poj1930 Dead Fraction

思路：

循环小数化分数，枚举所有可能的循环节，取分母最小的那个。

实现：

#include <iostream>
#include <cstdio>
#include <string>
using namespace std;

const int INF = 0x3f3f3f3f;

int gcd(int a, int b)
{
    return !b ? a : gcd(b, a % b);
}

int lcm(int a, int b)
{
    return a / gcd(a, b) * b;
}

int toNum(string s)
{
    int n = s.length();
    int res = 0;
    for (int i = 0; i < n; i++)
    {
        res += s[i] - '0';
        if (i != n - 1)
            res *= 10;
    }
    return res;
}

int main()
{
    string s;
    while (cin >> s, s != "0")
    {
        s = s.substr(2, s.length() - 5);
        int n = s.length();
        int minn = INF;
        int minm = 0;
        for (int i = 0; i < n; i++)
        {
            int x = toNum(s.substr(i, n - i));
            int y = 9;
            for (int j = 0; j < n - i - 1; j++)
            {
                y *= 10;
                y += 9;
            }
            for (int j = 0; j < i; j++)
            {
                y *= 10;
            }
            int p = toNum(s.substr(0, i));
            int q = 1;
            for (int j = 0; j < i; j++)
            {
                q *= 10;
            }
            int l = lcm(y, q);
            int tmp = l / y * x + l / q * p;
            int g = gcd(tmp, l);
            tmp /= g;
            l /= g;
            if (l < minn)
            {
                minn = l;
                minm = tmp;
            }
        }
        cout << minm << "/" << minn << endl;
    }
    return 0;
}