RhodeCode

LEMON code without an explicit copyright notice is covered by the following

copyright/license.

Kutatocsoport (Egervary Combinatorial Optimization Research Group,

EGRES).

===========================================================================

Boost Software License, Version 1.0

===========================================================================

Permission is hereby granted, free of charge, to any person or organization

obtaining a copy of the software and accompanying documentation covered by

this license (the "Software") to use, reproduce, display, distribute,

execute, and transmit the Software, and to prepare derivative works of the

Software, and to permit third-parties to whom the Software is furnished to

do so, all subject to the following:

The copyright notices in the Software and this entire statement, including

the above license grant, this restriction and the following disclaimer,

must be included in all copies of the Software, in whole or in part, and

all derivative works of the Software, unless such copies or derivative

works are solely in the form of machine-executable object code generated by

a source language processor.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT

SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE

FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,

ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER

DEALINGS IN THE SOFTWARE.

2009-05-13 Version 1.1 released

        This is the second stable release of the 1.x series. It

        features a better coverage of the tools available in the 0.x

        series, a thoroughly reworked LP/MIP interface plus various

        improvements in the existing tools.

        * Much improved M$ Windows support

          * Various improvements in the CMAKE build system

          * Compilation warnings are fixed/suppressed

        * Support IBM xlC compiler

        * New algorithms

          * Connectivity related algorithms (#61)

          * Euler walks (#65)

          * Preflow push-relabel max. flow algorithm (#176)

          * Circulation algorithm (push-relabel based) (#175)

          * Suurballe algorithm (#47)

          * Gomory-Hu algorithm (#66)

          * Hao-Orlin algorithm (#58)

          * Edmond's maximum cardinality and weighted matching algorithms

            in general graphs (#48,#265)

          * Minimum cost arborescence/branching (#60)

          * Network Simplex min. cost flow algorithm (#234)

        * New data structures

          * Full graph structure (#57)

          * Grid graph structure (#57)

          * Hypercube graph structure (#57)

          * Graph adaptors (#67)

          * ArcSet and EdgeSet classes (#67)

          * Elevator class (#174)

        * Other new tools

          * LP/MIP interface (#44)

            * Support for GLPK, CPLEX, Soplex, COIN-OR CLP and CBC

          * Reader for the Nauty file format (#55)

          * DIMACS readers (#167)

          * Radix sort algorithms (#72)

          * RangeIdMap and CrossRefMap (#160)

        * New command line tools

          * DIMACS to LGF converter (#182)

          * lgf-gen - a graph generator (#45)

          * DIMACS solver utility (#226)

        * Other code improvements

          * Lognormal distribution added to Random (#102)

          * Better (i.e. O(1) time) item counting in SmartGraph (#3)

          * The standard maps of graphs are guaranteed to be

            reference maps (#190)

        * Miscellaneous

          * Various doc improvements

          * Improved 0.x -> 1.x converter script

        * Several bugfixes (compared to release 1.0):

          #170: Bugfix SmartDigraph::split()

          #171: Bugfix in SmartGraph::restoreSnapshot()

          #172: Extended test cases for graphs and digraphs

          #173: Bugfix in Random

                * operator()s always return a double now

                * the faulty real<Num>(Num) and real<Num>(Num,Num)

                  have been removed

          #187: Remove DijkstraWidestPathOperationTraits

          #61:  Bugfix in DfsVisit

          #193: Bugfix in GraphReader::skipSection()

          #195: Bugfix in ConEdgeIt()

          #197: Bugfix in heap unionfind

                * This bug affects Edmond's general matching algorithms

          #207: Fix 'make install' without 'make html' using CMAKE

          #208: Suppress or fix VS2008 compilation warnings

          ----: Update the LEMON icon

          ----: Enable the component-based installer

                (in installers made by CPACK)

          ----: Set the proper version for CMAKE in the tarballs

                (made by autotools)

