POJ 1426 Find The Multiple(BFS 同余模定理)

题意 给你一个数n 输出一个仅由0，1组成的数m使得m是n的倍数

找到一个m 是m%n==0 就行了 初始让m=1 然后bfs扩展m的位数 只有两种情况 m = m * 10 或 m = m*10 + 1;

同余模定理 (a+b) % c = (a%c + b%c) % c, (a*b)%c = (a%c * b%c) % c;

运用同余模定理 可以只记录余数 这样就可以避免处理大数了 因为余数不会超过n 而n是小于两百的

对于已经得到过的余数 是可以跳过的 可以考虑下为什么

于是只用保存每一位选的是0还是1 只要保证最后余数为0就行了

1. 选0 m = m*10 % n;

2. 选1 m = (m*10 + 1) % n;

#include <cstdio>
using namespace std;
const int N = 205;
int q
, p
, d
, n;

int bfs()
{
    int le = 0, ri = 0, r = 1, cr;
    int v
 = {0};
    v[q[ri++] = r % n] = d[0] = 1;
    p[0] = -1;
    while(le < ri)
    {
        cr = q[le];
        if(cr == 0)  return le;
        if(!v[r = cr * 10 % n])
            v[r] = 1, p[ri] = le, d[ri] = 0, q[ri++] = r;
        if(!v[r = (cr * 10 + 1) % n])
            v[r] = 1, p[ri] = le, d[ri] = 1, q[ri++] = r;
        ++le;
    }
    return -1;
}

void print(int k)
{
    if(p[k] >= 0) print(p[k]);
    printf("%d", d[k]);
}

int main()
{
    while(scanf("%d", &n), n)
    {
        print(bfs());
        puts("");
    }
    return 0;
}

Find The Multiple

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 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

2
6
19
0

Sample Output

10
100100100100100100
111111111111111111