improves Strongly Connected Components

algorithms/graphs/Strongly Connected Components.cpp

@@ -0,0 +1,66 @@
+/*~================ BEGIN STRONGLY CONNECTED COMPONENTS ================~*/
+
+struct SCC {
+	int n, num_sccs;
+	vi2d adj;
+        vi scc_id;
+
+	SCC(int _n) :
+		n(_n),
+		num_sccs(0),
+		adj(n),
+		scc_id(n, -1) {}
+
+	void add_edge(int u, int v) {
+		adj[u].eb(v);
+	}
+
+	void find_sccs() {
+                int timer = 1;
+                vi tin(n), st;
+                st.reserve(n);
+                function<int(int)> dfs = [&](int u) -> int {
+                        int low = tin[u] = timer++,
+                            siz = len(st);
+                        st.eb(u);
+                        for (int v : adj[u])
+                                if (scc_id[v] < 0)
+                                        low = min(
+                                            low,
+                                            tin[v]
+                                                ? tin[v]
+                                                : dfs(v));
+                        if (tin[u] == low) {
+				rep(i, siz, len(st))
+					scc_id[st[i]] = num_sccs;
+                                st.resize(siz);
+                                num_sccs++;
+                        }
+                        return low;
+                };
+
+                for (int i = 0; i < n; i++)
+			if (!tin[i]) dfs(i);
+	}
+
+	vector<set<int>> build_gscc() {
+		vector<set<int>> gscc;
+                for (int i = 0; i < len(adj); ++i)
+                        for (auto j : adj[i])
+                                if (scc_id[i] != scc_id[j])
+                                        gscc[scc_id[i]]
+                                            .emplace(
+                                                scc_id[j]);
+		return gscc;
+	}
+
+	vi2d per_comp() {
+		vi2d ret(num_sccs);
+		rep(i, 0, n)
+			ret[scc_id[i]].eb(i);
+		reverse(all(ret)); // already in topological order ;)
+		return ret;
+	}
+};
+
+/*~================= END STRONGLY CONNECTED COMPONENTS =================~*/

algorithms/graphs/Strongly Connected Components.tex

@@ -0,0 +1,6 @@
+\subsection{Strongly Connected Components (struct)}
+
+Find the connected component for each edge (already in a topological order), some additional functions are also provided.
+
+time: build in $O(V + E)$
+