/* -*- 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_DINITZ_SLEATOR_TARJAN_H

 #define LEMON_DINITZ_SLEATOR_TARJAN_H

 /// \file 

 /// \ingroup max_flow 

 /// \brief Implementation the dynamic tree data structure of Sleator

 /// and Tarjan.

 #include <lemon/graph_utils.h>

 #include <lemon/tolerance.h>

 #include <lemon/dynamic_tree.h>

 #include <vector>

 #include <limits>

 #include <fstream>

 namespace lemon {

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

   ///

   /// Default traits class of DinitzSleatorTarjan class.

   /// \param _Graph Graph type.

   /// \param _CapacityMap Type of capacity map.

   template <typename _Graph, typename _CapacityMap>

   struct DinitzSleatorTarjanDefaultTraits {

     /// \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 Dinitz-Sleator-Tarjan algorithms class.

   ///

   /// This class provides an implementation of the \e

   /// Dinitz-Sleator-Tarjan \e algorithm producing a flow of maximum

   /// value in a directed graph. The DinitzSleatorTarjan algorithm is

   /// the fastest known max flow algorithms wich using blocking

   /// flow. It is an improvement of the Dinitz algorithm by using the

   /// \ref DynamicTree "dynamic tree" data structure of Sleator and

   /// Tarjan.

   ///

   /// This blocking flow algorithms builds a layered graph according

   /// to \ref Bfs "breadth-first search" distance from the target node

   /// in the reversed residual graph. The layered graph contains each

   /// residual edge which steps one level down. After that the

   /// algorithm constructs a blocking flow on the layered graph and

   /// augments the overall flow with it. The number of the levels in

   /// the layered graph is strictly increasing in each augmenting

   /// phase therefore the number of the augmentings is at most

   /// \f$n-1\f$.  The length of each phase is at most

   /// \f$O(m\log(n))\f$, that the overall time complexity is

   /// \f$O(nm\log(n))\f$.

   ///

   /// \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

   /// DinitzSleatorTarjanDefaultTraits.  See \ref

   /// DinitzSleatorTarjanDefaultTraits for the documentation of a

   /// Dinitz-Sleator-Tarjan traits class.

   ///

   /// \author Tamas Hamori and Balazs Dezso

 #ifdef DOXYGEN

   template <typename _Graph, typename _CapacityMap, typename _Traits>

 #else

   template <typename _Graph, 

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

 	    typename _Traits = 

 	    DinitzSleatorTarjanDefaultTraits<_Graph, _CapacityMap> >

 #endif

   class DinitzSleatorTarjan {

   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;

   private:

     GRAPH_TYPEDEFS(typename Graph);

     typedef typename Graph::template NodeMap<int> LevelMap;

     typedef typename Graph::template NodeMap<int> IntNodeMap;

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

     typedef DynamicTree<Value, IntNodeMap, Tolerance, false> DynTree;

   private:

     const Graph& _graph;

     const CapacityMap* _capacity;

     Node _source, _target;

     FlowMap* _flow;

     bool _local_flow;

     IntNodeMap* _level;

     EdgeNodeMap* _dt_edges;

     IntNodeMap* _dt_index;

     DynTree* _dt;

     std::vector<Node> _queue;

     Tolerance _tolerance;

     Value _flow_value;

     Value _max_value;

   public:

     typedef DinitzSleatorTarjan Create;

     ///\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 DinitzSleatorTarjan<Graph, CapacityMap, 

 			      DefFlowMapTraits<_FlowMap> > {

       typedef DinitzSleatorTarjan<Graph, CapacityMap, 

 			     DefFlowMapTraits<_FlowMap> > Create;

     };

     template <typename _Elevator>

     struct DefElevatorTraits : public Traits {

       typedef _Elevator Elevator;

       static Elevator *createElevator(const Graph&, int) {

 	throw UninitializedParameter();

       }

     };

     /// @}

     /// \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::DinitzSleatorTarjan::InvalidArgument";

       }

     };

   protected:

     DinitzSleatorTarjan() {}

   public:

     /// \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.

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

 			Node source, Node target)

       : _graph(graph), _capacity(&capacity),

 	_source(source), _target(target),

 	_flow(0), _local_flow(false),

 	_level(0), _dt_edges(0),

 	_dt_index(0), _dt(0), _queue(),

 	_tolerance(), _flow_value(), _max_value()

     {

       if (_source == _target) {

 	throw InvalidArgument();

       }

     }

     /// \brief Destrcutor.

