#ifndef ITALIANO_H_
#define ITALIANO_H_

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

#include <forward_list>

using namespace graph;

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;

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

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

  // Incoming / Outgoing edges
  struct Edges {
    std::forward_list<T> inc;
    std::forward_list<T> out;
  };
  std::map<T, Edges> E;
};

template<typename T>
void Italiano<T>::init() {
  for (const auto& u : std::views::keys(G.adjMatrix)) {
    for (const auto& v : G.adjMatrix[u]) {
      E[v].inc.push_front(u);
      E[u].out.push_front(v);
      TC[u][v] = false;
    }
    RT[u] = BreadthFirstTree(G, u);
    TC[u][u] = true;
    for (const auto& v : std::views::keys(RT[u].adjMatrix)) {
      TC[u][v] = true;
    }
  }
}

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

template<typename T>
void Italiano<T>::remove(const T& u, const T& v) {
  std::map<T, std::forward_list<T>> R;
  for (const auto& w : std::views::keys(G.adjMatrix)) {
    if (RT[w].contains(u, v) &&
        std::distance(E[w].inc.begin(), E[w].inc.end()) > 1) {
      if (E[v].inc.front() == u) {
        E[v].inc.pop_front();
        R[w].push_front(E[v].inc.front());
        E[v].inc.push_front(u);
      } else {
        R[w].push_front(E[v].inc.front());
      }
    }
  }
  E[u].inc.remove(v);
  E[u].out.remove(u);
  G.remove(u, v);

  for (const auto& w : std::views::keys(G.adjMatrix)) {
    bool hooked = false;
    // R contains all vertices that need a hook-parent
    while (!R[w].empty()) {
      // z is a candidate hook-parent if it is in RT[w]
      const auto& toHook = R[w].front();
      for (const auto& z : E[toHook].inc) {
        if (RT[w].contains(u, z)) {
          R[w].remove(toHook);
          hooked = true;
          break;
        }
      }
      if (!hooked) {
        TC[w][toHook] = false;
        for (const auto& z : E[toHook].out) {
          if (RT[w].contains(toHook, z))
            R[w].push_front(z);
        }
      }
    }
  }
}

} // namespace algo

#endif