uva 10555 - Dead Fraction)(数论)

来源：互联网发布：怎么把微店搬到淘宝编辑：程序博客网时间：2024/05/29 04:40

题目链接：uva 10555 - Dead Fraction

题目大意：给出一个小数，从...开始可以是任何数字，但是保证是无限循环小数，将该小数用分式的形式表示，并且要求分母尽量大。

解题思路：这题主要是怎么将无限循环小数转换成分式，这样的：

有小数0.abcdEEE，未循环部分长4，循环节为E，E的长度为i(假设)
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;}

1 0