[20250226] BOJ / D5 / Mountaineers / 권혁준

Author: oncsr

khj20006/202502/26 BOJ D5 Mountaineers.md

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+```cpp
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+#include <numeric>
+using namespace std;
+using ll = long long;
+
+int M, N, Q;
+
+int r[250000]{}, H[500][500]{};
+vector<vector<pair<int, int>>> V(250000);
+int dep[250000]{}, par[250000][18]{}, cost[250000][18]{};
+
+int f(int x) { return x == r[x] ? x : r[x] = f(r[x]); }
+int coord(int x, int y) { return x * M + y; }
+
+void makeTable() {
+	for (int k = 1; k < 18; k++) for (int i = 0; i < N*M; i++) {
+		par[i][k] = par[par[i][k - 1]][k - 1];
+		cost[i][k] = max(cost[i][k - 1], cost[par[i][k - 1]][k - 1]);
+	}
+}
+
+void dfs(int n, int p, int d) {
+	par[n][0] = p, dep[n] = d;
+	for (auto[i, c] : V[n]) if (i != p) {
+		cost[i][0] = c;
+		dfs(i, n, d + 1);
+	}
+}
+
+int solve(int a, int b) {
+	int res = 0;
+	if (dep[a] < dep[b]) swap(a, b);
+	int diff = dep[a] - dep[b];
+	for (int i = 0; i < 18; i++) if (diff & (1 << i)) {
+		res = max(res, cost[a][i]);
+		a = par[a][i];
+	}
+
+	while (par[a][0] != par[b][0]) {
+		for (int i = 17; i >= 0; i--) if (par[a][i] != par[b][i]) {
+			res = max({ res, cost[a][i], cost[b][i] });
+			a = par[a][i];
+			b = par[b][i];
+		}
+	}
+	if (a != b) res = max({ res, cost[a][0], cost[b][0] });
+
+	return res;
+
+}
+
+int main()
+{
+	cin.tie(0)->sync_with_stdio(0);
+
+	cin >> N >> M >> Q;
+
+	iota(r, r + N * M, 0);
+	vector<tuple<int, int, int>> E;
+	for (int i = 0; i < N; i++) for (int j = 0; j < M; j++) {
+		cin >> H[i][j];
+		int cur = coord(i, j);
+		if (i > 0) E.emplace_back(max(H[i - 1][j], H[i][j]), cur, coord(i - 1, j));
+		if (j > 0) E.emplace_back(max(H[i][j - 1], H[i][j]), cur, coord(i, j - 1));
+	}
+
+	sort(E.begin(), E.end());
+	for (auto[c, a, b] : E) {
+		int x = f(a), y = f(b);
+		if (x == y) continue;
+		V[a].emplace_back(b, c);
+		V[b].emplace_back(a, c);
+		r[x] = y;
+	}
+
+	dfs(0, -1, 0);
+	makeTable();
+
+	for (int a, b, c, d; Q--;) {
+		cin >> a >> b >> c >> d;
+		int s = coord(a - 1, b - 1), e = coord(c - 1, d - 1);
+
+		if (s == e) cout << H[a - 1][b - 1] << '\n';
+		else  cout << solve(s, e) << '\n';
+	}
+
+}
+
+```