/* -*- 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 flowalgs
///\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 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 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