deba@2514: /* -*- C++ -*-
deba@2514:  *
deba@2514:  * This file is a part of LEMON, a generic C++ optimization library
deba@2514:  *
alpar@2553:  * Copyright (C) 2003-2008
deba@2514:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@2514:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@2514:  *
deba@2514:  * Permission to use, modify and distribute this software is granted
deba@2514:  * provided that this copyright notice appears in all copies. For
deba@2514:  * precise terms see the accompanying LICENSE file.
deba@2514:  *
deba@2514:  * This software is provided "AS IS" with no warranty of any kind,
deba@2514:  * express or implied, and with no claim as to its suitability for any
deba@2514:  * purpose.
deba@2514:  *
deba@2514:  */
deba@2514: 
deba@2514: #ifndef LEMON_DINITZ_SLEATOR_TARJAN_H
deba@2514: #define LEMON_DINITZ_SLEATOR_TARJAN_H
deba@2514: 
deba@2514: /// \file 
deba@2514: /// \ingroup max_flow 
deba@2514: /// \brief Implementation the dynamic tree data structure of Sleator
deba@2514: /// and Tarjan.
deba@2514: 
deba@2514: #include <lemon/graph_utils.h>
deba@2514: #include <lemon/tolerance.h>
deba@2514: #include <lemon/dynamic_tree.h>
deba@2514: 
deba@2514: #include <vector>
deba@2514: #include <limits>
deba@2514: #include <fstream>
deba@2514: 
deba@2514: 
deba@2514: namespace lemon {
deba@2514: 
deba@2514:   /// \brief Default traits class of DinitzSleatorTarjan class.
deba@2514:   ///
deba@2514:   /// Default traits class of DinitzSleatorTarjan class.
deba@2514:   /// \param _Graph Graph type.
deba@2514:   /// \param _CapacityMap Type of capacity map.
deba@2514:   template <typename _Graph, typename _CapacityMap>
deba@2514:   struct DinitzSleatorTarjanDefaultTraits {
deba@2514: 
deba@2514:     /// \brief The graph type the algorithm runs on. 
deba@2514:     typedef _Graph Graph;
deba@2514: 
deba@2514:     /// \brief The type of the map that stores the edge capacities.
deba@2514:     ///
deba@2514:     /// The type of the map that stores the edge capacities.
deba@2514:     /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
deba@2514:     typedef _CapacityMap CapacityMap;
deba@2514: 
deba@2514:     /// \brief The type of the length of the edges.
deba@2514:     typedef typename CapacityMap::Value Value;
deba@2514: 
deba@2514:     /// \brief The map type that stores the flow values.
deba@2514:     ///
deba@2514:     /// The map type that stores the flow values. 
deba@2514:     /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
deba@2514:     typedef typename Graph::template EdgeMap<Value> FlowMap;
deba@2514: 
deba@2514:     /// \brief Instantiates a FlowMap.
deba@2514:     ///
deba@2514:     /// This function instantiates a \ref FlowMap. 
deba@2514:     /// \param graph The graph, to which we would like to define the flow map.
deba@2514:     static FlowMap* createFlowMap(const Graph& graph) {
deba@2514:       return new FlowMap(graph);
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief The tolerance used by the algorithm
deba@2514:     ///
deba@2514:     /// The tolerance used by the algorithm to handle inexact computation.
deba@2514:     typedef Tolerance<Value> Tolerance;
deba@2514: 
deba@2514:   };
deba@2514: 
deba@2514:   /// \ingroup max_flow
deba@2514:   ///
deba@2514:   /// \brief Dinitz-Sleator-Tarjan algorithms class.
deba@2514:   ///
deba@2514:   /// This class provides an implementation of the \e
deba@2514:   /// Dinitz-Sleator-Tarjan \e algorithm producing a flow of maximum
deba@2514:   /// value in a directed graph. The DinitzSleatorTarjan algorithm is
deba@2514:   /// the fastest known max flow algorithms wich using blocking
deba@2514:   /// flow. It is an improvement of the Dinitz algorithm by using the
deba@2514:   /// \ref DynamicTree "dynamic tree" data structure of Sleator and
deba@2514:   /// Tarjan.
