通过将 n 边多边形的顶点与公共边连接起来形成的三角形数

给定N边多边形，我们需要找到通过将给定多边形的顶点连接起来而形成的三角形的数量，其中只有一侧是公共的。
例子：

Input : 6 
Output : 12 
The image below is of a triangle forming inside a Hexagon by joining vertices as shown above. The two triangles formed has one side (AB) common with that of a polygon.It depicts that with one edge of a hexagon we can make two triangles with one side common. We can’t take C or F as our third vertex as it will make 2 sides common with the hexagon. 
 

Triangle with one side common of a hexagon

No of triangles formed ie equal to 12 as there are 6 edges in a hexagon.
Input : 5 
Output : 5 
 

方法 ：

• 为了使一个边与多边形共边的三角形，与所选公共顶点相邻的两个顶点不能被视为三角形的第三个顶点。
• 首先从多边形中选择任意一条边。将此边视为公共边。在多边形中选择边的方法数将等于 n。
• 现在，要形成一个三角形，请选择左侧的 (n-4) 个顶点中的任意一个。不能考虑公共边的两个顶点和与公共边相邻的两个顶点。
• 通过将 n 边多边形的顶点与公共边连接起来形成的三角形数将等于 n * ( n – 4) 。

下面是上述方法的实现：

C++

// C++ program to implement
// the above problem
#include 
using namespace std;
 
// Function to find the number of triangles
void findTriangles(int n)
{
    int num;
    num = n * (n - 4);
 
    // print the number of triangles
    cout << num;
}
 
// Driver code
int main()
{
    // initialize the number of sides of a polygon
    int n;
    n = 6;
 
    findTriangles(n);
 
    return 0;
}

Java

// Java program to implement
// the above problem
class GFG
{
     
// Function to find the number of triangles
static void findTriangles(int n)
{
    int num;
    num = n * (n - 4);
 
    // print the number of triangles
    System.out.println(num);
}
 
// Driver code
public static void main(String [] args)
{
    // initialize the number of sides of a polygon
    int n;
    n = 6;
 
    findTriangles(n);
 
}
}
 
// This code is contributed by ihritik

Python3

# Python3 program to implement
# the above problem
 
# Function to find the number of triangles
def findTriangles(n):
    num = n * (n - 4)
 
    # print the number of triangles
    print(num)
 
# Driver code
# initialize the number of sides of a polygon
n = 6
 
findTriangles(n)
 
# This codee is contributed by mohit kumar 29

C#

// C# program to implement
// the above problem
using System;
 
class GFG
{
     
// Function to find the number of triangles
static void findTriangles(int n)
{
    int num;
    num = n * (n - 4);
 
    // print the number of triangles
    Console.WriteLine(num);
}
 
// Driver code
public static void Main()
{
    // initialize the number of sides of a polygon
    int n;
    n = 6;
 
    findTriangles(n);
 
}
}
 
// This code is contributed by ihritik

Javascript

 
// JavaScript program to implement
// the above problem
 
     
// Function to find the number of triangles
function findTriangles(n)
{
    var num;
    num = n * (n - 4);
 
    // print the number of triangles
    document.write(num);
}
 
// Driver code
 
// initialize the number of sides of a polygon
var n;
n = 6;
 
findTriangles(n);
 
 
// This code contributed by shikhasingrajput
 

输出：

12

时间复杂度： O(1)

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