#ifndef MARCI_MAX_FLOW_HH

#define MARCI_MAX_FLOW_HH

#include <algorithm>

#include <marci_graph_traits.hh>

#include <marci_property_vector.hh>

#include <marci_bfs.hh>

namespace marci {

  template<typename graph_type, typename T>

  class res_graph_type { 

    typedef typename graph_traits<graph_type>::node_iterator node_iterator;

    typedef typename graph_traits<graph_type>::edge_iterator edge_iterator;

    typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;

    typedef typename graph_traits<graph_type>::sym_edge_iterator sym_edge_iterator;

    graph_type& G;

    edge_property_vector<graph_type, T>& flow;

    edge_property_vector<graph_type, T>& capacity;

  public:

    res_graph_type(graph_type& _G, edge_property_vector<graph_type, T>& _flow, edge_property_vector<graph_type, T>& _capacity) : G(_G), flow(_flow), capacity(_capacity) { }

    class res_edge_it {

      friend class res_graph_type<graph_type, T>;

    protected:

      res_graph_type<graph_type, T>* resG;

      sym_edge_iterator sym;

    public:

      res_edge_it() { }

      //bool is_free() {  

      //if (resG->G.a_node(sym)==resG->G.tail(sym)) { 

      //  return (resG->flow.get(sym)<resG->capacity.get(sym)); 

      //} else { 

      //  return (resG->flow.get(sym)>0); 

      //}

      //}

      T free() { 

	if (resG->G.a_node(sym)==resG->G.tail(sym)) { 

	  return (resG->capacity.get(sym)-resG->flow.get(sym)); 

	} else { 

	  return (resG->flow.get(sym)); 

	}

      }

      bool is_valid() { return sym.is_valid(); }

      void augment(T a) {

	if (resG->G.a_node(sym)==resG->G.tail(sym)) { 

	  resG->flow.put(sym, resG->flow.get(sym)+a);

	} else { 

	  resG->flow.put(sym, resG->flow.get(sym)-a);

	}

      }

    };

    class res_out_edge_it : public res_edge_it {

    public:

      res_out_edge_it() { }

      res_out_edge_it(res_graph_type<graph_type, T>& _resG, const node_iterator& v) { 

      	resG=&_resG;

	sym=resG->G.first_sym_edge(v);

	while( sym.is_valid() && !(free()>0) ) { ++sym; }

      }

      res_out_edge_it& operator++() { 

	++sym; 

	while( sym.is_valid() && !(free()>0) ) { ++sym; }

	return *this; 

      }

    };

    res_out_edge_it first_out_edge(const node_iterator& v) {

      return res_out_edge_it(*this, v);

    }

    each_node_iterator first_node() {

      return G.first_node();

    }

    node_iterator tail(const res_edge_it& e) { return G.a_node(e.sym); }

    node_iterator head(const res_edge_it& e) { return G.b_node(e.sym); }

    int id(const node_iterator& v) { return G.id(v); }

    node_iterator invalid_node() { return G.invalid_node(); }

    res_edge_it invalid_edge() { res_edge_it n; n.sym=G.invalid_sym_edge(); return n; }

  };

  template <typename graph_type, typename T>

  struct graph_traits< res_graph_type<graph_type, T> > {

    typedef typename graph_traits<graph_type>::node_iterator node_iterator;

    typedef typename res_graph_type<graph_type, T>::res_edge_it edge_iterator;

    typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;

    typedef typename res_graph_type<graph_type, T>::res_out_edge_it out_edge_iterator;

  };

  template <typename graph_type, typename pred_type, typename free_type>

  struct flow_visitor {

    typedef typename graph_traits<graph_type>::node_iterator node_iterator;

    typedef typename graph_traits<graph_type>::edge_iterator edge_iterator;

    typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;

    typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator;

    graph_type& G;

    pred_type& pred;

    free_type& free;

    flow_visitor(graph_type& _G, pred_type& _pred, free_type& _free) : G(_G), pred(_pred), free(_free) { }

    void at_previously_reached(out_edge_iterator& e) { 

      //node_iterator v=G.tail(e);

      //node_iterator w=G.head(e);

      //std::cout<<G.id(v)<<"->"<<G.id(w)<<", "<<G.id(w)<<" is already reached";

      //std::cout<<std::endl;

   }

    void at_newly_reached(out_edge_iterator& e) { 

      node_iterator v=G.tail(e);

      node_iterator w=G.head(e);

      //std::cout<<G.id(v)<<"->"<<G.id(w)<<", "<<G.id(w)<<" is newly reached";

      pred.put(w, e);

      if (pred.get(v).is_valid()) {

	free.put(w, std::min(free.get(v), e.free()));

	//std::cout <<" nem elso csucs: ";