deba@2514:   ///
deba@2514:   /// This blocking flow algorithms builds a layered graph according
deba@2514:   /// to \ref Bfs "breadth-first search" distance from the target node
deba@2514:   /// in the reversed residual graph. The layered graph contains each
deba@2514:   /// residual edge which steps one level down. After that the
deba@2514:   /// algorithm constructs a blocking flow on the layered graph and
deba@2514:   /// augments the overall flow with it. The number of the levels in
deba@2514:   /// the layered graph is strictly increasing in each augmenting
deba@2514:   /// phase therefore the number of the augmentings is at most
deba@2514:   /// \f$n-1\f$.  The length of each phase is at most
deba@2514:   /// \f$O(m\log(n))\f$, that the overall time complexity is
deba@2514:   /// \f$O(nm\log(n))\f$.
deba@2514:   ///
deba@2514:   /// \param _Graph The directed graph type the algorithm runs on.
deba@2514:   /// \param _CapacityMap The capacity map type.
deba@2514:   /// \param _Traits Traits class to set various data types used by
deba@2514:   /// the algorithm.  The default traits class is \ref
deba@2514:   /// DinitzSleatorTarjanDefaultTraits.  See \ref
deba@2514:   /// DinitzSleatorTarjanDefaultTraits for the documentation of a
deba@2514:   /// Dinitz-Sleator-Tarjan traits class.
deba@2514:   ///
deba@2514:   /// \author Tamas Hamori and Balazs Dezso
deba@2514: #ifdef DOXYGEN
deba@2514:   template <typename _Graph, typename _CapacityMap, typename _Traits>
deba@2514: #else
deba@2514:   template <typename _Graph, 
deba@2514: 	    typename _CapacityMap = typename _Graph::template EdgeMap<int>,
deba@2514: 	    typename _Traits = 
deba@2514: 	    DinitzSleatorTarjanDefaultTraits<_Graph, _CapacityMap> >
deba@2514: #endif
deba@2514:   class DinitzSleatorTarjan {
deba@2514:   public:
deba@2514: 
deba@2514:     typedef _Traits Traits;
deba@2514:     typedef typename Traits::Graph Graph;
deba@2514:     typedef typename Traits::CapacityMap CapacityMap;
deba@2514:     typedef typename Traits::Value Value; 
deba@2514: 
deba@2514:     typedef typename Traits::FlowMap FlowMap;
deba@2514:     typedef typename Traits::Tolerance Tolerance;
deba@2514: 
deba@2514: 
deba@2514:   private:
deba@2514: 
deba@2514:     GRAPH_TYPEDEFS(typename Graph);
deba@2514: 
deba@2514: 
deba@2514:     typedef typename Graph::template NodeMap<int> LevelMap;
deba@2514:     typedef typename Graph::template NodeMap<int> IntNodeMap;
deba@2514:     typedef typename Graph::template NodeMap<Edge> EdgeNodeMap;
deba@2514:     typedef DynamicTree<Value, IntNodeMap, Tolerance, false> DynTree;
deba@2514: 
deba@2514:   private:
deba@2514:     
deba@2514:     const Graph& _graph;
deba@2514:     const CapacityMap* _capacity;
deba@2514: 
deba@2514:     Node _source, _target;
deba@2514: 
deba@2514:     FlowMap* _flow;
deba@2514:     bool _local_flow;
deba@2514: 
deba@2514:     IntNodeMap* _level;
deba@2514:     EdgeNodeMap* _dt_edges;
deba@2514:     
deba@2514:     IntNodeMap* _dt_index;
deba@2514:     DynTree* _dt;
deba@2514: 
deba@2519:     std::vector<Node> _queue;
deba@2519: 
deba@2514:     Tolerance _tolerance;
deba@2514:     
deba@2514:     Value _flow_value;
deba@2514:     Value _max_value;
deba@2514: 
deba@2514: 
deba@2514:   public:
deba@2514: 
deba@2514:     typedef DinitzSleatorTarjan Create;
deba@2514: 
deba@2514:     ///\name Named template parameters
