From 0fff47d52d32283a2f7d92f67d762fb41ffa12c9 Mon Sep 17 00:00:00 2001
From: oncsr <khj20006@naver.com>
Date: Fri, 21 Feb 2025 10:10:21 +0900
Subject: [PATCH] =?UTF-8?q?[20250221]=20BOJ=20/=20P2=20/=20dgeu-learning?=
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+```cpp
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+#include <numeric>
+using namespace std;
+
+int N, M, Q;
+int r[200001]{}, dep[200001]{};
+int D[200001][18]{}, X[200001][18]{};
+vector<vector<pair<int, int>>> V(200001);
+
+int f(int x) { return x == r[x] ? x : r[x] = f(r[x]); }
+
+void dfs(int n, int p, int d) {
+	D[n][0] = p, dep[n] = d;
+	for (auto[i, c] : V[n]) if (i != p) dfs(i, n, d + 1), X[i][0] = c;
+}
+
+void make() {
+	for (int k = 1; k < 18; k++) for (int i = 1; i <= N; i++) {
+		D[i][k] = D[D[i][k - 1]][k - 1];
+		X[i][k] = min(X[i][k - 1], X[D[i][k - 1]][k - 1]);
+	}
+}
+
+int solve(int a, int b) {
+	if (dep[a] < dep[b]) swap(a, b);
+	int diff = dep[a] - dep[b], res = 2e9;
+	for (int i = 0; i < 18; i++) if (diff & (1 << i)) {
+		res = min(res, X[a][i]);
+		a = D[a][i];
+	}
+	if (a == b) return res;
+	while (D[a][0] != D[b][0]) {
+		for (int i = 0; i < 18; i++) if (D[a][i] == D[b][i]) {
+			i--;
+			res = min({ res, X[a][i], X[b][i] });
+			a = D[a][i], b = D[b][i];
+			break;
+		}
+	}
+	return min({ res, X[a][0], X[b][0] });
+}
+
+int main()
+{
+	cin.tie(0)->sync_with_stdio(0);
+
+	cin >> N >> M >> Q;
+	vector<tuple<int, int, int>> E(M);
+	for (auto &[v, x, y] : E) cin >> x >> y >> v;
+	sort(E.begin(), E.end(), greater<>());
+	
+	iota(r, r + N + 1, 0);
+	for (auto[v, a, b] : E) {
+		int x = f(a), y = f(b);
+		if (x == y) continue;
+		r[x] = y;
+		V[a].emplace_back(b, v);
+		V[b].emplace_back(a, v);
+	}
+
+	dfs(1, 0, 0);
+	make();
+
+	for (int a, b; Q--;) {
+		cin >> a >> b;
+		cout << solve(a, b) << '\n';
+	}
+
+}
+
+```