检查一个大数字是否可以被4整除-yiteyi-C++库

给定一个数字，任务是检查一个数字是否可以被4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 = 1124Output : YesInput  : n = 1234567589333862Output : NoInput  : n = 363588395960667043875487Output : No

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

由于输入的数字可能非常大，我们不能使用n%4来检查一个数字是否可以被4整除，尤其是在C/C++等语言中。这个想法基于以下事实。

如果一个数的最后两位数字可以被4整除，则该数可以被4整除。

插图：

For example, let us consider 76952 Number formed by last two digits = 52Since 52 is divisible by 4, answer is YES.

这是怎么回事？

Let us consider 76952, we can write it as76942 = 7*10000 + 6*1000 + 9*100 + 5*10 + 2The proof is based on below observation:Remainder of 10ⁱ divided by 4 is 0 if i greater than or equal to two. Note than 100, 1000,... etc lead to remainder 0 when divided by 4.So remainder of "7*10000 + 6*1000 + 9*100 + 5*10 + 2" divided by 4 is equivalent to remainder of following : 0 + 0 + 0 + 5*10 + 2 = 52Therefore we can say that the whole number is divisible by 4 if 52 is divisible by 4.

以下是上述想法的实施：

C++

                         // C++ program to find if a number is divisible by                       
                         // 4 or not                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find that number divisible by                       
                         // 4 or not                       
                         bool                                     check(string str)                       
                         {                       
                                                 int                                     n = str.length();                       
           
                                                 // Empty string                       
                                                 if                                     (n == 0)                       
                                                 return                                     false                                     ;                       
           
                                                 // If there is single digit                       
                                                 if                                     (n == 1)                       
                                                 return                                     ((str[0] -                                     '0'                                     ) % 4 == 0);                       
           
                                                 // If number formed by last two digits is                       
                                                 // divisible by 4.                       
                                                 int                                     last = str[n - 1] -                                     '0'                                     ;                       
                                                 int                                     second_last = str[n - 2] -                                     '0'                                     ;                       
                                                 return                                     ((second_last * 10 + last) % 4 == 0);                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 string str =                                     "76952"                                     ;                       
                                   
                                                 // Function call                       
                                                 check(str) ? cout <<                                     "Yes"                                     : cout <<                                     "No "                                     ;                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find if a number is                       
                         // divisible by 4 or not                       
                         class                                     IsDivisible                       
                         {                       
                                                 // Function to find that number                       
                                                 // is divisible by 4 or not                       
                                                 static                                     boolean                                     check(String str)                       
                                                 {                       
                                                 int                                     n = str.length();                       
           
                                                 // Empty string                       
                                                 if                                     (n ==                                     0                                     )                       
                                                 return                                     false                                     ;                       
           
                                                 // If there is single digit                       
                                                 if                                     (n ==                                     1                                     )                       
                                                 return                                     ((str.charAt(                                     0                                     ) -                                     '0'                                     ) %                                     4                                     ==                                     0                                     );                       
           
                                                 // If number formed by last two digits is                       
                                                 // divisible by 4.                       
                                                 int                                     last = str.charAt(n -                                     1                                     ) -                                     '0'                                     ;                       
                                                 int                                     second_last = str.charAt(n -                                     2                                     ) -                                     '0'                                     ;                       
                                                 return                                     ((second_last *                                     10                                     + last) %                                     4                                     ==                                     0                                     );                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     main(String[] args)                       
                                                 {                       
                                                 String str =                                     "76952"                                     ;                       
                                   
                                                 // Function call                       
                                                 if                                     (check(str))                       
                                                 System.out.println(                                     "Yes"                                     );                       
                                                 else                       
                                                 System.out.println(                                     "No"                                     );                       
                                                 }                       
                         }                       

Python3

                         # Python 3 program to find                       
                         # if a number is divisible                       
                         # by 4 or not                       
           
                         # Function to find that                       
                         # number divisible by                       
                         # 4 or not                       
           
           
                         def                                     check(st):                       
                                                 n                                     =                                     len                                     (st)                       
           
                                                 # Empty string                       
                                                 if                                     (n                                     =                                     =                                     0                                     ):                       
                                                 return                                     False                       
           
