/*

 *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