[20250225] BOJ / P2 / 트리의 외심 / 권혁준

Author: oncsr

khj20006/202502/26 BOJ P2 트리의 외심.md

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+```cpp
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+using ll = long long;
+
+int N, Q;
+vector<vector<int>> V(100001);
+int par[100001][17]{}, dep[100001]{};
+
+void dfs(int n, int p, int d) {
+	par[n][0] = p, dep[n] = d;
+	for (int i : V[n]) if (i != p) dfs(i, n, d + 1);
+}
+
+void makeTable() {
+	for (int k = 1; k < 17; k++) for (int i = 1; i <= N; i++) par[i][k] = par[par[i][k - 1]][k - 1];
+}
+
+pair<int, int> solve(int a, int b) {
+	int diff = abs(dep[a] - dep[b]);
+	int ma = 0, mb = 0;
+	int oa = a, ob = b;
+	for (int i = 0; i < 17; i++) if (diff & (1 << i)) {
+		if (dep[a] > dep[b]) a = par[a][i], ma += (1 << i);
+		else b = par[b][i], mb += (1 << i);
+	}
+
+	while (par[a][0] != par[b][0]) {
+		for (int i = 16; i >= 0; i--) if (par[a][i] != par[b][i]) {
+			a = par[a][i], ma += (1 << i);
+			b = par[b][i], mb += (1 << i);
+			break;
+		}
+	}
+	if (a != b) {
+		a = par[a][0], ma++;
+		b = par[b][0], mb++;
+	}
+
+	int d = ma + mb;
+	if (ma == mb) return { a, d };
+	if ((ma + mb) % 2) return { -1,d };
+
+	int from = ma > mb ? oa : ob, to = a, len = (ma + mb) / 2;
+	for (int i = 0; i < 17; i++) if (len & (1 << i)) from = par[from][i];
+	return { from, d };
+
+}
+
+int main()
+{
+	cin.tie(0)->sync_with_stdio(0);
+
+	cin >> N;
+	for (int i = 1, a, b; i < N; i++) {
+		cin >> a >> b;
+		V[a].push_back(b);
+		V[b].push_back(a);
+	}
+
+	dfs(1, 0, 0);
+	makeTable();
+
+	for (cin >> Q; Q--;) {
+		int a, b, c;
+		cin >> a >> b >> c;
+		int res = -1;
+
+		auto[m1, _x] = solve(a, b);
+		if (m1 != -1) {
+			auto[_1, l1] = solve(a, m1);
+			auto[_2, l2] = solve(b, m1);
+			auto[_3, l3] = solve(c, m1);
+			if (l1 == l2 && l2 == l3) res = m1;
+		}
+		auto[m2, _y] = solve(b, c);
+		if (m2 != -1) {
+			auto[_1, l1] = solve(a, m2);
+			auto[_2, l2] = solve(b, m2);
+			auto[_3, l3] = solve(c, m2);
+			if (l1 == l2 && l2 == l3) res = m2;
+		}
+		auto[m3, _z] = solve(a, c);
+		if (m3 != -1) {
+			auto[_1, l1] = solve(a, m3);
+			auto[_2, l2] = solve(b, m3);
+			auto[_3, l3] = solve(c, m3);
+			if (l1 == l2 && l2 == l3) res = m3;
+		}
+
+		cout << res << '\n';
+	}
+
+}
+
+```