检查一个大数字是否可以被25整除-yiteyi-C++库

给定一个数字，任务是检查这个数字是否可以被25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 = 56945250Output : YesInput  : n = 1234567589333100Output : YesInput  : 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%25来检查一个数字是否可以被25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 25 if its digits last two digits will be 0  or divisible by 25 .

插图：

For example, let us consider 769575 Number formed by last two digits is = 75Since 75 is divisible by 25 , answer is YES.

Let us consider 5325, we can write it as5325 = 5*1000 + 3*100 + 2*10 + 5The proof is based on below observation:Remainder of 10i divided by 25 is 0 if i greater than or equal to two. Note than 100, 1000,... etc lead to remainder 0 when divided by 25.So remainder of " 5*1000 + 3*100 + 2*10 + 5" divided by 25 is equivalent to remainder of following : 0 + 0 + 20 + 5 = 25Since 25 is divisible by 25, answer is yes.

C++

                         // C++ program to find if a number is                       
                         // divisible by 25 or not                       
                         #include<bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find that number divisible                       
                         // by 25 or not.                       
                         bool                                     isDivisibleBy25(string str)                       
                         {                       
                                                 // If length of string is single digit then                       
                                                 // it's not divisible by 25                       
                                                 int                                     n = str.length();                       
                                                 if                                     (n == 1)                       
                                                 return                                     false                                     ;                       
           
                                                 return                                     ( (str[n-1]-                                     '0'                                     == 0  &&                       
                                                 str[n-2]-                                     '0'                                     == 0) ||                       
                                                 ((str[n-2]-                                     '0'                                     )*10 + (str[n-1]-                                     '0'                                     ))%25 == 0 );                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 string str =                                     "76955"                                     ;                       
                                                 isDivisibleBy25(str)?  cout <<                                     "Yes"                                     :                       
                                                 cout <<                                     "No "                                     ;                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find if a number is                       
                         // divisible by 25 or not                       
                         class                                     IsDivisible                       
                         {                       
                                                 // Function to find that number divisible                       
                                                 // by 25 or not.                       
                                                 static                                     boolean                                     isDivisibleBy25(String str)                       
                                                 {                       
                                                 // If length of string is single digit then                       
                                                 // it's not divisible by 25                       
                                                 int                                     n = str.length();                       
                                                 if                                     (n ==                                     1                                     )                       
                                                 return                                     false                                     ;                       
                                   
                                                 return                                     ( (str.charAt(n-                                     1                                     )-                                     '0'                                     ==                                     0                                     &&                       
                                                 str.charAt(n-                                     2                                     )-                                     '0'                                     ==                                     0                                     ) ||                       
                                                 ((str.charAt(n-                                     2                                     )-                                     '0'                                     )*                                     10                                     + (str.charAt(n-                                     1                                     )-                                     '0'                                     ))%                                     25                                     ==                                     0                                     );                       
                                                 }                       
                                   
                                                 // main function                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 String str =                                     "76955"                                     ;                       
                                                 if                                     (isDivisibleBy25(str))                       
                                                 System.out.println(                                     "Yes"                                     );                       
                                                 else                       
                                                 System.out.println(                                     "No"                                     );                       
                                                 }                       
                         }                       

Python3

                         # Python 3 program to find if                       
                         # a number is divisible by 25                       
                         # or not                       
           
                         # Function to find that                       
                         # number divisible by 25 or not.                       
                         def                                     isDivisibleBy25(st) :                       
           
                                                 # If length of string is                       
                                                 # single digit then it's                       
                                                 # not divisible by 25                       
                                                 n                                     =                                     len                                     (st)                       
                                                 if                                     (n                                     =                                     =                                     1                                     ) :                       
                                                 return                                     False                       
           
                                                 return                                     ((                                     int                                     )(st[n                                     -                                     1                                     ])                                     =                                     =                                     0                                     and                                     ((                                     int                                     )(st[n                                     -                                     2                                     ])                                     =                                     =                                     0                                     )                                     or                       
                                                 ((                                     int                                     )(st[n                                     -                                     2                                     ])                                     *                                     10                                     +                                     (                                     int                                     )(st[n                                     -                                     1                                     ])                                     %                                     25                                     =                                     =                                     0                                     ))                       
           
