#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) {
  
  for (const auto& w : G.adjMatrix) {
    // Check if (u,v) edge of T(w) || p(w,v) points to (u,v)

    // If yes => set p(w, v) to point to the next edge (u',v) in Ein(v)
    // If (u,v) the last edge, then set it to point to null

    // If T(w) contains u' then the new edge reconnects v to T(w)
    // As this needs to be checked, we set R(w) <- {v}

    // If (u,v) is not edge of T(w) or is the last edge in Ein(v), R(w) <- phi

    // Remove (u,v) from Eout(u) and Ein(v)
  }

  for (const auto& w : G.adjMatrix) {

    // Check tentative pointers of the vertices in R(w).
    // While there is a vertex x in R(w), scan the edges in Ein(x), starting
    // from the edge pointed to by p(w,x), until an edge (u',x) for which
    // p(w,u') != null is found or Ein(x) is exhausted.

    // If such edge is found, x is removed from R(w).
    // If the list is exhausted, set p(w,x) to null and M(w,x) to 0

    // Then scan all Eout(x). If (x,x') is tree edge, add x' to R(w)
  }

}

} // namespace algo

#endif