     ///

     /// Destructor.

     ~DinitzSleatorTarjan() {

       destroyStructures();

     }

     /// \brief Sets the capacity map.

     ///

     /// Sets the capacity map.

     /// \return \c (*this)

     DinitzSleatorTarjan& capacityMap(const CapacityMap& map) {

       _capacity = ↦

       return *this;

     }

     /// \brief Sets the flow map.

     ///

     /// Sets the flow map.

     /// \return \c (*this)

     DinitzSleatorTarjan& 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)

     DinitzSleatorTarjan& source(const Node& node) {

       _source = node;

       return *this;

     }

     /// \brief Sets the target node.

     ///

     /// Sets the target node.

     /// \return \c (*this)

     DinitzSleatorTarjan& target(const Node& node) {

       _target = node;

       return *this;

     }

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

     ///

     /// Sets the tolerance used by algorithm.

     DinitzSleatorTarjan& tolerance(const Tolerance& tolerance) const {

       _tolerance = tolerance;

       if (_dt) {

 	_dt.tolerance(_tolerance);

       }

       return *this;

     } 

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

     ///

     /// Returns the tolerance used by algorithm.

     const Tolerance& tolerance() const {

       return tolerance;

     } 

   private:

     void createStructures() {

       if (!_flow) {

 	_flow = Traits::createFlowMap(_graph);

 	_local_flow = true;

       }

       if (!_level) {

 	_level = new LevelMap(_graph);

       }

       if (!_dt_index && !_dt) {

 	_dt_index = new IntNodeMap(_graph);

 	_dt = new DynTree(*_dt_index, _tolerance);

       }

       if (!_dt_edges) {

 	_dt_edges = new EdgeNodeMap(_graph);

       }

       _queue.resize(countNodes(_graph));

       _max_value = _dt->maxValue();

     }

     void destroyStructures() {

       if (_local_flow) {

 	delete _flow;

       }

       if (_level) {

 	delete _level;

       }

       if (_dt) {

 	delete _dt;

       }

       if (_dt_index) {

 	delete _dt_index;

       }

       if (_dt_edges) {

 	delete _dt_edges;

       }

     }

     bool createLayeredGraph() {

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

 	_level->set(n, -2);

       }

       int level = 0;

       _queue[0] = _target;

       _level->set(_target, level);

       int first = 0, last = 1, limit = 0;

       while (first != last && (*_level)[_source] == -2) {

 	if (first == limit) {

 	  limit = last;

 	  ++level;

 	}

 	Node n = _queue[first++];

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

 	  Node v = _graph.target(e);

 	  if ((*_level)[v] != -2) continue;

 	  Value rem = (*_flow)[e];

 	  if (!_tolerance.positive(rem)) continue;

 	  _level->set(v, level);

 	  _queue[last++] = v;

 	}

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

 	  Node v = _graph.source(e);

 	  if ((*_level)[v] != -2) continue;

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

 	  if (!_tolerance.positive(rem)) continue;

 	  _level->set(v, level);

 	  _queue[last++] = v;

 	}

       }

       return (*_level)[_source] != -2;

     }

     void initEdges() {

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

 	_graph.firstOut((*_dt_edges)[n], n);

       }

     }

     void augmentPath() {

       Value rem;

       Node n = _dt->findCost(_source, rem);

       _flow_value += rem;

       _dt->addCost(_source, - rem);

       _dt->cut(n);

       _dt->addCost(n, _max_value);

       Edge e = (*_dt_edges)[n];

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

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

 	_graph.nextOut(e);

 	if (e == INVALID) {

 	  _graph.firstIn(e, n);

 	}

       } else {

 	_flow->set(e, 0);

 	_graph.nextIn(e);

       }

       _dt_edges->set(n, e);

     }

     bool advance(Node n) {

       Edge e = (*_dt_edges)[n];

       if (e == INVALID) return false;

       Node u;

       Value rem;      

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

 	u = _graph.target(e);

 	while ((*_level)[n] != (*_level)[u] + 1 || 

 	       !_tolerance.positive((*_capacity)[e] - (*_flow)[e])) {

 	  _graph.nextOut(e);

 	  if (e == INVALID) break;

 	  u = _graph.target(e);

