lemon/preflow.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sun, 30 Nov 2008 00:50:31 +0100
changeset 408 37054b67d807
parent 407 db3251947eba
child 437 6a2a33ad261b
permissions -rw-r--r--
Many doc improvements for Preflow (#176)

- More precise doc for members.
- Add doc for public types.
- Hide the doc of the traits class parameter.
- Removing \author comments.
- Use \tparam for template parameters.
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2008
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_PREFLOW_H
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#define LEMON_PREFLOW_H
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#include <lemon/tolerance.h>
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#include <lemon/elevator.h>
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/// \file
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/// \ingroup max_flow
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/// \brief Implementation of the preflow algorithm.
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namespace lemon {
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  /// \brief Default traits class of Preflow class.
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  ///
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  /// Default traits class of Preflow class.
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  /// \tparam _Digraph Digraph type.
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  /// \tparam _CapacityMap Capacity map type.
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  template <typename _Digraph, typename _CapacityMap>
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  struct PreflowDefaultTraits {
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    /// \brief The type of the digraph the algorithm runs on.
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    typedef _Digraph Digraph;
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    /// \brief The type of the map that stores the arc capacities.
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    ///
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    /// The type of the map that stores the arc capacities.
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    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
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    typedef _CapacityMap CapacityMap;
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    /// \brief The type of the flow values.
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    typedef typename CapacityMap::Value Value;
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    /// \brief The type of the map that stores the flow values.
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    ///
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    /// The type of the map that stores the flow values.
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    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
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    typedef typename Digraph::template ArcMap<Value> FlowMap;
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    /// \brief Instantiates a FlowMap.
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    ///
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    /// This function instantiates a \ref FlowMap.
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    /// \param digraph The digraph, to which we would like to define
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    /// the flow map.
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    static FlowMap* createFlowMap(const Digraph& digraph) {
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      return new FlowMap(digraph);
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    }
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    /// \brief The elevator type used by Preflow algorithm.
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    ///
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    /// The elevator type used by Preflow algorithm.
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    ///
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    /// \sa Elevator
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    /// \sa LinkedElevator
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    typedef LinkedElevator<Digraph, typename Digraph::Node> Elevator;
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    /// \brief Instantiates an Elevator.
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    ///
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    /// This function instantiates an \ref Elevator.
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    /// \param digraph The digraph, to which we would like to define
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    /// the elevator.
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    /// \param max_level The maximum level of the elevator.
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    static Elevator* createElevator(const Digraph& digraph, int max_level) {
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      return new Elevator(digraph, max_level);
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    }
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    /// \brief The tolerance used by the algorithm
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    ///
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    /// The tolerance used by the algorithm to handle inexact computation.
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    typedef lemon::Tolerance<Value> Tolerance;
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  };
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  /// \ingroup max_flow
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  ///
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  /// \brief %Preflow algorithm class.
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  ///
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  /// This class provides an implementation of Goldberg-Tarjan's \e preflow
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  /// \e push-relabel algorithm producing a flow of maximum value in a
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  /// digraph. The preflow algorithms are the fastest known maximum
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  /// flow algorithms. The current implementation use a mixture of the
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  /// \e "highest label" and the \e "bound decrease" heuristics.
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  /// The worst case time complexity of the algorithm is \f$O(n^2\sqrt{e})\f$.
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  ///
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  /// The algorithm consists of two phases. After the first phase
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  /// the maximum flow value and the minimum cut is obtained. The
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  /// second phase constructs a feasible maximum flow on each arc.
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  ///
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  /// \tparam _Digraph The type of the digraph the algorithm runs on.
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  /// \tparam _CapacityMap The type of the capacity map. The default map
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  /// type is \ref concepts::Digraph::ArcMap "_Digraph::ArcMap<int>".
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#ifdef DOXYGEN
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  template <typename _Digraph, typename _CapacityMap, typename _Traits>
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#else
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  template <typename _Digraph,
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            typename _CapacityMap = typename _Digraph::template ArcMap<int>,
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            typename _Traits = PreflowDefaultTraits<_Digraph, _CapacityMap> >
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#endif
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  class Preflow {
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  public:
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    ///The \ref PreflowDefaultTraits "traits class" of the algorithm.
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    typedef _Traits Traits;
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    ///The type of the digraph the algorithm runs on.
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    typedef typename Traits::Digraph Digraph;
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    ///The type of the capacity map.
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    typedef typename Traits::CapacityMap CapacityMap;
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    ///The type of the flow values.
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    typedef typename Traits::Value Value;
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    ///The type of the flow map.
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    typedef typename Traits::FlowMap FlowMap;
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    ///The type of the elevator.
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    typedef typename Traits::Elevator Elevator;
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    ///The type of the tolerance.
