From 1d5b269c51371280f1ba3ca8291b82c1b4f1269e Mon Sep 17 00:00:00 2001
From: oncsr <khj20006@naver.com>
Date: Tue, 16 Sep 2025 21:11:51 +0900
Subject: [PATCH] =?UTF-8?q?[20250916]=20BOJ=20/=20D5=20/=20JOI=20=EA=B5=AD?=
 =?UTF-8?q?=EA=B0=80=EC=9D=98=20=ED=96=89=EC=82=AC=20/=20=EA=B6=8C?=
 =?UTF-8?q?=ED=98=81=EC=A4=80?=
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---
 ...0\354\235\230 \355\226\211\354\202\254.md" | 186 ++++++++++++++++++
 1 file changed, 186 insertions(+)
 create mode 100644 "khj20006/202509/16 BOJ D5 JOI \352\265\255\352\260\200\354\235\230 \355\226\211\354\202\254.md"

diff --git "a/khj20006/202509/16 BOJ D5 JOI \352\265\255\352\260\200\354\235\230 \355\226\211\354\202\254.md" "b/khj20006/202509/16 BOJ D5 JOI \352\265\255\352\260\200\354\235\230 \355\226\211\354\202\254.md"
new file mode 100644
index 00000000..8e3353f0
--- /dev/null
+++ "b/khj20006/202509/16 BOJ D5 JOI \352\265\255\352\260\200\354\235\230 \355\226\211\354\202\254.md"	
@@ -0,0 +1,186 @@
+```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 final int INF = (int)1e9 + 7;
+
+	static int N, M, K, Q;
+	static List<int[]>[] graph;
+	static List<Integer>[] tree;
+	static List<int[]> edges;
+	static int[][] min, par;
+	static int[] dep, root, dist;
+
+	public static int f(int x) { return x == root[x] ? x : (root[x] = f(root[x])); }
+
+	public static void main(String[] args) throws Exception {
+
+		io = new IOController();
+
+		N = io.nextInt();
+		M = io.nextInt();
+		K = io.nextInt();
+		Q = io.nextInt();
+		graph = new List[N+1];
+		tree = new List[N+1];
+		root = new int[N+1];
+		for(int i=1;i<=N;i++) {
+			graph[i] = new ArrayList<>();
+			tree[i] = new ArrayList<>();
+			root[i] = i;
+		}
+
+		edges = new ArrayList<>();
+		for(int i=1;i<=M;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});
+			edges.add(new int[]{a,b,0});
+		}
+
+		int[] starts = new int[K];
+		for(int i=0;i<K;i++) starts[i] = io.nextInt();
+		dijkstra(starts);
+
+
+		for(int[] edge : edges) edge[2] = Math.min(dist[edge[0]], dist[edge[1]]);
+		Collections.sort(edges, (a,b) -> b[2]-a[2]);
+
+		for(int[] edge : edges) {
+			int a = edge[0], b = edge[1], c = edge[2];
+			int x = f(a), y = f(b);
+			if(x == y) continue;
+			tree[a].add(b);
+			tree[b].add(a);
+			root[x] = y;
+		}
+
+		par = new int[N+1][17];
+		min = new int[N+1][17];
+		dep = new int[N+1];
+		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];
+			min[i][k] = Math.min(min[i][k-1], min[par[i][k-1]][k-1]);
+		}
+
+		while(Q-->0) {
+			int a = io.nextInt();
+			int b = io.nextInt();
+			int ans = Integer.MAX_VALUE;
+
+			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]) {
+					ans = Math.min(ans, min[a][k]);
+					a = par[a][k];
+				}
+				else {
+					ans = Math.min(ans, min[b][k]);
+					b = par[b][k];
+				}
+			}
+
+			for(int k=16;k>=0;k--) if(par[a][k] != par[b][k]) {
+				ans = Math.min(ans, Math.min(min[a][k], min[b][k]));
+				a = par[a][k];
+				b = par[b][k];
+			}
+
+			if(a != b) {
+				ans = Math.min(ans, Math.min(min[a][0], min[b][0]));
+				a = par[a][0];
+			}
+			ans = Math.min(ans, dist[a]);
+
+			io.write(ans + "\n");
+		}
+
+		io.close();
+
+	}
+
+	public static void dijkstra(int[] starts) {
+		dist = new int[N+1];
+		Arrays.fill(dist, INF);
+		PriorityQueue<int[]> pq = new PriorityQueue<>((a,b) -> a[0]-b[0]);
+		for(int i=0;i<starts.length;i++) {
+			dist[starts[i]] = 0;
+			pq.offer(new int[]{0, starts[i]});
+		}
+
+		while(!pq.isEmpty()) {
+			int[] cur = pq.poll();
+			int d = cur[0], n = cur[1];
+			if(d > dist[n]) continue;
+			for(int[] e:graph[n]) if(dist[e[0]] > d + e[1]) {
+				dist[e[0]] = d + e[1];
+				pq.offer(new int[]{dist[e[0]], e[0]});
+			}
+		}
+	}
+
+	public static void dfs(int n, int p, int d) {
+		dep[n] = d;
+		par[n][0] = p;
+		min[n][0] = dist[n];
+		for(int i:tree[n]) if(i != p) dfs(i, n, d+1);
+	}
+
+}
+```