lemon/preflow.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 20 Feb 2010 18:39:03 +0100
changeset 839 f3bc4e9b5f3a
parent 788 c92296660262
child 825 75e6020b19b1
permissions -rw-r--r--
New heuristics for MCF algorithms (#340)
and some implementation improvements.

- A useful heuristic is added to NetworkSimplex to make the
initial pivots faster.
- A powerful global update heuristic is added to CostScaling
and the implementation is reworked with various improvements.
- Better relabeling in CostScaling to improve numerical stability
and make the code faster.
- A small improvement is made in CapacityScaling for better
delta computation.
- Add notes to the classes about the usage of vector<char> instead
of vector<bool> for efficiency reasons.
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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) 2003-2009
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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 GR Digraph type.
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  /// \tparam CAP Capacity map type.
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  template <typename GR, typename CAP>
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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 GR 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 CAP 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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#ifdef DOXYGEN
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    typedef GR::ArcMap<Value> FlowMap;
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#else
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    typedef typename Digraph::template ArcMap<Value> FlowMap;
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#endif
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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 for 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, LinkedElevator
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#ifdef DOXYGEN
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    typedef lemon::Elevator<GR, GR::Node> Elevator;
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#else
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    typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator;
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#endif
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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 for 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 \ref max_flow
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  /// "flow of maximum value" in a digraph \ref clrs01algorithms,
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  /// \ref amo93networkflows, \ref goldberg88newapproach.
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  /// The preflow algorithms are the fastest known maximum
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  /// flow algorithms. The current implementation uses 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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  /// \warning This implementation cannot handle infinite or very large
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  /// capacities (e.g. the maximum value of \c CAP::Value).
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  ///
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  /// \tparam GR The type of the digraph the algorithm runs on.
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  /// \tparam CAP The type of the capacity map. The default map
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  /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
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#ifdef DOXYGEN
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  template <typename GR, typename CAP, typename TR>
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#else
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  template <typename GR,
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            typename CAP = typename GR::template ArcMap<int>,
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            typename TR = PreflowDefaultTraits<GR, CAP> >
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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 TR 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 T>
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    struct SetFlowMapTraits : public Traits {
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      typedef T 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 T>
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    struct SetFlowMap
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      : public Preflow<Digraph, CapacityMap, SetFlowMapTraits<T> > {
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      typedef Preflow<Digraph, CapacityMap,
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                      SetFlowMapTraits<T> > Create;
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    };
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    template <typename T>
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    struct SetElevatorTraits : public Traits {
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      typedef T 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 T>
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    struct SetElevator
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      : public Preflow<Digraph, CapacityMap, SetElevatorTraits<T> > {
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      typedef Preflow<Digraph, CapacityMap,
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                      SetElevatorTraits<T> > Create;
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    };
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    template <typename T>
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    struct SetStandardElevatorTraits : public Traits {
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      typedef T 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 T>
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    struct SetStandardElevator
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      : public Preflow<Digraph, CapacityMap,
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                       SetStandardElevatorTraits<T> > {
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      typedef Preflow<Digraph, CapacityMap,
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                      SetStandardElevatorTraits<T> > 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() const {
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      return *_level;
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    }
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    /// \brief Sets the tolerance used by the algorithm.
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    ///
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    /// Sets the tolerance object used by the algorithm.
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    /// \return <tt>(*this)</tt>
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    Preflow& tolerance(const Tolerance& tolerance) {
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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 object used by
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    /// the algorithm.
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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 better control on the initial solution or the execution,
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    /// you have to call one of the \ref init() functions first, then
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   407
    /// \ref startFirstPhase() and if you need it \ref startSecondPhase().
alpar@389
   408
alpar@389
   409
    ///@{
alpar@389
   410
alpar@389
   411
    /// \brief Initializes the internal data structures.
alpar@389
   412
    ///
kpeter@393
   413
    /// Initializes the internal data structures and sets the initial
kpeter@393
   414
    /// flow to zero on each arc.