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    typedef typename Traits::Tolerance Tolerance;
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  private:
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    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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    const Digraph& _graph;
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    const CapacityMap* _capacity;
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    int _node_num;
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    Node _source, _target;
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    FlowMap* _flow;
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    bool _local_flow;
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    Elevator* _level;
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    bool _local_level;
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    typedef typename Digraph::template NodeMap<Value> ExcessMap;
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    ExcessMap* _excess;
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    Tolerance _tolerance;
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    bool _phase;
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    void createStructures() {
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      _node_num = countNodes(_graph);
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      if (!_flow) {
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        _flow = Traits::createFlowMap(_graph);
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        _local_flow = true;
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      }
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      if (!_level) {
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        _level = Traits::createElevator(_graph, _node_num);
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        _local_level = true;
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      }
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      if (!_excess) {
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        _excess = new ExcessMap(_graph);
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      }
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    }
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    void destroyStructures() {
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      if (_local_flow) {
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        delete _flow;
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      }
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      if (_local_level) {
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        delete _level;
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      }
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      if (_excess) {
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        delete _excess;
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      }
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    }
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  public:
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    typedef Preflow Create;
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    ///\name Named Template Parameters
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    ///@{
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    template <typename _FlowMap>
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    struct SetFlowMapTraits : public Traits {
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      typedef _FlowMap FlowMap;
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      static FlowMap *createFlowMap(const Digraph&) {
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        LEMON_ASSERT(false, "FlowMap is not initialized");
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        return 0; // ignore warnings
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      }
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// FlowMap type
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    ///
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    /// \ref named-templ-param "Named parameter" for setting FlowMap
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    /// type.
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    template <typename _FlowMap>
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    struct SetFlowMap
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      : public Preflow<Digraph, CapacityMap, SetFlowMapTraits<_FlowMap> > {
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      typedef Preflow<Digraph, CapacityMap,
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                      SetFlowMapTraits<_FlowMap> > Create;
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    };
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    template <typename _Elevator>
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    struct SetElevatorTraits : public Traits {
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      typedef _Elevator Elevator;
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      static Elevator *createElevator(const Digraph&, int) {
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        LEMON_ASSERT(false, "Elevator is not initialized");
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        return 0; // ignore warnings
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      }
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// Elevator type
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    ///
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    /// \ref named-templ-param "Named parameter" for setting Elevator
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    /// type. If this named parameter is used, then an external
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    /// elevator object must be passed to the algorithm using the
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    /// \ref elevator(Elevator&) "elevator()" function before calling
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    /// \ref run() or \ref init().
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    /// \sa SetStandardElevator
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    template <typename _Elevator>
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    struct SetElevator
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      : public Preflow<Digraph, CapacityMap, SetElevatorTraits<_Elevator> > {
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      typedef Preflow<Digraph, CapacityMap,
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                      SetElevatorTraits<_Elevator> > Create;
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    };
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    template <typename _Elevator>
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    struct SetStandardElevatorTraits : public Traits {
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      typedef _Elevator Elevator;
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      static Elevator *createElevator(const Digraph& digraph, int max_level) {
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        return new Elevator(digraph, max_level);
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      }
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// Elevator type with automatic allocation
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    ///
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    /// \ref named-templ-param "Named parameter" for setting Elevator
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    /// type with automatic allocation.
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    /// The Elevator should have standard constructor interface to be
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    /// able to automatically created by the algorithm (i.e. the
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    /// digraph and the maximum level should be passed to it).
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    /// However an external elevator object could also be passed to the
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    /// algorithm with the \ref elevator(Elevator&) "elevator()" function
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    /// before calling \ref run() or \ref init().
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    /// \sa SetElevator
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    template <typename _Elevator>
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    struct SetStandardElevator
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      : public Preflow<Digraph, CapacityMap,
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                       SetStandardElevatorTraits<_Elevator> > {
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      typedef Preflow<Digraph, CapacityMap,
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                      SetStandardElevatorTraits<_Elevator> > Create;
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    };
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    /// @}
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  protected:
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    Preflow() {}
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  public:
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    /// \brief The constructor of the class.
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    ///
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    /// The constructor of the class.
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    /// \param digraph The digraph the algorithm runs on.
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    /// \param capacity The capacity of the arcs.
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    /// \param source The source node.
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    /// \param target The target node.
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    Preflow(const Digraph& digraph, const CapacityMap& capacity,
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            Node source, Node target)
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      : _graph(digraph), _capacity(&capacity),
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        _node_num(0), _source(source), _target(target),
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        _flow(0), _local_flow(false),
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        _level(0), _local_level(false),
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        _excess(0), _tolerance(), _phase() {}
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    /// \brief Destructor.
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    ///
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    /// Destructor.
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    ~Preflow() {
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      destroyStructures();
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    }
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    /// \brief Sets the capacity map.
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    ///
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    /// Sets the capacity map.
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    /// \return <tt>(*this)</tt>
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    Preflow& capacityMap(const CapacityMap& map) {
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      _capacity = &map;
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      return *this;
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    }
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    /// \brief Sets the flow map.
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    ///
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    /// Sets the flow map.
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    /// If you don't use this function before calling \ref run() or
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    /// \ref init(), an instance will be allocated automatically.
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    /// The destructor deallocates this automatically allocated map,
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    /// of course.
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    /// \return <tt>(*this)</tt>
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    Preflow& flowMap(FlowMap& map) {
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      if (_local_flow) {
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        delete _flow;
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        _local_flow = false;
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      }
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      _flow = &map;
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      return *this;
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    }
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    /// \brief Sets the source node.
