How to find the smallest number with just 0 and 1 which is divided by a given number?

Question

Every positive integer divide some number whose representation (base 10) contains only zeroes and ones.

One can prove that:

Consider the numbers 1, 11, 111,

Answer 1

The question equals to using 10ⁱ mod n (for each i, it can be used at most once) to get a sum m of n. It's like a knapsack problem or subset sum problem. In this way, dynamic programming will do the task.

In dynamic programming the complexity is O(k*n). k is the number of digits in answer. For n<10⁵, this code works perfectly.

Code:

#include 
#define NUM 2000

int main(int argc, char* argv[])
{
    signed long pow[NUM],val[NUM],x,num,ten;
    int i,j,count;
    for(num=2; numpow[x%num]-1)printf("0");
                count=pow[x%num]-1;
                printf("1");
                x=(num+x-val[pow[x%num]])%num;
            }
            while(count-->0)printf("0");
        }
        printf("\n");
    }
}

PS: This sequence in OEIS.