[20250313] BOJ / P2 / LCA와 쿼리 / 신희을

ShinHeeEul/202503/13 BOJ P2 LCA와 쿼리.md

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+```java
+import java.io.*;
+import java.util.*;
+
+public class Main {
+
+
+    static ArrayList<Integer>[] lists;
+
+    static int[][] parents;
+    static boolean[] visited;
+    static int[] depths;
+    static int logN;
+
+    public static void main(String[] args) throws Exception {
+        // TODO Auto-generated method stub
+
+        int N = read();
+
+        lists = new ArrayList[N + 1];
+        visited = new boolean[N + 1];
+        depths = new int[N + 1];
+        logN = (int) (Math.log(N) / Math.log(2));
+        parents = new int[N + 1][logN + 1];
+
+        for(int i = 0; i <= N; i++) {
+            lists[i] = new ArrayList<>();
+        }
+
+        // 트리 만들고       
+        for(int i = 1; i < N; i++) {
+
+            int a = read();
+            int b = read();
+
+            lists[a].add(b);
+            lists[b].add(a);
+        }
+
+        visited = new boolean[N + 1];
+        parents = new int[N + 1][logN + 1];
+
+        // dfs
+        dfs();
+
+        // parents 배열 만들기
+        for(int i = 1; i <= logN; i++) {
+        	for(int j = 2; j <= N; j++) {
+        		parents[j][i] = parents[parents[j][i-1]][i-1];
+        	}
+        }
+
+        int M = read();
+        StringBuilder sb = new StringBuilder();
+
+        for(int i = 0; i < M; i++) {
+
+        	int r = read();
+        	int u = read();
+        	int v = read();
+
+        	// depths 높이 맞추기
+
+        	// lca 3번
+        	int mr = lca(r, u);
+        	int mu = lca(r, v);
+        	int mv = lca(u, v);
+
+
+        	int ans = mr;
+        	if(depths[ans] < depths[mu]) {
+        		ans = mu;
+        	}
+        	if(depths[ans] < depths[mv]) {
+        		ans = mv;
+        	}
+        	sb.append(ans).append("\n");
+
+        }
+
+        System.out.println(sb);
+
+    }
+
+    public static int lca(int a, int b) {
+
+    	int depthA = depths[a];
+    	int depthB = depths[b];
+
+
+    	if(depthA < depthB) {
+    		b = diff(b, depthB - depthA);
+    	} else {
+    		a = diff(a, depthA - depthB);
+    	}
+
+    	if(a == b) return a;
+
+
+    	for(int i = logN; i >= 0; i--) {
+
+    		int aa = parents[a][i];
+    		int bb = parents[b][i];
+
+    		if(aa == bb) continue;
+
+
+    		a = aa;
+    		b = bb;
+    	}
+
+    	if(a == b) return a;
+
+    	return parents[a][0];
+    }
+
+    public static int diff(int a, int diff) {
+
+    	for(int i = 0; (1 << i) <= diff ; i++) {
+    		int de = (1 << i);
+
+    		if((de | diff) == diff) {
+    			a = parents[a][i];
+    		}
+    	}
+
+    	return a;
+    }
+
+    public static void dfs() {
+
+        Stack<Node> stack = new Stack<>();
+        stack.add(new Node(1, 1));
+        visited[1] = true;
+        while(!stack.isEmpty()) {
+            Node node = stack.pop();
+        	int val = node.val;
+        	int depth = node.depth;
+           depths[val] = depth;
+            for(int nxt : lists[val]) {
+            	if(visited[nxt]) continue;
+            	visited[nxt] = true;
+            	parents[nxt][0] = val;
+
+            	stack.add(new Node(nxt, depth + 1));
+            }
+
+        }
+    }
+
+    public static class Node implements Comparable<Node> {
+    	int depth;
+    	int val;
+
+    	Node(int val, int depth) {
+    		this.depth = depth;
+    		this.val = val;
+    	}
+
+    	public int compareTo(Node o) {
+    		return this.depth - o.depth;
+    	}
+    }
+
+    private static int read() throws Exception {
+        int d, o;
+        d = System.in.read();
+
+
+        o = d & 15;
+        while ((d = System.in.read()) > 32)
+            o = (o << 3) + (o << 1) + (d & 15);
+
+        return o;
+    }
+
+
+}
+```