lemon/hartmann_orlin.h
author Alpar Juttner <alpar@cs.elte.hu>
Wed, 03 Mar 2010 17:22:13 +0000
changeset 859 ac5f72c48367
parent 825 75e6020b19b1
child 863 a93f1a27d831
permissions -rw-r--r--
Merge #301
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/* -*- C++ -*-
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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_HARTMANN_ORLIN_H
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#define LEMON_HARTMANN_ORLIN_H
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/// \ingroup min_mean_cycle
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///
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/// \file
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/// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
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#include <vector>
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#include <limits>
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#include <lemon/core.h>
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#include <lemon/path.h>
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#include <lemon/tolerance.h>
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#include <lemon/connectivity.h>
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namespace lemon {
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  /// \brief Default traits class of HartmannOrlin algorithm.
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  ///
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  /// Default traits class of HartmannOrlin algorithm.
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  /// \tparam GR The type of the digraph.
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  /// \tparam LEN The type of the length map.
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  /// It must conform to the \ref concepts::Rea_data "Rea_data" concept.
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#ifdef DOXYGEN
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  template <typename GR, typename LEN>
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#else
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  template <typename GR, typename LEN,
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    bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
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#endif
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  struct HartmannOrlinDefaultTraits
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  {
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    /// The type of the digraph
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    typedef GR Digraph;
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    /// The type of the length map
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    typedef LEN LengthMap;
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    /// The type of the arc lengths
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    typedef typename LengthMap::Value Value;
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    /// \brief The large value type used for internal computations
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    ///
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    /// The large value type used for internal computations.
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    /// It is \c long \c long if the \c Value type is integer,
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    /// otherwise it is \c double.
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    /// \c Value must be convertible to \c LargeValue.
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    typedef double LargeValue;
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    /// The tolerance type used for internal computations
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    typedef lemon::Tolerance<LargeValue> Tolerance;
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    /// \brief The path type of the found cycles
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    ///
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    /// The path type of the found cycles.
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    /// It must conform to the \ref lemon::concepts::Path "Path" concept
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    /// and it must have an \c addFront() function.
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    typedef lemon::Path<Digraph> Path;
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  };
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  // Default traits class for integer value types
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  template <typename GR, typename LEN>
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  struct HartmannOrlinDefaultTraits<GR, LEN, true>
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  {
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    typedef GR Digraph;
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    typedef LEN LengthMap;
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    typedef typename LengthMap::Value Value;
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#ifdef LEMON_HAVE_LONG_LONG
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    typedef long long LargeValue;
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#else
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    typedef long LargeValue;
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#endif
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    typedef lemon::Tolerance<LargeValue> Tolerance;
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    typedef lemon::Path<Digraph> Path;
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  };
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  /// \addtogroup min_mean_cycle
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  /// @{
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  /// \brief Implementation of the Hartmann-Orlin algorithm for finding
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  /// a minimum mean cycle.
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  ///
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  /// This class implements the Hartmann-Orlin algorithm for finding
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  /// a directed cycle of minimum mean length (cost) in a digraph
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  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
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  /// It is an improved version of \ref Karp "Karp"'s original algorithm,
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  /// it applies an efficient early termination scheme.
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  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
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  ///
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  /// \tparam GR The type of the digraph the algorithm runs on.
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  /// \tparam LEN The type of the length map. The default
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  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
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  /// \tparam TR The traits class that defines various types used by the
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  /// algorithm. By default, it is \ref HartmannOrlinDefaultTraits
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  /// "HartmannOrlinDefaultTraits<GR, LEN>".
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  /// In most cases, this parameter should not be set directly,
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  /// consider to use the named template parameters instead.
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#ifdef DOXYGEN
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  template <typename GR, typename LEN, typename TR>
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#else
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  template < typename GR,
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             typename LEN = typename GR::template ArcMap<int>,
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             typename TR = HartmannOrlinDefaultTraits<GR, LEN> >
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#endif
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  class HartmannOrlin
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  {
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  public:
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    /// The type of the digraph
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    typedef typename TR::Digraph Digraph;
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    /// The type of the length map
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    typedef typename TR::LengthMap LengthMap;
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    /// The type of the arc lengths
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    typedef typename TR::Value Value;
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    /// \brief The large value type
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    ///
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    /// The large value type used for internal computations.