          ----: Minor clarification in the LICENSE file

          ----: Add missing unistd.h include to time_measure.h

          #204: Compilation bug fixed in graph_to_eps.h with VS2005

          #230: Build systems check the availability of 'long long' type

          #229: Default implementation of Tolerance<> is used for integer types

          #211,#212: Various fixes for compiling on AIX

          ----: Improvements in CMAKE config

                - docs is installed in share/doc/

                - detects newer versions of Ghostscript

          #239: Fix missing 'inline' specifier in time_measure.h

          #274,#280: Install lemon/config.h

          #275: Prefix macro names with LEMON_ in lemon/config.h

          ----: Small script for making the release tarballs added

          ----: Minor improvement in unify-sources.sh (a76f55d7d397)

2009-03-27 LEMON joins to the COIN-OR initiative

        COIN-OR (Computational Infrastructure for Operations Research,

        http://www.coin-or.org) project is an initiative to spur the

        development of open-source software for the operations research

        community.

2008-10-13 Version 1.0 released

          Migration Guide in the doc for more details)

          * Graph -> Digraph, UGraph -> Graph

          * Edge -> Arc, UEdge -> Edge

          * Concepts

              concepts/graph_components.h)

              (lgf_reader.h, lgf_writer.h)

            * tools to handle the anomalies of calculations with

            * tools to manage RGB colors (color.h)

  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);

  dijkstra.run(source, target);

\endcode

We have a length map and a maximum speed map on the arcs of a digraph.

The minimum time to pass the arc can be calculated as the division of

the two maps which can be done implicitly with the \c DivMap template

class. We use the implicit minimum time map as the length map of the

\c Dijkstra algorithm.

*/

/**

@defgroup paths Path Structures

@ingroup datas

\brief %Path structures implemented in LEMON.

This group contains the path structures implemented in LEMON.

LEMON provides flexible data structures to work with paths.

All of them have similar interfaces and they can be copied easily with

assignment operators and copy constructors. This makes it easy and

efficient to have e.g. the Dijkstra algorithm to store its result in

any kind of path structure.

\sa \ref concepts::Path "Path concept"

*/

/**

@defgroup heaps Heap Structures

@ingroup datas

\brief %Heap structures implemented in LEMON.

This group contains the heap structures implemented in LEMON.

LEMON provides several heap classes. They are efficient implementations

of the abstract data type \e priority \e queue. They store items with

specified values called \e priorities in such a way that finding and

removing the item with minimum priority are efficient.

The basic operations are adding and erasing items, changing the priority

of an item, etc.

Heaps are crucial in several algorithms, such as Dijkstra and Prim.

The heap implementations have the same interface, thus any of them can be

used easily in such algorithms.

\sa \ref concepts::Heap "Heap concept"

*/

/**

@defgroup auxdat Auxiliary Data Structures

@ingroup datas

\brief Auxiliary data structures implemented in LEMON.

This group contains some data structures implemented in LEMON in

order to make it easier to implement combinatorial algorithms.

*/

/**

@defgroup geomdat Geometric Data Structures

@ingroup auxdat

\brief Geometric data structures implemented in LEMON.

This group contains geometric data structures implemented in LEMON.

 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional

   vector with the usual operations.

 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the

   rectangular bounding box of a set of \ref lemon::dim2::Point

   "dim2::Point"'s.

*/

/**

@defgroup matrices Matrices

@ingroup auxdat

\brief Two dimensional data storages implemented in LEMON.

This group contains two dimensional data storages implemented in LEMON.

*/

/**

@defgroup algs Algorithms

\brief This group contains the several algorithms

implemented in LEMON.

This group contains the several algorithms

implemented in LEMON.

*/

/**

@defgroup search Graph Search

@ingroup algs

\brief Common graph search algorithms.

This group contains the common graph search algorithms, namely

\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)

\ref clrs01algorithms.

*/

\brief Algorithms for finding minimum cut in graphs.

This group contains the algorithms for finding minimum cut in graphs.

