3或7的倍数-yiteyi-C++库

给定一个正整数n，求小于或等于n的3或7的所有倍数的计数。 例如：

null

Input : n = 10Output : Count = 4The multiples are 3, 6, 7 and 9Input : n = 25Output : Count = 10The multiples are 3, 6, 7, 9, 12, 14, 15, 18, 21 and 24

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

一个简单的解决方案是迭代从1到n的所有数字，每当一个数字是3或7的倍数或两者的倍数时递增计数。

C++

                         // A Simple C++ program to find count of all                       
                         // numbers that multiples                       
                         #include<iostream>                       
                         using                                     namespace                                     std;                       
           
                         // Returns count of all numbers smaller than                       
                         // or equal to n and multiples of 3 or 7 or both                       
                         int                                     countMultiples(                                     int                                     n)                       
                         {                       
                                                 int                                     res = 0;                       
                                                 for                                     (                                     int                                     i=1; i<=n; i++)                       
                                                 if                                     (i%3==0 || i%7 == 0)                       
                                                 res++;                       
           
                                                 return                                     res;                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 cout <<                                     "Count = "                                     << countMultiples(25);                       
                         }                       

JAVA

                         // A Simple Java program to                       
                         // find count of all numbers                       
                         // that multiples                       
                         import                                     java.io.*;                       
           
                         class                                     GFG                       
                         {                       
                                   
                         // Returns count of all numbers                       
                         // smaller than or equal to n                       
                         // and multiples of 3 or 7 or both                       
                         static                                     int                                     countMultiples(                                     int                                     n)                       
                         {                       
                                                 int                                     res =                                     0                                     ;                       
                                                 for                                     (                                     int                                     i =                                     1                                     ; i <= n; i++)                       
                                                 if                                     (i %                                     3                                     ==                                     0                                     || i %                                     7                                     ==                                     0                                     )                       
                                                 res++;                       
           
                                                 return                                     res;                       
                         }                       
           
                         // Driver Code                       
                         public                                     static                                     void                                     main (String[] args)                       
                         {                       
                                                 System.out.print(                                     "Count = "                                     );                       
                                                 System.out.println(countMultiples(                                     25                                     ));                       
                         }                       
                         }                       
           
                         // This code is contributed by m_kit                       

Python3

                         # A Simple Python3 program to                       
                         # find count of all numbers                       
                         # that multiples                       
           
                         # Returns count of all numbers                       
                         # smaller than or equal to n                       
                         # and multiples of 3 or 7 or both                       
                         def                                     countMultiples(n):                       
                                                 res                                     =                                     0                                     ;                       
                                                 for                                     i                                     in                                     range                                     (                                     1                                     , n                                     +                                     1                                     ):                       
                                                 if                                     (i                                     %                                     3                                     =                                     =                                     0                                     or                                     i                                     %                                     7                                     =                                     =                                     0                                     ):                       
                                                 res                                     +                                     =                                     1                                     ;                       
                                   
                                                 return                                     res;                       
           
                         # Driver code                       
                         print                                     (                                     "Count ="                                     , countMultiples(                                     25                                     ));                       
           
                         # This code is contributed by mits                       

C#

                         // A Simple C# program to                       
                         // find count of all numbers                       
                         // that are multiples of 3 or 7                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
                                   
                         // Returns count of all                       
                         // numbers smaller than                       
                         // or equal to n  and                       
                         // are multiples of 3 or                       
                         // 7 or both                       
                         static                                     int                                     countMultiples(                                     int                                     n)                       
                         {                       
                                                 int                                     res = 0;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++)                       
                                                 if                                     (i % 3 == 0 || i % 7 == 0)                       
                                                 res++;                       
           
                                                 return                                     res;                       
                         }                       
           
                         // Driver Code                       
                         static                                     public                                     void                                     Main ()                       
                         {                       
                                                 Console.Write(                                     "Count = "                                     );                       
                                                 Console.WriteLine(countMultiples(25));                       
                         }                       
                         }                       
           
                         // This code is contributed by ajit                       

PHP

                         <?php                       
                         // A Simple PHP program to find count                       
                         // of all numbers that multiples                       
           
                         // Returns count of all numbers                       
                         // smaller than or equal to n                       
                         // and multiples of 3 or 7 or both                       
                         function                                     countMultiples(                                     $n                                     )                       
                         {                       
                                                 $res                                     = 0;                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <=                                     $n                                     ;                                     $i                                     ++)                       
                                                 if                                     (                                     $i                                     % 3 == 0 ||                                     $i                                     % 7 == 0)                       
                                                 $res                                     ++;                       
           
                                                 return                                     $res                                     ;                       
                         }                       
           
                         // Driver code                       
                         echo                                     "Count = "                                     ,countMultiples(25);                       
           
                         // This code is contributed by aj_36                       
                         ?>                       

Javascript

                         <script>                       
           
                         // A Simple JavaScript program to find count                       
                         // of all numbers that multiples                       
           