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    /// By default, it is \c long \c long if the \c Value type is integer,
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    /// otherwise it is \c double.
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    typedef typename TR::LargeValue LargeValue;
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    /// The tolerance type
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    typedef typename TR::Tolerance Tolerance;
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    /// \brief The path type of the found cycles
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    ///
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    /// The path type of the found cycles.
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    /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
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    /// it is \ref lemon::Path "Path<Digraph>".
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    typedef typename TR::Path Path;
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    /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm
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    typedef TR Traits;
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  private:
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    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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    // Data sturcture for path data
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    struct PathData
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    {
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      LargeValue dist;
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      Arc pred;
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      PathData(LargeValue d, Arc p = INVALID) :
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        dist(d), pred(p) {}
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    };
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    typedef typename Digraph::template NodeMap<std::vector<PathData> >
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      PathDataNodeMap;
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  private:
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    // The digraph the algorithm runs on
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    const Digraph &_gr;
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    // The length of the arcs
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    const LengthMap &_length;
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    // Data for storing the strongly connected components
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    int _comp_num;
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    typename Digraph::template NodeMap<int> _comp;
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    std::vector<std::vector<Node> > _comp_nodes;
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    std::vector<Node>* _nodes;
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    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
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    // Data for the found cycles
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    bool _curr_found, _best_found;
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    LargeValue _curr_length, _best_length;
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    int _curr_size, _best_size;
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    Node _curr_node, _best_node;
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    int _curr_level, _best_level;
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    Path *_cycle_path;
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    bool _local_path;
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    // Node map for storing path data
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    PathDataNodeMap _data;
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    // The processed nodes in the last round
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    std::vector<Node> _process;
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    Tolerance _tolerance;
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    // Infinite constant
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    const LargeValue INF;
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  public:
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    /// \name Named Template Parameters
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    /// @{
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    template <typename T>
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    struct SetLargeValueTraits : public Traits {
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      typedef T LargeValue;
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      typedef lemon::Tolerance<T> Tolerance;
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// \c LargeValue type.
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    ///
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    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
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    /// type. It is used for internal computations in the algorithm.
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    template <typename T>
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    struct SetLargeValue
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      : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
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      typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
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    };
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    template <typename T>
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    struct SetPathTraits : public Traits {
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      typedef T Path;
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// \c %Path type.
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    ///
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    /// \ref named-templ-param "Named parameter" for setting the \c %Path
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    /// type of the found cycles.
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    /// It must conform to the \ref lemon::concepts::Path "Path" concept
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    /// and it must have an \c addFront() function.
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    template <typename T>
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    struct SetPath
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      : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
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      typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
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    };
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    /// @}
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  public:
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    /// \brief Constructor.
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    ///
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    /// The constructor of the class.
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    ///
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    /// \param digraph The digraph the algorithm runs on.
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    /// \param length The lengths (costs) of the arcs.
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    HartmannOrlin( const Digraph &digraph,
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                   const LengthMap &length ) :
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      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
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      _best_found(false), _best_length(0), _best_size(1),
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      _cycle_path(NULL), _local_path(false), _data(digraph),
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      INF(std::numeric_limits<LargeValue>::has_infinity ?
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          std::numeric_limits<LargeValue>::infinity() :
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          std::numeric_limits<LargeValue>::max())
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    {}
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    /// Destructor.
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    ~HartmannOrlin() {
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      if (_local_path) delete _cycle_path;
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    }
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    /// \brief Set the path structure for storing the found cycle.
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    ///
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    /// This function sets an external path structure for storing the
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    /// found cycle.