The \e minimum \e cut \e problem is to find a non-empty and non-complete

\f$X\f$ subset of the nodes with minimum overall capacity on

outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a

\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum

cut is the \f$X\f$ solution of the next optimization problem:

\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}

    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]

LEMON contains several algorithms related to minimum cut problems:

- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut

  in directed graphs.

- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for

  calculating minimum cut in undirected graphs.

- \ref GomoryHu "Gomory-Hu tree computation" for calculating

  all-pairs minimum cut in undirected graphs.

If you want to find minimum cut just between two distinict nodes,

see the \ref max_flow "maximum flow problem".

*/

/**

@defgroup min_mean_cycle Minimum Mean Cycle Algorithms

@ingroup algs

\brief Algorithms for finding minimum mean cycles.

This group contains the algorithms for finding minimum mean cycles

\ref clrs01algorithms, \ref amo93networkflows.

The \e minimum \e mean \e cycle \e problem is to find a directed cycle

of minimum mean length (cost) in a digraph.

The mean length of a cycle is the average length of its arcs, i.e. the

ratio between the total length of the cycle and the number of arcs on it.

This problem has an important connection to \e conservative \e length

\e functions, too. A length function on the arcs of a digraph is called

conservative if and only if there is no directed cycle of negative total

length. For an arbitrary length function, the negative of the minimum

cycle mean is the smallest \f$\epsilon\f$ value so that increasing the

arc lengths uniformly by \f$\epsilon\f$ results in a conservative length

function.

LEMON contains three algorithms for solving the minimum mean cycle problem:

  \ref dasdan98minmeancycle.

  version of Karp's algorithm \ref dasdan98minmeancycle.

  \ref dasdan98minmeancycle.

*/

/**

@defgroup matching Matching Algorithms

@ingroup algs

\brief Algorithms for finding matchings in graphs and bipartite graphs.

This group contains the algorithms for calculating

matchings in graphs and bipartite graphs. The general matching problem is

finding a subset of the edges for which each node has at most one incident

edge.

There are several different algorithms for calculate matchings in

graphs.  The matching problems in bipartite graphs are generally

easier than in general graphs. The goal of the matching optimization

can be finding maximum cardinality, maximum weight or minimum cost

matching. The search can be constrained to find perfect or

maximum cardinality matching.

The matching algorithms implemented in LEMON:

- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm

  for calculating maximum cardinality matching in bipartite graphs.

- \ref PrBipartiteMatching Push-relabel algorithm

  for calculating maximum cardinality matching in bipartite graphs.

- \ref MaxWeightedBipartiteMatching

  Successive shortest path algorithm for calculating maximum weighted

  matching and maximum weighted bipartite matching in bipartite graphs.

- \ref MinCostMaxBipartiteMatching

  Successive shortest path algorithm for calculating minimum cost maximum

  matching in bipartite graphs.

- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating

  maximum cardinality matching in general graphs.

- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating

  maximum weighted matching in general graphs.

- \ref MaxWeightedPerfectMatching

  Edmond's blossom shrinking algorithm for calculating maximum weighted

  perfect matching in general graphs.

- \ref MaxFractionalMatching Push-relabel algorithm for calculating

  maximum cardinality fractional matching in general graphs.

- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating

  maximum weighted fractional matching in general graphs.

- \ref MaxWeightedPerfectFractionalMatching

  Augmenting path algorithm for calculating maximum weighted

  perfect fractional matching in general graphs.

\image html matching.png

\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth

*/

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2010

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_ARG_PARSER_H

#define LEMON_ARG_PARSER_H

#include <vector>

#include <map>

#include <list>

#include <string>

#include <iostream>

#include <sstream>

#include <algorithm>

#include <lemon/assert.h>

///\ingroup misc

///\file

///\brief A tool to parse command line arguments.

namespace lemon {

  ///Exception used by ArgParser

  class ArgParserException : public Exception {

  public:

    enum Reason {

    };

  private:

    Reason _reason;

  public:

    ///Constructor

    ArgParserException(Reason r) throw() : _reason(r) {}

    ///Virtual destructor

    virtual ~ArgParserException() throw() {}

    ///A short description of the exception

    virtual const char* what() const throw() {

      switch(_reason)

        {

        case HELP:

          return "lemon::ArgParseException: ask for help";

          break;

        case UNKNOWN_OPT:

          return "lemon::ArgParseException: unknown option";

          break;

        case INVALID_OPT:

          return "lemon::ArgParseException: invalid combination of options";

          break;

        }

      return "";

    }

    ///Return the reason for the failure

    Reason reason() const {return _reason; }

  };

  ///Command line arguments parser

  ///\ingroup misc

  ///Command line arguments parser.

  ///

  ///For a complete example see the \ref arg_parser_demo.cc demo file.

  class ArgParser {

    static void _showHelp(void *p);

  protected:

    int _argc;

    const char * const *_argv;

    enum OptType { UNKNOWN=0, BOOL=1, STRING=2, DOUBLE=3, INTEGER=4, FUNC=5 };

    class ParData {

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2010

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_BELLMAN_FORD_H

#define LEMON_BELLMAN_FORD_H

/// \ingroup shortest_path

/// \file

/// \brief Bellman-Ford algorithm.

#include <lemon/list_graph.h>

#include <lemon/bits/path_dump.h>

#include <lemon/core.h>

#include <lemon/error.h>

#include <lemon/maps.h>

#include <lemon/path.h>

#include <limits>

namespace lemon {

  ///

  /// This operation traits class defines all computational operations

  /// and constants that are used in the Bellman-Ford algorithm.

  /// The default implementation is based on the \c numeric_limits class.

  /// If the numeric type does not have infinity value, then the maximum

  /// value is used as extremal infinity value.

  template <

    typename V,

    bool has_inf = std::numeric_limits<V>::has_infinity>

  struct BellmanFordDefaultOperationTraits {

    typedef V Value;

    /// \brief Gives back the zero value of the type.

    static Value zero() {

      return static_cast<Value>(0);

    }

    /// \brief Gives back the positive infinity value of the type.

    static Value infinity() {

      return std::numeric_limits<Value>::infinity();

    }

    /// \brief Gives back the sum of the given two elements.

    static Value plus(const Value& left, const Value& right) {

      return left + right;

    }

    /// \brief Gives back \c true only if the first value is less than

    /// the second.

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  template <typename V>

  struct BellmanFordDefaultOperationTraits<V, false> {

    typedef V Value;

    static Value zero() {

      return static_cast<Value>(0);

    }

    static Value infinity() {

      return std::numeric_limits<Value>::max();

    }

    static Value plus(const Value& left, const Value& right) {

      if (left == infinity() || right == infinity()) return infinity();

      return left + right;

    }

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

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

  ///

  /// Default traits class of BellmanFord class.

  /// \param GR The type of the digraph.

  /// \param LEN The type of the length map.

  template<typename GR, typename LEN>

  struct BellmanFordDefaultTraits {

    /// The type of the digraph the algorithm runs on.

    typedef GR Digraph;

    /// \brief The type of the map that stores the arc lengths.

    ///

    /// The type of the map that stores the arc lengths.

    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.

    typedef LEN LengthMap;

    /// The type of the arc lengths.

    typedef typename LEN::Value Value;

    /// \brief Operation traits for Bellman-Ford algorithm.

    ///

    /// It defines the used operations and the infinity value for the

    /// given \c Value type.

    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;

    /// \brief The type of the map that stores the last arcs of the

    /// shortest paths.

    ///

    /// The type of the map that stores the last

    /// arcs of the shortest paths.

    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;

    /// \brief Instantiates a \c PredMap.

    ///

    /// This function instantiates a \ref PredMap.

    /// \param g is the digraph to which we would like to define the

    /// \ref PredMap.

    static PredMap *createPredMap(const GR& g) {

      return new PredMap(g);

    }

    /// \brief The type of the map that stores the distances of the nodes.

    ///

    /// The type of the map that stores the distances of the nodes.