                         // Returns count of all numbers                       
                         // smaller than or equal to n                       
                         // and multiples of 3 or 7 or both                       
                         function                                     countMultiples(n)                       
                         {                       
                                                 let res = 0;                       
                                                 for                                     (let i = 1; i <= n; i++)                       
                                                 if                                     (i % 3 == 0 || i % 7 == 0)                       
                                                 res++;                       
           
                                                 return                                     res;                       
                         }                       
           
                         // Driver code                       
                         document.write(                                     "Count = "                                     +countMultiples(25));                       
           
                         // This code is contributed by bobby                       
           
                         </script>                       

输出：

Count = 10

时间复杂性： O（n）一个有效的解决方案可以在O（1）时间内解决上述问题。这个想法是计算3的倍数，加上7的倍数，然后减去21的倍数，因为它们被计算两次。

count = n/3 + n/7 - n/21

C++

                         // A better C++ program to find count of all                       
                         // numbers that multiples                       
                         #include<iostream>                       
                         using                                     namespace                                     std;                       
           
                         // Returns count of all numbers smaller than                       
                         // or equal to n and multiples of 3 or 7 or both                       
                         int                                     countMultiples(                                     int                                     n)                       
                         {                       
                                                 return                                     n/3 + n/7 -n/21;                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 cout <<                                     "Count = "                                     << countMultiples(25);                       
                         }                       

JAVA

                         // A better Java program to                       
                         // find count of all numbers                       
                         // that multiples                       
                         import                                     java.io.*;                       
           
                         class                                     GFG                       
                         {                       
                                   
                         // Returns count of all numbers                       
                         // smaller than or equal to n                       
                         // and multiples of 3 or 7 or both                       
                         static                                     int                                     countMultiples(                                     int                                     n)                       
                         {                       
                                                 return                                     n /                                     3                                     + n /                                     7                                     - n /                                     21                                     ;                       
                         }                       
           
                         // Driver code                       
                         public                                     static                                     void                                     main (String args [] )                       
                         {                       
                                                 System.out.println(                                     "Count = "                                     +                       
                                                 countMultiples(                                     25                                     ));                       
                         }                       
                         }                       
           
                         // This code is contributed by aj_36                       

Python 3

                         # Python 3 program to find count of                       
                         # all numbers that multiples                       
           
                         # Returns count of all numbers                       
                         # smaller than or equal to n and                       
                         # multiples of 3 or 7 or both                       
                         def                                     countMultiples(n):                       
                                                 return                                     n                                     /                                     3                                     +                                     n                                     /                                     7                                     -                                     n                                     /                                     21                                     ;                       
           
                         # Driver code                       
                         n                                     =                                     ((                                     int                                     )(countMultiples(                                     25                                     )));                       
                         print                                     (                                     "Count ="                                     , n);                       
           
                         # This code is contributed                       
                         # by Shivi_Aggarwal                       

C#

                         // A better Java program to                       
                         // find count of all numbers                       
                         // that multiples                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
                                   
                         // Returns count of all numbers                       
                         // smaller than or equal to n                       
                         // and multiples of 3 or 7 or both                       
                         static                                     int                                     countMultiples(                                     int                                     n)                       
                         {                       
                                                 return                                     n / 3 + n / 7 - n / 21;                       
                         }                       
           
                         // Driver Code                       
                         static                                     public                                     void                                     Main ()                       
                         {                       
                                                 Console.WriteLine(                                     "Count = "                                     +                       
                                                 countMultiples(25));                       
                         }                       
                         }                       
           
                         // This code is contributed by m_kit                       

PHP

                         <?php                       
                         // A better PHP program to find count                       
                         // of all numbers that multiples                       
           
                         // Returns count of all numbers                       
                         // smaller than or equal to n                       
                         // and multiples of 3 or 7 or both                       
                         function                                     countMultiples(                                     $n                                     )                       
                         {                       
                         return                                     floor                                     (                                     $n                                     / 3 +                                     $n                                     / 7 -                                     $n                                     / 21);                       
                         }                       
           
                         // Driver code                       
                         echo                                     "Count = "                                     , countMultiples(25);                       
           
                         // This code is contributed by ajit                       
                         ?>                       

Javascript

                         <script>                       
           
                         // JavaScript program to find count                       
                         // of all numbers that multiples                       
           
                         // Returns count of all numbers                       
                         // smaller than or equal to n                       
                         // and multiples of 3 or 7 or both                       
                         function                                     countMultiples(n)                       
                         {                       
                         return                                     Math.floor(n / 3 + n / 7 - n / 21);                       
                         }                       
           
                         // Driver code                       
                         document.write(                                     "Count = "                                     +countMultiples(25));                       
           
                         // This code is contributed by bobby                       
           
                         </script>                       

输出：

Count = 10

时间复杂性： O（1） 练习： 现在试着在O（1）时间内找出所有小于或等于n的数的和，以及3或7或两者的倍数。本文由 苏拉布·古普塔 .如果你喜欢GeekSforgek，并想贡献自己的力量，你也可以写一篇文章，然后将文章邮寄给评论-team@geeksforgeeks.org.看到你的文章出现在Geeksforgeks主页上，并帮助其他极客。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，请写下评论。

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