检查一个大数字是否可以被9整除-yiteyi-C++库

给定一个数字，任务是找出这个数字是否可以被9整除。输入的数字可能很大，即使使用long int，也可能无法存储。

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例如：

Input  : n = 69354Output : YesInput  : n = 234567876799333Output : NoInput  : n = 3635883959606670431112222Output : No

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

由于输入的数字可能非常大，我们不能使用n%9来检查一个数字是否可以被9整除，尤其是在C/C++等语言中。这个想法基于以下事实。

A number is divisible by 9 if sum of its digits is divisible by 9.

插图：

For example n = 9432Sum of digits = 9 + 4 + 3 + 2             = 18Since sum is divisible by 9,answer is Yes.

这是怎么回事？

Let us consider 1332, we can write it as1332 = 1*1000 + 3*100 + 3*10 + 2The proof is based on below observation:Remainder of 10ⁱ divided by 9 is 1So powers of 10 only results in remainder 1 when divided by 9.Remainder of "1*1000 + 3*100 + 3*10 + 2"divided by 9 can be written as : 1*1 + 3*1 + 3*1 + 2 = 9The above expression is basically sum ofall digits.Since 9 is divisible by 9, answer is yes.

下面是上述想法的实现。

C++

                         // C++ program to find if a number is divisible by                       
                         // 9 or not                       
                         #include<bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find that number divisible by 9 or not                       
                         int                                     check(string str)                       
                         {                       
                                                 // Compute sum of digits                       
                                                 int                                     n = str.length();                       
                                                 int                                     digitSum = 0;                       
                                                 for                                     (                                     int                                     i=0; i<n; i++)                       
                                                 digitSum += (str[i]-                                     '0'                                     );                       
           
                                                 // Check if sum of digits is divisible by 9.                       
                                                 return                                     (digitSum % 9 == 0);                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 string str =                                     "99333"                                     ;                       
                                                 check(str)?  cout <<                                     "Yes"                                     : cout <<                                     "No "                                     ;                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find if a number is                       
                         // divisible by 9 or not                       
                         class                                     IsDivisible                       
                         {                       
                                                 // Function to find that number                       
                                                 // is divisible by 9 or not                       
                                                 static                                     boolean                                     check(String str)                       
                                                 {                       
                                                 // Compute sum of digits                       
                                                 int                                     n = str.length();                       
                                                 int                                     digitSum =                                     0                                     ;                       
                                                 for                                     (                                     int                                     i=                                     0                                     ; i<n; i++)                       
                                                 digitSum += (str.charAt(i)-                                     '0'                                     );                       
                                   
                                                 // Check if sum of digits is divisible by 9.                       
                                                 return                                     (digitSum %                                     9                                     ==                                     0                                     );                       
                                                 }                       
           
                                                 // main function                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 String str =                                     "99333"                                     ;                       
                                                 if                                     (check(str))                       
                                                 System.out.println(                                     "Yes"                                     );                       
                                                 else                       
                                                 System.out.println(                                     "No"                                     );                       
                                                 }                       
                         }                       

Python3

                         # Python 3 program to                       
                         # find if a number is                       
                         # divisible by                       
                         # 9 or not                       
           
                         # Function to find that                       
                         # number divisible by 9                       
                         # or not                       
                         def                                     check(st) :                       
           
                                                 # Compute sum of digits                       
                                                 n                                     =                                     len                                     (st)                       
                                                 digitSum                                     =                                     0                       
                                   
                                                 for                                     i                                     in                                     range                                     (                                     0                                     ,n) :                       
                                                 digitSum                                     =                                     digitSum                                     +                                     (                                     int                                     )(st[i])                       
           
                                                 # Check if sum of digits                       
                                                 # is divisible by 9.                       
                                                 return                                     (digitSum                                     %                                     9                                     =                                     =                                     0                                     )                       
           
                         # Driver code                       
                         st                                     =                                     "99333"                       
           
                         if                                     (check(st)) :                       
                                                 print                                     (                                     "Yes"                                     )                       
                         else                                     :                       
                                                 print                                     (                                     "No"                                     )                       
                                   
                         # This code is contributed by Nikita Tiwari.                       

C#

                         // C# program to find if a number is                       
                         // divisible by 9 or not.                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 // Function to find that number                       
                                                 // is divisible by 9 or not                       
                                                 static                                     bool                                     check(String str)                       
                                                 {                       
                                   
                                                 // Compute sum of digits                       
                                                 int                                     n = str.Length;                       
                                                 int                                     digitSum = 0;                       
                                                 for                                     (                                     int                                     i = 0; i < n; i++)                       
                                                 digitSum += (str[i] -                                     '0'                                     );                       
                                   
                                                 // Check if sum of digits is                       
                                                 // divisible by 9.                       
                                                 return                                     (digitSum % 9 == 0);                       
                                                 }                       
           
                                                 // main function                       
                                                 public                                     static                                     void                                     Main ()                       
                                                 {                       
                                                 String str =                                     "99333"                                     ;                       
                                                 if                                     (check(str))                       
                                                 Console.Write(                                     "Yes"                                     );                       
                                                 else                       
                                                 Console.Write(                                     "No"                                     );                       
                                                 }                       
                         }                       
           
                         // This code is Contributed by                       
                         // nitin mittal.                       

PHP

                         <?php                       
                         // PHP program to find if a number                       
                         // is divisible by 9 or not                       
           
                         // Function to find that                       
                         // number divisible by 9 or not                       
                         function                                     check(                                     $str                                     )                       
                         {                       
                                   
                                                 // Compute sum of digits                       
                                                 $n                                     =                                     strlen                                     (                                     $str                                     );                       
                                                 $digitSum                                     = 0;                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     <                                     $n                                     ;                                     $i                                     ++)                       
                                                 $digitSum                                     += (                                     $str                                     [                                     $i                                     ] -                                     '0'                                     );                       
           
                                                 // Check if sum of digits                       
                                                 // is divisible by 9.                       
                                                 return                                     (                                     $digitSum                                     % 9 == 0);                       
                         }                       
           
                         // Driver code                       
                         $str                                     =                                     "99333"                                     ;                       
                         $x                                     = check(                                     $str                                     ) ?                                     "Yes"                                     :                                     "No "                                     ;                       
                         echo                                     (                                     $x                                     );                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript program to find if a number                       
                         // is divisible by 9 or not                       
           
                         // Function to find that                       
                         // number divisible by 9 or not                       
                         function                                     check(str)                       
                         {                       
                                   
                                                 // Compute sum of digits                       
                                                 let n = str.length;                       
                                                 let digitSum = 0;                       
                                   
                                                 for                                     (let i = 0; i < n; i++)                       
                                                 digitSum += (str[i] -                                     '0'                                     );                       
           
                                                 // Check if sum of digits                       
                                                 // is divisible by 9.                       
                                                 return                                     (digitSum % 9 == 0);                       
                         }                       
           
                         // Driver code                       
                         let str =                                     "99333"                                     ;                       
                         let x = check(str) ?                                     "Yes"                                     :                                     "No "                                     ;                       
           
                         document.write(x);                       
           
                         // This code is contributed by _saurabh_jaiswal.                       
                                   
                         </script>                       

输出：

Yes

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