uva 10555 - Dead Fraction)(数论)

option=com_onlinejudge&Itemid=8&category=516&page=show_problem&problem=1496" style="">题目链接：uva 10555 - Dead Fraction

题目大意：给出一个小数，从...開始能够是不论什么数字，可是保证是无限循环小数。将该小数用分式的形式表示，而且要求分母尽量大。

解题思路：这题主要是怎么将无限循环小数转换成分式，这种：

• 有小数0.abcdEEE，未循环部分长4。循环节为E，E的长度为i(如果)
• abcd+E999…(i位9）10i

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
typedef long long ll;
const int maxn = 105;
const ll INF = 0x3f3f3f3f3f3f3f;

char s[maxn];

ll gcd (ll a, ll b) {
    return b ?

gcd(b, a%b) : a;
}

int main () {
    while (scanf("%s", s) == 1 && strcmp(s, "0")) {
        int len = strlen(s)-5;
        ll ansu, ansd = INF;
        for (int i = 0; i < len; i++)
            s[i] = s[i+2];

        for (int i = 0; i < len; i++) {
            ll d = 1, u = 0;
            for (int j = 0; j < i; j++) {
                d = d * 10;
                u = u * 10 + s[j] - '0';
            }

            ll x = 0, y = 0;
            for (int j = i; j < len; j++) {
                x = x * 10 + s[j] - '0';
                y = y * 10 + 9;
            }
            d = d * y;
            u = u * y + x;
            ll g = gcd(d, u);
            u /= g;
            d /= g;

            if (d < ansd) {
                ansd = d;
                ansu = u;
            }
        }
        printf("%lld/%lld\n", ansu, ansd);
    }
    return 0;
}