// -*- 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