从分别平行于X和Y轴的N和M直线中可以计算矩形

给定两个整数N和M ，其中N条直线平行于X轴， M条直线平行于Y轴，任务是计算可以由这些直线形成的矩形的数量。
例子：

Input: N = 3, M = 6 
Output: 45 
Explanation: 
There are total 45 rectangles possible with 3 lines parallel to x axis and 6 lines parallel to y axis.
Input: N = 2, M = 4 
Output: 6 
Explanation: 
There are total 6 rectangles possible with 2 lines parallel to x axis and 4 lines parallel to y axis. 
 

方法：
为解决上述问题，我们需要观察到一个矩形是由4条直线形成的，其中相对的边是平行的，并且任意两个边之间的角度都是90度。因此，对于每个矩形，需要使两个边平行于X-轴和其他两侧必须与Y轴平行。

• 选择两条平行于X轴的线的方式数目= ^N C ₂ 并且选择两条平行于Y轴的线的方式数= ^M C ₂ 。
• 因此矩形的总数= ^N C _{2 *} ^M C ₂ = [N *(N – 1)/ 2] * [M *(M – 1)/ 2]

下面是上述方法的实现：

C++

// C++ Program to count number of
// rectangles formed by N lines
// parallel to X axis M lines
// parallel to Y axis
#include 
using namespace std;
  
// Function to calculate
// number of rectangles
int count_rectangles(int N, int M)
{
    // Total number of ways to
    // select two lines
    // parallel to X axis
    int p_x = (N * (N - 1)) / 2;
  
    // Total number of ways
    // to select two lines
    // parallel to Y axis
    int p_y = (M * (M - 1)) / 2;
  
    // Total number of rectangles
    return p_x * p_y;
}
  
// Driver Program
int main()
{
  
    int N = 3;
  
    int M = 6;
  
    cout << count_rectangles(N, M);
}

Java

// Java Program to count number of
// rectangles formed by N lines
// parallel to X axis M lines
// parallel to Y axis
class GFG{
  
// Function to calculate
// number of rectangles
static int count_rectangles(int N, int M)
{
    // Total number of ways to
    // select two lines
    // parallel to X axis
    int p_x = (N * (N - 1)) / 2;
  
    // Total number of ways
    // to select two lines
    // parallel to Y axis
    int p_y = (M * (M - 1)) / 2;
  
    // Total number of rectangles
    return p_x * p_y;
}
  
// Driver Program
public static void main(String[] args)
{
    int N = 3;
    int M = 6;
  
    System.out.print(count_rectangles(N, M));
}
}
  
// This code is contributed by sapnasingh4991

Python3

# Python3 program to count number of rectangles
# formed by N lines parallel to X axis
# and M lines parallel to Y axis
def count_rectangles(N, M):
  
    # Total number of ways to select
    # two lines parallel to X axis
    p_x = (N * (N - 1)) // 2
  
    # Total number of ways to select
    # two lines parallel to Y axis
    p_y = (M * (M - 1)) // 2
  
    # Total number of rectangles
    return p_x * p_y
  
# Driver code
N = 3
M = 6
  
print(count_rectangles(N, M))
  
# This code is contributed by himanshu77

C#

// C# Program to count number of
// rectangles formed by N lines
// parallel to X axis M lines
// parallel to Y axis
using System;
class GFG{
  
// Function to calculate
// number of rectangles
static int count_rectangles(int N, int M)
{
    // Total number of ways to
    // select two lines
    // parallel to X axis
    int p_x = (N * (N - 1)) / 2;
  
    // Total number of ways
    // to select two lines
    // parallel to Y axis
    int p_y = (M * (M - 1)) / 2;
  
    // Total number of rectangles
    return p_x * p_y;
}
  
// Driver Program
public static void Main()
{
    int N = 3;
    int M = 6;
  
    Console.Write(count_rectangles(N, M));
}
}
  
// This code is contributed by Code_mech

输出：

45

时间复杂度： O(1)