UVa Multiplying by rotation: analog multiplication

550-multiplying by rotation

Time limit:3.000 seconds

Http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=100&page=show_ problem&problem=491

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

Multiplication of natural numbers in the general is a cumbersome operation. In some cases however the product can is obtained by moving the last digit to the front.
example:179487 * 4 = 717948
The course this property is depends on the numbersystem for you, in the above example we used the decimal representation. In base 9 We have a shorter example:

* 4 = (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 th E-Factor, and the second factor. This second factor are 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 a, the factor with the. 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

Learn English:

The least significant digit of the The

The least significant bit of the first multiplier (that is, the lowest bit)

Idea: Constantly multiply the two lowest bit a,b until the carry is a

Explain how the last example of 4 is calculated:

Complete code:

/*0.028s*/
    
#include <cstdio>  
    
int main ()  
{  
    int base, FIN, A, B, C, count, ans;  
    while (~SCANF ("%d%d%d", &base, &fin, &b))  
    {  
        a = fin;  
        c = Count = 0;  
        Do
        {  
            ans = a * b + C;  
            A = ans% base, C = Ans/base;  
            ++count;  
        }  
        while (ans!= fin);  
        printf ("%d\n", count);  
    }  
    return 0;  
}

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