    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename GR::template NodeMap<typename LEN::Value> DistMap;

    /// \brief Instantiates a \c DistMap.

    ///

    /// This function instantiates a \ref DistMap.

    /// \param g is the digraph to which we would like to define the

    /// \ref DistMap.

    static DistMap *createDistMap(const GR& g) {

      return new DistMap(g);

    }

  };

  /// \brief %BellmanFord algorithm class.

  ///

  /// \ingroup shortest_path

  /// This class provides an efficient implementation of the Bellman-Ford

  /// algorithm. The maximum time complexity of the algorithm is

  /// <tt>O(ne)</tt>.

  ///

  /// The Bellman-Ford algorithm solves the single-source shortest path

  /// problem when the arcs can have negative lengths, but the digraph

  /// should not contain directed cycles with negative total length.

  /// If all arc costs are non-negative, consider to use the Dijkstra

  /// algorithm instead, since it is more efficient.

      lemon::Path<Digraph> cycle;

      for (int i = 0; i < int(_process.size()); ++i) {

        if (state[_process[i]] != -1) continue;

        for (Node v = _process[i]; (*_pred)[v] != INVALID;

             v = _gr->source((*_pred)[v])) {

          if (state[v] == i) {

            cycle.addFront((*_pred)[v]);

            for (Node u = _gr->source((*_pred)[v]); u != v;

                 u = _gr->source((*_pred)[u])) {

              cycle.addFront((*_pred)[u]);

            }

            return cycle;

          }

          else if (state[v] >= 0) {

            break;

          }

          state[v] = i;

        }

      }

      return cycle;

    }

    ///@}

  };

  /// \brief Default traits class of bellmanFord() function.

  ///

  /// Default traits class of bellmanFord() function.

  /// \tparam GR The type of the digraph.

  /// \tparam LEN The type of the length map.

  template <typename GR, typename LEN>

  struct BellmanFordWizardDefaultTraits {

    /// The type of the digraph the algorithm runs on.

    typedef GR Digraph;

    /// \brief The type of the map that stores the arc lengths.

    ///

    /// The type of the map that stores the arc lengths.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef LEN LengthMap;

    /// The type of the arc lengths.

    typedef typename LEN::Value Value;

    /// \brief Operation traits for Bellman-Ford algorithm.

    ///

    /// It defines the used operations and the infinity value for the

    /// given \c Value type.

    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;

    /// \brief The type of the map that stores the last

    /// arcs of the shortest paths.

    ///

    /// The type of the map that stores the last arcs of the shortest paths.

    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;

    /// \brief Instantiates a \c PredMap.

    ///

    /// This function instantiates a \ref PredMap.

    /// \param g is the digraph to which we would like to define the

    /// \ref PredMap.

    static PredMap *createPredMap(const GR &g) {

      return new PredMap(g);

    }

    /// \brief The type of the map that stores the distances of the nodes.

    ///

    /// The type of the map that stores the distances of the nodes.

    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename GR::template NodeMap<Value> DistMap;

    /// \brief Instantiates a \c DistMap.

    ///

    /// This function instantiates a \ref DistMap.

    /// \param g is the digraph to which we would like to define the

    /// \ref DistMap.

    static DistMap *createDistMap(const GR &g) {

      return new DistMap(g);

    }

    ///The type of the shortest paths.

    ///The type of the shortest paths.

    ///It must meet the \ref concepts::Path "Path" concept.

    typedef lemon::Path<Digraph> Path;

  };

  /// \brief Default traits class used by BellmanFordWizard.

  ///

  /// Default traits class used by BellmanFordWizard.

  /// \tparam GR The type of the digraph.

  /// \tparam LEN The type of the length map.

  template <typename GR, typename LEN>

  class BellmanFordWizardBase

    : public BellmanFordWizardDefaultTraits<GR, LEN> {

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2010

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_HARTMANN_ORLIN_MMC_H

#define LEMON_HARTMANN_ORLIN_MMC_H

/// \ingroup min_mean_cycle

///

/// \file

/// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.

