数的超阶乘-yiteyi-C++库

给定一个数，任务是找到一个数的超阶乘。将给定数目的连续整数从1乘以给定数的结果，每一个整数都被提升到其自身的幂，称为 超因子 一个数字。

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H(n)= 1 ^ 1 * 2 ^ 2 * 3 ^ 3 * . . . . . * n ^ n

例如：

输入： 2. 输出： 4.

输入： 4. 输出： 27648 H（4）=1^1*2^2*3^3*4^4=27648

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

A. 幼稚的方法 使用两个循环，一个求i^i的和，另一个求i^i。但时间复杂度为O（n ^2. ). 一 有效的方法 就是使用内置的战俘（）功能或 O（logn）方法找到i^i，然后添加它。以下是上述方法的实施情况。

C++

                         /// C++ program to find the hyperfactorial                       
                         // of a number                       
                         #include <bits/stdc++.h>                       
           
                         using                                     namespace                                     std;                       
                         #define ll long long                       
           
                         // function to calculate the value of hyperfactorial                       
                         ll boost_hyperfactorial(ll num)                       
                         {                       
                                                 // initialise the val to 1                       
                                                 ll val = 1;                       
                                                 for                                     (                                     int                                     i = 1; i <= num; i++) {                       
                                                 val = val *                                     pow                                     (i,i);                       
                                                 }                       
                                                 // returns the hyperfactorial of a number                       
                                                 return                                     val;                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 int                                     num = 5;                       
                                                 cout << boost_hyperfactorial(num);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find the                       
                         // hyperfactorial of a number                       
           
                         // function to calculate the                       
                         // value of hyperfactorial                       
                         class                                     GFG                       
                         {                       
                         static                                     long                                     boost_hyperfactorial(                                     long                                     num)                       
                         {                       
                                                 // initialise the val to 1                       
                                                 long                                     val =                                     1                                     ;                       
                                                 for                                     (                                     int                                     i =                                     1                                     ; i <= num; i++)                       
                                                 {                       
                                                 val = val * (                                     long                                     )Math.pow(i, i);                       
                                                 }                       
                                   
                                                 // returns the hyperfactorial                       
                                                 // of a number                       
                                                 return                                     val;                       
                         }                       
           
                         // Driver code                       
                         public                                     static                                     void                                     main(String args[])                       
                         {                       
                                                 int                                     num =                                     5                                     ;                       
                                                 System.out.println(boost_hyperfactorial(num));                       
                         }                       
                         }                       
           
                         // This code is contributed                       
                         // by chandan_jnu                       

Python3

                         # Python3 program to find the                       
                         # hyperfactorial of a number                       
           
                         # function to calculate the                       
                         # value of hyperfactorial                       
                         def                                     boost_hyperfactorial(num):                       
           
                                                 # initialise the                       
                                                 # val to 1                       
                                                 val                                     =                                     1                                     ;                       
                                                 for                                     i                                     in                                     range                                     (                                     1                                     , num                                     +                                     1                                     ):                       
                                                 val                                     =                                     val                                     *                                     pow                                     (i, i);                       
                                   
                                                 # returns the hyperfactorial                       
                                                 # of a number                       
                                                 return                                     val;                       
           
                         # Driver code                       
                         num                                     =                                     5                                     ;                       
                         print                                     (boost_hyperfactorial(num));                       
           
                         # This code is contributed                       
                         # by mits                       

C#

                         // C# program to find the                       
                         // hyperfactorial of a number                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
           
                         // function to calculate the                       
                         // value of hyperfactorial                       
                         static                                     long                                     boost_hyperfactorial(                                     long                                     num)                       
                         {                       
                                                 // initialise the val to 1                       
                                                 long                                     val = 1;                       
                                                 for                                     (                                     long                                     i = 1; i <= num; i++)                       
                                                 {                       
                                                 val = val * (                                     long                                     )Math.Pow(i, i);                       
                                                 }                       
                                   
                                                 // returns the hyperfactorial                       
                                                 // of a number                       
                                                 return                                     val;                       
                         }                       
           
