#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