Poj 1426 find the multiple (BFS + same modulus theorem)

Find the multiple

Time limit:1000 ms		Memory limit:10000 K
Total submissions:18390		Accepted:7445		Special Judge

Description

Given a positive integer N, write a program to find out a nonzero Multiple m of N whose decimal representation contains only the digits 0 and 1. you may assume that N is not greater than 200 and there is a corresponding M containing no more than 100 decimal digits.

Input

The input file may contain in multiple test cases. Each line contains a value of N (1 <=n <= 200). A line containing a zero terminates the input.

Output

For each value of N in the input print a line containing the corresponding value of M. the decimal representation of M must not contain more than 100 digits. if there are multiple solutions for a given value of N, any one of them is acceptable.

Sample Input

26190

Sample output

10100100100100100100111111111111111111

Same modulus theorem:

(A * B) % N = (a % N * B % N) % N;

(A + B) % N = (a % N + B % N) % N;

The first 14 digits are: 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100...

1110% 6 = (110*10 + 0) % 6 = (110% 6) * 10) % 6 + (0% 6 );

MoD [x] = (mod [X/2] * 10 + x % 2) % N;

#include<stdio.h>#define N 600000int mod[N];int ans[200];int main(){    int i,k,n;    while(scanf("%d",&n),n)    {        mod[1]=1%n;         for(i=2;mod[i-1]!=0;i++)        {                                mod[i]=(mod[i/2]*10+i%2)%n;        }        i--;        k=0;        while(i)        {            ans[k++]=i%2;            i/=2;        }        for(i=k-1;i>=0;i--)            printf("%d",ans[i]);        puts("");    }    return 0;}

Poj 1426 find the multiple (BFS + same modulus theorem)