/* -*- C++ -*-

  * src/lemon/suurballe.h - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Combinatorial Optimization Research Group, 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 flowalgs

 ///\file

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

 #include <lemon/maps.h>

 #include <vector>

 #include <lemon/min_cost_flow.h>

 namespace lemon {

 /// \addtogroup flowalgs

 /// @{

   ///\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 if it is correct to call this method after

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

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

   ///wraps the MinCostFlow 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::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 MinCostFlow instance will actually solve the problem

     MinCostFlow<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. 

     Suurballe(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 lemon 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 Suurballe

   ///@}

 } //namespace lemon

 #endif //LEMON_SUURBALLE_H