Find The Multiple 二叉树 哈夫曼编码 经典，，，同余方程（(a*b)%n=(a%n*b%n)%n (a+b)%n=(a%n+b%n)%n）

Problem 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

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大神图片经典   领教啦！！

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#include<iostream>
#include<string>
#include<cstring>
#include<cmath>
#include<cstdio>
#include<queue>
using namespace std;
int mod[600001],res[600001];
int n,i,j,k;
int cnt;
int main()
{
   while(scanf("%d",&n)&&n)
   {
      mod[1]=1%n;
      for(i=2;mod[i-1];i++)
      {
          mod[i]=(mod[i/2]*10+i%2)%n;//哈夫曼树，模仿双向bfs();
      }
      i--;
      int id=0;
      while(i)
      {
          res[id++]=i%2;//哈夫曼编码
          i/=2;
      }
      for(i=id-1;i>=0;i--)
        printf("%d",res[i]);
      printf("
");
   }
   return 0;
}