使用位运算符检查数字是否为9的倍数-yiteyi-C++库

给定一个数字n，编写一个函数，如果n可被9整除，则返回true，否则返回false。检查n被9整除的最简单方法是执行n%9。另一种方法是对n的数字求和。如果数字之和是9的倍数，那么n是9的倍数。上述方法不是基于位运算符的方法，需要使用%和/。这个定义的位运算通常比模和除法运算符更快。下面是一个基于位运算符的方法来检查9的整除性。

null

C++

                         // C++ program to check if a number                       
                         // is multiple of 9 using bitwise operators                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Bitwise operator based function to check divisibility by 9                       
                         bool                                     isDivBy9(                                     int                                     n)                       
                         {                       
                                                 // Base cases                       
                                                 if                                     (n == 0 || n == 9)                       
                                                 return                                     true                                     ;                       
                                                 if                                     (n < 9)                       
                                                 return                                     false                                     ;                       
           
                                                 // If n is greater than 9, then recur for [floor(n/9) - n%8]                       
                                                 return                                     isDivBy9((                                     int                                     )(n >> 3) - (                                     int                                     )(n & 7));                       
                         }                       
           
                         // Driver program to test above function                       
                         int                                     main()                       
                         {                       
                                                 // Let us print all multiples of 9 from 0 to 100                       
                                                 // using above method                       
                                                 for                                     (                                     int                                     i = 0; i < 100; i++)                       
                                                 if                                     (isDivBy9(i))                       
                                                 cout << i <<                                     " "                                     ;                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to check if a number                       
                         // is multiple of 9 using bitwise operators                       
                         import                                     java.lang.*;                       
           
                         class                                     GFG {                       
           
                                                 // Bitwise operator based function                       
                                                 // to check divisibility by 9                       
                                                 static                                     boolean                                     isDivBy9(                                     int                                     n)                       
                                                 {                       
           
                                                 // Base cases                       
                                                 if                                     (n ==                                     0                                     || n ==                                     9                                     )                       
                                                 return                                     true                                     ;                       
                                                 if                                     (n <                                     9                                     )                       
                                                 return                                     false                                     ;                       
           
                                                 // If n is greater than 9, then                       
                                                 // recur for [floor(n/9) - n%8]                       
                                                 return                                     isDivBy9((                                     int                                     )(n >>                                     3                                     ) - (                                     int                                     )(n &                                     7                                     ));                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     main(String arg[])                       
                                                 {                       
           
                                                 // Let us print all multiples of 9 from                       
                                                 // 0 to 100 using above method                       
                                                 for                                     (                                     int                                     i =                                     0                                     ; i <                                     100                                     ; i++)                       
                                                 if                                     (isDivBy9(i))                       
                                                 System.out.print(i +                                     " "                                     );                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Anant Agarwal.                       

Python3

                         # Bitwise operator based                       
                         # function to check divisibility by 9                       
           
                         def                                     isDivBy9(n):                       
           
                                                 # Base cases                       
                                                 if                                     (n                                     =                                     =                                     0                                     or                                     n                                     =                                     =                                     9                                     ):                       
                                                 return                                     True                       
                                                 if                                     (n <                                     9                                     ):                       
                                                 return                                     False                       
                                   
                                                 # If n is greater than 9,                       
                                                 # then recur for [floor(n / 9) - n % 8]                       
                                                 return                                     isDivBy9((                                     int                                     )(n>>                                     3                                     )                                     -                                     (                                     int                                     )(n&                                     7                                     ))                       
           
                         # Driver code                       
           
                         # Let us print all multiples                       
                         # of 9 from 0 to 100                       
                         # using above method                       
                         for                                     i                                     in                                     range                                     (                                     100                                     ):                       
                                                 if                                     (isDivBy9(i)):                       
                                                 print                                     (i,                                     " "                                     , end                                     =                                     "")                       
           
                         # This code is contributed                       
                         # by Anant Agarwal.                       

C#

                         // C# program to check if a number                       
                         // is multiple of 9 using bitwise operators                       
                         using                                     System;                       
           
                         class                                     GFG {                       
           
                                                 // Bitwise operator based function                       
                                                 // to check divisibility by 9                       
                                                 static                                     bool                                     isDivBy9(                                     int                                     n)                       
                                                 {                       
                                                 // Base cases                       
                                                 if                                     (n == 0 || n == 9)                       
                                                 return                                     true                                     ;                       
                                                 if                                     (n < 9)                       
                                                 return                                     false                                     ;                       
           
