// -*- c++ -*-

 #ifndef HUGO_MINLENGTHPATHS_H

 #define HUGO_MINLENGTHPATHS_H

 ///\file

 ///\brief An algorithm for finding k paths of minimal total length.

 #include <iostream>

 #include <dijkstra.h>

 #include <graph_wrapper.h>

 #include <maps.h>

 #include <vector>

 namespace hugo {

   ///\brief Implementation of an algorithm for finding k paths between 2 nodes 

   /// of minimal total length 

   ///

   /// The class \ref hugo::MinLengthPaths "MinLengthPaths" implements

   /// an algorithm which finds k edge-disjoint paths

   /// from a given source node to a given target node in an

   /// edge-weighted directed graph having minimal total weigth (length).

   template <typename Graph, typename LengthMap>

   class MinLengthPaths {

     typedef typename LengthMap::ValueType Length;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     typedef typename Graph::EdgeMap<int> EdgeIntMap;

     typedef ConstMap<Edge,int> ConstMap;

     typedef ResGraphWrapper<const Graph,int,EdgeIntMap,ConstMap> ResGraphType;

     class ModLengthMap {   

       typedef typename ResGraphType::NodeMap<Length> NodeMap;

       const ResGraphType& G;

       const EdgeIntMap& rev;

       const LengthMap &ol;

       const NodeMap &pot;

     public :

       typedef typename LengthMap::KeyType KeyType;

       typedef typename LengthMap::ValueType ValueType;

       ValueType operator[](typename ResGraphType::Edge e) const {     

 	//if ( (1-2*rev[e])*ol[e]-(pot[G.head(e)]-pot[G.tail(e)] ) <0 ){

 	//  std::cout<<"Negative length!!"<<std::endl;

 	//}

 	return (1-2*rev[e])*ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   

       }     

       ModLengthMap(const ResGraphType& _G, const EdgeIntMap& _rev, 

 		   const LengthMap &o,  const NodeMap &p) : 

 	G(_G), rev(_rev), ol(o), pot(p){}; 

     };

     const Graph& G;

     const LengthMap& length;

     //auxiliry variables

     //The value is 1 iff the edge is reversed. 

     //If the algorithm has finished, the edges of the seeked paths are 

     //exactly those that are reversed 

     EdgeIntMap reversed; 

     //Container to store found paths

     std::vector< std::vector<Edge> > paths;

   public :

     MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), 

       length(_length), reversed(_G)/*, dijkstra_dist(_G)*/{ }

     ///Runs the algorithm

     ///Returns k if there are at least k edge-disjoint paths from s to t.

     ///Otherwise it returns the number of edge-disjoint paths from s to t.

     int run(Node s, Node t, int k) {

       ConstMap const1map(1);

       //We need a residual graph, in which some of the edges are reversed

       ResGraphType res_graph(G, reversed, const1map);

       //Initialize the copy of the Dijkstra potential to zero

       typename ResGraphType::NodeMap<Length> dijkstra_dist(res_graph);

       ModLengthMap mod_length(res_graph, reversed, length, dijkstra_dist);

       Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);

       int i;

       for (i=0; i<k; ++i){

 	dijkstra.run(s);

 	if (!dijkstra.reached(t)){

 	  //There are no k paths from s to t

 	  break;

 	};

 	{

 	  //We have to copy the potential

 	  typename ResGraphType::NodeIt n;

 	  for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {

 	      dijkstra_dist[n] += dijkstra.distMap()[n];

 	  }

 	}

 	//Reversing the sortest path

 	Node n=t;

 	Edge e;

 	while (n!=s){

 	  e = dijkstra.pred(n);

 	  n = dijkstra.predNode(n);

 	  reversed[e] = 1-reversed[e];

 	}

       }

       //Let's find the paths

       //We put the paths into vectors (just for now). In the meantime we lose 

       //the information stored in 'reversed'

       //We suppose the lengths to be positive now.

       paths.clear();

       paths.resize(k);

       for (int j=0; j<i; ++j){

 	Node n=s;

 	OutEdgeIt e;

 	while (n!=t){

 	  G.first(e,n);

 	  while (!reversed[e]){

 	    G.next(e);

 	  }

 	  n = G.head(e);

 	  paths[j].push_back(e);

 	  reversed[e] = 1-reversed[e];

 	}

       }

       return i;

     }

   }; //class MinLengthPaths

 } //namespace hugo

 #endif //HUGO_MINLENGTHPATHS_H