UVAOJ 550 基础题 移位乘法 数论

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=491
  Multiplying by Rotation 

Warning: Not all numbers in this problem are decimal numbers!

 


Multiplication of natural numbers in general is a cumbersome operation. In some cases however the product can be obtained by moving the last digit to the front.

 


Example: 179487 * 4 = 717948

 


Of course this property depends on the numbersystem you use, in the above example we used the decimal representation. In base 9 we have a shorter example:

 


17 * 4 = 71 (base 9)

 


as (9 * 1 + 7) * 4 = 7 * 9 + 1

 

Input 

The input for your program is a textfile. Each line consists of three numbers separated by a space: the base of the number system, the least significant digit of the first factor, and the second factor. This second factor is one digit only hence less than the base. The input file ends with the standard end-of-file marker.

 

Output 

Your program determines for each input line the number of digits of the smallest first factor with the rotamultproperty. The output-file is also a textfile. Each line contains the answer for the corresponding input line.

 

Sample Input 

10 7 4
9 7 4
17 14 12

 

Sample Output 

6
2
4

 

 

Miguel A. Revilla 
1998-03-10
 1 /*************************************************************************
 2     > File Name: 12345.cpp
 3     > Author: acmicpcstar
 4     > Mail: acmicpcstar@gmail.com
 5     > Created Time: 2014年04月24日 星期四 11时46分18秒
 6  ************************************************************************/
 7 
 8 #include<iostream>
 9 #include<string>
10 #include<cstdio>
11 #include<cmath>
12 #include<algorithm>
13 using namespace std;
14 const double pi=atan(1.0)*4.0;
15 int main()
16 {long long  n,a,b,c,tot,mod,x;
17 while(cin>>n>>a>>b)
18 {c=0;tot=1;
19 x=a;
20 while(1)
21  {mod=(a*b+c)%n;
22  c=(a*b+c)/n;
23  a=mod;
24  if (c==0&&mod==x)  {cout<<tot<<endl;break;}
25  tot++;
26  }
27 }
28 return 0;
29 }

XXXXXXX7*4=7XXXXXXXX

 

看起来好难。。。写出来就好水。。可以1位1位推出来。。。直到没有进位并且。。。结果的位数为7就终止～

posted @ 2014-04-24 20:28  acmicpcstar  阅读(130)  评论(0)  编辑  收藏  举报