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    ///
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    /// Sets the source node.
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    /// \return <tt>(*this)</tt>
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    Preflow& source(const Node& node) {
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      _source = node;
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      return *this;
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    }
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    /// \brief Sets the target node.
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    ///
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    /// Sets the target node.
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    /// \return <tt>(*this)</tt>
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    Preflow& target(const Node& node) {
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      _target = node;
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      return *this;
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    }
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    /// \brief Sets the elevator used by algorithm.
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    ///
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    /// Sets the elevator used by algorithm.
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    /// If you don't use this function before calling \ref run() or
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    /// \ref init(), an instance will be allocated automatically.
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    /// The destructor deallocates this automatically allocated elevator,
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    /// of course.
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    /// \return <tt>(*this)</tt>
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    Preflow& elevator(Elevator& elevator) {
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      if (_local_level) {
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        delete _level;
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        _local_level = false;
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      }
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      _level = &elevator;
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      return *this;
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    }
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    /// \brief Returns a const reference to the elevator.
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    ///
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    /// Returns a const reference to the elevator.
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    ///
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    /// \pre Either \ref run() or \ref init() must be called before
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    /// using this function.
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    const Elevator& elevator() {
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      return *_level;
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    }
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    /// \brief Sets the tolerance used by algorithm.
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    ///
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    /// Sets the tolerance used by algorithm.
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    Preflow& tolerance(const Tolerance& tolerance) const {
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      _tolerance = tolerance;
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      return *this;
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    }
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    /// \brief Returns a const reference to the tolerance.
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    ///
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    /// Returns a const reference to the tolerance.
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    const Tolerance& tolerance() const {
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      return tolerance;
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    }
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    /// \name Execution Control
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    /// The simplest way to execute the preflow algorithm is to use
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    /// \ref run() or \ref runMinCut().\n
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    /// If you need more control on the initial solution or the execution,
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    /// first you have to call one of the \ref init() functions, then
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    /// \ref startFirstPhase() and if you need it \ref startSecondPhase().
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    ///@{
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    /// \brief Initializes the internal data structures.
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    ///
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    /// Initializes the internal data structures and sets the initial
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    /// flow to zero on each arc.
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    void init() {
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      createStructures();
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      _phase = true;
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      for (NodeIt n(_graph); n != INVALID; ++n) {
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        _excess->set(n, 0);
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      }
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      for (ArcIt e(_graph); e != INVALID; ++e) {
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        _flow->set(e, 0);
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      }
alpar@404
   412
alpar@404
   413
      typename Digraph::template NodeMap<bool> reached(_graph, false);
alpar@404
   414
alpar@404
   415
      _level->initStart();
alpar@404
   416
      _level->initAddItem(_target);
alpar@404
   417
alpar@404
   418
      std::vector<Node> queue;
alpar@404
   419
      reached.set(_source, true);
alpar@404
   420
alpar@404
   421
      queue.push_back(_target);
alpar@404
   422
      reached.set(_target, true);
alpar@404
   423
      while (!queue.empty()) {
alpar@404
   424
        _level->initNewLevel();
alpar@404
   425
        std::vector<Node> nqueue;
alpar@404
   426
        for (int i = 0; i < int(queue.size()); ++i) {
alpar@404
   427
          Node n = queue[i];
alpar@404
   428
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   429
            Node u = _graph.source(e);
alpar@404
   430
            if (!reached[u] && _tolerance.positive((*_capacity)[e])) {
alpar@404
   431
              reached.set(u, true);
alpar@404
   432
              _level->initAddItem(u);
alpar@404
   433
              nqueue.push_back(u);
alpar@404
   434
            }
alpar@404
   435
          }
alpar@404
   436
        }
alpar@404
   437
        queue.swap(nqueue);
alpar@404
   438
      }
alpar@404
   439
      _level->initFinish();
alpar@404
   440
alpar@404
   441
      for (OutArcIt e(_graph, _source); e != INVALID; ++e) {
alpar@404
   442
        if (_tolerance.positive((*_capacity)[e])) {
alpar@404
   443
          Node u = _graph.target(e);
alpar@404
   444
          if ((*_level)[u] == _level->maxLevel()) continue;
alpar@404
   445
          _flow->set(e, (*_capacity)[e]);
alpar@404
   446
          _excess->set(u, (*_excess)[u] + (*_capacity)[e]);
alpar@404
   447
          if (u != _target && !_level->active(u)) {
alpar@404
   448
            _level->activate(u);
alpar@404
   449
          }
alpar@404
   450
        }
alpar@404
   451
      }
alpar@404
   452
    }
alpar@404
   453
kpeter@408
   454
    /// \brief Initializes the internal data structures using the
kpeter@408
   455
    /// given flow map.
alpar@404
   456
    ///
alpar@404
   457
    /// Initializes the internal data structures and sets the initial
alpar@404
   458
    /// flow to the given \c flowMap. The \c flowMap should contain a
kpeter@408
   459
    /// flow or at least a preflow, i.e. at each node excluding the
kpeter@408
   460
    /// source node the incoming flow should greater or equal to the
alpar@404
   461
    /// outgoing flow.
