From d017584adf6ded74412004c384e8c1b359d1ceb1 Mon Sep 17 00:00:00 2001
From: oncsr <khj20006@naver.com>
Date: Sun, 15 Jun 2025 23:54:15 +0900
Subject: [PATCH] =?UTF-8?q?[20250615]=20BOJ=20/=20D4=20/=20XOR=20MST=20/?=
 =?UTF-8?q?=20=EA=B6=8C=ED=98=81=EC=A4=80?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 khj20006/202506/15 BOJ D4 XOR MST.md | 192 +++++++++++++++++++++++++++
 1 file changed, 192 insertions(+)
 create mode 100644 khj20006/202506/15 BOJ D4 XOR MST.md

diff --git a/khj20006/202506/15 BOJ D4 XOR MST.md b/khj20006/202506/15 BOJ D4 XOR MST.md
new file mode 100644
index 00000000..af75bf05
--- /dev/null
+++ b/khj20006/202506/15 BOJ D4 XOR MST.md	
@@ -0,0 +1,192 @@
+```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);
+    }
+
+}
+
+class Node {
+    int count;
+    Node left, right;
+    Node(){ count = 0; }
+}
+
+class Trie {
+    Node root;
+    Trie(){ root = new Node(); }
+
+    void insert(int x) {
+        Node now = root;
+        int bit = 1<<29;
+        while(bit > 0) {
+            int val = x & bit;
+            if(val == 0) {
+                if(now.left == null) now.left = new Node();
+                now = now.left;
+            }
+            else {
+                if(now.right == null) now.right = new Node();
+                now = now.right;
+            }
+            now.count++;
+            bit >>= 1;
+        }
+    }
+
+    void erase(int x) {
+        Node now = root;
+        eraseDfs(now, x, 1<<29);
+    }
+
+    boolean eraseDfs(Node now, int x, int bit) {
+        if(bit == 0) return --now.count == 0;
+        int val = x & bit;
+        if(val == 0) {
+            if(eraseDfs(now.left, x, bit>>1)) now.left = null;
+        }
+        else {
+            if(eraseDfs(now.right, x, bit>>1)) now.right = null;
+        }
+        return --now.count == 0;
+    }
+
+}
+
+public class Main {
+
+    static IOController io;
+
+    //
+
+    static int N;
+    static int[] A;
+    static Trie P, Q;
+
+    public static void main(String[] args) throws Exception {
+
+        io = new IOController();
+
+        init();
+        solve();
+
+        io.close();
+
+    }
+
+    public static void init() throws Exception {
+
+        N = io.nextInt();
+        A = new int[N];
+        for(int i=0;i<N;i++) A[i] = io.nextInt();
+        P = new Trie();
+        Q = new Trie();
+
+    }
+
+    static void solve() throws Exception {
+
+        P.insert(A[0]);
+        for(int i=1;i<N;i++) Q.insert(A[i]);
+
+        long mst = 0;
+        for(int i=1;i<N;i++) mst += set();
+
+        io.write(mst + "\n");
+
+    }
+
+    static int set() {
+        int[] result = find(P.root, Q.root, 1<<29);
+        int cost = result[0], val = result[1];
+        Q.erase(val);
+        P.insert(val);
+        return cost;
+    }
+
+    static int[] find(Node p, Node q, int bit) {
+
+        if(bit == 0) return new int[]{0,0};
+
+        boolean c1 = p.left != null && q.left != null;
+        boolean c2 = p.right != null && q.right != null;
+        boolean c3 = p.left != null && q.right != null;
+        boolean c4 = p.right != null && q.left != null;
+
+        if(c1 || c2) {
+            if(c1 && c2) {
+                int[] res1 = find(p.left, q.left, bit>>1);
+                int[] res2 = find(p.right, q.right, bit>>1);
+                res2[1] |= bit;
+                if(res1[0] > res2[0]) return res2;
+                return res1;
+            }
+            if(c1) return find(p.left, q.left, bit>>1);
+            int[] res = find(p.right, q.right, bit>>1);
+            res[1] |= bit;
+            return res;
+        }
+        if(c3 && c4) {
+            int[] res1 = find(p.left, q.right, bit>>1);
+            res1[0] |= bit;
+            res1[1] |= bit;
+            int[] res2 = find(p.right, q.left, bit>>1);
+            res2[0] |= bit;
+            if(res1[0] > res2[0]) return res2;
+            return res1;
+        }
+        if(c3) {
+            int[] res = find(p.left, q.right, bit>>1);
+            res[0] |= bit;
+            res[1] |= bit;
+            return res;
+        }
+        int[] res = find(p.right, q.left, bit>>1);
+        res[0] |= bit;
+        return res;
+
+    }
+
+}
+```