#ifndef FRIGIONI_H_
#define FRIGIONI_H_

#include "algorithm/roditty_zwick.h"
#include "algorithm/tarjan.h"
#include "graph/breadth_first_tree.h"
#include "algorithm/decremental_scc.h"

#include <forward_list>
#include <utility>
#include <iostream>

using namespace graph;

namespace algo {

template<typename T>
class Frigioni : public RodittyZwick<T> {
public:
  Frigioni(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;

  // Transitive closure matrix, used to answer reachability queries in O(1)
  std::map<T, std::map<T, bool>> TC;

  // Connect each vertex with its representative SCC
  std::map<T, SCC<T>> C;

  // Each scc's representative vertex reachability tree
  std::map<T, BreadthFirstTree<T>> RT;

  // Incoming / Outgoing / Internal edges
  struct Edges {
    std::set<std::pair<T, T>> in;
    std::set<std::pair<T, T>> inc;
    std::set<std::pair<T, T>> out;
  };
  std::map<T, Edges> E;
};

template<typename T>
void Frigioni<T>::init() {
  auto SCCs = Tarjan<T>(G.adjMatrix).execute();

  for (auto& scc : SCCs) {
    RT[scc.id] = BreadthFirstTree<T>(G, scc.id);
    for (const auto& u : G.vertices()) {
      C[u] = scc;
      for (const auto& v : G.adjMatrix[u]) {
        TC[u][v] = false;
        if (scc.member(u)) {
          if (scc.member(v))
            E[scc.id].in.insert(std::make_pair(u, v));  
          else
            E[scc.id].out.insert(std::make_pair(u, v));
        } else if (scc.member(v)) {
          E[scc.id].inc.insert(std::make_pair(u, v));
        }
      }
    }
  }
  for (auto& scc : SCCs) {
    for (const auto& u : G.vertices()) {
      if (scc.member(u)) {
        for (const auto& v : RT[scc.id].vertices()) {
          TC[u][v] = true;
        }
      }
    }
  }
}

template<typename T>
bool Frigioni<T>::query(const T& u, const T& v) {
  return TC[u][v];
}

template<typename T>
void Frigioni<T>::remove(const T& u, const T& v) {

}

} // namespace algo

#endif