                         // Driver code                       
                         public                                     static                                     void                                     Main()                       
                         {                       
                                                 int                                     num = 5;                       
                                                 Console.WriteLine(boost_hyperfactorial(num));                       
                         }                       
                         }                       
           
                         // This code is contributed                       
                         // by chandan_jnu                       

PHP

                         <?php                       
                         // PHP program to find the                       
                         // hyperfactorial of a number                       
           
                         // function to calculate the                       
                         // value of hyperfactorial                       
                         function                                     boost_hyperfactorial(                                     $num                                     )                       
                         {                       
                                                 // initialise the                       
                                                 // val to 1                       
                                                 $val                                     = 1;                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <=                                     $num                                     ;                                     $i                                     ++)                       
                                                 {                       
                                                 $val                                     =                                     $val                                     * pow(                                     $i                                     ,                                     $i                                     );                       
                                                 }                       
                                   
                                                 // returns the hyperfactorial                       
                                                 // of a number                       
                                                 return                                     $val                                     ;                       
                         }                       
           
                         // Driver code                       
                         $num                                     = 5;                       
                         echo                                     boost_hyperfactorial(                                     $num                                     );                       
           
                         // This code is contributed                       
                         // by Akanksha Rai(Abby_akku)                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript program to find the                       
                         // hyperfactorial of a number                       
           
                         // function to calculate the                       
                         // value of hyperfactorial                       
                         function                                     boost_hyperfactorial(num)                       
                         {                       
                                                 // initialise the                       
                                                 // val to 1                       
                                                 let val = 1;                       
                                                 for                                     (let i = 1; i <= num; i++)                       
                                                 {                       
                                                 val = val * Math.pow(i, i);                       
                                                 }                       
                                   
                                                 // returns the hyperfactorial                       
                                                 // of a number                       
                                                 return                                     val;                       
                         }                       
           
                         // Driver code                       
                         let num = 5;                       
                         document.write(boost_hyperfactorial(num));                       
           
                         // This code is contributed                       
                         // by gfgking                       
           
                         </script>                       

输出：

86400000

时间复杂性： O（N*logn）由于数字的超因子可能是巨大的，因此数字将溢出。我们可以使用 C++中的库或 Java中的BigInteger 存储数字N的超阶乘。

C++

                         // C++ program to find the hyperfactorial                       
                         // of a number using boost libraries                       
                         #include <bits/stdc++.h>                       
                         #include <boost/multiprecision/cpp_int.hpp>                       
           
                         using                                     namespace                                     boost::multiprecision;                       
                         using                                     namespace                                     std;                       
           
                         // function to calculate the value of hyperfactorial                       
                         int1024_t boost_hyperfactorial(                                     int                                     num)                       
                         {                       
                                                 // initialise the val to 1                       
                                                 int1024_t val = 1;                       
                                                 for                                     (                                     int                                     i = 1; i <= num; i++) {                       
                                                 for                                     (                                     int                                     j = 1; j <= i; j++) {                       
                                                 // 1^1*2^2*3^3....                       
                                                 val *= i;                       
                                                 }                       
                                                 }                       
                                                 // returns the hyperfactorial of a number                       
                                                 return                                     val;                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 int                                     num = 5;                       
                                                 cout << boost_hyperfactorial(num);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find the hyperfactorial                       
                         // of a number using boost libraries                       
           
                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
           
                         // function to calculate the value of hyperfactorial                       
                         static                                     int                                     boost_hyperfactorial(                                     int                                     num)                       
                         {                       
                                                 // initialise the val to 1                       
                                                 int                                     val =                                     1                                     ;                       
                                                 for                                     (                                     int                                     i =                                     1                                     ; i <= num; i++) {                       
                                                 for                                     (                                     int                                     j =                                     1                                     ; j <= i; j++) {                       
                                                 // 1^1*2^2*3^3....                       
                                                 val *= i;                       
                                                 }                       
                                                 }                       
                                                 // returns the hyperfactorial of a number                       
                                                 return                                     val;                       
                         }                       
           
                         // Driver code                       
           
           
                                                 public                                     static                                     void                                     main (String[] args) {                       
                                                 int                                     num =                                     5                                     ;                       
                                                 System.out.println( boost_hyperfactorial(num));                       
                                                 }                       
                         }                       
                         // This code is contributed                       
                         // by chandan_jnu                       

