UVA550 Multiplying by Rotation

 Multiplying by Rotation 

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

Multiplication of natural numbers in general is a cumbersome operation. In somecases 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 aboveexample 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 standardend-of-file marker.

Output 

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

Sample Input 

10 7 49 7 417 14 12

Sample Output 

624题目意思就是一个数乘以另一个数得到的结果是自己本身最后以为数变到开头。如　１７９４８７　×　４　＝　７１７９４８；但这题并不是让你算１０进制，而是任意ｎ进制。题目给的三个数分别是　ｎ进制，要使乘完后最后一位变成第一位的那个乘数的最后一位，和要乘的数。。思路就是采用小学生乘法模拟，不过注意是满ｎ进１．按第一个样例，最后一位７乘以４为２８！＝７；那就下一位　（（２８　％　１０）＋（２８　／１０））　×　４是不是等于７．。循环到等于那最后一位为止。。。ＡＣ代码如下：
#include<iostream>using namespace std;int main () {int x,y,z;int count;int temp;while (cin >>x >>y >>z) {        count = 1;temp = y * z;while (temp != y ) {    count++;temp = (temp % x) * z + temp / x;}cout << count<<endl;}return 0;}