/* -*- 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/tolerance.h>

#include <vector>

namespace lemon {

  /// \brief Default traits class of EdmondsKarp class.

  ///

  /// Default traits class of EdmondsKarp class.

  /// \param _Graph Graph type.

  /// \param _CapacityMap Type of capacity map.

  template <typename _Graph, typename _CapacityMap>

  struct EdmondsKarpDefaultTraits {

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

    typedef _Graph Graph;

    /// \brief The type of the map that stores the edge capacities.

    ///

    /// The type of the map that stores the edge capacities.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef _CapacityMap CapacityMap;

    /// \brief The type of the length of the edges.

    typedef typename CapacityMap::Value Value;

    /// \brief The map type that stores the flow values.

    ///

    /// The map type that stores the flow values. 

    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    typedef typename Graph::template EdgeMap<Value> FlowMap;

    /// \brief Instantiates a FlowMap.

    ///

    /// This function instantiates a \ref FlowMap. 

    /// \param graph The graph, to which we would like to define the flow map.

    static FlowMap* createFlowMap(const Graph& graph) {

      return new FlowMap(graph);

    }

    /// \brief The tolerance used by the algorithm

    ///

    /// The tolerance used by the algorithm to handle inexact computation.

    typedef Tolerance<Value> Tolerance;

  };

  /// \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

  /// graphs. 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(nm^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 _CapacityMap The capacity map type.

  /// \param _Traits Traits class to set various data types used by

  /// the algorithm.  The default traits class is \ref

  /// EdmondsKarpDefaultTraits.  See \ref EdmondsKarpDefaultTraits for the

  /// documentation of a Edmonds-Karp traits class. 

  ///

  /// \author Balazs Dezso 

#ifdef DOXYGEN

  template <typename _Graph, typename _CapacityMap, typename _Traits>

#else 

  template <typename _Graph,

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

            typename _Traits = EdmondsKarpDefaultTraits<_Graph, _CapacityMap> >

#endif

  class EdmondsKarp {

  public:

    typedef _Traits Traits;

    typedef typename Traits::Graph Graph;

    typedef typename Traits::CapacityMap CapacityMap;

    typedef typename Traits::Value Value; 

    typedef typename Traits::FlowMap FlowMap;

    typedef typename Traits::Tolerance Tolerance;

    /// \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";

      }

    };

  private:

    GRAPH_TYPEDEFS(typename Graph);

    typedef typename Graph::template NodeMap<Edge> PredMap;

    const Graph& _graph;

    const CapacityMap* _capacity;

    Node _source, _target;

    FlowMap* _flow;

    bool _local_flow;

    PredMap* _pred;

    std::vector<Node> _queue;

    Tolerance _tolerance;

    Value _flow_value;

    void createStructures() {

      if (!_flow) {

	_flow = Traits::createFlowMap(_graph);

	_local_flow = true;

      }

      if (!_pred) {

	_pred = new PredMap(_graph);

      }

      _queue.resize(countNodes(_graph));

    }

    void destroyStructures() {

      if (_local_flow) {

	delete _flow;

      }

      if (_pred) {

	delete _pred;

      }

    }

  public:

    ///\name Named template parameters

    ///@{

    template <typename _FlowMap>

    struct DefFlowMapTraits : public Traits {

      typedef _FlowMap FlowMap;

      static FlowMap *createFlowMap(const Graph&) {

	throw UninitializedParameter();

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting

    /// FlowMap type

    ///

    /// \ref named-templ-param "Named parameter" for setting FlowMap

    /// type

    template <typename _FlowMap>

    struct DefFlowMap 

      : public EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > {

      typedef EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > 

      Create;

    };

    /// @}

    /// \brief The constructor of the class.

    ///

    /// The constructor of the class. 

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

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

    /// \param source The source node.

    /// \param target The target node.

    EdmondsKarp(const Graph& graph, const CapacityMap& capacity,

		Node source, Node target)

      : _graph(graph), _capacity(&capacity), _source(source), _target(target),

	_flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value()

    {

      if (_source == _target) {

        throw InvalidArgument();

      }

    }

    /// \brief Destrcutor.

    ///

    /// Destructor.

    ~EdmondsKarp() {

      destroyStructures();

    }

    /// \brief Sets the capacity map.

    ///

    /// Sets the capacity map.

    /// \return \c (*this)

    EdmondsKarp& capacityMap(const CapacityMap& map) {

      _capacity = ↦

      return *this;

    }

    /// \brief Sets the flow map.

    ///

    /// Sets the flow map.

    /// \return \c (*this)

    EdmondsKarp& flowMap(FlowMap& map) {

      if (_local_flow) {

	delete _flow;

	_local_flow = false;

      }

      _flow = ↦

      return *this;

    }

    /// \brief Returns the flow map.

    ///

    /// \return The flow map.

    const FlowMap& flowMap() {

      return *_flow;

    }

    /// \brief Sets the source node.

    ///

    /// Sets the source node.

    /// \return \c (*this)

    EdmondsKarp& source(const Node& node) {

      _source = node;

      return *this;

    }

    /// \brief Sets the target node.

    ///

    /// Sets the target node.

    /// \return \c (*this)

    EdmondsKarp& target(const Node& node) {

      _target = node;

      return *this;

    }

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

    ///

    /// Sets the tolerance used by algorithm.

