// -*- c++ -*-

#ifndef HUGO_MINCOSTFLOWS_H

#define HUGO_MINCOSTFLOWS_H

///\ingroup flowalgs

///\file

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

#include <hugo/dijkstra.h>

#include <hugo/graph_wrapper.h>

#include <hugo/maps.h>

#include <vector>

namespace hugo {

/// \addtogroup flowalgs

/// @{

  ///\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::MinCostFlow "MinCostFlow" implements

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

  /// having minimal total cost 

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

  /// edge-weighted directed graph. To this end, 

  /// the edge-capacities and edge-weitghs have to be nonnegative. 

  /// The edge-capacities should be integers, but the edge-weights can be 

  /// integers, reals or of other comparable numeric type.

  /// This algorithm is intended to use only for small values of \c k, 

  /// since it is only polynomial in k, 

  /// not in the length of k (which is log k). 

  /// In order to find the minimum cost flow of value \c k it 

  /// finds the minimum cost flow of value \c i for every 

  /// \c i between 0 and \c k. 

  ///

  ///\param Graph The directed graph type the algorithm runs on.

  ///\param LengthMap The type of the length map.

  ///\param CapacityMap The capacity map type.

  ///

  ///\author Attila Bernath

  template <typename Graph, typename LengthMap, typename CapacityMap>

  class MinCostFlow {

    typedef typename LengthMap::ValueType Length;

    //Warning: this should be integer type

    typedef typename CapacityMap::ValueType Capacity;

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

    typedef typename ResGraphType::Edge ResGraphEdge;

    class ModLengthMap {   

      typedef typename Graph::template NodeMap<Length> NodeMap;

      const ResGraphType& G;

      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 LengthMap &o,  const NodeMap &p) : 

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

    };//ModLengthMap

  protected:

    //Input

    const Graph& G;

    const LengthMap& length;

    const CapacityMap& capacity;

    //auxiliary variables

    //To store the flow

    EdgeIntMap flow; 

    //To store the potential (dual variables)

    typedef typename Graph::template NodeMap<Length> PotentialMap;

    PotentialMap potential;

    Length total_length;

  public :

    /// The constructor of the class.

    ///\param _G The directed graph the algorithm runs on. 

    ///\param _length The length (weight or cost) of the edges. 

    ///\param _cap The capacity of the edges. 

    MinCostFlow(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G), 

      length(_length), capacity(_cap), flow(_G), potential(_G){ }

    ///Runs the algorithm.

    ///Runs the algorithm.

    ///Returns k if there is a flow of value at least k edge-disjoint 

    ///from s to t.

    ///Otherwise it returns the maximum value of a flow from s to t.

    ///

    ///\param s The source node.

    ///\param t The target node.

    ///\param k The value of the flow we are looking for.

    ///

    ///\todo May be it does make sense to be able to start with a nonzero 

    /// feasible primal-dual solution pair as well.

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

      //Resetting variables from previous runs

      total_length = 0;

      for (typename Graph::EdgeIt e(G); e!=INVALID; ++e) flow.set(e, 0);

      //Initialize the potential to zero

      for (typename Graph::NodeIt n(G); n!=INVALID; ++n) potential.set(n, 0);

      //We need a residual graph

      ResGraphType res_graph(G, capacity, flow);

      ModLengthMap mod_length(res_graph, length, potential);

      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 flow of value k from s to t

	  break;

	};

	//We have to change the potential

        for(typename ResGraphType::NodeIt n(res_graph); n!=INVALID; ++n)

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

	//Augmenting on the sortest path

	Node n=t;

	ResGraphEdge e;

	while (n!=s){

	  e = dijkstra.pred(n);

	  n = dijkstra.predNode(n);

	  res_graph.augment(e,1);

	  //Let's update the total length

	  if (res_graph.forward(e))

	    total_length += length[e];

	  else 

	    total_length -= length[e];	    

	}

      }

      return i;

    }

    /// Gives back the total weight of the found flow.

    ///This function gives back the total weight of the found flow.

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

    Length totalLength(){

      return total_length;

    }

    ///Returns a const reference to the EdgeMap \c flow. 

    ///Returns a const reference to the EdgeMap \c flow. 

    ///\pre \ref run() must

    ///be called before using this function.

    const EdgeIntMap &getFlow() const { return flow;}

    ///Returns a const reference to the NodeMap \c potential (the dual solution).

    ///Returns a const reference to the NodeMap \c potential (the dual solution).

    /// \pre \ref run() must be called before using this function.

    const PotentialMap &getPotential() const { return potential;}

    /// Checking the complementary slackness optimality criteria

    ///This function checks, whether the given solution is optimal

    ///If executed after the call of \c run() then it should return with true.

    ///This function only checks optimality, doesn't bother with feasibility.

    ///It is meant for testing purposes.

    ///

    bool checkComplementarySlackness(){

      Length mod_pot;

      Length fl_e;

        for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) {

	//C^{\Pi}_{i,j}

	mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];

	fl_e = flow[e];

	if (0<fl_e && fl_e<capacity[e]) {

	  /// \todo better comparison is needed for real types, moreover, 

	  /// this comparison here is superfluous.

	  if (mod_pot != 0)

	    return false;

	} 

	else {

	  if (mod_pot > 0 && fl_e != 0)

	    return false;

	  if (mod_pot < 0 && fl_e != capacity[e])

	    return false;

	}

      }

      return true;

    }

  }; //class MinCostFlow

  ///@}

} //namespace hugo

#endif //HUGO_MINCOSTFLOWS_H