                                                 // If n is greater than 9, then                       
                                                 // recur for [floor(n/9) - n%8]                       
                                                 return                                     isDivBy9((                                     int                                     )(n >> 3) - (                                     int                                     )(n & 7));                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 // Let us print all multiples of 9 from                       
                                                 // 0 to 100 using above method                       
                                                 for                                     (                                     int                                     i = 0; i < 100; i++)                       
                                                 if                                     (isDivBy9(i))                       
                                                 Console.Write(i +                                     " "                                     );                       
                                                 }                       
                         }                       
           
                         // This code is contributed by nitin mittal.                       

PHP

                         <?php                       
                         // PHP program to check if a number                       
                         // is multiple of 9 using bitwise                       
                         // operators                       
           
                         // Bitwise operator based function                       
                         // to check divisibility by 9                       
                         function                                     isDivBy9(                                     $n                                     )                       
                         {                       
                                   
                                                 // Base cases                       
                                                 if                                     (                                     $n                                     == 0 ||                                     $n                                     == 9)                       
                                                 return                                     true;                       
                                                 if                                     (                                     $n                                     < 9)                       
                                                 return                                     false;                       
           
                                                 // If n is greater than 9,                       
                                                 // then recur for [floor(n/9) -                       
                                                 // n%8]                       
                                                 return                                     isDivBy9((                                     $n                                     >> 3) -                       
                                                 (                                     $n                                     & 7));                       
                         }                       
           
                                                 // Driver Code                       
                                                 // Let us print all multiples                       
                                                 // of 9 from 0 to 100                       
                                                 // using above method                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     < 100;                                     $i                                     ++)                       
                                                 if                                     (isDivBy9(                                     $i                                     ))                       
                                                 echo                                     $i                                     ,                                     " "                                     ;                       
                                   
                         // This code is contributed by nitin mittal                       
                         ?>                       

Javascript

                         <script>                       
                         // javascript program to check if a number                       
                         // is multiple of 9 using bitwise operators                       
           
                         // Bitwise operator based function                       
                         // to check divisibility by 9                       
                         function                                     isDivBy9(n)                       
                         {                       
           
                                                 // Base cases                       
                                                 if                                     (n == 0 || n == 9)                       
                                                 return                                     true                                     ;                       
                                                 if                                     (n < 9)                       
                                                 return                                     false                                     ;                       
           
                                                 // If n is greater than 9, then                       
                                                 // recur for [floor(n/9) - n%8]                       
                                                 return                                     isDivBy9(parseInt(n >> 3) - parseInt(n & 7));                       
                         }                       
           
                         // Driver code                       
           
                                                 // Let us print all multiples of 9 from                       
                         // 0 to 100 using above method                       
                         for                                     (i = 0; i < 100; i++)                       
                                                 if                                     (isDivBy9(i))                       
                                                 document.write(i +                                     " "                                     );                       
           
                         // This code is contributed by Princi Singh                       
                         </script>                       

输出：

0 9 18 27 36 45 54 63 72 81 90 99

这是怎么回事？ n/9 可以写成 n/8 使用下面的简单公式。

n/9 = n/8 - n/72

因为我们需要使用位运算符，所以我们得到 楼层（n/8） 使用 n> >3 并从中获得价值 n%8 使用 n&7 .我们需要写上面的表达方式 楼层（n/8） 和 n%8 . n/8 等于 “楼层（n/8）+（n%8）/8” .让我们把上面的表达式写成 楼层（n/8） 和 n%8

n/9 = floor(n/8) + (n%8)/8 - [floor(n/8) + (n%8)/8]/9n/9 = floor(n/8) - [floor(n/8) - 9(n%8)/8 + (n%8)/8]/9n/9 = floor(n/8) - [floor(n/8) - n%8]/9

从上面的等式中， N 是的倍数 9 只有当表达 楼层（n/8）–[楼层（n/8）–n%8]/9 是一个整数。如果子表达式 [楼层（n/8）–n%8]/9 是一个整数。子表达式只能是整数，如果 [楼层（n/8）–n%8] 是的倍数 9 因此，问题简化为一个较小的值，可以用位运算符来写。如果您发现任何不正确的地方，或者您想分享有关上述主题的更多信息，请写评论

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