📜  查找n边凸多边形中的对角线数

📅  最后修改于: 2021-05-05 02:14:39             🧑  作者: Mango

给定n> 3,找到n边凸多边形中的对角线数。
根据Wikipedia的说法,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,而这些顶点不在同一条边上。非正式地,任何倾斜线都称为对角线。

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 :

由于对于n边的凸多边形,我们可以从每个顶点绘制n-3个对角线,从而留下两个相邻的顶点及其本身。对于n个顶点,按照这种方式,将有n *(n-3)个对角线,但随后我们将对每个对角线进行两次计算,因此对角线总数变为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


PHP


Javascript


输出 :

5 sided convex polygon have 5 diagonals