    EdmondsKarp& tolerance(const Tolerance& tolerance) const {

      _tolerance = tolerance;

      return *this;

    } 

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

    ///

    /// Returns the tolerance used by algorithm.

    const Tolerance& tolerance() const {

      return tolerance;

    } 

    /// \name Execution control The simplest way to execute the

    /// algorithm is to use the \c run() member functions.

    /// \n

    /// If you need more control on initial solution or

    /// execution then you have to call one \ref init() function and then

    /// the start() or multiple times the \c augment() member function.  

    ///@{

    /// \brief Initializes the algorithm

    /// 

    /// It sets the flow to empty flow.

    void init() {

      createStructures();

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

        _flow->set(it, 0);

      }

      _flow_value = 0;

    }

    /// \brief Initializes the algorithm

    /// 

    /// Initializes the flow to the \c flowMap. The \c flowMap should

    /// contain a feasible flow, ie. in each node excluding the source

    /// and the target the incoming flow should be equal to the

    /// outgoing flow.

    template <typename FlowMap>

    void flowInit(const FlowMap& flowMap) {

      createStructures();

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

	_flow->set(e, flowMap[e]);

      }

      _flow_value = 0;

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

        _flow_value += (*_flow)[jt];

      }

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

        _flow_value -= (*_flow)[jt];

      }

    }

    /// \brief Initializes the algorithm

    /// 

    /// Initializes the flow to the \c flowMap. The \c flowMap should

    /// contain a feasible flow, ie. in each node excluding the source

    /// and the target the incoming flow should be equal to the

    /// outgoing flow.  

    /// \return %False when the given flowMap does not contain

    /// feasible flow.

    template <typename FlowMap>

    bool checkedFlowInit(const FlowMap& flowMap) {

      createStructures();

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

	_flow->set(e, flowMap[e]);

      }

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

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

        Value outFlow = 0;

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

          outFlow += (*_flow)[jt];

        }

        Value 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;

      }

      _flow_value = 0;

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

        _flow_value += (*_flow)[jt];

      }

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

        _flow_value -= (*_flow)[jt];

      }

      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() {

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

	_pred->set(n, INVALID);

      }

      int first = 0, last = 1;

      _queue[0] = _source;

      _pred->set(_source, OutEdgeIt(_graph, _source));

      while (first != last && (*_pred)[_target] == INVALID) {

	Node n = _queue[first++];

	for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

	  Value rem = (*_capacity)[e] - (*_flow)[e];

	  Node t = _graph.target(e);

	  if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {

	    _pred->set(t, e);

	    _queue[last++] = t;

	  }

	}

	for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

	  Value rem = (*_flow)[e];

	  Node t = _graph.source(e);

	  if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {

	    _pred->set(t, e);

	    _queue[last++] = t;

	  }

	}

      }

      if ((*_pred)[_target] != INVALID) {

	Node n = _target;

	Edge e = (*_pred)[n];

	Value prem = (*_capacity)[e] - (*_flow)[e];

	n = _graph.source(e);

	while (n != _source) {

	  e = (*_pred)[n];

	  if (_graph.target(e) == n) {

	    Value rem = (*_capacity)[e] - (*_flow)[e];

	    if (rem < prem) prem = rem;

	    n = _graph.source(e);

	  } else {

	    Value rem = (*_flow)[e];

	    if (rem < prem) prem = rem;

	    n = _graph.target(e);   

	  } 

	}

	n = _target;

	e = (*_pred)[n];

	_flow->set(e, (*_flow)[e] + prem);

	n = _graph.source(e);

	while (n != _source) {

	  e = (*_pred)[n];

	  if (_graph.target(e) == n) {

	    _flow->set(e, (*_flow)[e] + prem);

	    n = _graph.source(e);

	  } else {

	    _flow->set(e, (*_flow)[e] - prem);

	    n = _graph.target(e);   

	  } 

	}

	_flow_value += prem;	

	return true;

      } else {

	return false;

      }

    }

    /// \brief Executes the algorithm

    ///

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

    void start() {

      while (augment()) {}

    }

    /// \brief runs the algorithm.

    /// 

    /// It is just a shorthand for:

    ///

    ///\code 

    /// ek.init();

    /// ek.start();

    ///\endcode

    void run() {

      init();

      start();

    }

    /// @}

    /// \name Query Functions

    /// The result of the Edmonds-Karp algorithm can be obtained using these

    /// functions.\n

    /// Before the use of these functions,

    /// either run() or start() must be called.

    ///@{

    /// \brief Returns the value of the maximum flow.

    ///

    /// Returns the value of the maximum flow by returning the excess

    /// of the target node \c t. This value equals to the value of

    /// the maximum flow already after the first phase.

    Value flowValue() const {

      return _flow_value;

    }

    /// \brief Returns the flow on the edge.

    ///

    /// Sets the \c flowMap to the flow on the edges. This method can

    /// be called after the second phase of algorithm.

    Value flow(const Edge& edge) const {

      return (*_flow)[edge];

    }

    /// \brief Returns true when the node is on the source side of minimum cut.

    ///

    /// Returns true when the node is on the source side of minimum

    /// cut. This method can be called both after running \ref

    /// startFirstPhase() and \ref startSecondPhase().

    bool minCut(const Node& node) const {

      return (*_pred)[node] != INVALID;

    }

    /// \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 minCutMap(CutMap& cutMap) const {

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

	cutMap.set(n, (*_pred)[n] != INVALID);

      }

      cutMap.set(_source, true);

    }    

    /// @}

  };

}

#endif