alpar@389
   415
    void init() {
alpar@389
   416
      createStructures();
alpar@389
   417
alpar@389
   418
      _phase = true;
alpar@389
   419
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581
   420
        (*_excess)[n] = 0;
alpar@389
   421
      }
alpar@389
   422
alpar@389
   423
      for (ArcIt e(_graph); e != INVALID; ++e) {
alpar@389
   424
        _flow->set(e, 0);
alpar@389
   425
      }
alpar@389
   426
alpar@389
   427
      typename Digraph::template NodeMap<bool> reached(_graph, false);
alpar@389
   428
alpar@389
   429
      _level->initStart();
alpar@389
   430
      _level->initAddItem(_target);
alpar@389
   431
alpar@389
   432
      std::vector<Node> queue;
kpeter@581
   433
      reached[_source] = true;
alpar@389
   434
alpar@389
   435
      queue.push_back(_target);
kpeter@581
   436
      reached[_target] = true;
alpar@389
   437
      while (!queue.empty()) {
alpar@389
   438
        _level->initNewLevel();
alpar@389
   439
        std::vector<Node> nqueue;
alpar@389
   440
        for (int i = 0; i < int(queue.size()); ++i) {
alpar@389
   441
          Node n = queue[i];
alpar@389
   442
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@389
   443
            Node u = _graph.source(e);
alpar@389
   444
            if (!reached[u] && _tolerance.positive((*_capacity)[e])) {
kpeter@581
   445
              reached[u] = true;
alpar@389
   446
              _level->initAddItem(u);
alpar@389
   447
              nqueue.push_back(u);
alpar@389
   448
            }
alpar@389
   449
          }
alpar@389
   450
        }
alpar@389
   451
        queue.swap(nqueue);
alpar@389
   452
      }
alpar@389
   453
      _level->initFinish();
alpar@389
   454
alpar@389
   455
      for (OutArcIt e(_graph, _source); e != INVALID; ++e) {
alpar@389
   456
        if (_tolerance.positive((*_capacity)[e])) {
alpar@389
   457
          Node u = _graph.target(e);
alpar@389
   458
          if ((*_level)[u] == _level->maxLevel()) continue;
alpar@389
   459
          _flow->set(e, (*_capacity)[e]);
kpeter@581
   460
          (*_excess)[u] += (*_capacity)[e];
alpar@389
   461
          if (u != _target && !_level->active(u)) {
alpar@389
   462
            _level->activate(u);
alpar@389
   463
          }
alpar@389
   464
        }
alpar@389
   465
      }
alpar@389
   466
    }
alpar@389
   467
kpeter@393
   468
    /// \brief Initializes the internal data structures using the
kpeter@393
   469
    /// given flow map.
alpar@389
   470
    ///
alpar@389
   471
    /// Initializes the internal data structures and sets the initial
alpar@389
   472
    /// flow to the given \c flowMap. The \c flowMap should contain a
kpeter@393
   473
    /// flow or at least a preflow, i.e. at each node excluding the
kpeter@393
   474
    /// source node the incoming flow should greater or equal to the
alpar@389
   475
    /// outgoing flow.
kpeter@393
   476
    /// \return \c false if the given \c flowMap is not a preflow.
