查找 n 边凸多边形中的对角线数

给定 n > 3，找出 n 边凸多边形中的对角线数。
根据维基百科，在几何学中，对角线是连接多边形或多面体的两个顶点的线段，当这些顶点不在同一条边上时。非正式地，任何倾斜的线都称为对角线。

例子 ：

Input : 5
Output : 5

说明：五个可能的对角线是：AC、AD、BD、BE、CE

解决方案 ：

因为对于一个 n 边凸多边形，从每个顶点，我们可以绘制 n-3 条对角线，留下两个相邻的顶点和它自身。按照这种方式，对于 n 个顶点，将有 n*(n-3) 条对角线，但是我们将对每个对角线计算两次，因此对角线的总数变为 n*(n-3)/2
这是上述公式的代码。

C++

#include 
using namespace std;
 
// C++ function to find number of diagonals
// in n sided convex polygon
int numberOfDiagonals(int n)
{
    return n * (n - 3) / 2;
}
 
// driver code to test above function
int main()
{
    int n = 5;
    cout << n << " sided convex polygon have ";
    cout << numberOfDiagonals(n) << " diagonals";
    return 0;
}

Java

// Java function to find number of diagonals
// in n sided convex polygon
 
public class Diagonals {
 
    static int numberOfDiagonals(int n)
    {
        return n * (n - 3) / 2;
    }
 
    // driver code to test above function
    public static void main(String[] args)
    {
        int n = 5;
        System.out.print(n + " sided convex polygon have ");
        System.out.println(numberOfDiagonals(n) + " diagonals");
    }
}
 
// This code is contributed by Saket Kumar

Python3

# Python3 program to find number of diagonals
# in n sided convex polygon
def numberOfDiagonals(n):
    return n * (n - 3) / 2
 
  
# driver code to test above function
def main():
    n = 5
    print(n , " sided convex polygon have ")
    print(numberOfDiagonals(n) , " diagonals")
 
if __name__ == '__main__':
    main()
 
#this code contributed by 29AjayKumar

C#

// C# function to find number of diagonals
// in n sided convex polygon
using System;
 
class GFG {
     
    static int numberOfDiagonals(int n)
    {
        return n * (n - 3) / 2;
    }
 
    // driver code to test above function
    public static void Main()
    {
        int n = 5;
        Console.Write(n + " sided convex polygon have ");
         
        Console.WriteLine(numberOfDiagonals(n) +
                                  " diagonals");
    }
}
 
// This code is contributed by Sam007

Javascript

 
// Javascript function to find number of
// diagonals in n sided convex polygon
function numberOfDiagonals(n)
{
    return n * (n - 3) / 2;
}
 
// Driver code
var n = 5;
document.write(n + " sided convex polygon have ");
document.write(numberOfDiagonals(n) + " diagonals");
 
// This code is contributed by Ankita saini
 

输出 ：

5 sided convex polygon have 5 diagonals

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