[20250919] BOJ / G2 / 타임머신 / 이종환

0224LJH/202509/19 BOJ 타임머신.md

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+```java
+import java.io.BufferedReader;
+import java.io.IOException;
+import java.io.InputStreamReader;
+import java.util.*;
+
+class Main {
+
+    static int N, M, a, b, c;
+    static List<List<Integer>> graph;
+    static List<List<Integer>> reverseGraph;
+    static final long INF = Long.MAX_VALUE / 2;
+
+    static class Node implements Comparable<Node> {
+        int num;
+        long cost;
+
+        public Node(int num, long cost) {
+            this.num = num;
+            this.cost = cost;
+        }
+
+        @Override
+        public int compareTo(Node n) {
+            return Long.compare(this.cost, n.cost);
+        }
+    }
+
+    public static void main(String[] args) throws NumberFormatException, IOException {
+        init();
+        process();
+    }
+
+    public static void init() throws NumberFormatException, IOException {
+        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
+        StringTokenizer st = new StringTokenizer(br.readLine());
+
+        N = Integer.parseInt(st.nextToken());
+        M = Integer.parseInt(st.nextToken());
+        a = Integer.parseInt(st.nextToken());
+        b = Integer.parseInt(st.nextToken());
+        c = Integer.parseInt(st.nextToken());
+
+        graph = new ArrayList<>();
+        reverseGraph = new ArrayList<>();
+
+        for (int i = 0; i <= N; i++) {
+            graph.add(new ArrayList<>());
+            reverseGraph.add(new ArrayList<>());
+        }
+
+        for (int i = 0; i < M; i++) {
+            st = new StringTokenizer(br.readLine());
+            int u = Integer.parseInt(st.nextToken());
+            int v = Integer.parseInt(st.nextToken());
+
+            graph.get(u).add(v);
+            reverseGraph.get(v).add(u);
+        }
+    }
+
+    public static void process() {
+        // 1. 타임머신을 고려한 수정된 다익스트라
+        long[] dist = modifiedDijkstra();
+
+        // 2. 결과 출력
+        if (dist[N] == INF) {
+            System.out.println("x");
+        } else if (dist[N] <= -INF/2) {  // 음의 무한대로 발산
+            System.out.println("-inf");
+        } else {
+            System.out.println(dist[N]);
+        }
+    }
+
+    public static long[] modifiedDijkstra() {
+        long[] dist = new long[N + 1];
+        Arrays.fill(dist, INF);
+
+        // 타임머신 사이클 비용 계산을 위한 BFS
+        int distBtoA = bfs(b, a);
+        boolean cyclePossible = (distBtoA != -1);
+        long cycleCost = cyclePossible ? (distBtoA - c) : 0;
+
+        // N에서 역방향으로 도달 가능한 노드들 찾기
+        boolean[] reachableFromN = new boolean[N + 1];
+        findReachable(N, reverseGraph, reachableFromN);
+
+        PriorityQueue<Node> pq = new PriorityQueue<>();
+        dist[1] = 0;
+        pq.add(new Node(1, 0));
+
+        // 음의 사이클 체크를 위한 방문 횟수 카운트
+        int[] visitCount = new int[N + 1];
+
+        while (!pq.isEmpty()) {
+            Node cur = pq.poll();
+
+            // 너무 많이 방문했으면 음의 사이클
+            if (visitCount[cur.num] > N) {
+                if (reachableFromN[cur.num]) {
+                    dist[N] = -INF;
+                    return dist;
+                }
+                continue;
+            }
+
+            visitCount[cur.num]++;
+
+            // 일반 간선 처리
+            for (int next : graph.get(cur.num)) {
+                long newCost = dist[cur.num] + 1;
+                if (newCost < dist[next]) {
+                    dist[next] = newCost;
+                    pq.add(new Node(next, newCost));
+                }
+            }
+
+            // 타임머신 처리 (a번 정점에서만)
+            if (cur.num == a) {
+                long newCost = dist[a] - c;
+                if (newCost < dist[b]) {
+                    dist[b] = newCost;
+                    pq.add(new Node(b, newCost));
+
+                    // 음의 사이클 감지
+                    if (cyclePossible && cycleCost < 0 && reachableFromN[a]) {
+                        dist[N] = -INF;
+                        return dist;
+                    }
+                }
+            }
+        }
+
+        return dist;
+    }
+
+    // BFS로 최단 거리 찾기 (가중치가 모두 1이므로)
+    public static int bfs(int start, int end) {
+        if (start == end) return 0;
+
+        Queue<Integer> q = new LinkedList<>();
+        int[] dist = new int[N + 1];
+        Arrays.fill(dist, -1);
+
+        q.add(start);
+        dist[start] = 0;
+
+        while (!q.isEmpty()) {
+            int cur = q.poll();
+
+            for (int next : graph.get(cur)) {
+                if (dist[next] == -1) {
+                    dist[next] = dist[cur] + 1;
+                    q.add(next);
+
+                    if (next == end) {
+                        return dist[next];
+                    }
+                }
+            }
+        }
+
+        return -1;
+    }
+
+    // 특정 노드에서 도달 가능한 모든 노드 찾기
+    public static void findReachable(int start, List<List<Integer>> g, boolean[] reachable) {
+        Queue<Integer> q = new LinkedList<>();
+        q.add(start);
+        reachable[start] = true;
+
+        while (!q.isEmpty()) {
+            int cur = q.poll();
+
+            for (int next : g.get(cur)) {
+                if (!reachable[next]) {
+                    reachable[next] = true;
+                    q.add(next);
+                }
+            }
+        }
+    }
+}
+```