alpar@389
   477
    template <typename FlowMap>
kpeter@392
   478
    bool init(const FlowMap& flowMap) {
alpar@389
   479
      createStructures();
alpar@389
   480
alpar@389
   481
      for (ArcIt e(_graph); e != INVALID; ++e) {
alpar@389
   482
        _flow->set(e, flowMap[e]);
alpar@389
   483
      }
alpar@389
   484
alpar@389
   485
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@641
   486
        Value excess = 0;
alpar@389
   487
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@389
   488
          excess += (*_flow)[e];
alpar@389
   489
        }
alpar@389
   490
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@389
   491
          excess -= (*_flow)[e];
alpar@389
   492
        }
alpar@389
   493
        if (excess < 0 && n != _source) return false;
kpeter@581
   494
        (*_excess)[n] = excess;
alpar@389
   495
      }
alpar@389
   496
alpar@389
   497
      typename Digraph::template NodeMap<bool> reached(_graph, false);
alpar@389
   498
alpar@389
   499
      _level->initStart();
alpar@389
   500
      _level->initAddItem(_target);
alpar@389
   501
alpar@389
   502
      std::vector<Node> queue;
kpeter@581
   503
      reached[_source] = true;
alpar@389
   504
alpar@389
   505
      queue.push_back(_target);
kpeter@581
   506
      reached[_target] = true;
alpar@389
   507
      while (!queue.empty()) {
alpar@389
   508
        _level->initNewLevel();
alpar@389
   509
        std::vector<Node> nqueue;
alpar@389
   510
        for (int i = 0; i < int(queue.size()); ++i) {
alpar@389
   511
          Node n = queue[i];
alpar@389
   512
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@389
   513
            Node u = _graph.source(e);
alpar@389
   514
            if (!reached[u] &&
alpar@389
   515
                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
kpeter@581
   516
              reached[u] = true;
alpar@389
   517
              _level->initAddItem(u);
alpar@389
   518
              nqueue.push_back(u);
alpar@389
   519
            }
alpar@389
   520
          }
alpar@389
   521
          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@389
   522
            Node v = _graph.target(e);
alpar@389
   523
            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
kpeter@581
   524
              reached[v] = true;
alpar@389
   525
              _level->initAddItem(v);
alpar@389
   526
              nqueue.push_back(v);
alpar@389
   527
            }
alpar@389
   528
          }
alpar@389
   529
        }
alpar@389
   530
        queue.swap(nqueue);
alpar@389
   531
      }
alpar@389
   532
      _level->initFinish();
alpar@389
   533
alpar@389
   534
      for (OutArcIt e(_graph, _source); e != INVALID; ++e) {
kpeter@641
   535
        Value rem = (*_capacity)[e] - (*_flow)[e];
alpar@389
   536
        if (_tolerance.positive(rem)) {
alpar@389
   537
          Node u = _graph.target(e);
alpar@389
   538
          if ((*_level)[u] == _level->maxLevel()) continue;
alpar@389
   539
          _flow->set(e, (*_capacity)[e]);
kpeter@581
   540
          (*_excess)[u] += rem;
alpar@389
   541
          if (u != _target && !_level->active(u)) {
alpar@389
   542
            _level->activate(u);
alpar@389
   543
          }
alpar@389
   544
        }
alpar@389
   545
      }
alpar@389
   546
      for (InArcIt e(_graph, _source); e != INVALID; ++e) {
kpeter@641
   547
        Value rem = (*_flow)[e];
alpar@389
   548
        if (_tolerance.positive(rem)) {
alpar@389
   549
          Node v = _graph.source(e);
alpar@389
   550
          if ((*_level)[v] == _level->maxLevel()) continue;
alpar@389
   551
          _flow->set(e, 0);
kpeter@581
   552
          (*_excess)[v] += rem;
alpar@389
   553
          if (v != _target && !_level->active(v)) {
alpar@389
   554
            _level->activate(v);
alpar@389
   555
          }
alpar@389
   556
        }
alpar@389
   557
      }
alpar@389
   558
      return true;
alpar@389
   559
    }
alpar@389
   560
alpar@389
   561
    /// \brief Starts the first phase of the preflow algorithm.
alpar@389
   562
    ///
alpar@389
   563
    /// The preflow algorithm consists of two phases, this method runs
alpar@389
   564
    /// the first phase. After the first phase the maximum flow value
alpar@389
   565
    /// and a minimum value cut can already be computed, although a
alpar@389
   566
    /// maximum flow is not yet obtained. So after calling this method
alpar@389
   567
    /// \ref flowValue() returns the value of a maximum flow and \ref
alpar@389
   568
    /// minCut() returns a minimum cut.
kpeter@393
   569
    /// \pre One of the \ref init() functions must be called before
kpeter@393
   570
    /// using this function.
