/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2008

  * 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