deba@2514: 
deba@2514:     ///@{
deba@2514: 
deba@2514:     template <typename _FlowMap>
deba@2514:     struct DefFlowMapTraits : public Traits {
deba@2514:       typedef _FlowMap FlowMap;
deba@2514:       static FlowMap *createFlowMap(const Graph&) {
deba@2514: 	throw UninitializedParameter();
deba@2514:       }
deba@2514:     };
deba@2514: 
deba@2514:     /// \brief \ref named-templ-param "Named parameter" for setting
deba@2514:     /// FlowMap type
deba@2514:     ///
deba@2514:     /// \ref named-templ-param "Named parameter" for setting FlowMap
deba@2514:     /// type
deba@2514:     template <typename _FlowMap>
deba@2514:     struct DefFlowMap 
deba@2514:       : public DinitzSleatorTarjan<Graph, CapacityMap, 
deba@2514: 			      DefFlowMapTraits<_FlowMap> > {
deba@2514:       typedef DinitzSleatorTarjan<Graph, CapacityMap, 
deba@2514: 			     DefFlowMapTraits<_FlowMap> > Create;
deba@2514:     };
deba@2514: 
deba@2514:     template <typename _Elevator>
deba@2514:     struct DefElevatorTraits : public Traits {
deba@2514:       typedef _Elevator Elevator;
deba@2514:       static Elevator *createElevator(const Graph&, int) {
deba@2514: 	throw UninitializedParameter();
deba@2514:       }
deba@2514:     };
deba@2514: 
deba@2514:     /// @}
deba@2514: 
deba@2514:     /// \brief \ref Exception for the case when the source equals the target.
deba@2514:     ///
deba@2514:     /// \ref Exception for the case when the source equals the target.
deba@2514:     ///
deba@2514:     class InvalidArgument : public lemon::LogicError {
deba@2514:     public:
deba@2514:       virtual const char* what() const throw() {
deba@2514: 	return "lemon::DinitzSleatorTarjan::InvalidArgument";
deba@2514:       }
deba@2514:     };
deba@2514: 
deba@2527:   protected:
deba@2527:     
deba@2527:     DinitzSleatorTarjan() {}
deba@2527: 
deba@2527:   public:
deba@2527: 
deba@2514:     /// \brief The constructor of the class.
deba@2514:     ///
deba@2514:     /// The constructor of the class. 
deba@2514:     /// \param graph The directed graph the algorithm runs on. 
deba@2514:     /// \param capacity The capacity of the edges. 
deba@2514:     /// \param source The source node.
deba@2514:     /// \param target The target node.
deba@2514:     DinitzSleatorTarjan(const Graph& graph, const CapacityMap& capacity,
deba@2514: 			Node source, Node target)
deba@2514:       : _graph(graph), _capacity(&capacity),
deba@2514: 	_source(source), _target(target),
deba@2514: 	_flow(0), _local_flow(false),
deba@2514: 	_level(0), _dt_edges(0),
deba@2519: 	_dt_index(0), _dt(0), _queue(),
deba@2514: 	_tolerance(), _flow_value(), _max_value()
deba@2514:     {
deba@2514:       if (_source == _target) {
deba@2514: 	throw InvalidArgument();
deba@2514:       }
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Destrcutor.
deba@2514:     ///
deba@2514:     /// Destructor.
deba@2514:     ~DinitzSleatorTarjan() {
deba@2514:       destroyStructures();
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Sets the capacity map.
deba@2514:     ///
deba@2514:     /// Sets the capacity map.
deba@2514:     /// \return \c (*this)
deba@2514:     DinitzSleatorTarjan& capacityMap(const CapacityMap& map) {
deba@2514:       _capacity = &map;
deba@2514:       return *this;
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Sets the flow map.
deba@2514:     ///
deba@2514:     /// Sets the flow map.