                                                 # If there is single                       
                                                 # digit                       
                                                 if                                     (n                                     =                                     =                                     1                                     ):                       
                                                 return                                     ((st[                                     0                                     ]                                     -                                     '0'                                     )                                     %                                     4                                     =                                     =                                     0                                     )                       
           
                                                 # If number formed by                       
                                                 # last two digits is                       
                                                 # divisible by 4.                       
                                                 last                                     =                                     (                                     int                                     )(st[n                                     -                                     1                                     ])                       
                                                 second_last                                     =                                     (                                     int                                     )(st[n                                     -                                     2                                     ])                       
           
                                                 return                                     ((second_last                                     *                                     10                                     +                                     last)                                     %                                     4                                     =                                     =                                     0                                     )                       
           
           
                         # Driver code                       
                         st                                     =                                     "76952"                       
           
                         # Function call                       
                         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 4 or not                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
                                                 // Function to find that number                       
                                                 // is divisible by 4 or not                       
                                                 static                                     bool                                     check(String str)                       
                                                 {                       
                                                 int                                     n = str.Length;                       
           
                                                 // Empty string                       
                                                 if                                     (n == 0)                       
                                                 return                                     false                                     ;                       
           
                                                 // If there is single digit                       
                                                 if                                     (n == 1)                       
                                                 return                                     ((str[0] -                                     '0'                                     ) % 4 == 0);                       
           
                                                 // If number formed by last two                       
                                                 // digits is divisible by 4.                       
                                                 int                                     last = str[n - 1] -                                     '0'                                     ;                       
                                                 int                                     second_last = str[n - 2] -                                     '0'                                     ;                       
           
                                                 return                                     ((second_last * 10 + last) % 4 == 0);                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 String str =                                     "76952"                                     ;                       
           
                                                 // Function call                       
                                                 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                       
                         // 4 or not                       
           
                         // Function to find that                       
                         // number divisible by                       
                         // 4 or not                       
                         function                                     check(                                     $str                                     )                       
                         {                       
                                                 $n                                     =                                     strlen                                     (                                     $str                                     );                       
           
                                                 // Empty string                       
                                                 if                                     (                                     $n                                     == 0)                       
                                                 return                                     false;                       
           
                                                 // If there is single digit                       
                                                 if                                     (                                     $n                                     == 1)                       
                                                 return                                     ((                                     $str                                     [0] -                                     '0'                                     ) % 4 == 0);                       
           
                                                 // If number formed by                       
                                                 // last two digits is                       
                                                 // divisible by 4.                       
                                                 $last                                     =                                     $str                                     [                                     $n                                     - 1] -                                     '0'                                     ;                       
                                                 $second_last                                     =                                     $str                                     [                                     $n                                     - 2] -                                     '0'                                     ;                       
                                                 return                                     ((                                     $second_last                                     * 10 +                                     $last                                     ) % 4 == 0);                       
                         }                       
           
                         // Driver code                       
                         $str                                     =                                     "76952"                                     ;                       
           
                         // Function call                       
                         $x                                     = check(                                     $str                                     )?                                     "Yes"                                     :                                     "No"                                     ;                       
                         echo                                     (                                     $x                                     );                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         //Javascript program to check whether a string is divisible by 4 or not                       
           
                         // function to check the divisibility                       
                         function                                     check(str)                       
                         {                       
                                                 // checking the length for future reference                       
                                                 var                                     n = str.length;                       
           
                                                 // if it is empty then directly returning false                       
                                                 if                                     ( n == 0)                       
                                                 {                       
                                                 return                                     false                                     ;                       
                                                 }                       
                                   
                                                 if                                     ( n == 1)                       
                                                 {                       
                                                 return                                     ((str[0] -                                     '0'                                     ) % 4 == 0);                       
                                                 }                       
                                                 var                                     lastNumber = str[n-1] -                                     '0'                                     ;                       
                                                 var                                     lastSecondNUmber = str[n-2] -                                     '0'                                     ;                       
                                                 return                                     ((lastSecondNUmber * 10  + lastNumber) % 4 == 0);                       
                         }                       
           
                         // Driver code                       
                         var                                     str=                                     "76952"                                     ;                       
           
                         //checking the value by passing it into the function                       
                         // Function call                       
                         if                                     (check(str)){                       
                                                 console.log(                                     "Yes"                                     );                       
                         }                       
                         else                                     {                       
                                                 console.log(                                     "No"                                     );                       
                         }                       

输出

Yes

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