🧑‍💻 improves the topological sorting algorithm

algorithms/graphs/topological-sorting-(tarjan).cpp

@@ -0,0 +1,35 @@
+const int maxn(1'00'000);
+int n, m;
+vi g[maxn];
+
+int not_found = 0, found = 1, processed = 2;
+int state[maxn];
+
+bool dfs(int u, vi &order) {
+  if (state[u] == processed) return true;
+  if (state[u] == found) return false;
+
+  state[u] = found;
+
+  for (auto v : g[u]) {
+    if (not dfs(v, order)) return false;
+  }
+
+  state[u] = processed;
+  order.emplace_back(u);
+
+  return true;
+}
+
+vi topo_sort() {
+  vi order;
+  memset(state, 0, sizeof state);
+
+  for (int u = 0; u < n; u++) {
+    if (state[u] == not_found and not dfs(u, order))
+      return {};
+  }
+
+  reverse(all(order));
+  return order;
+}

algorithms/graphs/topological-sorting-(tarjan).tex

@@ -0,0 +1,5 @@
+\subsection{Topological Sorting (Tarjan)}
+
+Finds a the topological order for the graph, if there is no such order it means the graph is cyclic, then it returns an empty vector
+
+$O(V + E)$