alpar@389
   571
    void startFirstPhase() {
alpar@389
   572
      _phase = true;
alpar@389
   573
alpar@389
   574
      Node n = _level->highestActive();
alpar@389
   575
      int level = _level->highestActiveLevel();
alpar@389
   576
      while (n != INVALID) {
alpar@389
   577
        int num = _node_num;
alpar@389
   578
alpar@389
   579
        while (num > 0 && n != INVALID) {
kpeter@641
   580
          Value excess = (*_excess)[n];
alpar@389
   581
          int new_level = _level->maxLevel();
alpar@389
   582
alpar@389
   583
          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
kpeter@641
   584
            Value rem = (*_capacity)[e] - (*_flow)[e];
alpar@389
   585
            if (!_tolerance.positive(rem)) continue;
alpar@389
   586
            Node v = _graph.target(e);
alpar@389
   587
            if ((*_level)[v] < level) {
alpar@389
   588
              if (!_level->active(v) && v != _target) {
alpar@389
   589
                _level->activate(v);
alpar@389
   590
              }
alpar@389
   591
              if (!_tolerance.less(rem, excess)) {
alpar@389
   592
                _flow->set(e, (*_flow)[e] + excess);
kpeter@581
   593
                (*_excess)[v] += excess;
alpar@389
   594
                excess = 0;
alpar@389
   595
                goto no_more_push_1;
alpar@389
   596
              } else {
alpar@389
   597
                excess -= rem;
kpeter@581
   598
                (*_excess)[v] += rem;
alpar@389
   599
                _flow->set(e, (*_capacity)[e]);
alpar@389
   600
              }
alpar@389
   601
            } else if (new_level > (*_level)[v]) {
alpar@389
   602
              new_level = (*_level)[v];
alpar@389
   603
            }
alpar@389
   604
          }
alpar@389
   605
alpar@389
   606
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
kpeter@641
   607
            Value rem = (*_flow)[e];
alpar@389
   608
            if (!_tolerance.positive(rem)) continue;
alpar@389
   609
            Node v = _graph.source(e);
alpar@389
   610
            if ((*_level)[v] < level) {
alpar@389
   611
              if (!_level->active(v) && v != _target) {
alpar@389
   612
                _level->activate(v);
alpar@389
   613
              }
alpar@389
   614
              if (!_tolerance.less(rem, excess)) {
alpar@389
   615
                _flow->set(e, (*_flow)[e] - excess);
kpeter@581
   616
                (*_excess)[v] += excess;
alpar@389
   617
                excess = 0;
alpar@389
   618
                goto no_more_push_1;
alpar@389
   619
              } else {
alpar@389
   620
                excess -= rem;
kpeter@581
   621
                (*_excess)[v] += rem;
alpar@389
   622
                _flow->set(e, 0);
alpar@389
   623
              }
alpar@389
   624
            } else if (new_level > (*_level)[v]) {
alpar@389
   625
              new_level = (*_level)[v];
alpar@389
   626
            }
alpar@389
   627
          }
alpar@389
   628
alpar@389
   629
        no_more_push_1:
alpar@389
   630
kpeter@581
   631
          (*_excess)[n] = excess;
alpar@389
   632
alpar@389
   633
          if (excess != 0) {
alpar@389
   634
            if (new_level + 1 < _level->maxLevel()) {
alpar@389
   635
              _level->liftHighestActive(new_level + 1);
alpar@389
   636
            } else {
alpar@389
   637
              _level->liftHighestActiveToTop();
alpar@389
   638
            }
alpar@389
   639
            if (_level->emptyLevel(level)) {
alpar@389
   640
              _level->liftToTop(level);
alpar@389
   641
            }
alpar@389
   642
          } else {
alpar@389
   643
            _level->deactivate(n);
alpar@389
   644
          }
alpar@389
   645
alpar@389
   646
          n = _level->highestActive();
alpar@389
   647
          level = _level->highestActiveLevel();
alpar@389
   648
          --num;
alpar@389
   649
        }
alpar@389
   650
alpar@389
   651
        num = _node_num * 20;
alpar@389
   652