kpeter@408
   462
    /// \return \c false if the given \c flowMap is not a preflow.
alpar@404
   463
    template <typename FlowMap>
kpeter@407
   464
    bool init(const FlowMap& flowMap) {
alpar@404
   465
      createStructures();
alpar@404
   466
alpar@404
   467
      for (ArcIt e(_graph); e != INVALID; ++e) {
alpar@404
   468
        _flow->set(e, flowMap[e]);
alpar@404
   469
      }
alpar@404
   470
alpar@404
   471
      for (NodeIt n(_graph); n != INVALID; ++n) {
alpar@404
   472
        Value excess = 0;
alpar@404
   473
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   474
          excess += (*_flow)[e];
alpar@404
   475
        }
alpar@404
   476
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   477
          excess -= (*_flow)[e];
alpar@404
   478
        }
alpar@404
   479
        if (excess < 0 && n != _source) return false;
alpar@404
   480
        _excess->set(n, excess);
alpar@404
   481
      }
alpar@404
   482
alpar@404
   483
      typename Digraph::template NodeMap<bool> reached(_graph, false);
alpar@404
   484
alpar@404
   485
      _level->initStart();
alpar@404
   486
      _level->initAddItem(_target);
alpar@404
   487
alpar@404
   488
      std::vector<Node> queue;
alpar@404
   489
      reached.set(_source, true);
alpar@404
   490
alpar@404
   491
      queue.push_back(_target);
alpar@404
   492
      reached.set(_target, true);
alpar@404
   493
      while (!queue.empty()) {
alpar@404
   494
        _level->initNewLevel();
alpar@404
   495
        std::vector<Node> nqueue;
alpar@404
   496
        for (int i = 0; i < int(queue.size()); ++i) {
alpar@404
   497
          Node n = queue[i];
alpar@404
   498
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   499
            Node u = _graph.source(e);
alpar@404
   500
            if (!reached[u] &&
alpar@404
   501
                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
alpar@404
   502
              reached.set(u, true);
alpar@404
   503
              _level->initAddItem(u);
alpar@404
   504
              nqueue.push_back(u);
alpar@404
   505
            }
alpar@404
   506
          }
alpar@404
   507
          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   508
            Node v = _graph.target(e);
alpar@404
   509
            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
alpar@404
   510
              reached.set(v, true);
alpar@404
   511
              _level->initAddItem(v);
alpar@404
   512
              nqueue.push_back(v);
alpar@404
   513
            }
alpar@404
   514
          }
alpar@404
   515
        }
alpar@404
   516
        queue.swap(nqueue);
alpar@404
   517
      }
alpar@404
   518
      _level->initFinish();
alpar@404
   519
alpar@404
   520
      for (OutArcIt e(_graph, _source); e != INVALID; ++e) {
alpar@404
   521
        Value rem = (*_capacity)[e] - (*_flow)[e];
alpar@404
   522
        if (_tolerance.positive(rem)) {
alpar@404
   523
          Node u = _graph.target(e);
alpar@404
   524
          if ((*_level)[u] == _level->maxLevel()) continue;
alpar@404
   525
          _flow->set(e, (*_capacity)[e]);
alpar@404
   526
          _excess->set(u, (*_excess)[u] + rem);
alpar@404
   527
          if (u != _target && !_level->active(u)) {
alpar@404
   528
            _level->activate(u);
alpar@404
   529
          }
alpar@404
   530
        }
alpar@404
   531
      }
alpar@404
   532
      for (InArcIt e(_graph, _source); e != INVALID; ++e) {
alpar@404
   533
        Value rem = (*_flow)[e];
alpar@404
   534
        if (_tolerance.positive(rem)) {
alpar@404
   535
          Node v = _graph.source(e);
alpar@404
   536
          if ((*_level)[v] == _level->maxLevel()) continue;
alpar@404
   537
          _flow->set(e, 0);
alpar@404
   538
          _excess->set(v, (*_excess)[v] + rem);
alpar@404
   539
          if (v != _target && !_level->active(v)) {
alpar@404
   540
            _level->activate(v);
alpar@404
   541
          }
alpar@404
   542
        }
alpar@404
   543
      }
alpar@404
   544
      return true;
alpar@404
   545
    }
alpar@404
   546
alpar@404
   547
    /// \brief Starts the first phase of the preflow algorithm.
alpar@404
   548
    ///
alpar@404
   549
    /// The preflow algorithm consists of two phases, this method runs
alpar@404
   550
    /// the first phase. After the first phase the maximum flow value
alpar@404
   551
    /// and a minimum value cut can already be computed, although a
alpar@404
   552
    /// maximum flow is not yet obtained. So after calling this method
alpar@404
   553
    /// \ref flowValue() returns the value of a maximum flow and \ref
alpar@404
   554
    /// minCut() returns a minimum cut.
kpeter@408
   555
    /// \pre One of the \ref init() functions must be called before
kpeter@408
   556
    /// using this function.