deba@2514:     /// \return \c (*this)
deba@2514:     DinitzSleatorTarjan& flowMap(FlowMap& map) {
deba@2514:       if (_local_flow) {
deba@2514: 	delete _flow;
deba@2514: 	_local_flow = false;
deba@2514:       }
deba@2514:       _flow = &map;
deba@2514:       return *this;
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Returns the flow map.
deba@2514:     ///
deba@2514:     /// \return The flow map.
deba@2514:     const FlowMap& flowMap() {
deba@2514:       return *_flow;
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Sets the source node.
deba@2514:     ///
deba@2514:     /// Sets the source node.
deba@2514:     /// \return \c (*this)
deba@2514:     DinitzSleatorTarjan& source(const Node& node) {
deba@2514:       _source = node;
deba@2514:       return *this;
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Sets the target node.
deba@2514:     ///
deba@2514:     /// Sets the target node.
deba@2514:     /// \return \c (*this)
deba@2514:     DinitzSleatorTarjan& target(const Node& node) {
deba@2514:       _target = node;
deba@2514:       return *this;
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Sets the tolerance used by algorithm.
deba@2514:     ///
deba@2514:     /// Sets the tolerance used by algorithm.
deba@2514:     DinitzSleatorTarjan& tolerance(const Tolerance& tolerance) const {
deba@2514:       _tolerance = tolerance;
deba@2514:       if (_dt) {
deba@2514: 	_dt.tolerance(_tolerance);
deba@2514:       }
deba@2514:       return *this;
deba@2514:     } 
deba@2514: 
deba@2514:     /// \brief Returns the tolerance used by algorithm.
deba@2514:     ///
deba@2514:     /// Returns the tolerance used by algorithm.
deba@2514:     const Tolerance& tolerance() const {
deba@2514:       return tolerance;
deba@2514:     } 
deba@2514: 
deba@2514:   private:
deba@2514:         
deba@2514:     void createStructures() {
deba@2514:       if (!_flow) {
deba@2514: 	_flow = Traits::createFlowMap(_graph);
deba@2514: 	_local_flow = true;
deba@2514:       }
deba@2514:       if (!_level) {
deba@2514: 	_level = new LevelMap(_graph);
deba@2514:       }
deba@2514:       if (!_dt_index && !_dt) {
deba@2514: 	_dt_index = new IntNodeMap(_graph);
deba@2514: 	_dt = new DynTree(*_dt_index, _tolerance);
deba@2514:       }
deba@2514:       if (!_dt_edges) {
deba@2514: 	_dt_edges = new EdgeNodeMap(_graph);
deba@2514:       }
deba@2519:       _queue.resize(countNodes(_graph));
deba@2514:       _max_value = _dt->maxValue();
deba@2514:     }
deba@2514: 
deba@2514:     void destroyStructures() {
deba@2514:       if (_local_flow) {
deba@2514: 	delete _flow;
deba@2514:       }
deba@2514:       if (_level) {
deba@2514: 	delete _level;
deba@2514:       }
deba@2514:       if (_dt) {
deba@2514: 	delete _dt;
deba@2514:       }
deba@2514:       if (_dt_index) {
deba@2514: 	delete _dt_index;
deba@2514:       }
deba@2514:       if (_dt_edges) {
deba@2514: 	delete _dt_edges;
deba@2514:       }
deba@2514:     }
deba@2514: 
deba@2514:     bool createLayeredGraph() {
deba@2514: 
deba@2514:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2514: 	_level->set(n, -2);
deba@2514:       }
deba@2514:       
deba@2514:       int level = 0;
deba@2514: 
deba@2519:       _queue[0] = _target;
