poj 2551 Ones

OnesTime Limit: 1000MS Memory Limit: 65536K
Total Submissions: 10306 Accepted: 5869


Description
Given any integer 0 <= n <= 10000 not divisible by 2 or 5, some multiple of n is a number which in decimal notation is a sequence of 1's. How many digits are in the smallest such a multiple of n?

Input
Each line contains a number n.

Output
Output the number of digits.

Sample Input
3
7
9901

Sample Output
3
6
12

Source
Waterloo local 2001.06.02

//136K    16MS    C++    273B
//题意：求最少个连续的1 mod n为0    
//思路：设i个1 %n 余数为 e，i+1个1 为(e*10+1)%n 
//      当e为0时得到最少个1的数量 
#include<stdio.h>
int main(void)
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        int e=1;
        int cnt=1;
        while(e!=0){
           e=10*e+1;
           e%=n;
           cnt++;
        }
        printf("%d\n",cnt);
    }
    return 0;
}