中心十二面体数-yiteyi-C++库

给定一个数字n，找到 第n位 居中十二面体数。 A. 中心十二面体数 是一类比喻数字。它由一个中心点构成，周围是连续的十二面体（12个平面的多面体）层。前几个中心十二面体数 （其中n=0,1,2,3……） 是： 1, 33, 155, 427, 909, 1661 …………… 例如：

null

Input : 5Output : 1661Input :1Output :33

数学公式 N 居中十二面体数由下式给出：

以下是上述理念的基本实现：

C++

                         // Program to find nth centered                       
                         // dodecahedral number                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find                       
                         // centered dodecahedral number                       
                         int                                     CenteredDodecahedral_num(                                     long                                     int                                     n)                       
                         {                       
                                                 // Formula to calculate nth                       
                                                 // centered dodecahedral number                       
                                                 // and return it into main function.                       
                                                 return                                     (2 * n + 1) * (5 * n * n + 5 * n + 1);                       
                         }                       
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 long                                     int                                     n = 3;                       
                                                 // print result                       
                                                 cout << n <<                                     "th Centered Dodecahedral number : "                                     ;                       
                                                 cout << CenteredDodecahedral_num(n) << endl;                       
           
                                                 n = 10;                       
                                                 // print result                       
                                                 cout << n <<                                     "th Centered Dodecahedral number : "                                     ;                       
                                                 cout << CenteredDodecahedral_num(n);                       
           
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java Program to find nth                       
                         // centered dodecahedral number                       
                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
           
                                                 // Function to find centered                       
                                                 // dodecahedral number                       
                                                 static                                     int                                     CenteredDodecahedral_num(                                     int                                     n)                       
                                                 {                       
                                   
                                                 // Formula to calculate nth                       
                                                 // centered dodecahedral number                       
                                                 // and return it into main function.                       
                                   
                                                 return                                     (                                     2                                     * n +                                     1                                     ) *                       
                                                 (                                     5                                     * n * n +                                     5                                     * n +                                     1                                     );                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
           
                                                 int                                     n =                                     3                                     ;                       
                                   
                                                 // print result                       
                                                 System.out.print( n +                                     "th Centered "                       
                                                 +                                     "Dodecahedral number : "                                     );                       
                                                 System.out.println (                       
                                                 CenteredDodecahedral_num(n));                       
           
                                                 n =                                     10                                     ;                       
                                   
                                                 // print result                       
                                                 System.out.print( n +                                     "th Centered "                       
                                                 +                                     "Dodecahedral number : "                                     );                       
                                                 System.out.println(                       
                                                 CenteredDodecahedral_num(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by m_kit.                       

Python3

                         # Program to find nth centered                       
                         # dodecahedral number                       
           
                         # Function to find centered                       
                         # dodecahedral number                       
                         def                                     CenteredDodecahedral_num(n) :                       
                                   
                                                 # Formula to calculate nth                       
                                                 # centered dodecahedral number                       
                                                 return                                     (                                     2                                     *                                     n                                     +                                     1                                     )                                     *                                     (                                     5                                     *                                     n                                     *                                     n                                     +                                     5                                     *                                     n                                     +                                     1                                     )                       
           
                         # Driver Code                       
                         if                                     __name__                                     =                                     =                                     '__main__'                                     :                       
                                   
                                                 n                                     =                                     3                       
                                                 print                                     (n,                                     "rd centered dodecahedral number: "                                     ,                       
                                                 CenteredDodecahedral_num(n))                       
                                                 n                                     =                                     10                       
                                                 print                                     (n,                                     "th centered dodecahedral number : "                                     ,                       
                                                 CenteredDodecahedral_num(n))                       
                                   
                         # This code is contributed by aj_36                       

C#

                         // C# Program to find                       
                         // nth centered                       
                         // dodecahedral number                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
                                   
                                                 // Function to find                       
                                                 // nth centered                       
                                                 // dodecahedral number                       
                                                 static                                     int                                     CenteredDodecahedral_num(                                     int                                     n)                       
                                                 {                       
                                   
                                                 // Formula to calculate                       
                                                 // nth centered dodecahedral                       
                                                 // number and return it                       
                                                 // into main function.                       
                                                 return                                     (2 * n + 1) *                       
                                                 (5 * n * n +                       
                                                 5 * n + 1);                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 static                                     public                                     void                                     Main ()                       
                                                 {                       
                                                 int                                     n = 3;                       
                                   
                                                 // print result                       
                                                 Console.Write( n +                                     "th Centered "                                     +                       
                                                 "Dodecahedral number : "                                     );                       
                                                 Console.WriteLine(                       
                                                 CenteredDodecahedral_num(n));                       
           
                                                 n = 10;                       
                                   
                                                 // print result                       
                                                 Console.Write( n +                                     "th Centered "                                     +                       
                                                 "Dodecahedral number : "                                     );                       
                                                 Console.WriteLine(                       
                                                 CenteredDodecahedral_num(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by ajit                       

PHP

                         <?php                       
                         // Program to find nth centered                       
                         // dodecahedral number                       
           
                         // Function to find                       
                         // centered dodecahedral number                       
                         function                                     CenteredDodecahedral_num(                                     $n                                     )                       
                         {                       
                                                 // Formula to calculate nth                       
                                                 // centered dodecahedral number                       
                                                 // and return it into main function.                       
                                                 return                                     (2 *                                     $n                                     + 1) *                       
                                                 (5 *                                     $n                                     *                                     $n                                     +                       
                                                 5 *                                     $n                                     + 1);                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 3;                       
                         // print result                       
                         echo                                     $n                                     ,                                     "th Centered Dodecahedral "                                     .                       
                                                 "number : "                                     ;                       
                         echo                                     CenteredDodecahedral_num(                                     $n                                     ),                                     ""                                     ;                       
           
                         $n                                     = 10;                       
                         // print result                       
                         echo                                     $n                                     ,                                     "th Centered Dodecahedral "                                     .                       
                                                 "number : "                                     ;                       
                         echo                                     CenteredDodecahedral_num(                                     $n                                     );                       
           
                         // This code is contributed by akt_mit                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript Program to find nth                       
                         // centered dodecahedral number                       
           
                         // Function to find centered                       
                         // dodecahedral number                       
                         function                                     CenteredDodecahedral_num(n)                       
                         {                       
                                   
                                                 // Formula to calculate nth                       
                                                 // centered dodecahedral number                       
                                                 // and return it into main function.                       
                                                 return                                     (2 * n + 1) *                       
                                                 (5 * n * n + 5 * n + 1);                       
                         }                       
                                   
                         // Driver code                       
                         var                                     n = 3;                       
                                   
                         // print result                       
                         document.write(n +                                     "th Centered "                                     +                       
                                                 "Dodecahedral number : "                                     );                       
                         document.write(CenteredDodecahedral_num(n) +                                     "<br>"                                     );                       
           
                         n = 10;                       
           
                         // print result                       
                         document.write(n +                                     "th Centered "                                     +                       
                                                 "Dodecahedral number : "                                     );                       
                         document.write(CenteredDodecahedral_num(n));                       
           
                         // This code is contributed by Khushboogoyal499                       
           
                         </script>                       

输出：

3th Centered Dodecahedral number : 42710th Centered Dodecahedral number : 11571

时间复杂性： O（1） 辅助空间： O（1）

参考资料： https://en.wikipedia.org/wiki/Centered_dodecahedral_number

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