n边凸对角多边形的个数-yiteyi-C++库

给定n>3，求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。非正式地说，任何倾斜的线都被称为对角线。

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例如：

Input : 5
Output : 5

说明：五种可能的对角线是：AC、AD、BD、BE、CE

number of diagonals in n sided convex polygon

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

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本身。按照这种方法，对于n个顶点，将有n*（n-3）条对角线，但是我们将计算每个对角线两次，这样对角线的总数将变成n*（n-3）/2 下面是上述公式的代码。

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

                         // 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

                         <?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                       
                         ?>                       

Javascript

                         <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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