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    ///
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    /// If you don't call this function before calling \ref run() or
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    /// \ref findMinMean(), it will allocate a local \ref Path "path"
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    /// structure. The destuctor deallocates this automatically
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    /// allocated object, of course.
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    ///
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    /// \note The algorithm calls only the \ref lemon::Path::addFront()
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    /// "addFront()" function of the given path structure.
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    ///
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    /// \return <tt>(*this)</tt>
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    HartmannOrlin& cycle(Path &path) {
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      if (_local_path) {
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        delete _cycle_path;
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        _local_path = false;
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      }
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      _cycle_path = &path;
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      return *this;
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    }
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    /// \brief Set the tolerance used by the algorithm.
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    ///
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    /// This function sets the tolerance object used by the algorithm.
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    ///
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    /// \return <tt>(*this)</tt>
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    HartmannOrlin& 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 Return a const reference to the tolerance.
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    ///
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    /// This function returns a const reference to the tolerance object
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    /// used by 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 algorithm is to call the \ref run()
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    /// function.\n
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    /// If you only need the minimum mean length, you may call
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    /// \ref findMinMean().
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    /// @{
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    /// \brief Run the algorithm.
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    ///
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    /// This function runs the algorithm.
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    /// It can be called more than once (e.g. if the underlying digraph
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    /// and/or the arc lengths have been modified).
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    ///
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    /// \return \c true if a directed cycle exists in the digraph.
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    ///
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    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
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    /// \code
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    ///   return mmc.findMinMean() && mmc.findCycle();
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    /// \endcode
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    bool run() {
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      return findMinMean() && findCycle();
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    }
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    /// \brief Find the minimum cycle mean.
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    ///
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    /// This function finds the minimum mean length of the directed
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    /// cycles in the digraph.
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    ///
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    /// \return \c true if a directed cycle exists in the digraph.
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    bool findMinMean() {
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      // Initialization and find strongly connected components
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      init();
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      findComponents();
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      // Find the minimum cycle mean in the components
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      for (int comp = 0; comp < _comp_num; ++comp) {
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        if (!initComponent(comp)) continue;
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        processRounds();
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        // Update the best cycle (global minimum mean cycle)
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        if ( _curr_found && (!_best_found || 
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             _curr_length * _best_size < _best_length * _curr_size) ) {
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          _best_found = true;
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          _best_length = _curr_length;
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          _best_size = _curr_size;
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          _best_node = _curr_node;
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          _best_level = _curr_level;
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        }
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      }
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      return _best_found;
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    }
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    /// \brief Find a minimum mean directed cycle.
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    ///
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    /// This function finds a directed cycle of minimum mean length
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    /// in the digraph using the data computed by findMinMean().
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    ///
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    /// \return \c true if a directed cycle exists in the digraph.
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    ///
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    /// \pre \ref findMinMean() must be called before using this function.
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    bool findCycle() {
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      if (!_best_found) return false;
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      IntNodeMap reached(_gr, -1);
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      int r = _best_level + 1;
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      Node u = _best_node;
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      while (reached[u] < 0) {
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        reached[u] = --r;
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        u = _gr.source(_data[u][r].pred);
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      }
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      r = reached[u];
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      Arc e = _data[u][r].pred;
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      _cycle_path->addFront(e);
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      _best_length = _length[e];
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      _best_size = 1;
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      Node v;
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      while ((v = _gr.source(e)) != u) {
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        e = _data[v][--r].pred;
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   386
        _cycle_path->addFront(e);
kpeter@766
   387
        _best_length += _length[e];
kpeter@766
   388
        ++_best_size;
kpeter@766
   389
      }
kpeter@766
   390
      return true;
kpeter@766
   391
    }
kpeter@766
   392
kpeter@766
   393
    /// @}
kpeter@766
   394
kpeter@766
   395
    /// \name Query Functions
kpeter@766
   396
    /// The results of the algorithm can be obtained using these
kpeter@766
   397
    /// functions.\n
kpeter@766
   398
    /// The algorithm should be executed before using them.
