B, l, b);
 
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
 
class GFG{
 
// Function to count smaller rectangles
// within the larger rectangle
static int No_of_rectangles(int L, int B,
                            int l, int b)
{
     
    // If the dimension of the smaller
    // rectangle is greater than the
    // bigger one
    if ((l > L) || (b > B))
    {
        return -1;
    }
 
    else
    {
         
        // Return the number of smaller
        // rectangles possible
        return (L - l + 1) * (B - b + 1);
    }
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Dimension of bigger rectangle
    int L = 5, B = 3;
 
    // Dimension of smaller rectangle
    int l = 4, b = 1;
 
    // Function call
    System.out.println(No_of_rectangles(L, B, l, b));
}
}
 
// This code is contributed by jana_sayantan

Python3

# Python3 program for the above approach
 
# Function to count smaller rectangles
# within the larger rectangle
def No_of_rectangles( L, B, l, b):
 
    # If the dimension of the smaller
    # rectangle is greater than the
    # bigger one
    if (l > L) or (b > B):
        return -1;
         
    else:
 
        # Return the number of smaller
        # rectangles possible
        return (L - l + 1) * (B - b + 1);
     
# Driver code
if __name__ == '__main__':
     
    # Dimension of bigger rectangle
    L = 5
    B = 3
 
    # Dimension of smaller rectangle
    l = 4
    b = 1
 
    # Function call
    print(No_of_rectangles(L, B, l, b))
 
# This code is contributed by jana_sayantan

C#

// C# program for the above approach
using System;
 
class GFG{
 
// Function to count smaller rectangles
// within the larger rectangle
static int No_of_rectangles(int L, int B,
                            int l, int b)
{
     
    // If the dimension of the smaller
    // rectangle is greater than the
    // bigger one
    if ((l > L) || (b > B))
    {
        return -1;
    }
    else
    {
         
        // Return the number of smaller
        // rectangles possible
        return (L - l + 1) * (B - b + 1);
    }
}
 
// Driver Code
public static void Main(String[] args)
{
     
    // Dimension of bigger rectangle
    int L = 5, B = 3;
     
    // Dimension of smaller rectangle
    int l = 4, b = 1;
     
    // Function call
    Console.Write(No_of_rectangles(L, B, l, b));
}
}
 
// This code is contributed by jana_sayantan

Javascript

 
// JavaScript implementation of the above approach
 
// Function to count smaller rectangles
// within the larger rectangle
function No_of_rectangles(L, B,
                            l, b)
{
       
    // If the dimension of the smaller
    // rectangle is greater than the
    // bigger one
    if ((l > L) || (b > B))
    {
        return -1;
    }
   
    else
    {
           
        // Return the number of smaller
        // rectangles possible
        return (L - l + 1) * (B - b + 1);
    }
}
 
// Driver code
         
    // Dimension of bigger rectangle
    let L = 5, B = 3;
   
    // Dimension of smaller rectangle
    let l = 4, b = 1;
   
    // Function call
    document.write(No_of_rectangles(L, B, l, b));
       
    // This code is contributed by code_hunt.

输出：

6

时间复杂度： O(1)
辅助空间： O(1)