蛋糕号-yiteyi-C++库

考虑3D立方体和N平面。我们可以用给定的平面在立方体上切割。给定n的饼数是n个平面可以形成的最大区域数。 n个平面切割后的系列（0≤ n） : 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697…

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例如：

Input : 1Output : 2Explanation : With 1 plane cut the cube is divided into 2 regionsInput : 2Output : 4Explanation: With 2 plane cuts, we can divide the cube into 4 regionsInput : 4Output : 15Input : 5Output : 26

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

饼数n项公式：

第n个蛋糕编号= ^N C ^3. + ^N C ^2. + ^N C ^1. + ^N C ⁰ =（n） ^3. +5*n+6）/6

以下是上述方法的实施情况：

C++

                         // CPP Program to find the                       
                         // nth Cake number                       
                         #include <iostream>                       
                         using                                     namespace                                     std;                       
           
                         // function for Cake number                       
                         int                                     number_cake(                                     int                                     n)                       
                         {                       
                                                 // formula for find  Cake number                       
                                                 // nth term                       
                                                 return                                     (n * n * n + 5 * n + 6) / 6;                       
                         }                       
           
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 // For 2nd cake Number                       
                                                 int                                     n = 2;                       
                                                 cout << number_cake(n) << endl;                       
           
                                                 // For 8th cake Number                       
                                                 n = 8;                       
                                                 cout << number_cake(n) << endl;                       
                                                 // For 25th cake Number                       
                                                 n = 25;                       
                                                 cout << number_cake(n) << endl;                       
           
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java Program to find the nth Cake number                       
                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
                                   
                                                 // function for Cake number                       
                                                 static                                     int                                     number_cake(                                     int                                     n)                       
                                                 {                       
                                   
                                                 // formula for find Cake number                       
                                                 // nth term                       
                                                 return                                     (n * n * n +                                     5                                     * n +                                     6                                     ) /                                     6                                     ;                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 // For 2nd cake Number                       
                                                 int                                     n =                                     2                                     ;                       
                                                 System.out.println( number_cake(n));                       
                                   
                                                 // For 8th cake Number                       
                                                 n =                                     8                                     ;                       
                                                 System.out.println( number_cake(n));                       
                                   
                                                 // For 25th cake Number                       
                                                 n =                                     25                                     ;                       
                                                 System.out.println( number_cake(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

Python3

                         # Python program to find                       
                         # nth Cake number                       
           
                         # Function to calculate                       
                         # Cake number                       
                         def                                     number_cake(n):                       
           
                                                 # Formula to calculate nth                       
                                                 # Cake number                       
                                   
                                                 return                                     (n                                     *                                     n                                     *                                     n                                     +                                     5                                     *                                     n                                     +                                     6                                     )                                     /                                     /                                     6                       
           
                         # Driver Code                       
                         n                                     =                                     2                       
                         print                                     (number_cake(n))                       
           
                         n                                     =                                     8                       
                         print                                     (number_cake(n))                       
           
                         n                                     =                                     25                       
                         print                                     (number_cake(n))                       
                                   
                         # This code is contributed by aj_36                       

C#

                         // C# Program to find the nth Cake number                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 // function for Cake number                       
                                                 static                                     int                                     number_cake(                                     int                                     n)                       
                                                 {                       
                                   
                                                 // formula for find Cake number                       
                                                 // nth term                       
                                                 return                                     (n * n * n + 5 * n + 6) / 6;                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main ()                       
                                                 {                       
                                                 // For 2nd cake Number                       
                                                 int                                     n = 2;                       
                                                 Console.WriteLine( number_cake(n));                       
                                   
                                                 // For 8th cake Number                       
                                                 n = 8;                       
                                                 Console.WriteLine( number_cake(n));                       
                                   
                                                 // For 25th cake Number                       
                                                 n = 25;                       
                                                 Console.WriteLine( number_cake(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

PHP

                         <?php                       
                         // PHP Program to find the                       
                         // nth Cake number                       
           
           
                         // function for Cake number                       
                         function                                     number_cake(                                     $n                                     )                       
                         {                       
                                                 // formula for find Cake                       
                                                 // number nth term                       
                                                 return                                     (                                     $n                                     *                                     $n                                     *                                     $n                                     +                       
                                                 5 *                                     $n                                     + 6) / 6;                       
                         }                       
           
                         // Driver Code                       
           
                         // For 2nd cake Number                       
                         $n                                     = 2;                       
                         echo                                     number_cake(                                     $n                                     ) ,                                     ""                                     ;                       
           
                         // For 8th cake Number                       
                         $n                                     = 8;                       
                         echo                                     number_cake(                                     $n                                     ),                                     " "                                     ;                       
                         // For 25th cake Number                       
                         $n                                     = 25;                       
                         echo                                     number_cake(                                     $n                                     );                       
           
                         // This code is contributed by anuj_67.                       
                         ?>                       

Javascript

                         <script>                       
                                                 // Javascript Program to find the nth Cake number                       
                                   
                                                 // function for Cake number                       
                                                 function                                     number_cake(n)                       
                                                 {                       
                                   
                                                 // formula for find Cake number                       
                                                 // nth term                       
                                                 return                                     parseInt((n * n * n + 5 * n + 6) / 6, 10);                       
                                                 }                       
                                   
                                                 // For 2nd cake Number                       
                                                 let n = 2;                       
                                                 document.write( number_cake(n) +                                     "</br>"                                     );                       
           
                                                 // For 8th cake Number                       
                                                 n = 8;                       
                                                 document.write( number_cake(n) +                                     "</br>"                                     );                       
           
                                                 // For 25th cake Number                       
                                                 n = 25;                       
                                                 document.write( number_cake(n));                       
           
                         </script>                       

输出：

时间复杂性： O（1） 辅助空间： O（1）

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