#include <vector>

#include <limits>

#include <lemon/core.h>

#include <lemon/path.h>

#include <lemon/tolerance.h>

#include <lemon/connectivity.h>

namespace lemon {

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

  ///

  /// Default traits class of HartmannOrlinMmc class.

  /// \tparam GR The type of the digraph.

  /// \tparam CM The type of the cost map.

#ifdef DOXYGEN

  template <typename GR, typename CM>

#else

  template <typename GR, typename CM,

    bool integer = std::numeric_limits<typename CM::Value>::is_integer>

#endif

  struct HartmannOrlinMmcDefaultTraits

  {

    /// The type of the digraph

    typedef GR Digraph;

    /// The type of the cost map

    typedef CM CostMap;

    /// The type of the arc costs

    typedef typename CostMap::Value Cost;

    /// \brief The large cost type used for internal computations

    ///

    /// The large cost type used for internal computations.

    /// It is \c long \c long if the \c Cost type is integer,

    /// otherwise it is \c double.

    /// \c Cost must be convertible to \c LargeCost.

    typedef double LargeCost;

    /// The tolerance type used for internal computations

    typedef lemon::Tolerance<LargeCost> Tolerance;

    /// \brief The path type of the found cycles

    ///

    /// The path type of the found cycles.

    /// It must conform to the \ref lemon::concepts::Path "Path" concept

    /// and it must have an \c addFront() function.

    typedef lemon::Path<Digraph> Path;

  };

  // Default traits class for integer cost types

  template <typename GR, typename CM>

  struct HartmannOrlinMmcDefaultTraits<GR, CM, true>

  {

    typedef GR Digraph;

    typedef CM CostMap;

    typedef typename CostMap::Value Cost;

#ifdef LEMON_HAVE_LONG_LONG

    typedef long long LargeCost;

#else

    typedef long LargeCost;

#endif

    typedef lemon::Tolerance<LargeCost> Tolerance;

    typedef lemon::Path<Digraph> Path;

  };

  /// \addtogroup min_mean_cycle

  /// @{

  /// \brief Implementation of the Hartmann-Orlin algorithm for finding

  /// a minimum mean cycle.

  ///

  /// This class implements the Hartmann-Orlin algorithm for finding

  /// a directed cycle of minimum mean cost in a digraph

  /// \ref amo93networkflows, \ref dasdan98minmeancycle.

  /// it applies an efficient early termination scheme.

  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).

  ///

  /// \tparam GR The type of the digraph the algorithm runs on.

  /// \tparam CM The type of the cost map. The default

  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".

  /// \tparam TR The traits class that defines various types used by the

  /// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits

  /// "HartmannOrlinMmcDefaultTraits<GR, CM>".

  /// In most cases, this parameter should not be set directly,

  /// consider to use the named template parameters instead.

#ifdef DOXYGEN

  template <typename GR, typename CM, typename TR>

#else

  template < typename GR,

             typename CM = typename GR::template ArcMap<int>,

             typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >

#endif

  class HartmannOrlinMmc

  {

  public:

    /// The type of the digraph

    typedef typename TR::Digraph Digraph;

    /// The type of the cost map

    typedef typename TR::CostMap CostMap;

    /// The type of the arc costs

    typedef typename TR::Cost Cost;

    /// \brief The large cost type

    ///

    /// The large cost type used for internal computations.

    /// By default, it is \c long \c long if the \c Cost type is integer,

    /// otherwise it is \c double.

    typedef typename TR::LargeCost LargeCost;

    /// The tolerance type

    typedef typename TR::Tolerance Tolerance;

    /// \brief The path type of the found cycles

    ///

    /// The path type of the found cycles.

    /// Using the \ref HartmannOrlinMmcDefaultTraits "default traits class",

    /// it is \ref lemon::Path "Path<Digraph>".

    typedef typename TR::Path Path;

    /// The \ref HartmannOrlinMmcDefaultTraits "traits class" of the algorithm

    typedef TR Traits;