Codeforces Round #377 (Div. 2) F. Tourist Reform
問題
http://codeforces.com/contest/732/problem/F
N 頂点 M 辺の連結な無向グラフが与えられます。すべての辺の向きをそれぞれどちらか 1 方向に限定した時に頂点 i から到達可能な頂点の数を mi とします。mi の最小値を最大化するとき、その値と、その時の各辺の向きを出力してください。
解法
2重辺連結成分の中では上手く巡回するように辺の向きを決めると、連結成分内の全ての頂点を行き来することができます。逆に、橋となる辺の向きを固定するとき、連結成分 v->u へ橋の向きを固定することを考えると、mi の最小値 m は 必ず m<=|u| となります。よって、最大の連結成分 u を選び、各連結成分からは u に向けて橋を固定すれば良いです。
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 F { private static class Task { long N; TreeMap<Long, int[]> direction = new TreeMap<>(); ArrayList<ArrayList<Integer>> graph; void disconnectedDfs(int v, int p, boolean[] vis) { vis[v] = true; for (int u : graph.get(v)) { if (u == p) continue; if (direction.containsKey(edgeValue(u, v))) continue; direction.put(edgeValue(u, v), new int[]{v, u}); if (!vis[u]) { disconnectedDfs(u, v, vis); } } } void superDfs(int v, int p, int[] ord) { for (int u : graph.get(v)) { if (u == p) continue; ord[u] = ord[v] + 1;//v <- u superDfs(u, v, ord); } } void solve(FastScanner in, PrintWriter out) throws Exception { N = in.nextInt(); int M = in.nextInt(); int[][] edges = new int[2][M]; graph = new ArrayList<>(); for (int i = 0; i < N; i++) graph.add(new ArrayList<>()); for (int i = 0; i < M; i++) { int u = in.nextInt() - 1; int v = in.nextInt() - 1; graph.get(u).add(v); graph.get(v).add(u); edges[0][i] = u; edges[1][i] = v; } int k; int[] cmp; ArrayList<int[]> bridges; { BiconnectedComponents bic = new BiconnectedComponents(graph); k = bic.k; cmp = bic.cmp; bridges = bic.bridges; } for (int i = 0; i < N; i++) graph.get(i).clear(); int[] sizes = new int[k]; for (int c : cmp) sizes[c]++; int maxSize = 0; int maxComponentId = 0; for (int i = 0; i < sizes.length; i++) if (maxSize < sizes[i]) { maxSize = sizes[i]; maxComponentId = i; } for (ArrayList<Integer> g : graph) g.clear(); for (int[] bridge : bridges) { int u = bridge[0]; int v = bridge[1]; graph.get(cmp[u]).add(cmp[v]); graph.get(cmp[v]).add(cmp[u]); } int[] ord = new int[k]; superDfs(maxComponentId, -1, ord); for (ArrayList<Integer> g : graph) g.clear(); for (int[] bridge : bridges) { int u = bridge[0]; int v = bridge[1]; if (ord[cmp[v]] < ord[cmp[u]]) { //u->v direction.put(edgeValue(u, v), new int[]{u, v}); } else { //v->u direction.put(edgeValue(u, v), new int[]{v, u}); } } for (int i = 0; i < M; i++) { if (!direction.containsKey(edgeValue(edges[0][i], edges[1][i]))) { graph.get(edges[0][i]).add(edges[1][i]); graph.get(edges[1][i]).add(edges[0][i]); } } boolean[] vis = new boolean[(int) N]; for (int i = 0; i < N; i++) { if (!vis[i]) disconnectedDfs(i, -1, vis); } out.println(maxSize); for (int i = 0; i < M; i++) { int[] vu = direction.get(edgeValue(edges[0][i], edges[1][i])); out.println((vu[0] + 1) + " " + (vu[1] + 1)); } } long edgeValue(int u, int v) { return N * Math.min(u, v) + Math.max(u, v); } class BiconnectedComponents { private int[] order; private ArrayDeque<Integer> stack = new ArrayDeque<>(); private ArrayDeque<Integer> path = new ArrayDeque<>(); private boolean[] inStack; private int idx; private int k; private final ArrayList<ArrayList<Integer>> G; public ArrayList<int[]> bridges = new ArrayList<>(); public int[] cmp; BiconnectedComponents(ArrayList<ArrayList<Integer>> g) { int n = g.size(); this.G = g; idx = 0; k = 0; order = new int[n]; Arrays.fill(order, -1); inStack = new boolean[n]; cmp = new int[n]; for (int v = 0; v < n; v++) { if (order[v] == -1) { dfs(v, n); // [v, N] が追加されてしまっているので削除 bridges.remove(bridges.size() - 1); } } } private void dfs(int v, int p) { order[v] = idx++; stack.addLast(v); inStack[v] = true; path.addLast(v); for (Integer to : G.get(v)) { if (to == p) continue; if (order[to] == -1) dfs(to, v); else if (inStack[to]) while (order[path.peekLast()] > order[to]) path.pollLast(); } if (v == path.peekLast()) { bridges.add(new int[]{p, v}); while (true) { int w = stack.pollLast(); inStack[w] = false; cmp[w] = k; if (v == w) break; } path.pollLast(); ++k; } } } } /** * ここから下はテンプレートです。 */ public static void main(String[] args) throws Exception { 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; } public int[][] nextIntMap(int n, int m) { int[][] map = new int[n][]; for (int i = 0; i < n; i++) { map[i] = nextIntArray(m); } return map; } } }