Digital Roots

最新推荐文章于 2022-02-06 17:11:13 发布

原创最新推荐文章于 2022-02-06 17:11:13 发布 · 125 阅读

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本文详细介绍了数字根的概念，即通过重复累加整数的各个位直到得到一位数的过程，并提供了一段使用C语言编写的代码实现。该算法适用于处理任意长度的正整数，通过将输入转换为字符串来避免数据溢出问题。

Problem Description

The digital root of a positive integer is found by summing the digits of the integer. If the resulting value is a single digit then that digit is the digital root. If the resulting value contains two or more digits, those digits are summed and the process is repeated. This is continued as long as necessary to obtain a single digit.

For example, consider the positive integer 24. Adding the 2 and the 4 yields a value of 6. Since 6 is a single digit, 6 is the digital root of 24. Now consider the positive integer 39. Adding the 3 and the 9 yields 12. Since 12 is not a single digit, the process must be repeated. Adding the 1 and the 2 yeilds 3, a single digit and also the digital root of 39.

Input

The input file will contain a list of positive integers, one per line. The end of the input will be indicated by an integer value of zero.

Output

For each integer in the input, output its digital root on a separate line of the output.

Sample Input

24
39
0

Sample Output

6
3

代码

#include <stdio.h>
#include <string.h>
int sum(long long n)
{
	int sum=0;
	int t;
	while(n!=0)
	{
		t=n%10;
		sum+=t;
		n/=10;
	}
	return sum;
}
int main()
{
	char a[10000];
	while(gets(a)&&strcmp(a,"0"))
	{
		int i;
		int s=0;
		for(i=0;a[i]!='\0';i++)
			s+=a[i]-'0';
		while(s/10!=0)
		{
			s=sum(s);
		}
		printf("%d\n",s);
	} 
	return 0;
}