import java.io.*; import java.util.*; public class clique2_nosquared { static int n, m; public static void main(String[] args) throws Exception { if (args.length < 2) { System.err.println("Usage: java clique2_fixb "); } final double EPS = Double.parseDouble(args[0]); Scanner r; try { r = new Scanner(new FileReader(args[1])); } catch (IOException e) { System.err.println("Could not open " + args[1] + ". Falling back to stdin."); r = new Scanner(System.in); } n = r.nextInt(); m = r.nextInt(); @SuppressWarnings("unchecked") List[] adj = new ArrayList[n + 1]; for (int i = 1; i <= n; i++) adj[i] = new ArrayList<>(); for (int i = 0; i < m; i++) { int a = r.nextInt(), b = r.nextInt(); adj[a].add(b); adj[b].add(a); } r.close(); long t0 = System.nanoTime(); Result res = runLaplacianRMC(adj, EPS); long t1 = System.nanoTime(); System.out.printf(Locale.US, "%.6f, %d%n", res.bestSL, res.bestRoot); System.out.printf(Locale.US, "Runtime: %.3f ms%n", (t1 - t0) / 1_000_000.0); } static Result runLaplacianRMC(List[] adj, double EPS) { // Phase 1: peel by nondecreasing degree with stale-check heap int[] deg = new int[n + 1]; PriorityQueue pq = new PriorityQueue<>(); for (int i = 1; i <= n; i++) { deg[i] = adj[i].size(); pq.add(new Pair(i, deg[i])); } Deque stack = new ArrayDeque<>(n); while (!pq.isEmpty()) { Pair p = pq.poll(); if (p.degree != deg[p.node]) continue; // stale stack.push(p); for (int v : adj[p.node]) { if (deg[v] > 0) { deg[v]--; pq.add(new Pair(v, deg[v])); } } deg[p.node] = 0; } // Phase 2: reverse reconstruction with batched Laplacian update DSU dsu = new DSU(n); boolean[] inGraph = new boolean[n + 1]; // Internal degree inside the evolving graph int[] d = new int[n + 1]; // Component energy E[root] long[] compEnergy = new long[n + 1]; // Stamps for distinct-root accumulation and for marking A int[] rootSeenStamp = new int[n + 1]; int stamp = 1; int[] inAStamp = new int[n + 1]; int aStamp = 1; double bestSL = 0.0; int bestRoot = 0; while (!stack.isEmpty()) { Pair item = stack.pop(); int u = item.node; // Collect already-in neighbors A List A = new ArrayList<>(); for (int v : adj[u]) if (inGraph[v]) A.add(v); // Sum energies from distinct neighbor roots BEFORE union long mergedEnergy = 0L; stamp++; for (int v : A) { int rv = dsu.find(v); if (rootSeenStamp[rv] != stamp) { rootSeenStamp[rv] = stamp; mergedEnergy += compEnergy[rv]; } } // Mark A for O(1) membership tests aStamp++; for (int v : A) inAStamp[v] = aStamp; // Compute delta on old edges touching A, but only within current in-graph long deltaOld = 0L; for (int w : A) { for (int x : adj[w]) { if (!inGraph[x]) continue; // not in current graph if (inAStamp[x] == aStamp) continue; // x also in A, change = 0 deltaOld += 2L * ((long) d[w] - (long) d[x]) + 1L; } } // Contribution from the |A| new edges (u, w) with w in A int degU = A.size(); long deltaNew = 0L; for (int w : A) { long t = (long) degU - ((long) d[w] + 1L); deltaNew += t * t; } // Create u and union with all neighbors in A dsu.makeIfNeeded(u); int root = u; for (int v : A) root = dsu.union(root, v); // Activate u and update degrees inGraph[u] = true; d[u] = degU; for (int w : A) d[w]++; // The new component's energy compEnergy[root] = mergedEnergy + deltaOld + deltaNew; // Score int compRoot = dsu.find(u); int compSize = dsu.size[compRoot]; double sL = compSize / (compEnergy[compRoot] + EPS); if (sL > bestSL) { bestSL = sL; bestRoot = compRoot; } } Result out = new Result(); out.bestSL = bestSL; out.bestRoot = bestRoot; return out; } // Helpers static class Result { double bestSL; int bestRoot; } static class Pair implements Comparable { final int node, degree; Pair(int node, int degree) { this.node = node; this.degree = degree; } public int compareTo(Pair o) { if (degree != o.degree) return Integer.compare(degree, o.degree); return Integer.compare(node, o.node); } } static class DSU { final int[] parent; final int[] size; final boolean[] made; DSU(int n) { parent = new int[n + 1]; size = new int[n + 1]; made = new boolean[n + 1]; } void makeIfNeeded(int v) { if (!made[v]) { made[v] = true; parent[v] = v; size[v] = 1; } } int find(int v) { if (!made[v]) return v; // treat as isolated until made if (parent[v] != v) parent[v] = find(parent[v]); return parent[v]; } int union(int a, int b) { makeIfNeeded(a); makeIfNeeded(b); int ra = find(a), rb = find(b); if (ra == rb) return ra; if (size[ra] < size[rb]) { int t = ra; ra = rb; rb = t; } parent[rb] = ra; size[ra] += size[rb]; return ra; } } }