                         # Driver code                       
                         st                                     =                                     "76955"                       
                         if                                     (isDivisibleBy25(st)) :                       
                                                 print                                     (                                     "Yes"                                     )                       
                         else                                     :                       
                                                 print                                     (                                     "No"                                     )                       
                                   
           
                         # This code is contributed by Nikita Tiwari.                       

C#

                         // C# program to find if a number                       
                         // is divisible by 25 or not                       
                         using                                     System;                       
           
                         class                                     IsDivisible                       
                         {                       
                                                 // Function to find that number                       
                                                 // divisible by 25 or not.                       
                                                 static                                     bool                                     isDivisibleBy25(String str)                       
                                                 {                       
                                                 // If length of string is single digit then                       
                                                 // then it's not divisible by 25                       
                                                 int                                     n = str.Length;                       
                                                 if                                     (n == 1)                       
                                                 return                                     false                                     ;                       
                                   
                                                 return                                     ((str[n - 1] -                                     '0'                                     == 0 &&                       
                                                 str[n - 2] -                                     '0'                                     == 0) ||                       
                                                 ((str[n - 2] -                                     '0'                                     ) * 10 +                       
                                                 (str[n - 1] -                                     '0'                                     )) % 25 == 0);                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main ()                       
                                                 {                       
                                                 String str =                                     "76955"                                     ;                       
                                                 if                                     (isDivisibleBy25(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 25 or not                       
           
                         // Function to find that number                       
                         //  divisible by 25 or not.                       
                         function                                     isDivisibleBy25(                                     $str                                     )                       
                         {                       
                                   
                                                 // If length of string                       
                                                 // is single digit then                       
                                                 // it's not divisible by 25                       
                                                 $n                                     =                                     strlen                                     (                                     $str                                     );                       
                                                 if                                     (                                     $n                                     == 1)                       
                                                 return                                     false;                       
           
                                                 return                                     ( (                                     $str                                     [                                     $n                                     - 1] -                                     '0'                                     == 0 &&                       
                                                 $str                                     [                                     $n                                     - 2] -                                     '0'                                     == 0) ||                       
                                                 ((                                     $str                                     [                                     $n                                     - 2] -                                     '0'                                     ) * 10 +                       
                                                 (                                     $str                                     [                                     $n                                     - 1] -                                     '0'                                     )) % 25 == 0 );                       
                         }                       
           
                         // Driver code                       
                         $str                                     =                                     "76955"                                     ;                       
                         $x                                     = isDivisibleBy25(                                     $str                                     ) ?                                     "Yes"                                     :                                     "No "                                     ;                       
                         echo                                     (                                     $x                                     );                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript program to find if a number                       
                         // is divisible by 25 or not                       
                                   
                         // Function to find that number                       
                         // divisible by 25 or not                       
                         function                                     isDivisibleBy25(str)                       
                         {                       
                                   
                                                 // If length of string                       
                                                 // is single digit then                       
                                                 // it's not divisible by 25                       
                                                 n = str.length;                       
                                   
                                                 if                                     (n == 1)                       
                                                 return                                     false                                     ;                       
                                   
                                                 return                                     ((str[n - 1] -'0                                     ' == 0 &&                       
                                                 str[n - 2] -'                                     0                                     ' == 0) ||                       
                                                 ((str[n - 2] -'                                     0                                     ') * 10 +                       
                                                 (str[n - 1] - '                                     0')) % 25 == 0);                       
                         }                       
                                   
                         // Driver Code                       
                         var                                     str =                                     "76955"                                     ;                       
                         var                                     x = isDivisibleBy25(str) ?                                     "Yes"                                     :                                     "No"                                     ;                       
           
                         document.write (x);                       
           
                         // This code is contributed by bunnyram19                       
           
                         </script>                       

输出：

No

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