/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2006

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_SUURBALLE_H

#define LEMON_SUURBALLE_H

///\ingroup shortest_path

///\file

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

#include <lemon/maps.h>

#include <vector>

#include <lemon/path.h>

#include <lemon/ssp_min_cost_flow.h>

namespace lemon {

/// \addtogroup shortest_path

/// @{

  ///\brief Implementation of an algorithm for finding k edge-disjoint

  /// paths between 2 nodes of minimal total length

  ///

  /// The class \ref lemon::Suurballe 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).

  ///

  ///\note It it questionable whether it is correct to call this method after

  ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm

  ///for finding minimum cost flows. In fact, this implementation just

  ///wraps the SspMinCostFlow algorithms. The paper of both %Suurballe and

  ///Edmonds-Karp published in 1972, therefore it is possibly right to

  ///state that they are

  ///independent results. Most frequently this special case is referred as

  ///%Suurballe method in the literature, especially in communication

  ///network context.

  ///\author Attila Bernath

  template <typename Graph, typename LengthMap>

  class Suurballe{

    typedef typename LengthMap::Value 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;

    const Graph& G;

    Node s;

    Node t;

    //Auxiliary variables

    //This is the capacity map for the mincostflow problem

    ConstMap const1map;

    //This MinCostFlow instance will actually solve the problem

    SspMinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow;

    //Container to store found paths

    std::vector<SimplePath<Graph> > paths;

  public :

    /// \brief 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 _s Source node.

    /// \param _t Target node.

    Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) : 

      G(_G), s(_s), t(_t), const1map(1), 

      min_cost_flow(_G, _length, const1map, _s, _t) { }

    /// \brief 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 edge-disjoint paths found 

    /// from s to t.

    ///

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

    ///

    int run(int k) {

      int i = min_cost_flow.run(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 min_cost_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] = min_cost_flow.getFlow()[e];

      paths.clear();

      paths.resize(k);

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

	Node n=s;

	while (n!=t){

	  OutEdgeIt e(G, n);

	  while (!reversed[e]){

	    ++e;

	  }

	  n = G.target(e);

	  paths[j].addBack(e);

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

	}

      }

      return i;

    }

    /// \brief Returns the total length of the paths.

    ///

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

    Length totalLength(){

      return min_cost_flow.totalLength();

    }

    /// \brief Returns the found flow.

    ///

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

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

    /// \brief Returns the optimal dual solution

    ///

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

    /// potential (the dual solution).

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

    /// \brief Checks whether the complementary slackness holds.

    ///

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

    /// Currently this function only checks optimality, doesn't bother

    /// with feasibility.  It is meant for testing purposes.

    bool checkComplementarySlackness(){

      return min_cost_flow.checkComplementarySlackness();

    }

    typedef SimplePath<Graph> Path; 

    /// \brief 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 has 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 j Which path you want to get from the found paths (in a

    /// real application you would get the found paths iteratively).

    Path path(int j) const {

      return paths[j];

    }

    /// \brief Gives back the number of the paths.

    ///

    /// Gives back the number of the constructed paths.

    int pathNum() const {

      return paths.size();

    }

  }; //class Suurballe

  ///@}

} //namespace lemon

#endif //LEMON_SUURBALLE_H