kpeter@766
   399
kpeter@766
   400
    /// @{
kpeter@766
   401
kpeter@766
   402
    /// \brief Return the total length of the found cycle.
kpeter@766
   403
    ///
kpeter@766
   404
    /// This function returns the total length of the found cycle.
kpeter@766
   405
    ///
kpeter@766
   406
    /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@766
   407
    /// using this function.
kpeter@841
   408
    Value cycleLength() const {
kpeter@841
   409
      return static_cast<Value>(_best_length);
kpeter@766
   410
    }
kpeter@766
   411
kpeter@766
   412
    /// \brief Return the number of arcs on the found cycle.
kpeter@766
   413
    ///
kpeter@766
   414
    /// This function returns the number of arcs on the found cycle.
kpeter@766
   415
    ///
kpeter@766
   416
    /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@766
   417
    /// using this function.
kpeter@766
   418
    int cycleArcNum() const {
kpeter@766
   419
      return _best_size;
kpeter@766
   420
    }
kpeter@766
   421
kpeter@766
   422
    /// \brief Return the mean length of the found cycle.
kpeter@766
   423
    ///
kpeter@766
   424
    /// This function returns the mean length of the found cycle.
kpeter@766
   425
    ///
kpeter@766
   426
    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@766
   427
    /// following code.
kpeter@766
   428
    /// \code
kpeter@766
   429
    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
kpeter@766
   430
    /// \endcode
kpeter@766
   431
    ///
kpeter@766
   432
    /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@766
   433
    /// using this function.
kpeter@766
   434
    double cycleMean() const {
kpeter@766
   435
      return static_cast<double>(_best_length) / _best_size;
kpeter@766
   436
    }
kpeter@766
   437
kpeter@766
   438
    /// \brief Return the found cycle.
kpeter@766
   439
    ///
kpeter@766
   440
    /// This function returns a const reference to the path structure
kpeter@766
   441
    /// storing the found cycle.
kpeter@766
   442
    ///
kpeter@766
   443
    /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@766
   444
    /// this function.
kpeter@766
   445
    const Path& cycle() const {
kpeter@766
   446
      return *_cycle_path;
kpeter@766
   447
    }
kpeter@766
   448
kpeter@766
   449
    ///@}
kpeter@766
   450
kpeter@766
   451
  private:
kpeter@766
   452
kpeter@766
   453
    // Initialization
kpeter@766
   454
    void init() {
kpeter@766
   455
      if (!_cycle_path) {
kpeter@766
   456
        _local_path = true;
kpeter@766
   457
        _cycle_path = new Path;
kpeter@766
   458
      }
kpeter@766
   459
      _cycle_path->clear();
kpeter@766
   460
      _best_found = false;
kpeter@766
   461
      _best_length = 0;
kpeter@766
   462
      _best_size = 1;
kpeter@766
   463
      _cycle_path->clear();
kpeter@766
   464
      for (NodeIt u(_gr); u != INVALID; ++u)
kpeter@766
   465
        _data[u].clear();
kpeter@766
   466
    }
kpeter@766
   467
kpeter@766
   468
    // Find strongly connected components and initialize _comp_nodes
kpeter@766
   469
    // and _out_arcs
kpeter@766
   470
    void findComponents() {
kpeter@766
   471
      _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@766
   472
      _comp_nodes.resize(_comp_num);
kpeter@766
   473
      if (_comp_num == 1) {
kpeter@766
   474
        _comp_nodes[0].clear();
kpeter@766
   475
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@766
   476
          _comp_nodes[0].push_back(n);
kpeter@766
   477
          _out_arcs[n].clear();
kpeter@766
   478
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@766
   479
            _out_arcs[n].push_back(a);
kpeter@766
   480
          }
kpeter@766
   481
        }
kpeter@766
   482
      } else {
kpeter@766
   483
        for (int i = 0; i < _comp_num; ++i)
kpeter@766
   484
          _comp_nodes[i].clear();
kpeter@766
   485
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@766
   486
          int k = _comp[n];
kpeter@766
   487
          _comp_nodes[k].push_back(n);
kpeter@766
   488
          _out_arcs[n].clear();
kpeter@766
   489
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@766
   490
            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
kpeter@766
   491
          }
kpeter@766
   492
        }
kpeter@766
   493
      }
kpeter@766
   494
    }
kpeter@766
   495
kpeter@766
   496
    // Initialize path data for the current component
kpeter@766
   497
    bool initComponent(int comp) {
kpeter@766
   498
      _nodes = &(_comp_nodes[comp]);
kpeter@766
   499
      int n = _nodes->size();
kpeter@766
   500
      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@766
   501
        return false;
kpeter@766
   502
      }      
kpeter@766
   503
      for (int i = 0; i < n; ++i) {
kpeter@767
   504
        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
kpeter@766
   505
      }
kpeter@766
   506
      return true;
kpeter@766
   507
    }
kpeter@766
   508
kpeter@766
   509
    // Process all rounds of computing path data for the current component.
