求一个数的位数之和，直到和变成一位数-yiteyi-C++库

给定一个数字 N ，我们需要找到它的数字之和，以便：

null

If n < 10        digSum(n) = nElse             digSum(n) = Sum(digSum(n))

例如：

Input : 1234Output : 1Explanation : The sum of 1+2+3+4 = 10,               digSum(x) == 10              Hence ans will be 1+0 = 1Input : 5674Output : 4

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

A. 蛮力方法是将所有数字相加，直到总和小于10。 流程图：

图片[1]-求一个数的位数之和，直到和变成一位数-yiteyi-C++库

下面是寻找总和的蛮力程序。

C++

                         // C++ program to find sum of                       
                         // digits of a number until                       
                         // sum becomes single digit.                       
                         #include<bits/stdc++.h>                       
                                   
                         using                                     namespace                                     std;                       
           
                         int                                     digSum(                                     int                                     n)                       
                         {                       
                                                 int                                     sum = 0;                       
                                   
                                                 // Loop to do sum while                       
                                                 // sum is not less than                       
                                                 // or equal to 9                       
                                                 while                                     (n > 0 || sum > 9)                       
                                                 {                       
                                                 if                                     (n == 0)                       
                                                 {                       
                                                 n = sum;                       
                                                 sum = 0;                       
                                                 }                       
                                                 sum += n % 10;                       
                                                 n /= 10;                       
                                                 }                       
                                                 return                                     sum;                       
                         }                       
           
                         // Driver program to test the above function                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 1234;                       
                                                 cout << digSum(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find sum of                       
                         // digits of a number until                       
                         // sum becomes single digit.                       
                         import                                     java.util.*;                       
           
                         public                                     class                                     GfG {                       
                                   
                                                 static                                     int                                     digSum(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum =                                     0                                     ;                       
           
                                                 // Loop to do sum while                       
                                                 // sum is not less than                       
                                                 // or equal to 9                       
                                                 while                                     (n >                                     0                                     || sum >                                     9                                     )                       
                                                 {                       
                                                 if                                     (n ==                                     0                                     ) {                       
                                                 n = sum;                       
                                                 sum =                                     0                                     ;                       
                                                 }                       
                                                 sum += n %                                     10                                     ;                       
                                                 n /=                                     10                                     ;                       
                                                 }                       
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver code                       
                                                 public                                     static                                     void                                     main(String argc[])                       
                                                 {                       
                                                 int                                     n =                                     1234                                     ;                       
                                                 System.out.println(digSum(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Gitanjali.                       

python

                         # Python program to find sum of                       
                         # digits of a number until                       
                         # sum becomes single digit.                       
                         import                                     math                       
           
                         # method to find sum of digits                       
                         # of a number until sum becomes                       
                         # single digit                       
                         def                                     digSum( n):                       
                                                 sum                                     =                                     0                       
                                   
                                                 while                                     (n >                                     0                                     or                                     sum                                     >                                     9                                     ):                       
                                   
                                                 if                                     (n                                     =                                     =                                     0                                     ):                       
                                                 n                                     =                                     sum                       
                                                 sum                                     =                                     0                       
                                   
                                                 sum                                     +                                     =                                     n                                     %                                     10                       
                                                 n                                     /                                     =                                     10                       
                                   
                                                 return                                     sum                       
           
                         # Driver method                       
                         n                                     =                                     1234                       
                         print                                     (digSum(n))                       
           
                         # This code is contributed by Gitanjali.                       

C#

                         // C# program to find sum of                       
                         // digits of a number until                       
                         // sum becomes single digit.                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 static                                     int                                     digSum(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum = 0;                       
           
                                                 // Loop to do sum while                       
                                                 // sum is not less than                       
                                                 // or equal to 9                       
                                                 while                                     (n > 0 || sum > 9)                       
                                                 {                       
                                                 if                                     (n == 0)                       
                                                 {                       
                                                 n = sum;                       
                                                 sum = 0;                       
                                                 }                       
                                                 sum += n % 10;                       
                                                 n /= 10;                       
                                                 }                       
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 1234;                       
                                                 Console.Write(digSum(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by nitin mittal                       

PHP

                         <?php                       
                         // PHP program to find sum of                       
                         // digits of a number until                       
                         // sum becomes single digit.                       
           
