/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2007

  * 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_EDMONDS_KARP_H

 #define LEMON_EDMONDS_KARP_H

 /// \file

 /// \ingroup max_flow

 /// \brief Implementation of the Edmonds-Karp algorithm.

 #include <lemon/graph_adaptor.h>

 #include <lemon/tolerance.h>

 #include <lemon/bfs.h>

 namespace lemon {

   /// \ingroup max_flow

   /// \brief Edmonds-Karp algorithms class.

   ///

   /// This class provides an implementation of the \e Edmonds-Karp \e

   /// algorithm producing a flow of maximum value in a directed

   /// graph. The Edmonds-Karp algorithm is slower than the Preflow algorithm

   /// but it has an advantage of the step-by-step execution control with

   /// feasible flow solutions. The \e source node, the \e target node, the \e

   /// capacity of the edges and the \e starting \e flow value of the

   /// edges should be passed to the algorithm through the

   /// constructor.

   ///

   /// The time complexity of the algorithm is \f$ O(n * e^2) \f$ in

   /// worst case.  Always try the preflow algorithm instead of this if

   /// you just want to compute the optimal flow.

   ///

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

   /// \param _Number The number type of the capacities and the flow values.

   /// \param _CapacityMap The capacity map type.

   /// \param _FlowMap The flow map type.

   /// \param _Tolerance The tolerance class to handle computation problems.

   ///

   /// \author Balazs Dezso 

 #ifdef DOXYGEN

   template <typename _Graph, typename _Number,

 	    typename _CapacityMap, typename _FlowMap, typename _Tolerance>

 #else

   template <typename _Graph, typename _Number,

 	    typename _CapacityMap = typename _Graph::template EdgeMap<_Number>,

             typename _FlowMap = typename _Graph::template EdgeMap<_Number>,

 	    typename _Tolerance = Tolerance<_Number> >

 #endif

   class EdmondsKarp {

   public:

     /// \brief \ref Exception for the case when the source equals the target.

     ///

     /// \ref Exception for the case when the source equals the target.

     ///

     class InvalidArgument : public lemon::LogicError {

     public:

       virtual const char* what() const throw() {

 	return "lemon::EdmondsKarp::InvalidArgument";

       }

     };

     /// \brief The graph type the algorithm runs on. 

     typedef _Graph Graph;

     /// \brief The value type of the algorithms.

     typedef _Number Number;

     /// \brief The capacity map on the edges.

     typedef _CapacityMap CapacityMap;

     /// \brief The flow map on the edges.

     typedef _FlowMap FlowMap;

     /// \brief The tolerance used by the algorithm.

     typedef _Tolerance Tolerance;

     typedef ResGraphAdaptor<Graph, Number, CapacityMap, 

                             FlowMap, Tolerance> ResGraph;

   private:

     typedef typename Graph::Node Node;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::EdgeIt EdgeIt;

     typedef typename Graph::InEdgeIt InEdgeIt;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

   public:

     /// \brief The constructor of the class.

     ///

     /// The constructor of the class. 

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

     /// \param source The source node.

     /// \param target The target node.

     /// \param capacity The capacity of the edges. 

     /// \param flow The flow of the edges. 

     /// \param tolerance Tolerance class.

     EdmondsKarp(const Graph& graph, Node source, Node target,

                 const CapacityMap& capacity, FlowMap& flow, 

                 const Tolerance& tolerance = Tolerance())

       : _graph(graph), _capacity(capacity), _flow(flow), 

         _tolerance(tolerance), _resgraph(graph, capacity, flow, tolerance), 

         _source(source), _target(target) 

     {

       if (_source == _target) {

         throw InvalidArgument();

       }

     }

     /// \brief Initializes the algorithm

     /// 

     /// It sets the flow to empty flow.

     void init() {

       for (EdgeIt it(_graph); it != INVALID; ++it) {

         _flow.set(it, 0);

       }

       _value = 0;

     }

     /// \brief Initializes the algorithm

     /// 

     /// If the flow map initially flow this let the flow map

     /// unchanged but the flow value will be set by the flow

     /// on the outedges from the source.

     void flowInit() {

       _value = 0;

       for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {

         _value += _flow[jt];

       }

       for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {

         _value -= _flow[jt];

       }

     }

     /// \brief Initializes the algorithm

     /// 

     /// If the flow map initially flow this let the flow map

     /// unchanged but the flow value will be set by the flow

     /// on the outedges from the source. It also checks that

     /// the flow map really contains a flow.

     /// \return %True when the flow map really a flow.

     bool checkedFlowInit() {

       _value = 0;

       for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {

         _value += _flow[jt];

       }

       for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {

         _value -= _flow[jt];

       }

       for (NodeIt it(_graph); it != INVALID; ++it) {

         if (it == _source || it == _target) continue;

         Number outFlow = 0;

         for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) {

           outFlow += _flow[jt];

         }

         Number inFlow = 0;

         for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) {

           inFlow += _flow[jt];

         }

         if (_tolerance.different(outFlow, inFlow)) {

           return false;

         }

       }

       for (EdgeIt it(_graph); it != INVALID; ++it) {

         if (_tolerance.less(_flow[it], 0)) return false;

         if (_tolerance.less(_capacity[it], _flow[it])) return false;

       }

       return true;

     }

     /// \brief Augment the solution on an edge shortest path.