kpeter@766
   510
    // _data[v][k] is the length of a shortest directed walk from the root
kpeter@766
   511
    // node to node v containing exactly k arcs.
kpeter@766
   512
    void processRounds() {
kpeter@766
   513
      Node start = (*_nodes)[0];
kpeter@767
   514
      _data[start][0] = PathData(0);
kpeter@766
   515
      _process.clear();
kpeter@766
   516
      _process.push_back(start);
kpeter@766
   517
kpeter@766
   518
      int k, n = _nodes->size();
kpeter@766
   519
      int next_check = 4;
kpeter@766
   520
      bool terminate = false;
kpeter@766
   521
      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
kpeter@766
   522
        processNextBuildRound(k);
kpeter@766
   523
        if (k == next_check || k == n) {
kpeter@766
   524
          terminate = checkTermination(k);
kpeter@766
   525
          next_check = next_check * 3 / 2;
kpeter@766
   526
        }
kpeter@766
   527
      }
kpeter@766
   528
      for ( ; k <= n && !terminate; ++k) {
kpeter@766
   529
        processNextFullRound(k);
kpeter@766
   530
        if (k == next_check || k == n) {
kpeter@766
   531
          terminate = checkTermination(k);
kpeter@766
   532
          next_check = next_check * 3 / 2;
kpeter@766
   533
        }
kpeter@766
   534
      }
kpeter@766
   535
    }
kpeter@766
   536
kpeter@766
   537
    // Process one round and rebuild _process
kpeter@766
   538
    void processNextBuildRound(int k) {
kpeter@766
   539
      std::vector<Node> next;
kpeter@766
   540
      Node u, v;
kpeter@766
   541
      Arc e;
kpeter@766
   542
      LargeValue d;
kpeter@766
   543
      for (int i = 0; i < int(_process.size()); ++i) {
kpeter@766
   544
        u = _process[i];
kpeter@766
   545
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@766
   546
          e = _out_arcs[u][j];
kpeter@766
   547
          v = _gr.target(e);
kpeter@766
   548
          d = _data[u][k-1].dist + _length[e];
kpeter@767
   549
          if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@767
   550
            if (_data[v][k].dist == INF) next.push_back(v);
kpeter@767
   551
            _data[v][k] = PathData(d, e);
kpeter@766
   552
          }
kpeter@766
   553
        }
kpeter@766
   554
      }
kpeter@766
   555
      _process.swap(next);
kpeter@766
   556
    }
kpeter@766
   557
kpeter@766
   558
    // Process one round using _nodes instead of _process
kpeter@766
   559
    void processNextFullRound(int k) {
kpeter@766
   560
      Node u, v;
kpeter@766
   561
      Arc e;
kpeter@766
   562
      LargeValue d;
kpeter@766
   563
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@766
   564
        u = (*_nodes)[i];
kpeter@766
   565
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@766
   566
          e = _out_arcs[u][j];
kpeter@766
   567
          v = _gr.target(e);
kpeter@766
   568
          d = _data[u][k-1].dist + _length[e];
kpeter@767
   569
          if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@767
   570
            _data[v][k] = PathData(d, e);
kpeter@766
   571
          }
kpeter@766
   572
        }
kpeter@766
   573
      }
kpeter@766
   574
    }
kpeter@766
   575
    
kpeter@766
   576
    // Check early termination
kpeter@766
   577
    bool checkTermination(int k) {
kpeter@766