        while (num > 0 && n != INVALID) {
kpeter@641
   653
          Value excess = (*_excess)[n];
alpar@389
   654
          int new_level = _level->maxLevel();
alpar@389
   655
alpar@389
   656
          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
kpeter@641
   657
            Value rem = (*_capacity)[e] - (*_flow)[e];
alpar@389
   658
            if (!_tolerance.positive(rem)) continue;
alpar@389
   659
            Node v = _graph.target(e);
alpar@389
   660
            if ((*_level)[v] < level) {
alpar@389
   661
              if (!_level->active(v) && v != _target) {
alpar@389
   662
                _level->activate(v);
alpar@389
   663
              }
alpar@389
   664
              if (!_tolerance.less(rem, excess)) {
alpar@389
   665
                _flow->set(e, (*_flow)[e] + excess);
kpeter@581
   666
                (*_excess)[v] += excess;
alpar@389
   667
                excess = 0;
alpar@389
   668
                goto no_more_push_2;
alpar@389
   669
              } else {
alpar@389
   670
                excess -= rem;
kpeter@581
   671
                (*_excess)[v] += rem;
alpar@389
   672
                _flow->set(e, (*_capacity)[e]);
alpar@389
   673
              }
alpar@389
   674
            } else if (new_level > (*_level)[v]) {
alpar@389
   675
              new_level = (*_level)[v];
alpar@389
   676
            }
alpar@389
   677
          }
alpar@389
   678
alpar@389
   679
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
kpeter@641
   680
            Value rem = (*_flow)[e];
alpar@389
   681
            if (!_tolerance.positive(rem)) continue;
alpar@389
   682
            Node v = _graph.source(e);
alpar@389
   683
            if ((*_level)[v] < level) {
alpar@389
   684
              if (!_level->active(v) && v != _target) {
alpar@389
   685
                _level->activate(v);
alpar@389
   686
              }
alpar@389
   687
              if (!_tolerance.less(rem, excess)) {
alpar@389
   688
                _flow->set(e, (*_flow)[e] - excess);
kpeter@581
   689
                (*_excess)[v] += excess;
alpar@389
   690
                excess = 0;
alpar@389
   691
                goto no_more_push_2;
alpar@389
   692
              } else {
alpar@389
   693
                excess -= rem;
kpeter@581
   694
                (*_excess)[v] += rem;
alpar@389
   695
                _flow->set(e, 0);
alpar@389
   696
              }
alpar@389
   697
            } else if (new_level > (*_level)[v]) {
alpar@389
   698
              new_level = (*_level)[v];
alpar@389
   699
            }
alpar@389
   700
          }
alpar@389
   701
alpar@389
   702
        no_more_push_2:
alpar@389
   703
kpeter@581
   704
          (*_excess)[n] = excess;
alpar@389
   705
alpar@389
   706
          if (excess != 0) {
alpar@389
   707
            if (new_level + 1 < _level->maxLevel()) {
alpar@389
   708
              _level->liftActiveOn(level, new_level + 1);
alpar@389
   709
            } else {
alpar@389
   710
              _level->liftActiveToTop(level);
alpar@389
   711
            }
alpar@389
   712
            if (_level->emptyLevel(level)) {
alpar@389
   713
              _level->liftToTop(level);
alpar@389
   714
            }
alpar@389
   715
          } else {
alpar@389
   716
            _level->deactivate(n);
alpar@389
   717
          }
alpar@389
   718
alpar@389
   719
          while (level >= 0 && _level->activeFree(level)) {
alpar@389
   720
            --level;
alpar@389
   721
          }
alpar@389
   722
          if (level == -1) {
alpar@389
   723
            n = _level->highestActive();
alpar@389
   724
            level = _level->highestActiveLevel();
alpar@389
   725
          } else {
alpar@389
   726
            n = _level->activeOn(level);
alpar@389
   727
          }
alpar@389
   728
          --num;
alpar@389
   729
        }
alpar@389
   730
      }
alpar@389
   731
    }
alpar@389
   732
alpar@389
   733
    /// \brief Starts the second phase of the preflow algorithm.