deba@2514:       _level->set(_target, level);
deba@2519: 
deba@2519:       int first = 0, last = 1, limit = 0;
deba@2514:       
deba@2519:       while (first != last && (*_level)[_source] == -2) {
deba@2519: 	if (first == limit) {
deba@2519: 	  limit = last;
deba@2519: 	  ++level;
deba@2519: 	}
deba@2514: 	
deba@2519: 	Node n = _queue[first++];
deba@2514: 	  
deba@2519: 	for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2519: 	  Node v = _graph.target(e);
deba@2519: 	  if ((*_level)[v] != -2) continue;
deba@2519: 	  Value rem = (*_flow)[e];
deba@2519: 	  if (!_tolerance.positive(rem)) continue;
deba@2519: 	  _level->set(v, level);
deba@2519: 	  _queue[last++] = v;
deba@2514: 	}
deba@2519: 	
deba@2519: 	for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2519: 	  Node v = _graph.source(e);
deba@2519: 	  if ((*_level)[v] != -2) continue;
deba@2519: 	  Value rem = (*_capacity)[e] - (*_flow)[e];
deba@2519: 	  if (!_tolerance.positive(rem)) continue;
deba@2519: 	  _level->set(v, level);
deba@2519: 	  _queue[last++] = v;
deba@2519: 	}
deba@2514:       }
deba@2514:       return (*_level)[_source] != -2;
deba@2514:     }
deba@2514: 
deba@2514:     void initEdges() {
deba@2514:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2514: 	_graph.firstOut((*_dt_edges)[n], n);
deba@2514:       }
deba@2514:     }
deba@2514:         
deba@2514:     
deba@2514:     void augmentPath() {
deba@2514:       Value rem;
deba@2514:       Node n = _dt->findCost(_source, rem);
deba@2514:       _flow_value += rem;
deba@2514:       _dt->addCost(_source, - rem);
deba@2514: 
deba@2514:       _dt->cut(n);
deba@2514:       _dt->addCost(n, _max_value);
deba@2514: 
deba@2514:       Edge e = (*_dt_edges)[n];
deba@2514:       if (_graph.source(e) == n) {
deba@2514: 	_flow->set(e, (*_capacity)[e]);
deba@2514: 	
deba@2514: 	_graph.nextOut(e);
deba@2514: 	if (e == INVALID) {
deba@2514: 	  _graph.firstIn(e, n);
deba@2514: 	}
deba@2514:       } else {
deba@2514: 	_flow->set(e, 0);
deba@2514: 	_graph.nextIn(e);
deba@2514:       }
deba@2514:       _dt_edges->set(n, e);
deba@2514: 
deba@2514:     }
deba@2514: 
deba@2514:     bool advance(Node n) {
deba@2514:       Edge e = (*_dt_edges)[n];
deba@2514:       if (e == INVALID) return false;
deba@2514: 
deba@2514:       Node u;
deba@2514:       Value rem;      
deba@2514:       if (_graph.source(e) == n) {
deba@2514: 	u = _graph.target(e);
deba@2514: 	while ((*_level)[n] != (*_level)[u] + 1 || 
deba@2514: 	       !_tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
deba@2514: 	  _graph.nextOut(e);
deba@2514: 	  if (e == INVALID) break;
deba@2514: 	  u = _graph.target(e);
deba@2514: 	}
deba@2514: 	if (e != INVALID) {
deba@2514: 	  rem = (*_capacity)[e] - (*_flow)[e];
deba@2514: 	} else {
deba@2514: 	  _graph.firstIn(e, n);
deba@2514: 	  if (e == INVALID) {
deba@2514: 	    _dt_edges->set(n, INVALID);
deba@2514: 	    return false;
deba@2514: 	  }
deba@2514: 	  u = _graph.source(e);
deba@2514: 	  while ((*_level)[n] != (*_level)[u] + 1 ||
deba@2514: 		 !_tolerance.positive((*_flow)[e])) {
deba@2514: 	    _graph.nextIn(e);
deba@2514: 	    if (e == INVALID) {
deba@2514: 	      _dt_edges->set(n, INVALID);
deba@2514: 	      return false;
