// -*- c++ -*-

#ifndef HUGO_MINLENGTHPATHS_H

#define HUGO_MINLENGTHPATHS_H

///\ingroup flowalgs

///\file

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

#include <hugo/maps.h>

#include <vector>

#include <hugo/min_cost_flows.h>

namespace hugo {

/// \addtogroup flowalgs

/// @{

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

  /// of minimal total length 

  ///

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

  /// an algorithm for finding k edge-disjoint paths

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

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

  ///

  ///\warning Length values should be nonnegative.

  /// 

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

  ///\param LengthMap The type of the length map (values should be nonnegative).

  ///

  ///\author Attila Bernath

  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::template EdgeMap<int> EdgeIntMap;

    typedef ConstMap<Edge,int> ConstMap;

    //Input

    const Graph& G;

    //Auxiliary variables

    //This is the capacity map for the mincostflow problem

    ConstMap const1map;

    //This MinCostFlows instance will actually solve the problem

    MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow;

    //Container to store found paths

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

  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. 

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

      const1map(1), mincost_flow(_G, _length, const1map){}

    ///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.

    ///

    ///\param s The source node.

    ///\param t The target node.

    ///\param k How many paths are we looking for?

    ///

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

      int i = mincost_flow.run(s,t,k);

      //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.

      //We don't want to change the flow of mincost_flow, so we make a copy

      //The name here suggests that the flow has only 0/1 values.

      EdgeIntMap reversed(G); 

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

	reversed[e] = mincost_flow.getFlow()[e];

      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]){

	    ++e;

	  }

	  n = G.head(e);

	  paths[j].push_back(e);

	  //total_length += length[e];

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

	}

      }

      return i;

    }

    ///Returns the total length of the paths

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

    ///\pre \ref run() must

    ///be called before using this function.

    Length totalLength(){

      return mincost_flow.totalLength();

    }

    ///Returns the found flow.

    ///This function returns a const reference to the EdgeMap \c flow.

    ///\pre \ref run() must

    ///be called before using this function.

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

    /// Returns the optimal dual solution

    ///This function returns a const reference to the NodeMap

    ///\c potential (the dual solution).

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

    const EdgeIntMap &getPotential() const { return mincost_flow.potential;}

    ///Checks whether the complementary slackness holds.

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

    ///It should return true after calling \ref run() 

    ///Currently this function only checks optimality,

    ///doesn't bother with feasibility

    ///It is meant for testing purposes.

    ///

    bool checkComplementarySlackness(){

      return mincost_flow.checkComplementarySlackness();

    }

    ///Read the found paths.

    ///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 not less than the result of previous \c run,

    ///then the result here will be an empty path (\c j can be 0 as well).

    ///

    ///\param Path The type of the path structure to put the result to (must meet hugo path concept).

    ///\param p The path to put the result to 

    ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively)

    template<typename Path>

    void getPath(Path& p, size_t j){

      p.clear();

      if (j>paths.size()-1){

	return;

      }

      typename Path::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_MINLENGTHPATHS_H