QOJ: 有限小数

QOJ/9622.cpp

@@ -0,0 +1,70 @@
+/**
+ * @file 9622.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-11-12
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+const int64_t lim = 1e9;
+
+int64_t exgcd(int64_t a, int64_t b, int64_t &x, int64_t &y) {
+    if (b == 0) return x = 1, y = 0, a;
+    int64_t d = exgcd(b, a % b, y, x);
+    return y -= a / b * x, d;
+}
+
+void solve(void) {
+    int64_t a, b;
+    cin >> a >> b;
+
+    int64_t beta1 = 1;
+    while (b % 2 == 0) b /= 2, beta1 *= 2;
+    while (b % 5 == 0) b /= 5, beta1 *= 5;
+
+    if (b == 1) return cout << "0 1" << endl, void();
+    a %= b;
+
+    int ansc = INT_MAX, ansd = 1;
+    for (int64_t beta2 = 1; beta2 * b <= lim; beta2 *= 2)
+        for (int64_t beta3 = 1; beta2 * beta3 * b <= lim; beta3 *= 5) {
+            int64_t v = (b - beta2 * beta3 % b * a % b) % b, x, y;
+            exgcd(beta1, b, x, y);
+            x = (v * x % b + b) % b, y = beta2 * beta3 * b;
+            int64_t gg = gcd(x, y);
+            x /= gg, y /= gg;
+            if (ansc > x) ansc = x, ansd = y;
+        }
+
+    cout << ansc << ' ' << ansd << endl;
+
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    int _ = 1;
+    cin >> _;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}