alpar@404
   557
    void startFirstPhase() {
alpar@404
   558
      _phase = true;
alpar@404
   559
alpar@404
   560
      Node n = _level->highestActive();
alpar@404
   561
      int level = _level->highestActiveLevel();
alpar@404
   562
      while (n != INVALID) {
alpar@404
   563
        int num = _node_num;
alpar@404
   564
alpar@404
   565
        while (num > 0 && n != INVALID) {
alpar@404
   566
          Value excess = (*_excess)[n];
alpar@404
   567
          int new_level = _level->maxLevel();
alpar@404
   568
alpar@404
   569
          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   570
            Value rem = (*_capacity)[e] - (*_flow)[e];
alpar@404
   571
            if (!_tolerance.positive(rem)) continue;
alpar@404
   572
            Node v = _graph.target(e);
alpar@404
   573
            if ((*_level)[v] < level) {
alpar@404
   574
              if (!_level->active(v) && v != _target) {
alpar@404
   575
                _level->activate(v);
alpar@404
   576
              }
alpar@404
   577
              if (!_tolerance.less(rem, excess)) {
alpar@404
   578
                _flow->set(e, (*_flow)[e] + excess);
alpar@404
   579
                _excess->set(v, (*_excess)[v] + excess);
alpar@404
   580
                excess = 0;
alpar@404
   581
                goto no_more_push_1;
alpar@404
   582
              } else {
alpar@404
   583
                excess -= rem;
alpar@404
   584
                _excess->set(v, (*_excess)[v] + rem);
alpar@404
   585
                _flow->set(e, (*_capacity)[e]);
alpar@404
   586
              }
alpar@404
   587
            } else if (new_level > (*_level)[v]) {
alpar@404
   588
              new_level = (*_level)[v];
alpar@404
   589
            }
alpar@404
   590
          }
alpar@404
   591
alpar@404
   592
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   593
            Value rem = (*_flow)[e];
alpar@404
   594
            if (!_tolerance.positive(rem)) continue;
alpar@404
   595
            Node v = _graph.source(e);
alpar@404
   596
            if ((*_level)[v] < level) {
alpar@404
   597
              if (!_level->active(v) && v != _target) {
alpar@404
   598
                _level->activate(v);
alpar@404
   599
              }
alpar@404
   600
              if (!_tolerance.less(rem, excess)) {
alpar@404
   601
                _flow->set(e, (*_flow)[e] - excess);
alpar@404
   602
                _excess->set(v, (*_excess)[v] + excess);
alpar@404
   603
                excess = 0;
alpar@404
   604
                goto no_more_push_1;
alpar@404
   605
              } else {
alpar@404
   606
                excess -= rem;
alpar@404
   607
                _excess->set(v, (*_excess)[v] + rem);
alpar@404
   608
                _flow->set(e, 0);
alpar@404
   609
              }
alpar@404
   610
            } else if (new_level > (*_level)[v]) {
alpar@404
   611
              new_level = (*_level)[v];
alpar@404
   612
            }
alpar@404
   613
          }
alpar@404
   614
alpar@404
   615
        no_more_push_1:
alpar@404
   616
alpar@404
   617
          _excess->set(n, excess);
alpar@404
   618
alpar@404
   619
          if (excess != 0) {
alpar@404
   620
            if (new_level + 1 < _level->maxLevel()) {
alpar@404
   621
              _level->liftHighestActive(new_level + 1);
alpar@404
   622
            } else {
alpar@404
   623
              _level->liftHighestActiveToTop();
alpar@404
   624
            }
alpar@404
   625
            if (_level->emptyLevel(level)) {
alpar@404
   626
              _level->liftToTop(level);
alpar@404
   627
            }
alpar@404
   628
          } else {
alpar@404
   629
            _level->deactivate(n);
alpar@404
   630
          }
alpar@404
   631
alpar@404
   632
          n = _level->highestActive();
alpar@404
   633
          level = _level->highestActiveLevel();
alpar@404
   634
          --num;
alpar@404
   635
        }
alpar@404
   636
alpar@404
   637
        num = _node_num * 20;
alpar@404
   638
        while (num > 0 && n != INVALID) {
alpar@404
   639
          Value excess = (*_excess)[n];
alpar@404
   640
          int new_level = _level->maxLevel();
alpar@404
   641
alpar@404
   642
          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   643
            Value rem = (*_capacity)[e] - (*_flow)[e];
alpar@404
   644
            if (!_tolerance.positive(rem)) continue;
alpar@404
   645
            Node v = _graph.target(e);
alpar@404
   646
            if ((*_level)[v] < level) {
alpar@404
   647
              if (!_level->active(v) && v != _target) {
alpar@404
   648
                _level->activate(v);
alpar@404
   649
              }
alpar@404
   650
              if (!_tolerance.less(rem, excess)) {
alpar@404
   651
                _flow->set(e, (*_flow)[e] + excess);
alpar@404
   652
                _excess->set(v, (*_excess)[v] + excess);
alpar@404
   653
                excess = 0;
alpar@404
   654
                goto no_more_push_2;
alpar@404
   655
              } else {
alpar@404
   656
                excess -= rem;
alpar@404
   657
