// -*- c++ -*-

 #ifndef HUGO_MINCOSTFLOWS_H

 #define HUGO_MINCOSTFLOWS_H

 ///\ingroup galgs

 ///\file

 ///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost 

 #include <iostream>

 #include <dijkstra.h>

 #include <graph_wrapper.h>

 #include <maps.h>

 #include <vector.h>

 namespace hugo {

 /// \addtogroup galgs

 /// @{

   ///\brief Implementation of an algorithm for finding a flow of value \c k 

   ///(for small values of \c k) having minimal total cost between 2 nodes 

   /// 

   ///

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

   /// an algorithm for finding a flow of value \c k 

   ///(for small values of \c k) having minimal total cost  

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

   /// edge-weighted directed graph having nonnegative integer capacities.

   /// The range of the length (weight) function is nonnegative reals but 

   /// the range of capacity function is the set of nonnegative integers. 

   /// It is not a polinomial time algorithm for counting the minimum cost

   /// maximal flow, since it counts the minimum cost flow for every value 0..M

   /// where \c M is the value of the maximal flow.

   ///

   ///\author Attila Bernath

   template <typename Graph, typename LengthMap>

   class MinCostFlows {

     typedef typename LengthMap::ValueType Length;

     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::template EdgeMap<int> EdgeIntMap;

     //    typedef ConstMap<Edge,int> ConstMap;

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

     class ModLengthMap {   

       typedef typename ResGraphType::template 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 (G.forward(e))

 	  return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   

 	else

 	  return -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){}; 

     };//ModLengthMap

     //Input

     const Graph& G;

     const LengthMap& length;

     const EdgeIntMap& capacity;

     //auxiliary 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 flow; 

     //Container to store found paths

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

     //typedef DirPath<Graph> DPath;

     //DPath paths;

     Length total_length;

   public :

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

       length(_length), capacity(_cap), flow(_G)/*, dijkstra_dist(_G)*/{ }

     ///Runs the algorithm.

     ///Runs the algorithm.

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

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

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

       //We need a residual graph

       ResGraphType res_graph(G, capacity, flow);

       //Initialize the copy of the Dijkstra potential to zero

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

       ModLengthMap mod_length(res_graph, 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];

 	  }

 	}

 	//Augmenting on the sortest path

 	Node n=t;

 	Edge e;

 	while (n!=s){

 	  e = dijkstra.pred(n);

 	  n = dijkstra.predNode(n);

 	  G.augment(e,1);

 	}

       }

       /*

 	///\TODO To be implemented later

       //Let's find the paths

       //We put the paths into stl vectors (as an inner representation). 

       //In the meantime we lose the information stored in 'reversed'.

       //We suppose the lengths to be positive now.

       //Meanwhile we put the total length of the found paths 

       //in the member variable total_length

       paths.clear();

       total_length=0;

       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);

 	  total_length += length[e];

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

 	}

       }

       */

       return i;

     }

     ///This function gives back the total length of the found paths.

     ///Assumes that \c run() has been run and nothing changed since then.

     Length totalLength(){

       return total_length;

     }

     ///This function gives back the \c j-th path in argument p.

     ///Assumes that \c run() has been run and nothing changed since then.

     /// \warning It is assumed that \c p is constructed to be a path of graph \c G. If \c j is greater than the result of previous \c run, then the result here will be an empty path.

     template<typename DirPath>

     void getPath(DirPath& p, int j){

       p.clear();

       typename DirPath::Builder B(p);

       for(typename std::vector<Edge>::iterator i=paths[j].begin(); 

 	  i!=paths[j].end(); ++i ){

 	B.pushBack(*i);

       }

       B.commit();

     }

   }; //class MinLengthPaths

   ///@}

 } //namespace hugo

 #endif //HUGO_MINCOSTFLOW_H