deba@2514: 	    }
deba@2514: 	    u = _graph.source(e);
deba@2514: 	  }
deba@2514: 	  rem = (*_flow)[e];
deba@2514: 	}
deba@2514:       } else {
deba@2514: 	u = _graph.source(e);
deba@2514: 	while ((*_level)[n] != (*_level)[u] + 1 ||
deba@2514: 	       !_tolerance.positive((*_flow)[e])) {
deba@2514: 	  _graph.nextIn(e);
deba@2514: 	  if (e == INVALID) {
deba@2514: 	    _dt_edges->set(n, INVALID);
deba@2514: 	    return false;
deba@2514: 	  }
deba@2514: 	  u = _graph.source(e);
deba@2514: 	}
deba@2514: 	rem = (*_flow)[e];
deba@2514:       }
deba@2514: 
deba@2514:       _dt->addCost(n, - std::numeric_limits<Value>::max());
deba@2514:       _dt->addCost(n, rem);
deba@2514:       _dt->link(n, u);
deba@2514:       _dt_edges->set(n, e);
deba@2514:       return true;
deba@2514:     }
deba@2514: 
deba@2514:     void retreat(Node n) {
deba@2514:       _level->set(n, -1);
deba@2514:       
deba@2514:       for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2514: 	Node u = _graph.target(e);
deba@2514: 	if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) {
deba@2514: 	  Value rem;
deba@2514: 	  _dt->findCost(u, rem);
deba@2514: 	  _flow->set(e, rem);
deba@2514: 	  _dt->cut(u);
deba@2514: 	  _dt->addCost(u, - rem);
deba@2514: 	  _dt->addCost(u, _max_value);
deba@2514: 	}
deba@2514:       }
deba@2514:       for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2514: 	Node u = _graph.source(e);
deba@2514: 	if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) {
deba@2514: 	  Value rem;
deba@2514: 	  _dt->findCost(u, rem);
deba@2514: 	  _flow->set(e, (*_capacity)[e] - rem);
deba@2514: 	  _dt->cut(u);
deba@2514: 	  _dt->addCost(u, - rem);
deba@2514: 	  _dt->addCost(u, _max_value);
deba@2514: 	}
deba@2514:       }
deba@2514:     }
deba@2514: 
deba@2514:     void extractTrees() {
deba@2514:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2514: 	
deba@2514: 	Node w = _dt->findRoot(n);
deba@2514:       
deba@2514: 	while (w != n) {
deba@2514:       
deba@2514: 	  Value rem;      
deba@2514: 	  Node u = _dt->findCost(n, rem);
deba@2514: 
deba@2514: 	  _dt->cut(u);
deba@2514: 	  _dt->addCost(u, - rem);
deba@2514: 	  _dt->addCost(u, _max_value);
deba@2514: 	  
deba@2514: 	  Edge e = (*_dt_edges)[u];
deba@2514: 	  _dt_edges->set(u, INVALID);
deba@2514: 	  
deba@2514: 	  if (u == _graph.source(e)) {
deba@2514: 	    _flow->set(e, (*_capacity)[e] - rem);
deba@2514: 	  } else {
deba@2514: 	    _flow->set(e, rem);
deba@2514: 	  }
deba@2514: 	  
deba@2514: 	  w = _dt->findRoot(n);
deba@2514: 	}      
deba@2514:       }
deba@2514:     }
deba@2514: 
deba@2514: 
deba@2514:   public:
deba@2514:     
deba@2514:     /// \name Execution control The simplest way to execute the
deba@2514:     /// algorithm is to use the \c run() member functions.
deba@2514:     /// \n
deba@2514:     /// If you need more control on initial solution or
deba@2514:     /// execution then you have to call one \ref init() function and then
deba@2514:     /// the start() or multiple times the \c augment() member function.  
deba@2514:     
deba@2514:     ///@{
deba@2514: 
deba@2514:     /// \brief Initializes the algorithm
deba@2514:     /// 
deba@2514:     /// It sets the flow to empty flow.