	//std::cout <<"szabad kap eddig: "<< free.get(w) << " ";

      } else {

	free.put(w, e.free()); 

	//std::cout <<" elso csucs: ";

	//std::cout <<"szabad kap eddig: "<< free.get(w) << " ";

      }

      //std::cout<<std::endl;

    }

  };

  template <typename graph_type, typename T>

  struct max_flow_type {

    typedef typename graph_traits<graph_type>::node_iterator node_iterator;

    typedef typename graph_traits<graph_type>::edge_iterator edge_iterator;

    typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;

    typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator;

    typedef typename graph_traits<graph_type>::in_edge_iterator in_edge_iterator;

    graph_type& G;

    node_iterator s;

    node_iterator t;

    edge_property_vector<graph_type, T> flow;

    edge_property_vector<graph_type, T>& capacity;

    max_flow_type(graph_type& _G, node_iterator _s, node_iterator _t, edge_property_vector<graph_type, T>& _capacity) : G(_G), s(_s), t(_t), flow(_G), capacity(_capacity) { 

      for(each_node_iterator i=G.first_node(); i.is_valid(); ++i) 

	for(out_edge_iterator j=G.first_out_edge(i); j.is_valid(); ++j) 

	  flow.put(j, 0);

    }

    void run() {

      typedef res_graph_type<graph_type, T> aug_graph_type;

      aug_graph_type res_graph(G, flow, capacity);

      typedef std::queue<graph_traits<aug_graph_type>::out_edge_iterator> bfs_queue_type;

      bfs_queue_type bfs_queue;

      //bfs_queue.push(res_graph.first_out_edge(s));

      typedef node_property_vector<aug_graph_type, bool> reached_type;

      //reached_type reached(res_graph, false);

      reached_type reached(res_graph);

      //reached.put(s, true);

      typedef node_property_vector<aug_graph_type, graph_traits<aug_graph_type>::edge_iterator> pred_type;

      pred_type pred(res_graph);

      pred.put(s, res_graph.invalid_edge());

      typedef node_property_vector<aug_graph_type, int> free_type;

      free_type free(res_graph);

      typedef flow_visitor<aug_graph_type, pred_type, free_type> visitor_type;

      visitor_type vis(res_graph, pred, free);

      bfs_iterator< aug_graph_type, reached_type, visitor_type > 

	res_bfs(res_graph, bfs_queue, reached, vis);

      //for(graph_traits<aug_graph_type>::each_node_iterator i=res_graph.first_node(); i.is_valid(); ++i) { 

      //for(graph_traits<aug_graph_type>::out_edge_iterator j=res_graph.first_out_edge(i); j.is_valid(); ++j) {

      //  std::cout<<"("<<res_graph.tail(j)<< "->"<<res_graph.head(j)<<") ";

      //}

      //}

      //std::cout<<std::endl;

      //char c; 

      bool augment;

      do {

	augment=false;

	while (!bfs_queue.empty()) { bfs_queue.pop(); }

	bfs_queue.push(res_graph.first_out_edge(s));

	for(graph_traits<aug_graph_type>::each_node_iterator i=res_graph.first_node(); i.is_valid(); ++i) { reached.put(i, false); }

	reached.put(s, true); 

	//searching for augmenting path

	while ( /*std::cin>>c &&*/ res_bfs.is_valid() ) { 

	  res_bfs.process(); 

	  //if (res_graph.head(graph_traits<aug_graph_type>::out_edge_iterator(res_bfs))==t) break;

	  if (res_graph.head(res_bfs)==t) break;

	  //res_bfs.next();

	  ++res_bfs;

	}

	//for (; std::cin>>c && !res_bfs.finished() && res_graph.head(res_bfs.current())!=t; res_bfs.next()) { res_bfs.process(); } 

	if (reached.get(t)) {

	  augment=true;

	  node_iterator n=t;

	  T augment_value=free.get(t);

	  std::cout<<"augmentation: ";

	  while (pred.get(n).is_valid()) { 

	    graph_traits<aug_graph_type>::edge_iterator e=pred.get(n);

	    e.augment(augment_value); 

	    std::cout<<"("<<res_graph.tail(e)<< "->"<<res_graph.head(e)<<") ";

	    n=res_graph.tail(e);

	  }

	  std::cout<<std::endl;

	}

	std::cout << "max flow:"<< std::endl;

	for(graph_traits<graph_type>::each_edge_iterator e=G.first_edge(); e.is_valid(); ++e) { 

	  std::cout<<"("<<G.tail(e)<< "-"<<flow.get(e)<<"->"<<G.head(e)<<") ";

	}

	std::cout<<std::endl;

      } while (augment);

    }

  };

} // namespace marci

#endif //MARCI_MAX_FLOW_HH