HDU_1013 Digital Roots

Digital Roots

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 40201 Accepted Submission(s): 12398

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
  

Source

Greater New York 2000 

本以为可以直接递归水过，谁知道没那么简单，有陷阱！数据没有范围！！！

自己的错误递归代码：

#include<stdio.h>
int SUM(int n)
{
	int k,sum=0;
	while(n)
	{
		k=n%10;
		n=n/10;
		sum+=k;
	}
	if(sum<10)
	return sum;
	else
		return SUM(sum);
}
int main()
{
	int n;
	while(scanf("%d",&n)!=EOF && n!=0)
	{
		int r;
		r=SUM(n);
		printf("%d\n",r);
	}
	return 0;
}

AC代码：

#include<stdio.h>
int main()
{
 int i,m;
 char s[1000];
 while(scanf("%s",s)==1&&s[0]!='0'){
   for(m=i=0;s[i];i++)
     m+=s[i]-'0';
 printf("%d\n",m%9==0?9:m%9);
 }
 return 0;
}

超简代码：

#include<stdio.h>
int main()
{
    int a,c;
    for(;scanf("%1d",&a),a>0;printf("%d\n",--a%9u+1))
        while((c=getchar())-48u<10)
            a+=c-48;
    return 0;
}

代码解释：

1.一位数模9是它本身(9除外);整十数模9是它十位的数字(90除外);整百数摸9是它百位的数字(900除外)......
2.对于一个一般的数,可以分拆成几个10的幂的和;一般的数模9的结果,实质就是题目所描述的"数字根"(9的倍数除外).
3.反复提到9的倍数除外,那这个除外的结果是什么?想一下就清楚.所以楼主先--a再%9最后+1就是在处理这种情况
4.数字后面跟u后缀代表无符号整数,至于9啊48啊还要加这个，那是楼主在炫耀他的代码能力，大家可无视之
5.最后提醒 48 == ‘0’

这个代码只是我从杭电搬运来的，分享一下.....