[20250815] BOJ / D5 / 정기 모임 / 권혁준

khj20006/202508/15 BOJ D5 정기 모임.md

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+# C++
+```cpp
+#include <bits/stdc++.h>
+using namespace std;
+
+int N, Q;
+vector<vector<pair<int, int>>> v(300001);
+int par[300001][19]{}, mx[300001][19]{}, dep[300001]{};
+int lca[1048576]{}, dist[1048576]{};
+
+void dfs(int n, int p, int d) {
+	par[n][0] = p, dep[n] = d;
+	for(auto [i,c]:v[n]) if(i != p) {
+		mx[i][0] = c;
+		dfs(i,n,d+1);
+	}
+}
+
+pair<int,int> mrg(pair<int,int> A, pair<int,int> B) {
+	if(A.first == -1) return B;
+	if(B.first == -1) return A;
+	int a = A.first, b = B.first, res = max(A.second, B.second);
+	int diff = abs(dep[a]-dep[b]);
+	for(int k=0;k<19;k++) if(diff & (1<<k)) {
+		if(dep[a] > dep[b]) res = max(res, mx[a][k]), a = par[a][k];
+		else res = max(res, mx[b][k]), b = par[b][k];
+	}
+	for(int k=18;k>=0;k--) if(par[a][k] != par[b][k]) {
+		res = max({res, mx[a][k], mx[b][k]});
+		a = par[a][k], b = par[b][k];
+	}
+	if(a != b) res = max({res, mx[a][0], mx[b][0]}), a = par[a][0];
+	return {a, res};
+}
+
+void init(int s, int e, int n) {
+	if(s == e) {
+		lca[n] = s;
+		return;
+	}
+	int m = (s+e)>>1;
+	init(s,m,n*2);	init(m+1,e,n*2+1);
+	auto [a, b] = mrg({lca[n*2], dist[n*2]}, {lca[n*2+1], dist[n*2+1]});
+	lca[n] = a, dist[n] = b;
+}
+
+pair<int,int> find(int s, int e, int l, int r, int n) {
+	if(l>r || l>e || r<s) return {-1,0};
+	if(l<=s && e<=r) return {lca[n], dist[n]};
+	int m = (s+e)>>1;
+	auto a = find(s,m,l,r,n*2);
+	auto b = find(m+1,e,l,r,n*2+1);
+	return mrg(a,b);
+}
+
+int main(){
+	cin.tie(0)->sync_with_stdio(0);
+
+	cin>>N>>Q;
+	for(int i=1,a,b,c;i<N;i++) {
+		cin>>a>>b>>c;
+		v[a].emplace_back(b,c);
+		v[b].emplace_back(a,c);
+	}
+
+	dfs(1,0,0);
+	for(int k=1;k<19;k++) for(int i=1;i<=N;i++) {
+		par[i][k] = par[par[i][k-1]][k-1];
+		mx[i][k] = max(mx[i][k-1], mx[par[i][k-1]][k-1]);
+	}
+	init(1,N,1);
+	for(int a,b;Q--;cout<<find(1,N,a,b,1).second<<'\n') cin>>a>>b;
+
+}
+```
+
+# Java
+```java
+import java.util.*;
+import java.io.*;
+
+class IOController {
+	BufferedReader br;
+	BufferedWriter bw;
+	StringTokenizer st;
+
+	public IOController() {
+		br = new BufferedReader(new InputStreamReader(System.in));
+		bw = new BufferedWriter(new OutputStreamWriter(System.out));
+		st = new StringTokenizer("");
+	}
+
+	String nextLine() throws Exception {
+		String line = br.readLine();
+		st = new StringTokenizer(line);
+		return line;
+	}
+
+	String nextToken() throws Exception {
+		while (!st.hasMoreTokens()) nextLine();
+		return st.nextToken();
+	}
+
+	int nextInt() throws Exception {
+		return Integer.parseInt(nextToken());
+	}
+
+	long nextLong() throws Exception {
+		return Long.parseLong(nextToken());