alpar@389
   734
    ///
alpar@389
   735
    /// The preflow algorithm consists of two phases, this method runs
kpeter@393
   736
    /// the second phase. After calling one of the \ref init() functions
kpeter@393
   737
    /// and \ref startFirstPhase() and then \ref startSecondPhase(),
kpeter@393
   738
    /// \ref flowMap() returns a maximum flow, \ref flowValue() returns the
alpar@389
   739
    /// value of a maximum flow, \ref minCut() returns a minimum cut
kpeter@393
   740
    /// \pre One of the \ref init() functions and \ref startFirstPhase()
kpeter@393
   741
    /// must be called before using this function.
alpar@389
   742
    void startSecondPhase() {
alpar@389
   743
      _phase = false;
alpar@389
   744
alpar@389
   745
      typename Digraph::template NodeMap<bool> reached(_graph);
alpar@389
   746
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581
   747
        reached[n] = (*_level)[n] < _level->maxLevel();
alpar@389
   748
      }
alpar@389
   749
alpar@389
   750
      _level->initStart();
alpar@389
   751
      _level->initAddItem(_source);
alpar@389
   752
alpar@389
   753
      std::vector<Node> queue;
alpar@389
   754
      queue.push_back(_source);
kpeter@581
   755
      reached[_source] = true;
alpar@389
   756
alpar@389
   757
      while (!queue.empty()) {
alpar@389
   758
        _level->initNewLevel();
alpar@389
   759
        std::vector<Node> nqueue;
alpar@389
   760
        for (int i = 0; i < int(queue.size()); ++i) {
alpar@389
   761
          Node n = queue[i];
alpar@389
   762
          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
alpar@389
   763
            Node v = _graph.target(e);
alpar@389
   764
            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
kpeter@581
   765
              reached[v] = true;
alpar@389
   766
              _level->initAddItem(v);
alpar@389
   767
              nqueue.push_back(v);
alpar@389
   768
            }
alpar@389
   769
          }
alpar@389
   770
          for (InArcIt e(_graph, n); e != INVALID; ++e) {
alpar@389
   771
            Node u = _graph.source(e);
alpar@389
   772
            if (!reached[u] &&
alpar@389
   773
                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
kpeter@581
   774
              reached[u] = true;
alpar@389
   775
              _level->initAddItem(u);
alpar@389
   776
              nqueue.push_back(u);
alpar@389
   777
            }
alpar@389
   778
          }
alpar@389
   779
        }
alpar@389
   780
        queue.swap(nqueue);
alpar@389
   781
      }
alpar@389
   782
      _level->initFinish();
alpar@389
   783
alpar@389
   784
      for (NodeIt n(_graph); n != INVALID; ++n) {
alpar@389
   785
        if (!reached[n]) {
alpar@389
   786
          _level->dirtyTopButOne(n);
alpar@389
   787
        } else if ((*_excess)[n] > 0 && _target != n) {
alpar@389
   788
          _level->activate(n);
alpar@389
   789
        }
alpar@389
   790
      }
alpar@389
   791
alpar@389
   792
      Node n;
alpar@389
   793
      while ((n = _level->highestActive()) != INVALID) {
kpeter@641
   794
        Value excess = (*_excess)[n];
alpar@389
   795
        int level = _level->highestActiveLevel();
alpar@389
   796
        int new_level = _level->maxLevel();
alpar@389
   797
alpar@389
   798
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
kpeter@641
   799
          Value rem = (*_capacity)[e] - (*_flow)[e];
alpar@389
   800
          if (!_tolerance.positive(rem)) continue;
alpar@389
   801
          Node v = _graph.target(e);
alpar@389
   802
          if ((*_level)[v] < level) {
alpar@389
   803
            if (!_level->active(v) && v != _source) {
alpar@389
   804
              _level->activate(v);
alpar@389
   805
            }
alpar@389
   806
            if (!_tolerance.less(rem, excess)) {
alpar@389
   807
              _flow->set(e, (*_flow)[e] + excess);
kpeter@581
   808
              (*_excess)[v] += excess;
alpar@389
   809
              excess = 0;
alpar@389
   810
              goto no_more_push;
alpar@389
   811
