求n个幻数-yiteyi-C++库

幻数的定义是一个可以表示为5的幂或5的唯一幂之和的数。前几个数字是5，25，30（5+25），125，130（125+5）…。写一个函数来求第n个幻数。例子：

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Input: n = 2Output: 25Input: n = 5Output: 130

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

如果我们仔细注意，幻数可以表示为001、010、011、100、101、110等，其中001是0*pow（5,3）+0*pow（5,2）+1*pow（5,1）。所以基本上我们需要为给定的整数n中的每一位加上5的幂。下面是基于这个想法的实现。

C++

                         // C++ program to find nth magic number                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find nth magic number                       
                         int                                     nthMagicNo(                                     int                                     n)                       
                         {                       
                                                 int                                     pow                                     = 1, answer = 0;                       
           
                                                 // Go through every bit of n                       
                                                 while                                     (n)                       
                                                 {                       
                                                 pow                                     =                                     pow                                     *5;                       
           
                                                 // If last bit of n is set                       
                                                 if                                     (n & 1)                       
                                                 answer +=                                     pow                                     ;                       
           
                                                 // proceed to next bit                       
                                                 n >>= 1;                                     // or n = n/2                       
                                                 }                       
                                                 return                                     answer;                       
                         }                       
           
                         // Driver program to test above function                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 5;                       
                                                 cout <<                                     "nth magic number is "                                     << nthMagicNo(n) << endl;                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find nth                       
                         // magic number                       
                         import                                     java.io.*;                       
           
                         class                                     GFG                       
                         {                       
                                                 // Function to find nth magic number                       
                                                 static                                     int                                     nthMagicNo(                                     int                                     n)                       
                                                 {                       
                                                 int                                     pow =                                     1                                     , answer =                                     0                                     ;                       
                                   
                                                 // Go through every bit of n                       
                                                 while                                     (n !=                                     0                                     )                       
                                                 {                       
                                                 pow = pow*                                     5                                     ;                       
                                   
                                                 // If last bit of n is set                       
                                                 if                                     ((                                     int                                     )(n &                                     1                                     ) ==                                     1                                     )                       
                                                 answer += pow;                       
                                   
                                                 // proceed to next bit                       
                                                 // or n = n/2                       
                                                 n >>=                                     1                                     ;                       
                                                 }                       
                                                 return                                     answer;                       
                                                 }                       
                                   
                                                 // Driver program to test                       
                                                 // above function                       
                                                 public                                     static                                     void                                     main(String[] args)                       
                                                 {                       
                                                 int                                     n =                                     5                                     ;                       
                                                 System.out.println(                                     "nth magic"                                     +                       
                                                 " number is "                                     + nthMagicNo(n));                       
                                                 }                       
                         }                       
           
           
                         // This code is contributed by                       
                         // prerna saini                       

Python3

                         # Python program to find nth magic number                       
           
                         # Function to find nth magic number                       
                         def                                     nthMagicNo(n):                       
           
                                                 pow                                     =                                     1                       
                                                 answer                                     =                                     0                       
           
                                                 # Go through every bit of n                       
                                                 while                                     (n):                       
           
                                                 pow                                     =                                     pow                                     *                                     5                       
           
                                                 # If last bit of n is set                       
                                                 if                                     (n &                                     1                                     ):                       
                                                 answer                                     +                                     =                                     pow                       
           
                                                 # proceed to next bit                       
                                                 n >>                                     =                                     1                                     # or n = n/2                       
                                   
                                                 return                                     answer                       
           
           
                         # Driver program to test above function                       
                         n                                     =                                     5                       
                         print                                     (                                     "nth magic number is"                                     , nthMagicNo(n))                       
           
                         # This code is contributed by                       
                         # Smitha Dinesh Semwal                       

C#

                         // C# program to find nth                       
                         // magic number                       
                         using                                     System;                       
           
                         public                                     class                                     GFG                       
                         {                       
                                   
                         // Function to find nth magic number                       
                         static                                     int                                     nthMagicNo(                                     int                                     n)                       
                         {                       
                                                 int                                     pow = 1, answer = 0;                       
           
                                                 // Go through every bit of n                       
                                                 while                                     (n != 0)                       
                                                 {                       
                                                 pow = pow * 5;                       
           
                                                 // If last bit of n is set                       
                                                 if                                     ((                                     int                                     )(n & 1) == 1)                       
                                                 answer += pow;                       
                                   
                                                 // proceed to next bit                       
                                                 // or n = n/2                       
                                                 n >>= 1;                       
                                                 }                       
                                                 return                                     answer;                       
                         }                       
           
                         // Driver Code                       
                         public                                     static                                     void                                     Main()                       
                         {                       
                                                 int                                     n = 5;                       
                                                 Console.WriteLine(                                     "nth magic"                                     +                                     " number is "                       
                                                 + nthMagicNo(n));                       
           
                         }                       
                         }                       
           
                         // This code is contributed by Sam007                       

PHP

                         <?php                       
                         // PHP program to find nth                       
                         // magic number                       
           
                         // Function to find nth                       
                         // magic number                       
                         function                                     nthMagicNo(                                     $n                                     )                       
                         {                       
                                                 $pow                                     = 1;                       
                                                 $answer                                     = 0;                       
           
                                                 // Go through every bit of n                       
                                                 while                                     (                                     $n                                     )                       
                                                 {                       
                                                 $pow                                     =                                     $pow                                     * 5;                       
           
                                                 // If last bit of n is set                       
                                                 if                                     (                                     $n                                     & 1)                       
                                                 $answer                                     +=                                     $pow                                     ;                       
           
                                                 // proceed to next bit                       
                                                 $n                                     >>= 1;                                     // or $n = $n/2                       
                                                 }                       
                                                 return                                     $answer                                     ;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 5;                       
                         echo                                     "nth magic number is "                                     ,                       
                                                 nthMagicNo(                                     $n                                     ),                                     ""                                     ;                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         <script>                       
           
                                                 // Javascript program to find nth                       
                                                 // magic number                       
                                   
                                                 // Function to find nth magic number                       
                                                 function                                     nthMagicNo(n)                       
                                                 {                       
                                                 let pow = 1, answer = 0;                       
           
                                                 // Go through every bit of n                       
                                                 while                                     (n != 0)                       
                                                 {                       
                                                 pow = pow * 5;                       
           
                                                 // If last bit of n is set                       
                                                 if                                     ((n & 1) == 1)                       
                                                 answer += pow;                       
           
                                                 // proceed to next bit                       
                                                 // or n = n/2                       
                                                 n >>= 1;                       
                                                 }                       
                                                 return                                     answer;                       
                                                 }                       
                                   
                                                 let n = 5;                       
                                                 document.write(                                     "nth magic"                                     +                                     " number is "                                     + nthMagicNo(n));                       
                                   
                         </script>                       

输出：

 nth magic number is 130

感谢曼拉辛格提出上述解决方案。

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