deba@2514:     void init() {
deba@2514:       createStructures();
deba@2514: 
deba@2514:       _dt->clear();
deba@2514:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2514:         _dt->makeTree(n);
deba@2514:         _dt->addCost(n, _max_value);
deba@2514:       }
deba@2514: 
deba@2514:       for (EdgeIt it(_graph); it != INVALID; ++it) {
deba@2514:         _flow->set(it, 0);
deba@2514:       }
deba@2514:       _flow_value = 0;
deba@2514:     }
deba@2514:     
deba@2514:     /// \brief Initializes the algorithm
deba@2514:     /// 
deba@2514:     /// Initializes the flow to the \c flowMap. The \c flowMap should
deba@2514:     /// contain a feasible flow, ie. in each node excluding the source
deba@2514:     /// and the target the incoming flow should be equal to the
deba@2514:     /// outgoing flow.
deba@2514:     template <typename FlowMap>
deba@2514:     void flowInit(const FlowMap& flowMap) {
deba@2514:       createStructures();
deba@2514: 
deba@2514:       _dt->clear();
deba@2514:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2514:         _dt->makeTree(n);
deba@2514:         _dt->addCost(n, _max_value);
deba@2514:       }
deba@2514: 
deba@2514:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@2514: 	_flow->set(e, flowMap[e]);
deba@2514:       }
deba@2514:       _flow_value = 0;
deba@2514:       for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
deba@2514:         _flow_value += (*_flow)[jt];
deba@2514:       }
deba@2514:       for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
deba@2514:         _flow_value -= (*_flow)[jt];
deba@2514:       }
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Initializes the algorithm
deba@2514:     /// 
deba@2514:     /// Initializes the flow to the \c flowMap. The \c flowMap should
deba@2514:     /// contain a feasible flow, ie. in each node excluding the source
deba@2514:     /// and the target the incoming flow should be equal to the
deba@2514:     /// outgoing flow.  
deba@2514:     /// \return %False when the given flowMap does not contain
deba@2514:     /// feasible flow.
deba@2514:     template <typename FlowMap>
deba@2514:     bool checkedFlowInit(const FlowMap& flowMap) {
deba@2514:       createStructures();
deba@2514: 
deba@2514:       _dt->clear();
deba@2514:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2514:         _dt->makeTree(n);
deba@2514:         _dt->addCost(n, _max_value);
deba@2514:       }
deba@2514: 
deba@2514:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@2514: 	_flow->set(e, flowMap[e]);
deba@2514:       }
deba@2514:       for (NodeIt it(_graph); it != INVALID; ++it) {
deba@2514:         if (it == _source || it == _target) continue;
deba@2514:         Value outFlow = 0;
deba@2514:         for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) {
deba@2514:           outFlow += (*_flow)[jt];
deba@2514:         }
deba@2514:         Value inFlow = 0;
deba@2514:         for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) {
deba@2514:           inFlow += (*_flow)[jt];
deba@2514:         }
deba@2514:         if (_tolerance.different(outFlow, inFlow)) {
deba@2514:           return false;
deba@2514:         }
deba@2514:       }
deba@2514:       for (EdgeIt it(_graph); it != INVALID; ++it) {
deba@2514:         if (_tolerance.less((*_flow)[it], 0)) return false;
deba@2514:         if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false;
deba@2514:       }
deba@2514:       _flow_value = 0;
deba@2514:       for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
deba@2514:         _flow_value += (*_flow)[jt];
deba@2514:       }
deba@2514:       for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
deba@2514:         _flow_value -= (*_flow)[jt];
deba@2514:       }
deba@2514:       return true;
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Executes the algorithm
deba@2514:     ///
deba@2514:     /// It runs augmenting phases by adding blocking flow until the
deba@2514:     /// optimal solution is reached.
deba@2514:     void start() {
deba@2514:       while (augment());
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Augments the flow with a blocking flow on a layered
deba@2514:     /// graph.
deba@2514:     /// 
deba@2514:     /// This function builds a layered graph and then find a blocking
deba@2514:     /// flow on this graph. The number of the levels in the layered
deba@2514:     /// graph is strictly increasing in each augmenting phase
deba@2514:     /// therefore the number of the augmentings is at most \f$ n-1
deba@2514:     /// \f$.  The length of each phase is at most \f$ O(m \log(n))
deba@2514:     /// \f$, that the overall time complexity is \f$ O(nm \log(n)) \f$.