 	}

 	if (e != INVALID) {

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

 	} else {

 	  _graph.firstIn(e, n);

 	  if (e == INVALID) {

 	    _dt_edges->set(n, INVALID);

 	    return false;

 	  }

 	  u = _graph.source(e);

 	  while ((*_level)[n] != (*_level)[u] + 1 ||

 		 !_tolerance.positive((*_flow)[e])) {

 	    _graph.nextIn(e);

 	    if (e == INVALID) {

 	      _dt_edges->set(n, INVALID);

 	      return false;

 	    }

 	    u = _graph.source(e);

 	  }

 	  rem = (*_flow)[e];

 	}

       } else {

 	u = _graph.source(e);

 	while ((*_level)[n] != (*_level)[u] + 1 ||

 	       !_tolerance.positive((*_flow)[e])) {

 	  _graph.nextIn(e);

 	  if (e == INVALID) {

 	    _dt_edges->set(n, INVALID);

 	    return false;

 	  }

 	  u = _graph.source(e);

 	}

 	rem = (*_flow)[e];

       }

       _dt->addCost(n, - std::numeric_limits<Value>::max());

       _dt->addCost(n, rem);

       _dt->link(n, u);

       _dt_edges->set(n, e);

       return true;

     }

     void retreat(Node n) {

       _level->set(n, -1);

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

 	Node u = _graph.target(e);

 	if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) {

 	  Value rem;

 	  _dt->findCost(u, rem);

 	  _flow->set(e, rem);

 	  _dt->cut(u);

 	  _dt->addCost(u, - rem);

 	  _dt->addCost(u, _max_value);

 	}

       }

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

 	Node u = _graph.source(e);

 	if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) {

 	  Value rem;

 	  _dt->findCost(u, rem);

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

 	  _dt->cut(u);

 	  _dt->addCost(u, - rem);

 	  _dt->addCost(u, _max_value);

 	}

       }

     }

     void extractTrees() {

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

 	Node w = _dt->findRoot(n);

 	while (w != n) {

 	  Value rem;      

 	  Node u = _dt->findCost(n, rem);

 	  _dt->cut(u);

 	  _dt->addCost(u, - rem);

 	  _dt->addCost(u, _max_value);

 	  Edge e = (*_dt_edges)[u];

 	  _dt_edges->set(u, INVALID);

 	  if (u == _graph.source(e)) {

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

 	  } else {

 	    _flow->set(e, rem);

 	  }

 	  w = _dt->findRoot(n);

 	}      

       }

     }

   public:

     /// \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();

       _dt->clear();

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

         _dt->makeTree(n);

         _dt->addCost(n, _max_value);

       }

       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();

       _dt->clear();

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

         _dt->makeTree(n);

         _dt->addCost(n, _max_value);

       }

       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();

       _dt->clear();

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

         _dt->makeTree(n);

         _dt->addCost(n, _max_value);

       }

       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 Executes the algorithm

     ///

     /// It runs augmenting phases by adding blocking flow until the

     /// optimal solution is reached.

     void start() {

       while (augment());

     }

     /// \brief Augments the flow with a blocking flow on a layered

     /// graph.

     /// 

     /// This function builds a layered graph and then find a blocking

     /// flow on this graph. The number of the levels in the layered

     /// graph is strictly increasing in each augmenting phase

     /// therefore the number of the augmentings is at most \f$ n-1

     /// \f$.  The length of each phase is at most \f$ O(m \log(n))

     /// \f$, that the overall time complexity is \f$ O(nm \log(n)) \f$.

     /// \return %False when there is not residual path between the

     /// source and the target so the current flow is a feasible and

     /// optimal solution.

     bool augment() {

       Node n;

       if (createLayeredGraph()) {

 	Timer bf_timer;

 	initEdges();

 	n = _dt->findRoot(_source);

 	while (true) {

 	  Edge e;

 	  if (n == _target) {

 	    augmentPath();

 	  } else if (!advance(n)) {

 	    if (n != _source) {

 	      retreat(n);

 	    } else {

 	      break;

 	    }

 	  }

 	  n = _dt->findRoot(_source);

 	}     

 	extractTrees();

 	return true;

       } else {

 	return false;

       }

     }

     /// \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 Dinitz-Sleator-Tarjan 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 (*_level)[node] == -2;

     }

     /// \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, (*_level)[n] == -2);

       }

       cutMap.set(_source, true);

     }    

     /// @}

   };

 }

 #endif