中心立方数-yiteyi-C++库

给定一个数字n，找到 第n位 居中的立方体数。这个 中心立方数 计算由一个点形成的点的数量，该点在3D中由同心立方体层包围，并带有i ^2. 第i层方形面上的点。来源 [维基] .请看这图像更清晰。前几个居中的立方体数是： 1, 9, 35, 91, 189, 341, 559, 855, 1241, 172………………………… 例如：

null

Input :  n = 1Output : 9Input  : n = 7Output : 855

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

数学公式 N 居中立方体编号由以下公式给出：

n-th Centered Cube Number = (2n + 1)(n² + n + 1)

以下是上述公式的基本实现：

C++

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

JAVA

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

Python3

                         # Python 3 Program to find                       
                         # nth Centered cube number                       
           
                         # Centered cube                       
                         # number function                       
                         def                                     centered_cube(n) :                       
                                   
                                                 # Formula to calculate                       
                                                 # nth Centered cube                       
                                                 # number return it                       
                                                 # into main function.                       
                                                 return                                     (                                     2                                     *                                     n                                     +                                     1                                     )                                     *                                     (                       
                                                 n                                     *                                     n                                     +                                     n                                     +                                     1                                     )                       
           
                         # Driver Code                       
                         if                                     __name__                                     =                                     =                                     '__main__'                                     :                       
                                   
                                                 n                                     =                                     3                       
                                                 print                                     (n,                                     "th Centered cube "                                     +                       
                                                 "number : "                                     ,                       
                                                 centered_cube(n))                       
           
                                                 n                                     =                                     10                       
                                                 print                                     (n,                                     "th Centered cube "                                     +                       
                                                 "number : "                                     ,                       
                                                 centered_cube(n))                       
           
                         # This code is contributed by ajit                       

C#

                         // C# Program to find nth                       
                         // Centered cube number                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
                                   
                                                 // Function to find                       
                                                 // Centered cube number                       
                                                 static                                     int                                     centered_cube(                                     int                                     n)                       
                                                 {                       
                                                 // Formula to calculate                       
                                                 // nth Centered cube                       
                                                 // number & return it                       
                                                 // into main function.                       
                                                 return                                     (2 * n + 1) *                       
                                                 (n * n + n + 1);                       
                                                 }                       
                                   
                                                 // Driver code                       
                                                 static                                     public                                     void                                     Main ()                       
                                                 {                       
                                                 int                                     n = 3;                       
                                                 Console.Write(n +                                     "th Centered"                                     +                       
                                                 " cube number: "                                     );                       
                                                 Console.WriteLine (centered_cube(n));                       
                                   
                                                 n = 10;                       
                                                 Console.Write( n +                                     "th Centered"                                     +                       
                                                 " cube number: "                                     );                       
                                                 Console.WriteLine(centered_cube(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by aj_36                       

PHP

                         <?php                       
                         // Program to find nth                       
                         // Centered cube number                       
           
                         // Function to find                       
                         // Centered cube number                       
                         function                                     centered_cube(                                     $n                                     )                       
                         {                       
                                                 // Formula to calculate nth                       
                                                 // Centered cube number &                       
                                                 // return it into main function.                       
                                                 return                                     (2 *                                     $n                                     + 1) *                       
                                                 (                                     $n                                     *                                     $n                                     +                                     $n                                     + 1);                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 3;                       
                         echo                                     $n                                     ,                                     "th Centered cube number: "                                     ;                       
                         echo                                     centered_cube(                                     $n                                     );                       
                         echo                                     ""                                     ;                       
           
                         $n                                     = 10;                       
                         echo                                     $n                                     ,                                     "th Centered cube number: "                                     ;                       
                         echo                                     centered_cube(                                     $n                                     );                       
           
                         // This code is contributed by m_kit                       
                         ?>                       

Javascript

                         <script>                       
                         // Program to find nth Centered cube                       
                         // number                       
           
                         // Function to find                       
                         // Centered cube number                       
                         function                                     centered_cube(n)                       
                         {                       
                                                 // Formula to calculate nth                       
                                                 // Centered cube number &                       
                                                 // return it into main function.                       
                                                 return                                     (2 * n + 1) * ( n * n + n + 1);                       
                         }                       
           
                         // Driver Code                       
                         let n = 3;                       
                         document.write(n +                                     "th Centered cube number: "                                     );                       
                         document.write(centered_cube(n));                       
                         document.write(                                     "<br>"                                     );                       
           
                         n = 10;                       
                         document.write(n +                                     "th Centered cube number: "                                     );                       
                         document.write(centered_cube(n));                       
           
                         // This code is contributed by rishavmahato348.                       
                         </script>                       

输出：

 3th Centered cube number: 91 10th Centered cube number: 2331

时间复杂性： O（1） 辅助空间： O（1）

文章版权归作者所有，未经允许请勿转载。

THE END

技术文章