                         function                                     digSum(                                     $n                                     )                       
                         {                       
                                                 $sum                                     = 0;                       
                                   
                                                 // Loop to do sum while                       
                                                 // sum is not less than                       
                                                 // or equal to 9                       
                                                 while                                     (                                     $n                                     > 0 ||                                     $sum                                     > 9)                       
                                                 {                       
                                                 if                                     (                                     $n                                     == 0)                       
                                                 {                       
                                                 $n                                     =                                     $sum                                     ;                       
                                                 $sum                                     = 0;                       
                                                 }                       
                                                 $sum                                     +=                                     $n                                     % 10;                       
                                                 $n                                     = (int)                                     $n                                     / 10;                       
                                                 }                       
                                                 return                                     $sum                                     ;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 1234;                       
                         echo                                     digSum(                                     $n                                     );                       
           
                         // This code is contributed                       
                         // by aj_36                       
                         ?>                       

Javascript

                         <script>                       
                         // Javascript program to find sum of                       
                         // digits of a number until                       
                         // sum becomes single digit.                       
                                                 let n = 1234;                       
                                                 //Function to get sum of digits                       
                                                 function                                     getSum(n) {                       
                                                 let sum = 0;                       
                                                 while                                     (n > 0 || sum > 9) {                       
                                                 if                                     (n == 0) {                       
                                                 n = sum;                       
                                                 sum = 0;                       
                                                 }                       
                                                 sum = sum + n % 10;                       
                                                 n = Math.floor(n / 10);                       
                                                 }                       
                                                 return                                     sum;                       
                                                 }                       
                                                 //function call                       
                                                 document.write(getSum(n));                       
                                   
                         //This code is contributed by Surbhi Tyagi                       
                         </script>                       

输出：

所以，另一个挑战是“你能在O（1）运行时不使用任何循环/递归吗？”

对存在一个 简单优雅的O（1）解决方案 也为了这个。答案很简单：-

If n == 0   return 0;If n % 9 == 0          digSum(n) = 9Else                   digSum(n) = n % 9

上述逻辑是如何运作的？

这种方法背后的逻辑是：

要检查一个数字是否可被9整除，请将数字的位数相加，然后检查总和是否可被9整除。如果是，那么这个数字可以被9整除，否则不是。

我们取27，即（2+7=9），因此可以被9整除。如果一个数n可以被9整除，那么它的数字之和直到变成一个数字时总是9。例如设n=2880 数字之和=2+8+8=18:18=1+8=9

因此数字的形式可以是9x或9x+k。对于第一种情况，答案总是9。对于第二种情况，始终是k，这是剩下的余数。

这个问题被广泛称为数字根问题。

你可能会发现这篇维基百科文章很有用。-> https://en.wikipedia.org/wiki/Digital_root

以下是上述理念的实施情况：

C++

                         #include<bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         int                                     digSum(                                     int                                     n)                       
                         {                       
                                                 if                                     (n == 0)                       
                                                 return                                     0;                       
                                                 return                                     (n % 9 == 0) ? 9 : (n % 9);                       
                         }                       
           
                         // Driver program to test the above function                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 9999;                       
                                                 cout<<digSum(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
           
                                                 static                                     int                                     digSum(                                     int                                     n)                       
                                                 {                       
                                                 if                                     (n ==                                     0                                     )                       
                                                 return                                     0                                     ;                       
                                                 return                                     (n %                                     9                                     ==                                     0                                     ) ?                                     9                                     : (n %                                     9                                     );                       
                                                 }                       
                                   
                                                 // Driver program to test the above function                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 int                                     n =                                     9999                                     ;                       
                                                 System.out.println(digSum(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

Python3

                         def                                     digSum(n):                       
           
                                                 if                                     (n                                     =                                     =                                     0                                     ):                       
                                                 return                                     0                       
                                                 if                                     (n                                     %                                     9                                     =                                     =                                     0                                     ):                       
                                                 return                                     9                       
                                                 else                                     :                       
                                                 return                                     (n                                     %                                     9                                     )                       
           
                         # Driver program to test the above function                       
                         n                                     =                                     9999                       
                         print                                     (digSum(n))                       
           
                         # This code is contributed by                       
                         # Smitha Dinesh Semwal                       

C#

                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
                                                 static                                     int                                     digSum(                                     int                                     n)                       
                                                 {                       
                                                 if                                     (n == 0)                       
                                                 return                                     0;                       
                                                 return                                     (n % 9 == 0) ? 9 : (n % 9);                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main ()                       
                                                 {                       
                                                 int                                     n = 9999;                       
                                                 Console.Write(digSum(n));                       
                                   
                                                 }                       
                         }                       
           
                         // This code is contributed by aj_36                       

PHP

                         <?php                       
           
                         function                                     digSum(                                     $n                                     )                       
                         {                       
                                                 if                                     (                                     $n                                     == 0)                       
                                                 return                                     0;                       
                                                 return                                     (                                     $n                                     % 9 == 0) ? 9 : (                                     $n                                     % 9);                       
                         }                       
           
                         // Driver program to test the above function                       
                         $n                                     = 9999;                       
                         echo                                     digSum(                                     $n                                     );                       
           
                         //This code is contributed by anuj_67.                       
                         ?>                       

Javascript

                         <script>                       
                                   
                         function                                     digSum(n)                       
                         {                       
                                                 if                                     (n == 0)                       
                                                 return                                     0;                       
                                   
                                                 return                                     (n % 9 == 0) ? 9 : (n % 9);                       
                         }                       
           
                         // Driver code                       
                         n = 9999;                       
                         document.write(digSum(n));                       
           
                         // This code is contributed by code_hunt                       
           
                         </script>                       

输出：

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