[20251102] BOJ / P1 / Imperial roads / 권혁준

khj20006/202511/02 BOJ P1 Imperial roads.md

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+```java
+import java.io.*;
+import java.util.*;
+
+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, R, Q;
+	static int[][] edges;
+	static List<int[]>[] graph;
+	static int[] root, dep;
+	static int[][] par, max;
+	static TreeMap<Integer, TreeMap<Integer, Integer>> help;
+
+	public static int f(int x) { return x == root[x] ? x : (root[x] = f(root[x])); }
+
+	public 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) {
+			dfs(e[0], n, d+1);
+			max[e[0]][0] = e[1];
+		}
+	}
+
+	public static void main(String[] args) throws Exception {
+
+		io = new IOController();
+
+		N = io.nextInt();
+		R = io.nextInt();
+		edges = new int[R][];
+		for(int i=0;i<R;i++) edges[i] = new int[]{io.nextInt(),io.nextInt(),io.nextInt()};
+		Arrays.sort(edges, (a,b) -> a[2]-b[2]);
+
+		graph = new List[N+1];
+		root = new int[N+1];
+		for(int i=1;i<=N;i++) {
+			graph[i] = new ArrayList<>();
+			root[i] = i;
+		}
+
+		help = new TreeMap<>();
+		int mst = 0;
+		for(int[] edge : edges) {
+			int a = edge[0], b = edge[1], c = edge[2];
+			if(!help.containsKey(a)) help.put(a, new TreeMap<>());
+			help.get(a).put(b, c);
+			if(!help.containsKey(b)) help.put(b, new TreeMap<>());
+			help.get(b).put(a, c);
+			int x = f(a), y = f(b);
+			if(x == y) continue;
+			mst += c;
+			root[x] = y;
+			graph[a].add(new int[]{b,c});
+			graph[b].add(new int[]{a,c});
+		}
+
+		par = new int[N+1][17];
+		dep = new int[N+1];
+		max = new int[N+1][17];
+		dfs(1,0,0);
+		for(int k=1;k<17;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]);
+		}
+
+		for(Q = io.nextInt(); Q-->0;) {
+			int a = io.nextInt(), b = io.nextInt();
+			int c = help.get(a).get(b);
+
+			int rem = 0;
+			int diff = Math.abs(dep[a] - dep[b]);
+			for(int k=0;k<17;k++) if((diff & (1<<k)) != 0) {
+				if(dep[a] > dep[b]) {
+					rem = Math.max(rem, max[a][k]);
+					a = par[a][k];
+				}
+				else {
+					rem = Math.max(rem, max[b][k]);
+					b = par[b][k];
+				}
+			}
+
+			for(int k=16;k>=0;k--) if(par[a][k] != par[b][k]) {
+				rem = Math.max(rem, Math.max(max[a][k], max[b][k]));
+				a = par[a][k];
+				b = par[b][k];
+			}
+
+			if(a != b) {
+				rem = Math.max(rem, Math.max(max[a][0], max[b][0]));
+			}
+
+			io.write((mst + c - rem) + "\n");
+		}
+
+		io.close();
+
+	}
+
+}
+```