FZU Problem 2102 Solve equation （数学啊 ）

题目链接：http://acm.fzu.edu.cn/problem.php?pid=2102

Problem Description

You are given two positive integers A and B in Base C. For the equation:

A=k*B+d

We know there always existing many non-negative pairs (k, d) that satisfy the equation above. Now in this problem, we want to maximize k.

For example, A="123" and B="100", C=10. So both A and B are in Base 10. Then we have:

(1) A=0*B+123

(2) A=1*B+23

As we want to maximize k, we finally get one solution: (1, 23)

The range of C is between 2 and 16, and we use ‘a‘, ‘b‘, ‘c‘, ‘d‘, ‘e‘, ‘f‘ to represent 10, 11, 12, 13, 14, 15, respectively.

Input

The first line of the input contains an integer T (T≤10), indicating the number of test cases.

Then T cases, for any case, only 3 positive integers A, B and C (2≤C≤16) in a single line. You can assume that in Base 10, both A and B is less than 2^31.

Output

For each test case, output the solution “(k,d)” to the equation in Base 10.

Sample Input

32bc 33f 16123 100 101 1 2

Sample Output

(0,700)(1,23)(1,0)

Source

“高教社杯”第三届福建省大学生程序设计竞赛

题意：

给出 A 和 B 求满足 A = k * B + d，的最大的K；

c表示A, 和B是几进制！

代码如下：

#include <cstdio>
#include <cstring>
int main()
{
    int t;
    int cas = 0;
    int c;
    char a[47], b[47];
    scanf("%d",&t);
    while(t--)
    {
        int t1 = 0, t2 = 0;
        scanf("%s%s%d",a,b,&c);
        int len1 = strlen(a);
        int len2 = strlen(b);
        for(int i = 0; i < len1; i++)
        {
            t1 *= c;
            if(a[i]<='9' && a[i]>='0')
                t1+=a[i]-'0';
            else
                t1+=a[i]-'a'+10;
        }

        for(int i = 0; i < len2; i++)
        {
            t2 *= c;
            if(b[i]<='9' && b[i]>='0')
                t2+=b[i]-'0';
            else
                t2+=b[i]-'a'+10;
        }
        printf("(%d,%d)\n",t1/t2,t1%t2);
    }
    return 0;
}