   578
      typedef std::pair<int, int> Pair;
kpeter@766
   579
      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
kpeter@766
   580
      typename GR::template NodeMap<LargeValue> pi(_gr);
kpeter@766
   581
      int n = _nodes->size();
kpeter@766
   582
      LargeValue length;
kpeter@766
   583
      int size;
kpeter@766
   584
      Node u;
kpeter@766
   585
      
kpeter@766
   586
      // Search for cycles that are already found
kpeter@766
   587
      _curr_found = false;
kpeter@766
   588
      for (int i = 0; i < n; ++i) {
kpeter@766
   589
        u = (*_nodes)[i];
kpeter@767
   590
        if (_data[u][k].dist == INF) continue;
kpeter@766
   591
        for (int j = k; j >= 0; --j) {
kpeter@766
   592
          if (level[u].first == i && level[u].second > 0) {
kpeter@766
   593
            // A cycle is found
kpeter@766
   594
            length = _data[u][level[u].second].dist - _data[u][j].dist;
kpeter@766
   595
            size = level[u].second - j;
kpeter@766
   596
            if (!_curr_found || length * _curr_size < _curr_length * size) {
kpeter@766
   597
              _curr_length = length;
kpeter@766
   598
              _curr_size = size;
kpeter@766
   599
              _curr_node = u;
kpeter@766
   600
              _curr_level = level[u].second;
kpeter@766
   601
              _curr_found = true;
kpeter@766
   602
            }
kpeter@766
   603
          }
kpeter@766
   604
          level[u] = Pair(i, j);
deba@795
   605
          if (j != 0) {
deba@795
   606
	    u = _gr.source(_data[u][j].pred);
deba@795
   607
	  }
kpeter@766
   608
        }
kpeter@766
   609
      }
kpeter@766
   610
kpeter@766
   611
      // If at least one cycle is found, check the optimality condition
kpeter@766
   612
      LargeValue d;
kpeter@766
   613
      if (_curr_found && k < n) {
kpeter@766
   614
        // Find node potentials
kpeter@766
   615
        for (int i = 0; i < n; ++i) {
kpeter@766
   616
          u = (*_nodes)[i];
kpeter@767
   617
          pi[u] = INF;
kpeter@766
   618
          for (int j = 0; j <= k; ++j) {
kpeter@767
   619
            if (_data[u][j].dist < INF) {
kpeter@767
   620
              d = _data[u][j].dist * _curr_size - j * _curr_length;
kpeter@767
   621
              if (_tolerance.less(d, pi[u])) pi[u] = d;
kpeter@766
   622
            }
kpeter@766
   623
          }
kpeter@766
   624
        }
kpeter@766
   625
kpeter@766
   626
        // Check the optimality condition for all arcs
kpeter@766
   627
        bool done = true;
kpeter@766
   628
        for (ArcIt a(_gr); a != INVALID; ++a) {
kpeter@766
   629
          if (_tolerance.less(_length[a] * _curr_size - _curr_length,
kpeter@766
   630
                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
kpeter@766
   631
            done = false;
kpeter@766
   632
            break;
kpeter@766
   633
          }
kpeter@766
   634
        }
kpeter@766
   635
        return done;
kpeter@766
   636
      }
kpeter@766
   637
      return (k == n);
kpeter@766
   638
    }
kpeter@766
   639
kpeter@766
   640
  }; //class HartmannOrlin
kpeter@766
   641
kpeter@766
   642
  ///@}
kpeter@766
   643
kpeter@766
   644
} //namespace lemon
kpeter@766
   645
kpeter@766
   646
#endif //LEMON_HARTMANN_ORLIN_H