                _excess->set(v, (*_excess)[v] + rem);
alpar@404
   658
                _flow->set(e, (*_capacity)[e]);
alpar@404
   659
              }
alpar@404
   660
            } else if (new_level > (*_level)[v]) {
alpar@404
   661
              new_level = (*_level)[v];
alpar@404
   662
            }
alpar@404
   663
          }
alpar@404
   664
alpar@404
   665
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   666
            Value rem = (*_flow)[e];
alpar@404
   667
            if (!_tolerance.positive(rem)) continue;
alpar@404
   668
            Node v = _graph.source(e);
alpar@404
   669
            if ((*_level)[v] < level) {
alpar@404
   670
              if (!_level->active(v) && v != _target) {
alpar@404
   671
                _level->activate(v);
alpar@404
   672
              }
alpar@404
   673
              if (!_tolerance.less(rem, excess)) {
alpar@404
   674
                _flow->set(e, (*_flow)[e] - excess);
alpar@404
   675
                _excess->set(v, (*_excess)[v] + excess);
alpar@404
   676
                excess = 0;
alpar@404
   677
                goto no_more_push_2;
alpar@404
   678
              } else {
alpar@404
   679
                excess -= rem;
alpar@404
   680
                _excess->set(v, (*_excess)[v] + rem);
alpar@404
   681
                _flow->set(e, 0);
alpar@404
   682
              }
alpar@404
   683
            } else if (new_level > (*_level)[v]) {
alpar@404
   684
              new_level = (*_level)[v];
alpar@404
   685
            }
alpar@404
   686
          }
alpar@404
   687
alpar@404
   688
        no_more_push_2:
alpar@404
   689
alpar@404
   690
          _excess->set(n, excess);
alpar@404
   691
alpar@404
   692
          if (excess != 0) {
alpar@404
   693
            if (new_level + 1 < _level->maxLevel()) {
alpar@404
   694
              _level->liftActiveOn(level, new_level + 1);
alpar@404
   695
            } else {
alpar@404
   696
              _level->liftActiveToTop(level);
alpar@404
   697
            }
alpar@404
   698
            if (_level->emptyLevel(level)) {
alpar@404
   699
              _level->liftToTop(level);
alpar@404
   700
            }
alpar@404
   701
          } else {
alpar@404
   702
            _level->deactivate(n);
alpar@404
   703
          }
alpar@404
   704
alpar@404
   705
          while (level >= 0 && _level->activeFree(level)) {
alpar@404
   706
            --level;
alpar@404
   707
          }
alpar@404
   708
          if (level == -1) {
alpar@404
   709
            n = _level->highestActive();
alpar@404
   710
            level = _level->highestActiveLevel();
alpar@404
   711
          } else {
alpar@404
   712
            n = _level->activeOn(level);
alpar@404
   713
          }
alpar@404
   714
          --num;
alpar@404
   715
        }
alpar@404
   716
      }
alpar@404
   717
    }
alpar@404
   718
alpar@404
   719
    /// \brief Starts the second phase of the preflow algorithm.
alpar@404
   720
    ///
alpar@404
   721
    /// The preflow algorithm consists of two phases, this method runs
kpeter@408
   722
    /// the second phase. After calling one of the \ref init() functions
kpeter@408
   723
    /// and \ref startFirstPhase() and then \ref startSecondPhase(),
kpeter@408
   724
    /// \ref flowMap() returns a maximum flow, \ref flowValue() returns the
alpar@404
   725
    /// value of a maximum flow, \ref minCut() returns a minimum cut
kpeter@408
   726
    /// \pre One of the \ref init() functions and \ref startFirstPhase()
kpeter@408
   727
    /// must be called before using this function.
alpar@404
   728
    void startSecondPhase() {
alpar@404
   729
      _phase = false;
alpar@404
   730
alpar@404
   731
      typename Digraph::template NodeMap<bool> reached(_graph);
alpar@404
   732
      for (NodeIt n(_graph); n != INVALID; ++n) {
alpar@404
   733
        reached.set(n, (*_level)[n] < _level->maxLevel());
alpar@404
   734
      }
alpar@404
   735
alpar@404
   736
      _level->initStart();
alpar@404
   737
      _level->initAddItem(_source);
alpar@404
   738
alpar@404
   739
      std::vector<Node> queue;
alpar@404
   740
      queue.push_back(_source);
alpar@404
   741
      reached.set(_source, true);
alpar@404
   742
alpar@404
   743
      while (!queue.empty()) {
alpar@404
   744
        _level->initNewLevel();
alpar@404
   745
        std::vector<Node> nqueue;
alpar@404
   746
        for (int i = 0; i < int(queue.size()); ++i) {
alpar@404
   747
          Node n = queue[i];
alpar@404
   748
          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   749
            Node v = _graph.target(e);
alpar@404
   750
            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
alpar@404
   751
              reached.set(v, true);
alpar@404
   752
              _level->initAddItem(v);
alpar@404
   753
              nqueue.push_back(v);
alpar@404
   754
            }
alpar@404
   755
          }
alpar@404
   756
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   757
            Node u = _graph.source(e);
alpar@404
   758
            if (!reached[u] &&