deba@2514:     /// \return %False when there is not residual path between the
deba@2514:     /// source and the target so the current flow is a feasible and
deba@2514:     /// optimal solution.
deba@2514:     bool augment() {
deba@2514:       Node n;
deba@2514: 
deba@2514:       if (createLayeredGraph()) {
deba@2514: 	
deba@2514: 	Timer bf_timer;
deba@2514: 	initEdges();
deba@2514: 
deba@2514: 	n = _dt->findRoot(_source);
deba@2514: 	while (true) {
deba@2514: 	  Edge e;
deba@2514: 	  if (n == _target) {
deba@2514: 	    augmentPath();
deba@2514: 	  } else if (!advance(n)) {
deba@2514: 	    if (n != _source) {
deba@2514: 	      retreat(n);
deba@2514: 	    } else {
deba@2514: 	      break;
deba@2514: 	    }
deba@2514: 	  }
deba@2514: 	  n = _dt->findRoot(_source);
deba@2514: 	}     
deba@2514: 	extractTrees();
deba@2514: 
deba@2514: 	return true;
deba@2514:       } else {
deba@2514: 	return false;
deba@2514:       }
deba@2514:     }
deba@2514:     
deba@2514:     /// \brief runs the algorithm.
deba@2514:     /// 
deba@2514:     /// It is just a shorthand for:
deba@2514:     ///
deba@2514:     ///\code 
deba@2514:     /// ek.init();
deba@2514:     /// ek.start();
deba@2514:     ///\endcode
deba@2514:     void run() {
deba@2514:       init();
deba@2514:       start();
deba@2514:     }
deba@2514: 
deba@2514:     /// @}
deba@2514: 
deba@2522:     /// \name Query Functions 
deba@2522:     /// The result of the Dinitz-Sleator-Tarjan algorithm can be
deba@2522:     /// obtained using these functions.
deba@2522:     /// \n
deba@2514:     /// Before the use of these functions,
deba@2514:     /// either run() or start() must be called.
deba@2514:     
deba@2514:     ///@{
deba@2514: 
deba@2514:     /// \brief Returns the value of the maximum flow.
deba@2514:     ///
deba@2514:     /// Returns the value of the maximum flow by returning the excess
deba@2514:     /// of the target node \c t. This value equals to the value of
deba@2514:     /// the maximum flow already after the first phase.
deba@2514:     Value flowValue() const {
deba@2514:       return _flow_value;
deba@2514:     }
deba@2514: 
deba@2514: 
deba@2514:     /// \brief Returns the flow on the edge.
deba@2514:     ///
deba@2514:     /// Sets the \c flowMap to the flow on the edges. This method can
deba@2514:     /// be called after the second phase of algorithm.
deba@2514:     Value flow(const Edge& edge) const {
deba@2514:       return (*_flow)[edge];
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Returns true when the node is on the source side of minimum cut.
deba@2514:     ///
deba@2514: 
deba@2514:     /// Returns true when the node is on the source side of minimum
deba@2514:     /// cut. This method can be called both after running \ref
deba@2514:     /// startFirstPhase() and \ref startSecondPhase().
deba@2514:     bool minCut(const Node& node) const {
deba@2514:       return (*_level)[node] == -2;
deba@2514:     }
deba@2514: 
deba@2514:     /// \brief Returns a minimum value cut.
deba@2514:     ///
deba@2514:     /// Sets \c cut to the characteristic vector of a minimum value cut
deba@2514:     /// It simply calls the minMinCut member.
deba@2514:     /// \retval cut Write node bool map. 
deba@2514:     template <typename CutMap>
deba@2514:     void minCutMap(CutMap& cutMap) const {
deba@2514:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2514: 	cutMap.set(n, (*_level)[n] == -2);
deba@2514:       }
deba@2514:       cutMap.set(_source, true);
deba@2514:     }    
deba@2514: 
deba@2514:     /// @}
deba@2514: 
deba@2514:   };
deba@2514: }
deba@2514: 
deba@2514: #endif