Python3

                         # Python3 program to find the hyperfactorial                       
                         # of a number using boost libraries                       
           
                         # function to calculate the value of hyperfactorial                       
                         def                                     boost_hyperfactorial(num):                       
                                   
                                                 # initialise the val to 1                       
                                                 val                                     =                                     1                                     ;                       
                                                 for                                     i                                     in                                     range                                     (                                     1                                     ,num                                     +                                     1                                     ):                       
                                                 for                                     j                                     in                                     range                                     (                                     1                                     ,i                                     +                                     1                                     ):                       
                                   
                                                 # 1^1*2^2*3^3....                       
                                                 val                                     *                                     =                                     i;                       
                                   
                                                 # returns the hyperfactorial of a number                       
                                                 return                                     val;                       
           
                         # Driver code                       
                         num                                     =                                     5                                     ;                       
                         print                                     ( boost_hyperfactorial(num));                       
           
                         # This code is contributed by mits                       

C#

                         // C# program to find the hyperfactorial                       
                         // of a number using boost libraries                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
           
                         // function to calculate the                       
                         // value of hyperfactorial                       
                         static                                     int                                     boost_hyperfactorial(                                     int                                     num)                       
                         {                       
                                                 // initialise the val to 1                       
                                                 int                                     val = 1;                       
                                                 for                                     (                                     int                                     i = 1; i <= num; i++)                       
                                                 {                       
                                                 for                                     (                                     int                                     j = 1; j <= i; j++)                       
                                                 {                       
                                                 // 1^1*2^2*3^3....                       
                                                 val *= i;                       
                                                 }                       
                                                 }                       
                                   
                                                 // returns the hyperfactorial                       
                                                 // of a number                       
                                                 return                                     val;                       
                         }                       
           
                         // Driver code                       
                         public                                     static                                     void                                     Main ()                       
                         {                       
                                                 int                                     num = 5;                       
                                                 Console.WriteLine(boost_hyperfactorial(num));                       
                         }                       
                         }                       
           
                         // This code is contributed                       
                         // by chandan_jnu                       

PHP

                         <?php                       
                         // PHP program to find the hyperfactorial                       
                         // of a number using boost libraries                       
           
                         // function to calculate the value                       
                         // of hyperfactorial                       
                         function                                     boost_hyperfactorial(                                     $num                                     )                       
                         {                       
                                                 // initialise the val to 1                       
                                                 $val                                     = 1;                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <=                                     $num                                     ;                                     $i                                     ++)                       
                                                 {                       
                                                 for                                     (                                     $j                                     = 1;                                     $j                                     <=                                     $i                                     ;                                     $j                                     ++)                       
                                                 {                       
                                                 // 1^1*2^2*3^3....                       
                                                 $val                                     *=                                     $i                                     ;                       
                                                 }                       
                                                 }                       
                                   
                                                 // returns the hyperfactorial                       
                                                 // of a number                       
                                                 return                                     $val                                     ;                       
                         }                       
           
                         // Driver code                       
                         $num                                     = 5;                       
                         echo                                     boost_hyperfactorial(                                     $num                                     );                       
           
                         // This code is contributed                       
                         // by Mukul Singh                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript program to find the hyperfactorial                       
                         // of a number using boost libraries                       
           
                         // function to calculate the value of hyperfactorial                       
                         function                                     boost_hyperfactorial(num)                       
                         {                       
                                                 // initialise the val to 1                       
                                                 var                                     val = 1;                       
                                                 for                                     (                                     var                                     i = 1; i <= num; i++) {                       
                                                 for                                     (                                     var                                     j = 1; j <= i; j++) {                       
                                                 // 1^1*2^2*3^3....                       
                                                 val *= i;                       
                                                 }                       
                                                 }                       
                                                 // returns the hyperfactorial of a number                       
                                                 return                                     val;                       
                         }                       
           
                         // Driver code                       
                         var                                     num = 5;                       
                         document.write( boost_hyperfactorial(num));                       
           
           
                         </script>                       

输出：

86400000

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