Split frigioni and italiano algorithms and add query function

algorithm/italiano.h

@@ -0,0 +1,60 @@
+#ifndef ITALIANO_H_
+#define ITALIANO_H_
+
+#include "algorithm/roditty_zwick.h"
+#include "algorithm/tarjan.h"
+#include "tree/breadth_first_tree.h"
+
+#include <forward_list>
+
+using namespace graph;
+using namespace tree;
+
+namespace algo {
+
+template<typename T>
+class Italiano : public RodittyZwick<T> {
+public:
+  Italiano(Digraph<T> G) : G(G) {}
+
+  void init();
+
+  bool query(const T& u, const T& v);
+
+  void remove(const T& u, const T& v);
+private:
+  Digraph<T> G;
+
+  // Connect each vertex with its representative SCC
+  std::map<T, SCC<T>> TC;
+
+  // Reachability trees
+  std::map<T, std::set<T>> RT;
+
+  // Incoming / Outgoing edges
+  struct Edges {
+    std::forward_list<T> Ein;
+    std::forward_list<T> Eout;
+  };
+  std::map<SCC<T>, Edges> E;
+};
+
+
+template<typename T>
+void Italiano<T>::init() {
+
+}
+
+template<typename T>
+bool Italiano<T>::query(const T& u, const T& v) {
+  return TC[u] == TC[v];
+}
+
+template<typename T>
+void Italiano<T>::remove(const T& u, const T& v) {
+
+}
+
+} // namespace algo
+
+#endif