+	}
+
+	double nextDouble() throws Exception {
+		return Double.parseDouble(nextToken());
+	}
+
+	void close() throws Exception {
+		bw.flush();
+		bw.close();
+	}
+
+	void write(String content) throws Exception {
+		bw.write(content);
+	}
+
+}
+
+public class Main {
+
+	static IOController io;
+
+	//
+
+	static int N, Q;
+	static List<int[]>[] graph;
+	static int[][] par, max;
+	static int[] dep;
+
+	static int[][] seg;
+
+	public static void main(String[] args) throws Exception {
+
+		io = new IOController();
+
+		init();
+		solve();
+
+		io.close();
+
+	}
+
+	static void init() throws Exception {
+
+		N = io.nextInt();
+		Q = io.nextInt();
+		graph = new List[N+1];
+		for(int i=1;i<=N;i++) graph[i] = new ArrayList<>();
+		for(int i=1;i<N;i++) {
+			int a = io.nextInt();
+			int b = io.nextInt();
+			int c = io.nextInt();
+			graph[a].add(new int[]{b,c});
+			graph[b].add(new int[]{a,c});
+		}
+		par = new int[N+1][19];
+		max = new int[N+1][19];
+		dep = new int[N+1];
+		seg = new int[4*N][2];
+
+	}
+
+	static void solve() throws Exception {
+
+		dfs(1,0,0);
+		for(int k=1;k<19;k++) for(int i=1;i<=N;i++) {
+			par[i][k] = par[par[i][k-1]][k-1];
+			max[i][k] = Math.max(max[i][k-1], max[par[i][k-1]][k-1]);
+		}
+
+		initSeg(1,N,1);
+
+		for(int a, b;Q-->0;) {
+			a = io.nextInt();
+			b = io.nextInt();
+			io.write(find(1,N,a,b,1)[1] + "\n");
+		}
+
+	}
+
+	static void dfs(int n, int p, int d) {
+		par[n][0] = p;
+		dep[n] = d;
+		for(int[] e:graph[n]) if(e[0] != p) {
+			max[e[0]][0] = e[1];
+			dfs(e[0],n,d+1);
+		}
+	}
+
+	static int[] lca(int[] A, int[] B) {
+		if(A[0] == -1) return B;
+		if(B[0] == -1) return A;
+
+		int a = A[0], b = B[0];
+		int res = Math.max(A[1], B[1]);
+
+		int diff = Math.abs(dep[a]-dep[b]);
+		for(int k=0;k<19;k++) if((diff & (1<<k)) != 0) {
+			if(dep[a] > dep[b]) {
+				res = Math.max(res, max[a][k]);
+				a = par[a][k];
+			}
+			else {
+				res = Math.max(res, max[b][k]);
+				b = par[b][k];
+			}
+		}
+		for(int k=18;k>=0;k--) if(par[a][k] != par[b][k]) {
+			res = Math.max(res, Math.max(max[a][k], max[b][k]));
+			a = par[a][k];
+			b = par[b][k];
+		}
+		if(a != b) {
+			res = Math.max(res, Math.max(max[a][0], max[b][0]));
+			a = par[a][0];
+		}
+		return new int[]{a, res};
+	}
+
+	static void initSeg(int s, int e, int n) {
+		if(s == e) {
+			seg[n][0] = s;
+			return;
+		}
+		int m = (s+e)>>1;
+		initSeg(s,m,n*2);
+		initSeg(m+1,e,n*2+1);
+		seg[n] = lca(seg[n*2], seg[n*2+1]);
+	}
+
+	static int[] find(int s, int e, int l, int r, int n) {
+		if(l>r || l>e || r<s) return new int[]{-1,0};
+		if(l<=s && e<=r) return seg[n];
+		int m = (s+e)>>1;
+		return lca(find(s,m,l,r,n*2), find(m+1,e,l,r,n*2+1));
+	}
+
+}
+```