alpar@404
   759
                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
alpar@404
   760
              reached.set(u, true);
alpar@404
   761
              _level->initAddItem(u);
alpar@404
   762
              nqueue.push_back(u);
alpar@404
   763
            }
alpar@404
   764
          }
alpar@404
   765
        }
alpar@404
   766
        queue.swap(nqueue);
alpar@404
   767
      }
alpar@404
   768
      _level->initFinish();
alpar@404
   769
alpar@404
   770
      for (NodeIt n(_graph); n != INVALID; ++n) {
alpar@404
   771
        if (!reached[n]) {
alpar@404
   772
          _level->dirtyTopButOne(n);
alpar@404
   773
        } else if ((*_excess)[n] > 0 && _target != n) {
alpar@404
   774
          _level->activate(n);
alpar@404
   775
        }
alpar@404
   776
      }
alpar@404
   777
alpar@404
   778
      Node n;
alpar@404
   779
      while ((n = _level->highestActive()) != INVALID) {
alpar@404
   780
        Value excess = (*_excess)[n];
alpar@404
   781
        int level = _level->highestActiveLevel();
alpar@404
   782
        int new_level = _level->maxLevel();
alpar@404
   783
alpar@404
   784
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   785
          Value rem = (*_capacity)[e] - (*_flow)[e];
alpar@404
   786
          if (!_tolerance.positive(rem)) continue;
alpar@404
   787
          Node v = _graph.target(e);
alpar@404
   788
          if ((*_level)[v] < level) {
alpar@404
   789
            if (!_level->active(v) && v != _source) {
alpar@404
   790
              _level->activate(v);
alpar@404
   791
            }
alpar@404
   792
            if (!_tolerance.less(rem, excess)) {
alpar@404
   793
              _flow->set(e, (*_flow)[e] + excess);
alpar@404
   794
              _excess->set(v, (*_excess)[v] + excess);
alpar@404
   795
              excess = 0;
alpar@404
   796
              goto no_more_push;
alpar@404
   797
            } else {
alpar@404
   798
              excess -= rem;
alpar@404
   799
              _excess->set(v, (*_excess)[v] + rem);
alpar@404
   800
              _flow->set(e, (*_capacity)[e]);
alpar@404
   801
            }
alpar@404
   802
          } else if (new_level > (*_level)[v]) {
alpar@404
   803
            new_level = (*_level)[v];
alpar@404
   804
          }
alpar@404
   805
        }
alpar@404
   806
alpar@404
   807
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@404
   808
          Value rem = (*_flow)[e];
alpar@404
   809
          if (!_tolerance.positive(rem)) continue;
alpar@404
   810
          Node v = _graph.source(e);
alpar@404
   811
          if ((*_level)[v] < level) {
alpar@404
   812
            if (!_level->active(v) && v != _source) {
alpar@404
   813
              _level->activate(v);
alpar@404
   814
            }
alpar@404
   815
            if (!_tolerance.less(rem, excess)) {
alpar@404
   816
              _flow->set(e, (*_flow)[e] - excess);
alpar@404
   817
              _excess->set(v, (*_excess)[v] + excess);
alpar@404
   818
              excess = 0;
alpar@404
   819
              goto no_more_push;
alpar@404
   820
            } else {
alpar@404
   821
              excess -= rem;
alpar@404
   822
              _excess->set(v, (*_excess)[v] + rem);
alpar@404
   823
              _flow->set(e, 0);
alpar@404
   824
            }
alpar@404
   825
          } else if (new_level > (*_level)[v]) {
alpar@404
   826
            new_level = (*_level)[v];
alpar@404
   827
          }
alpar@404
   828
        }
alpar@404
   829
alpar@404
   830
      no_more_push:
alpar@404
   831
alpar@404
   832
        _excess->set(n, excess);
alpar@404
   833
alpar@404
   834
        if (excess != 0) {
alpar@404
   835
          if (new_level + 1 < _level->maxLevel()) {
alpar@404
   836
            _level->liftHighestActive(new_level + 1);
alpar@404
   837
          } else {
alpar@404
   838
            // Calculation error
alpar@404
   839
            _level->liftHighestActiveToTop();
alpar@404
   840
          }
alpar@404
   841
          if (_level->emptyLevel(level)) {
alpar@404
   842
            // Calculation error
alpar@404
   843
            _level->liftToTop(level);
alpar@404
   844
          }
alpar@404
   845
        } else {
alpar@404
   846
          _level->deactivate(n);
alpar@404
   847
        }
alpar@404
   848
alpar@404
   849
      }
alpar@404
   850
    }
alpar@404
   851
alpar@404
   852
    /// \brief Runs the preflow algorithm.
alpar@404
   853
    ///
alpar@404
   854
    /// Runs the preflow algorithm.
alpar@404
   855
    /// \note pf.run() is just a shortcut of the following code.
alpar@404
   856
    /// \code
alpar@404
   857
    ///   pf.init();
alpar@404
   858
    ///   pf.startFirstPhase();
alpar@404
   859
    ///   pf.startSecondPhase();
alpar@404
   860
    /// \endcode
alpar@404
   861
    void run() {
alpar@404
   862
      init();
alpar@404
   863
      startFirstPhase();
alpar@404
   864
      startSecondPhase();
alpar@404
   865
    }
alpar@404
   866
alpar@404
   867
    /// \brief Runs the preflow algorithm to compute the minimum cut.
