Codeforces Beta Round #55 Div2 E. Shortest Path
問題
社内の勉強会で出題された。
http://codeforces.com/contest/59/problem/E
N 個の頂点と M 本の重み 1 の無向辺からなるグラフがある。K 個の (a, b, c) の組が与えられる。各 (a, b, c) について a, b, c の順で連続して頂点を通ることができないとした時、1 から N までの最短距離とその経路を求めよ。
解法
各頂点 v について幅優先するのではなく、v の 1 個前の頂点 p と合わせて、(p, v) を 1 つの頂点と考えて幅優先する。例えば、x->y->z という経路を通るとき、(x, y) から (y, z) に移動するイメージである。(a, b) から (b, c) へ移動しないようにしながら BFS して距離を出す。
コード
import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintWriter; import java.util.*; /* _ooOoo_ o8888888o 88" . "88 (| -_- |) O\ = /O ____/`---'\____ .' \\| |// `. / \\||| : |||// \ / _||||| -:- |||||- \ | | \\\ - /// | | | \_| ''\---/'' | | \ .-\__ `-` ___/-. / ___`. .' /--.--\ `. . __ ."" '< `.___\_<|>_/___.' >'"". | | : `- \`.;`\ _ /`;.`/ - ` : | | \ \ `-. \_ __\ /__ _/ .-` / / ======`-.____`-.___\_____/___.-`____.-'====== `=---=' ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ pass System Test! */ public class E { private static class Task { void solve(FastScanner in, PrintWriter out) { int N = in.nextInt(); int M = in.nextInt(); int K = in.nextInt(); ArrayList<Integer>[] graph = new ArrayList[N]; for (int i = 0; i < N; i++) { graph[i] = new ArrayList<>(); } for (int i = 0; i < M; i++) { int v = in.nextInt() - 1, u = in.nextInt() - 1; graph[v].add(u); graph[u].add(v); } //<a*N+b, [c]> TreeMap<Integer, TreeSet<Integer>> triples = new TreeMap<>(); for (int i = 0; i < K; i++) { int a = in.nextInt() - 1; int b = in.nextInt() - 1; int c = in.nextInt() - 1; int key = a * N + b; TreeSet<Integer> cs = triples.get(key); if (cs == null) triples.put(key, cs = new TreeSet<>()); cs.add(c); } ArrayDeque<Integer> deque = new ArrayDeque<>(); int[][] dist = new int[N][N]; for (int[] d : dist) Arrays.fill(d, Integer.MAX_VALUE); deque.add(0); dist[0][0] = 0; outer: while (!deque.isEmpty()) { Integer key = deque.poll(); int v = key % N;// now int p = key / N;// parent for (int next : graph[v]) { if (triples.containsKey(key) && triples.get(key).contains(next)) continue; if (dist[v][next] > dist[p][v] + 1) { dist[v][next] = dist[p][v] + 1; deque.add(v * N + next); if (next == N - 1) break outer; } } } int min = Integer.MAX_VALUE; for (int i = 0; i < N; i++) min = Math.min(min, dist[i][N - 1]); if (min == Integer.MAX_VALUE) { out.println(-1); return; } out.println(min); ArrayList<Integer> ans = new ArrayList<>(); int cur = N - 1; while (cur > 0) { ans.add(cur + 1); for (int v : graph[cur]) { if (dist[v][cur] == min) { cur = v; min--; break; } } } Collections.reverse(ans); out.print(1); for (int v : ans) { out.print(" " + v); } out.println(); } } /** * ここから下はテンプレートです。 */ public static void main(String[] args) { OutputStream outputStream = System.out; FastScanner in = new FastScanner(); PrintWriter out = new PrintWriter(outputStream); Task solver = new Task(); solver.solve(in, out); out.close(); } private static class FastScanner { private final InputStream in = System.in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int bufferLength = 0; private boolean hasNextByte() { if (ptr < bufferLength) { return true; } else { ptr = 0; try { bufferLength = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } if (bufferLength <= 0) { return false; } } return true; } private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1; } private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126; } private void skipUnprintable() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; } boolean hasNext() { skipUnprintable(); return hasNextByte(); } public String next() { if (!hasNext()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while (isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } long nextLong() { if (!hasNext()) throw new NoSuchElementException(); long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } if (b < '0' || '9' < b) { throw new NumberFormatException(); } while (true) { if ('0' <= b && b <= '9') { n *= 10; n += b - '0'; } else if (b == -1 || !isPrintableChar(b)) { return minus ? -n : n; } else { throw new NumberFormatException(); } b = readByte(); } } double nextDouble() { return Double.parseDouble(next()); } double[] nextDoubleArray(int n) { double[] array = new double[n]; for (int i = 0; i < n; i++) { array[i] = nextDouble(); } return array; } double[][] nextDoubleMap(int n, int m) { double[][] map = new double[n][]; for (int i = 0; i < n; i++) { map[i] = nextDoubleArray(m); } return map; } public int nextInt() { return (int) nextLong(); } public int[] nextIntArray(int n) { int[] array = new int[n]; for (int i = 0; i < n; i++) array[i] = nextInt(); return array; } public long[] nextLongArray(int n) { long[] array = new long[n]; for (int i = 0; i < n; i++) array[i] = nextLong(); return array; } public String[] nextStringArray(int n) { String[] array = new String[n]; for (int i = 0; i < n; i++) array[i] = next(); return array; } public char[][] nextCharMap(int n) { char[][] array = new char[n][]; for (int i = 0; i < n; i++) array[i] = next().toCharArray(); return array; } } }