在N * N棋盘中计算不同的矩形

给定一个N x N的棋盘。任务是计算棋盘上不同的矩形。例如，如果输入为8，则输出应为36。

例子：

Input: N = 4 
Output: 10

Input: N = 6
Output: 21

方法：
假设N = 8，即给出了8 x 8的棋盘，那么可以形成的不同矩形是：

1 x 1, 1 x 2, 1 x 3, 1 x 4, 1 x 5, 1 x 6, 1 x 7, 1 x 8 = 8
      2 x 2, 2 x 3, 2 x 4, 2 x 5, 2 x 6, 2 x 7, 2 x 8 = 7 
            3 x 3, 3 x 4, 3 x 5, 3 x 6, 2 x 7, 3 x 8 = 6 
                  4 x 4, 4 x 5, 4 x 6, 4 x 7, 4 x 8 = 5 
                        5 x 5, 5 x 6, 5 x 7, 5 x 8 = 4
                              6 x 6, 6 x 7, 6 x 8 = 3
                                    7 x 7, 7 x 8 = 2
                                          8 x 8 = 1

因此形成的总唯一矩形= 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36，这是前8个自然数的总和。因此，通常，可以在N x N棋盘中形成的不同矩形是：

Sum of the first N natural numbers = N*(N+1)/2
                                   = 8*(8+1)/2
                                   = 36

下面是上述方法的实现：

C++

// C++ code to count distinct rectangle in a chessboard
#include  
using namespace std; 
  
// Function to return the count 
// of distinct rectangles 
int count(int N)
{
    int a = 0;
    a = (N * (N + 1)) / 2;
    return a;
}
  
// Driver Code
int main()
{
    int N = 4;
    cout<

---

Java

// Java program to count unique rectangles in a chessboard
class Rectangle {
  
    // Function to count distinct rectangles
    static int count(int N)
    {
        int a = 0;
  
        a = (N * (N + 1)) / 2;
  
        return a;
    }
  
    // Driver Code
    public static void main(String args[])
    {
        int n = 4;
        System.out.print(count(n)); 
    }
}

Python3

# Python code to count distinct rectangle in a chessboard
  
# Function to return the count 
# of distinct rectangles 
def count(N):
    a = 0;
    a = (N * (N + 1)) / 2;
    return int(a);
  
  
# Driver Code
N = 4;
print(count(N)); 
  
# This code has been contributed by 29AjayKumar

C#

// C# program to count unique rectangles in a chessboard 
using System;
  
class Rectangle 
{ 
  
    // Function to count distinct rectangles 
    static int count(int N) 
    { 
        int a = 0; 
  
        a = (N * (N + 1)) / 2; 
  
        return a; 
    } 
  
    // Driver Code 
    public static void Main() 
    { 
        int n = 4; 
        Console.Write(count(n)); 
    } 
} 
  
// This code is contributed by AnkitRai01

输出：

10