     /// 

     /// Augment the solution on an edge shortest path. It search an

     /// edge shortest path between the source and the target

     /// in the residual graph with the bfs algoritm.

     /// Then it increase the flow on this path with the minimal residual

     /// capacity on the path. If there is not such path it gives back

     /// false.

     /// \return %False when the augmenting is not success so the

     /// current flow is a feasible and optimal solution.

     bool augment() {

       typename Bfs<ResGraph>

       ::template DefDistMap<NullMap<Node, int> >

       ::Create bfs(_resgraph);

       NullMap<Node, int> distMap;

       bfs.distMap(distMap);

       bfs.init();

       bfs.addSource(_source);

       bfs.start(_target);

       if (!bfs.reached(_target)) {

         return false;

       }

       Number min = _resgraph.rescap(bfs.predEdge(_target));

       for (Node it = bfs.predNode(_target); it != _source; 

            it = bfs.predNode(it)) {

         if (min > _resgraph.rescap(bfs.predEdge(it))) {

           min = _resgraph.rescap(bfs.predEdge(it));

         }

       } 

       for (Node it = _target; it != _source; it = bfs.predNode(it)) {

         _resgraph.augment(bfs.predEdge(it), min);

       }

       _value += min;

       return true;

     }

     /// \brief Executes the algorithm

     ///

     /// It runs augmenting phases until the optimal solution is reached. 

     void start() {

       while (augment()) {}

     }

     /// \brief Gives back the current flow value.

     ///

     /// Gives back the current flow _value.

     Number flowValue() const {

       return _value;

     }

     /// \brief runs the algorithm.

     /// 

     /// It is just a shorthand for:

     ///

     ///\code 

     /// ek.init();

     /// ek.start();

     ///\endcode

     void run() {

       init();

       start();

     }

     /// \brief Returns a minimum value cut.

     ///

     /// Sets \c cut to the characteristic vector of a minimum value cut

     /// It simply calls the minMinCut member.

     /// \retval cut Write node bool map. 

     template <typename CutMap>

     void minCut(CutMap& cut) const {

       minMinCut(cut);

     }

     /// \brief Returns the inclusionwise minimum of the minimum value cuts.

     ///

     /// Sets \c cut to the characteristic vector of the minimum value cut

     /// which is inclusionwise minimum. It is computed by processing a

     /// bfs from the source node \c source in the residual graph.  

     /// \retval cut Write node bool map. 

     template <typename CutMap>

     void minMinCut(CutMap& cut) const {

       typename Bfs<ResGraph>

       ::template DefDistMap<NullMap<Node, int> >

       ::template DefProcessedMap<CutMap>

       ::Create bfs(_resgraph);

       NullMap<Node, int> distMap;

       bfs.distMap(distMap);

       bfs.processedMap(cut);

       bfs.run(_source);

     }

     /// \brief Returns the inclusionwise minimum of the minimum value cuts.

     ///

     /// Sets \c cut to the characteristic vector of the minimum value cut

     /// which is inclusionwise minimum. It is computed by processing a

     /// bfs from the source node \c source in the residual graph.  

     /// \retval cut Write node bool map. 

     template <typename CutMap>

     void maxMinCut(CutMap& cut) const {

       typedef RevGraphAdaptor<const ResGraph> RevGraph;

       RevGraph revgraph(_resgraph);

       typename Bfs<RevGraph>

       ::template DefDistMap<NullMap<Node, int> >

       ::template DefPredMap<NullMap<Node, Edge> >

       ::template DefProcessedMap<NotWriteMap<CutMap> >

       ::Create bfs(revgraph);

       NullMap<Node, int> distMap;

       bfs.distMap(distMap);

       NullMap<Node, Edge> predMap;

       bfs.predMap(predMap);

       NotWriteMap<CutMap> notcut(cut);

       bfs.processedMap(notcut);

       bfs.run(_target);

     }

     /// \brief Returns the source node.

     ///

     /// Returns the source node.

     /// 

     Node source() const { 

       return _source;

     }

     /// \brief Returns the target node.

     ///

     /// Returns the target node.

     /// 

     Node target() const { 

       return _target;

     }

     /// \brief Returns a reference to capacity map.

     ///

     /// Returns a reference to capacity map.

     /// 

     const CapacityMap &capacityMap() const { 

       return *_capacity;

     }

     /// \brief Returns a reference to flow map.

     ///

     /// Returns a reference to flow map.

     /// 

     const FlowMap &flowMap() const { 

       return *_flow;

     }

     /// \brief Returns the tolerance used by algorithm.

     ///

     /// Returns the tolerance used by algorithm.

     const Tolerance& tolerance() const {

       return tolerance;

     } 

   private:

     const Graph& _graph;

     const CapacityMap& _capacity;

     FlowMap& _flow;

     Tolerance _tolerance;

     ResGraph _resgraph;

     Node _source, _target;

     Number _value;

   };

 }

 #endif