            } else {
alpar@389
   812
              excess -= rem;
kpeter@581
   813
              (*_excess)[v] += rem;
alpar@389
   814
              _flow->set(e, (*_capacity)[e]);
alpar@389
   815
            }
alpar@389
   816
          } else if (new_level > (*_level)[v]) {
alpar@389
   817
            new_level = (*_level)[v];
alpar@389
   818
          }
alpar@389
   819
        }
alpar@389
   820
alpar@389
   821
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
kpeter@641
   822
          Value rem = (*_flow)[e];
alpar@389
   823
          if (!_tolerance.positive(rem)) continue;
alpar@389
   824
          Node v = _graph.source(e);
alpar@389
   825
          if ((*_level)[v] < level) {
alpar@389
   826
            if (!_level->active(v) && v != _source) {
alpar@389
   827
              _level->activate(v);
alpar@389
   828
            }
alpar@389
   829
            if (!_tolerance.less(rem, excess)) {
alpar@389
   830
              _flow->set(e, (*_flow)[e] - excess);
kpeter@581
   831
              (*_excess)[v] += excess;
alpar@389
   832
              excess = 0;
alpar@389
   833
              goto no_more_push;
alpar@389
   834
            } else {
alpar@389
   835
              excess -= rem;
kpeter@581
   836
              (*_excess)[v] += rem;
alpar@389
   837
              _flow->set(e, 0);
alpar@389
   838
            }
alpar@389
   839
          } else if (new_level > (*_level)[v]) {
alpar@389
   840
            new_level = (*_level)[v];
alpar@389
   841
          }
alpar@389
   842
        }
alpar@389
   843
alpar@389
   844
      no_more_push:
alpar@389
   845
kpeter@581
   846
        (*_excess)[n] = excess;
alpar@389
   847
alpar@389
   848
        if (excess != 0) {
alpar@389
   849
          if (new_level + 1 < _level->maxLevel()) {
alpar@389
   850
            _level->liftHighestActive(new_level + 1);
alpar@389
   851
          } else {
alpar@389
   852
            // Calculation error
alpar@389
   853
            _level->liftHighestActiveToTop();
alpar@389
   854
          }
alpar@389
   855
          if (_level->emptyLevel(level)) {
alpar@389
   856
            // Calculation error
alpar@389
   857
            _level->liftToTop(level);
alpar@389
   858
          }
alpar@389
   859
        } else {
alpar@389
   860
          _level->deactivate(n);
alpar@389
   861
        }
alpar@389
   862
alpar@389
   863
      }
alpar@389
   864
    }
alpar@389
   865
alpar@389
   866
    /// \brief Runs the preflow algorithm.
alpar@389
   867
    ///
alpar@389
   868
    /// Runs the preflow algorithm.
alpar@389
   869
    /// \note pf.run() is just a shortcut of the following code.
alpar@389
   870
    /// \code
alpar@389
   871
    ///   pf.init();
alpar@389
   872
    ///   pf.startFirstPhase();
alpar@389
   873
    ///   pf.startSecondPhase();
alpar@389
   874
    /// \endcode
alpar@389
   875
    void run() {
alpar@389
   876
      init();
alpar@389
   877
      startFirstPhase();
alpar@389
   878
      startSecondPhase();
alpar@389
   879
    }
alpar@389
   880
alpar@389
   881
    /// \brief Runs the preflow algorithm to compute the minimum cut.
alpar@389
   882
    ///
alpar@389
   883
    /// Runs the preflow algorithm to compute the minimum cut.
alpar@389
   884
    /// \note pf.runMinCut() is just a shortcut of the following code.
alpar@389
   885
    /// \code
alpar@389
   886
    ///   pf.init();
alpar@389
   887
    ///   pf.startFirstPhase();
alpar@389
   888
    /// \endcode
alpar@389
   889
    void runMinCut() {
alpar@389
   890
      init();
alpar@389
   891
      startFirstPhase();
alpar@389
   892
    }
alpar@389
   893
alpar@389
   894
    /// @}
alpar@389
   895
alpar@389
   896
    /// \name Query Functions
kpeter@393
   897
    /// The results of the preflow algorithm can be obtained using these
alpar@389
   898
    /// functions.\n
kpeter@393
   899
    /// Either one of the \ref run() "run*()" functions or one of the
kpeter@393
   900
    /// \ref startFirstPhase() "start*()" functions should be called
kpeter@393
   901
    /// before using them.
