From d4930597c497880238b131868cbb8fbc7387f4f6 Mon Sep 17 00:00:00 2001
From: Ren Baoshuo <i@baoshuo.ren>
Date: Fri, 16 Jul 2021 10:23:57 +0800
Subject: [PATCH] =?UTF-8?q?P2502=20[HAOI2006]=E6=97=85=E8=A1=8C?=
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R53268659
---
 Luogu/problem/P2502/P2502.cpp | 102 ++++++++++++++++++++++++++++++++++
 1 file changed, 102 insertions(+)
 create mode 100644 Luogu/problem/P2502/P2502.cpp

diff --git a/Luogu/problem/P2502/P2502.cpp b/Luogu/problem/P2502/P2502.cpp
new file mode 100644
index 00000000..be15f072
--- /dev/null
+++ b/Luogu/problem/P2502/P2502.cpp
@@ -0,0 +1,102 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+struct edge {
+    int from, to, v;
+
+    bool operator<(const edge& x) const {
+        return v < x.v;
+    }
+} e[5005];
+
+struct data {
+    int a, b;
+
+    data() {
+        a = b = 0;
+    }
+    data(int _a, int _b) {
+        int g = __gcd(_a, _b);
+        a = _a / g;
+        b = _b / g;
+    }
+
+    bool operator<(const data& x) const {
+        return a * x.b < b * x.a;
+    }
+    bool operator>(const data& x) const {
+        return a * x.b > b * x.a;
+    }
+    bool operator==(const data& x) const {
+        return a * x.b == b * x.a;
+    }
+} ans(100000, 1);
+
+int n, m, s, t, fa[510], rnk[510];
+
+int find(int x) {
+    if (fa[x] != x) return find(fa[x]);
+    return x;
+}
+
+void merge(int x, int y) {
+    x = find(x);
+    y = find(y);
+    if (x == y) return;
+    if (rnk[x] < rnk[y]) swap(x, y);
+    fa[y] = x;
+    rnk[x] = max(rnk[x], rnk[y] + 1);
+}
+
+bool check(int l, int r) {
+    for (int i = 1; i <= n; i++) {
+        fa[i] = i, rnk[i] = 1;
+    }
+    for (int i = l; i <= r; i++) {
+        merge(e[i].from, e[i].to);
+    }
+    return find(s) == find(t);
+}
+
+int main() {
+    cin >> n >> m;
+    for (int i = 1; i <= m; i++) {
+        cin >> e[i].from >> e[i].to >> e[i].v;
+    }
+    cin >> s >> t;
+    sort(e + 1, e + 1 + m);
+    for (int i = 1; i <= m; i++) {
+        if (e[i].v != e[i - 1].v) {
+            int l = i - 1;
+            int r = m + 1;
+            int mid = l + r >> 1;
+            while (data(e[mid].v, e[i].v) > ans) {
+                r = mid;
+                mid = (l + r) >> 1;
+            }
+            if (!check(i, r)) continue;
+            while (l + 1 < r) {
+                mid = (l + r) >> 1;
+                if (check(i, mid)) {
+                    r = mid;
+                } else {
+                    l = mid;
+                }
+            }
+            if (data(e[r].v, e[i].v) < ans) {
+                ans = data(e[r].v, e[i].v);
+            }
+        }
+    }
+    if (ans.a == 100000) {
+        cout << "IMPOSSIBLE" << endl;
+    } else {
+        cout << ans.a;
+        if (ans.b != 1) {
+            cout << '/' << ans.b;
+        }
+        cout << endl;
+    }
+    return 0;
+}