alpar@404
   868
    ///
alpar@404
   869
    /// Runs the preflow algorithm to compute the minimum cut.
alpar@404
   870
    /// \note pf.runMinCut() is just a shortcut of the following code.
alpar@404
   871
    /// \code
alpar@404
   872
    ///   pf.init();
alpar@404
   873
    ///   pf.startFirstPhase();
alpar@404
   874
    /// \endcode
alpar@404
   875
    void runMinCut() {
alpar@404
   876
      init();
alpar@404
   877
      startFirstPhase();
alpar@404
   878
    }
alpar@404
   879
alpar@404
   880
    /// @}
alpar@404
   881
alpar@404
   882
    /// \name Query Functions
kpeter@408
   883
    /// The results of the preflow algorithm can be obtained using these
alpar@404
   884
    /// functions.\n
kpeter@408
   885
    /// Either one of the \ref run() "run*()" functions or one of the
kpeter@408
   886
    /// \ref startFirstPhase() "start*()" functions should be called
kpeter@408
   887
    /// before using them.
alpar@404
   888
alpar@404
   889
    ///@{
alpar@404
   890
alpar@404
   891
    /// \brief Returns the value of the maximum flow.
alpar@404
   892
    ///
alpar@404
   893
    /// Returns the value of the maximum flow by returning the excess
kpeter@408
   894
    /// of the target node. This value equals to the value of
kpeter@408
   895
    /// the maximum flow already after the first phase of the algorithm.
kpeter@408
   896
    ///
kpeter@408
   897
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@408
   898
    /// using this function.
alpar@404
   899
    Value flowValue() const {
alpar@404
   900
      return (*_excess)[_target];
alpar@404
   901
    }
alpar@404
   902
kpeter@408
   903
    /// \brief Returns the flow on the given arc.
alpar@404
   904
    ///
kpeter@408
   905
    /// Returns the flow on the given arc. This method can
kpeter@408
   906
    /// be called after the second phase of the algorithm.
kpeter@408
   907
    ///
kpeter@408
   908
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@408
   909
    /// using this function.
kpeter@408
   910
    Value flow(const Arc& arc) const {
kpeter@408
   911
      return (*_flow)[arc];
kpeter@408
   912
    }
kpeter@408
   913
kpeter@408
   914
    /// \brief Returns a const reference to the flow map.
kpeter@408
   915
    ///
kpeter@408
   916
    /// Returns a const reference to the arc map storing the found flow.
kpeter@408
   917
    /// This method can be called after the second phase of the algorithm.
kpeter@408
   918
    ///
kpeter@408
   919
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@408
   920
    /// using this function.
kpeter@408
   921
    const FlowMap& flowMap() {
kpeter@408
   922
      return *_flow;
kpeter@408
   923
    }
kpeter@408
   924
kpeter@408
   925
    /// \brief Returns \c true when the node is on the source side of the
kpeter@408
   926
    /// minimum cut.
kpeter@408
   927
    ///
kpeter@408
   928
    /// Returns true when the node is on the source side of the found
kpeter@408
   929
    /// minimum cut. This method can be called both after running \ref
alpar@404
   930
    /// startFirstPhase() and \ref startSecondPhase().
kpeter@408
   931
    ///
kpeter@408
   932
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@408
   933
    /// using this function.
alpar@404
   934
    bool minCut(const Node& node) const {
alpar@404
   935
      return ((*_level)[node] == _level->maxLevel()) == _phase;
alpar@404
   936
    }
alpar@404
   937
kpeter@408
   938
    /// \brief Gives back a minimum value cut.
alpar@404
   939
    ///
kpeter@408
   940
    /// Sets \c cutMap to the characteristic vector of a minimum value
kpeter@408
   941
    /// cut. \c cutMap should be a \ref concepts::WriteMap "writable"
kpeter@408
   942
    /// node map with \c bool (or convertible) value type.
kpeter@408
   943
    ///
kpeter@408
   944
    /// This method can be called both after running \ref startFirstPhase()
kpeter@408
   945
    /// and \ref startSecondPhase(). The result after the second phase
kpeter@408
   946
    /// could be slightly different if inexact computation is used.
kpeter@408
   947
    ///
kpeter@408
   948
    /// \note This function calls \ref minCut() for each node, so it runs in
kpeter@408
   949
    /// \f$O(n)\f$ time.
kpeter@408
   950
    ///
kpeter@408
   951
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@408
   952
    /// using this function.
alpar@404
   953
    template <typename CutMap>
alpar@404
   954
    void minCutMap(CutMap& cutMap) const {
alpar@404
   955
      for (NodeIt n(_graph); n != INVALID; ++n) {
alpar@404
   956
        cutMap.set(n, minCut(n));
alpar@404
   957
      }
alpar@404
   958
    }
alpar@404
   959
alpar@404
   960
    /// @}
alpar@404
   961
  };
alpar@404
   962
}
alpar@404
   963
alpar@404
   964
#endif