alpar@389
   902
alpar@389
   903
    ///@{
alpar@389
   904
alpar@389
   905
    /// \brief Returns the value of the maximum flow.
alpar@389
   906
    ///
alpar@389
   907
    /// Returns the value of the maximum flow by returning the excess
kpeter@393
   908
    /// of the target node. This value equals to the value of
kpeter@393
   909
    /// the maximum flow already after the first phase of the algorithm.
kpeter@393
   910
    ///
kpeter@393
   911
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@393
   912
    /// using this function.
kpeter@641
   913
    Value flowValue() const {
alpar@389
   914
      return (*_excess)[_target];
alpar@389
   915
    }
alpar@389
   916
kpeter@641
   917
    /// \brief Returns the flow value on the given arc.
alpar@389
   918
    ///
kpeter@641
   919
    /// Returns the flow value on the given arc. This method can
kpeter@393
   920
    /// be called after the second phase of the algorithm.
kpeter@393
   921
    ///
kpeter@393
   922
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@393
   923
    /// using this function.
kpeter@641
   924
    Value flow(const Arc& arc) const {
kpeter@393
   925
      return (*_flow)[arc];
kpeter@393
   926
    }
kpeter@393
   927
kpeter@393
   928
    /// \brief Returns a const reference to the flow map.
kpeter@393
   929
    ///
kpeter@393
   930
    /// Returns a const reference to the arc map storing the found flow.
kpeter@393
   931
    /// This method can be called after the second phase of the algorithm.
kpeter@393
   932
    ///
kpeter@393
   933
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@393
   934
    /// using this function.
kpeter@420
   935
    const FlowMap& flowMap() const {
kpeter@393
   936
      return *_flow;
kpeter@393
   937
    }
kpeter@393
   938
kpeter@393
   939
    /// \brief Returns \c true when the node is on the source side of the
kpeter@393
   940
    /// minimum cut.
kpeter@393
   941
    ///
kpeter@393
   942
    /// Returns true when the node is on the source side of the found
kpeter@393
   943
    /// minimum cut. This method can be called both after running \ref
alpar@389
   944
    /// startFirstPhase() and \ref startSecondPhase().
kpeter@393
   945
    ///
kpeter@393
   946
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@393
   947
    /// using this function.
alpar@389
   948
    bool minCut(const Node& node) const {
alpar@389
   949
      return ((*_level)[node] == _level->maxLevel()) == _phase;
alpar@389
   950
    }
alpar@389
   951
kpeter@393
   952
    /// \brief Gives back a minimum value cut.
alpar@389
   953
    ///
kpeter@393
   954
    /// Sets \c cutMap to the characteristic vector of a minimum value
kpeter@393
   955
    /// cut. \c cutMap should be a \ref concepts::WriteMap "writable"
kpeter@393
   956
    /// node map with \c bool (or convertible) value type.
kpeter@393
   957
    ///
kpeter@393
   958
    /// This method can be called both after running \ref startFirstPhase()
kpeter@393
   959
    /// and \ref startSecondPhase(). The result after the second phase
kpeter@393
   960
    /// could be slightly different if inexact computation is used.
kpeter@393
   961
    ///
kpeter@393
   962
    /// \note This function calls \ref minCut() for each node, so it runs in
kpeter@559
   963
    /// O(n) time.
kpeter@393
   964
    ///
kpeter@393
   965
    /// \pre Either \ref run() or \ref init() must be called before
kpeter@393
   966
    /// using this function.
alpar@389
   967
    template <typename CutMap>
alpar@389
   968
    void minCutMap(CutMap& cutMap) const {
alpar@389
   969
      for (NodeIt n(_graph); n != INVALID; ++n) {
alpar@389
   970
        cutMap.set(n, minCut(n));
alpar@389
   971
      }
alpar@389
   972
    }
alpar@389
   973
alpar@389
   974
    /// @}
alpar@389
   975
  };
alpar@389
   976
}
alpar@389
   977
alpar@389
   978
#endif