求 n 边凸多边形的对角线数
原文:https://www . geesforgeks . org/find-number-对角线-n 边-凸-多边形/
给定 n > 3，求 n 边凸多边形的对角线数。 根据维基百科的说法，在几何学中，当多边形或多面体的两个顶点不在同一条边上时，对角线是连接这两个顶点的线段。非正式地说，任何斜线都称为对角线。
示例:
Input : 5
Output : 5
说明:五种可能的对角线为:AC、AD、BD、BE、CE
解决方案:
因为对于 n 边凸多边形，从每个顶点，我们可以画出 n-3 条对角线，留下两个相邻的顶点和它自己。按照这种方式，对于 n 个顶点，将有 n(n-3)条对角线，但是我们将计算每条对角线两次，因此对角线总数变为 n(n-3)/2 这里是上述公式的代码。
C++
#include <iostream>
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 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP function to find number
// of diagonals in n sided
// convex polygon
function numberOfDiagonals($n)
{
return $n * ($n - 3) / 2;
}
// Driver Code
$n = 5;
echo $n , " sided convex polygon have ";
echo numberOfDiagonals($n) ,
" diagonals";
// This code is contributed by aj_36
?>
java 描述语言
<script>
// 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
</script>
输出:
5 sided convex polygon have 5 diagonals
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