/*
 *dijkstra
 *by jacint
 *Performs Dijkstra's algorithm from Node s. 
 *
 *Constructor: 
 *
 *dijkstra(graph_type& G, NodeIt s, EdgeMap& distance)
 *
 *
 *
 *Member functions:
 *
 *void run()
 *
 *  The following function should be used after run() was already run.
 *
 *
 *T dist(NodeIt v) : returns the distance from s to v. 
 *   It is 0 if v is not reachable from s.
 *
 *
 *EdgeIt pred(NodeIt v)
 *   Returns the last Edge of a shortest s-v path. 
 *   Returns an invalid iterator if v=s or v is not
 *   reachable from s.
 *
 *
 *bool reach(NodeIt v) : true if v is reachable from s
 *
 *
 *
 *
 *
 *Problems: 
 * 
 *Heap implementation is needed, because the priority queue of stl
 *does not have a mathod for key-decrease, so we had to use here a 
 *g\'any solution.
 * 
 *The implementation of infinity would be desirable, see after line 100. 
 */

#ifndef DIJKSTRA_HH
#define DIJKSTRA_HH

#include <queue>
#include <algorithm>

#include <marci_graph_traits.hh>
#include <marciMap.hh>


namespace std {
  namespace marci {





    template <typename graph_type, typename T>
    class dijkstra{
      typedef typename graph_traits<graph_type>::NodeIt NodeIt;
      typedef typename graph_traits<graph_type>::EdgeIt EdgeIt;
      typedef typename graph_traits<graph_type>::EachNodeIt EachNodeIt;
      typedef typename graph_traits<graph_type>::InEdgeIt InEdgeIt;
      typedef typename graph_traits<graph_type>::OutEdgeIt OutEdgeIt;
      
      
      graph_type& G;
      NodeIt s;
      NodeMap<graph_type, EdgeIt> predecessor;
      NodeMap<graph_type, T> distance;
      EdgeMap<graph_type, T> length;
      NodeMap<graph_type, bool> reached;
          
  public :

    /*
      The distance of all the Nodes is 0.
    */
    dijkstra(graph_type& _G, NodeIt _s, EdgeMap<graph_type, T>& _length) : 
      G(_G), s(_s), predecessor(G, 0), distance(G, 0), length(_length), reached(G, false) { }
    

      
      /*By Misi.*/
      struct Node_dist_comp
      {
	NodeMap<graph_type, T> &d;
	Node_dist_comp(NodeMap<graph_type, T> &_d) : d(_d) {} 
	
	bool operator()(const NodeIt& u, const NodeIt& v) const 
	{ return d.get(u) < d.get(v); }
      };


      
      void run() {
	
	NodeMap<graph_type, bool> scanned(G, false);
	std::priority_queue<NodeIt, vector<NodeIt>, Node_dist_comp> 
	  heap(( Node_dist_comp(distance) ));
      
	heap.push(s);
	reached.put(s, true);

	while (!heap.empty()) {

	  NodeIt v=heap.top();	
	  heap.pop();


	  if (!scanned.get(v)) {
	
	    for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) {
	      NodeIt w=G.head(e);

	      if (!scanned.get(w)) {
		if (!reached.get(w)) {
		  reached.put(w,true);
		  distance.put(w, distance.get(v)-length.get(e));
		  predecessor.put(w,e);
		} else if (distance.get(v)-length.get(e)>distance.get(w)) {
		  distance.put(w, distance.get(v)-length.get(e));
		  predecessor.put(w,e);
		}
		
		heap.push(w);
	      
	      } 

	    } 
	    scanned.put(v,true);
	    
	  } // if (!scanned.get(v))
	  
	  
	  
	} // while (!heap.empty())

	
      } //void run()
      
      
      


      /*
       *Returns the distance of the Node v.
       *It is 0 for the root and for the Nodes not
       *reachable form the root.
       */      
      T dist(NodeIt v) {
	return -distance.get(v);
      }



      /*
       *  Returns the last Edge of a shortest s-v path. 
       *  Returns an invalid iterator if v=root or v is not
       *  reachable from the root.
       */      
      EdgeIt pred(NodeIt v) {
	if (v!=s) { return predecessor.get(v);}
	else {return EdgeIt();}
      }
     

      
      bool reach(NodeIt v) {
	return reached.get(v);
      }









    };// class dijkstra



  } // namespace marci
}
#endif //DIJKSTRA_HH