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Sol
分情况讨论
-
直接取 -
那么
直接取 -
且
那么递归处理 -
那么递归处理
形式上类似于欧几里得算法,把 转化成 可能就是是类欧几里得算法的精髓
# include <bits/stdc++.h>
using namespace std;
typedef long long ll;
inline ll Gcd(ll x, ll y) {
if (!x || !y) return x | y;
return !y ? x : Gcd(y, x % y);
}
inline void Solve(ll a, ll b, ll c, ll d, ll &x, ll &y) {
register ll g = Gcd(a, b), nx, ny;
a /= g, b /= g, g = Gcd(c, d), c /= g, d /= g;
nx = a / b + 1, ny = c / d + (c % d > 0) - 1;
if (nx <= ny) x = nx, y = 1;
else if (!a) x = 1, y = d / c + 1;
else if (a < b && c <= d) Solve(d, c, b, a, y, x);
else Solve(a % b, b, c - d * (a / b), d, x, y), x += y * (a / b);
}
ll a, b, c, d, x, y;
int main() {
while (scanf("%lld%lld%lld%lld", &a, &b, &c, &d) != EOF) Solve(a, b, c, d, x, y), printf("%lld/%lld\n", x, y);
return 0;
}