lemon/karp.h
author Peter Kovacs <kpeter@inf.elte.hu>
Mon, 08 Mar 2010 08:33:41 +0100
changeset 941 a93f1a27d831
parent 914 aa8c9008b3de
permissions -rw-r--r--
Fix gcc 3.3 compilation error (#354)

gcc 3.3 requires that a class has a default constructor if it has
template named parameters. (That constructor can be protected.)
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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_KARP_H
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#define LEMON_KARP_H
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/// \ingroup min_mean_cycle
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///
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/// \file
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/// \brief Karp'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 Karp algorithm.
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  ///
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  /// Default traits class of Karp 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::ReadMap "ReadMap" 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 KarpDefaultTraits
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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 KarpDefaultTraits<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 Karp's algorithm for finding a minimum
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  /// mean cycle.
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  ///
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  /// This class implements Karp's algorithm for finding a directed
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  /// cycle of minimum mean length (cost) in a digraph
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  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
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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 KarpDefaultTraits
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  /// "KarpDefaultTraits<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 = KarpDefaultTraits<GR, LEN> >
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#endif
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  class Karp
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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 KarpDefaultTraits "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 KarpDefaultTraits "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 cycle
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    LargeValue _cycle_length;
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    int _cycle_size;
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    Node _cycle_node;
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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 Karp<GR, LEN, SetLargeValueTraits<T> > {
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      typedef Karp<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 Karp<GR, LEN, SetPathTraits<T> > {
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      typedef Karp<GR, LEN, SetPathTraits<T> > Create;
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    };
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    /// @}
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  protected:
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    Karp() {}
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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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    Karp( 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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      _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
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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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    ~Karp() {
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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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    Karp& 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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    Karp& 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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        updateMinMean();
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      }
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      return (_cycle_node != INVALID);
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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 (_cycle_node == INVALID) return false;
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      IntNodeMap reached(_gr, -1);
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      int r = _data[_cycle_node].size();
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      Node u = _cycle_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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      _cycle_length = _length[e];
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      _cycle_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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        _cycle_path->addFront(e);
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        _cycle_length += _length[e];
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        ++_cycle_size;
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      }
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      return true;
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    }
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    /// @}
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    /// \name Query Functions
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    /// The results of the algorithm can be obtained using these
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    /// functions.\n
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    /// The algorithm should be executed before using them.
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    /// @{
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    /// \brief Return the total length of the found cycle.
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    ///
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    /// This function returns the total length of the found cycle.
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    ///
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    /// \pre \ref run() or \ref findMinMean() must be called before
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    /// using this function.
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    Value cycleLength() const {
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      return static_cast<Value>(_cycle_length);
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    }
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    /// \brief Return the number of arcs on the found cycle.
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    ///
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    /// This function returns the number of arcs on the found cycle.
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    ///
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    /// \pre \ref run() or \ref findMinMean() must be called before
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    /// using this function.
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    int cycleArcNum() const {
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      return _cycle_size;
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    }
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    /// \brief Return the mean length of the found cycle.
kpeter@812
   414
    ///
kpeter@812
   415
    /// This function returns the mean length of the found cycle.
kpeter@812
   416
    ///
kpeter@812
   417
    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@812
   418
    /// following code.
kpeter@812
   419
    /// \code
kpeter@812
   420
    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
kpeter@812
   421
    /// \endcode
kpeter@812
   422
    ///
kpeter@812
   423
    /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@812
   424
    /// using this function.
kpeter@812
   425
    double cycleMean() const {
kpeter@812
   426
      return static_cast<double>(_cycle_length) / _cycle_size;
kpeter@812
   427
    }
kpeter@812
   428
kpeter@812
   429
    /// \brief Return the found cycle.
kpeter@812
   430
    ///
kpeter@812
   431
    /// This function returns a const reference to the path structure
kpeter@812
   432
    /// storing the found cycle.
kpeter@812
   433
    ///
kpeter@812
   434
    /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@812
   435
    /// this function.
kpeter@812
   436
    const Path& cycle() const {
kpeter@812
   437
      return *_cycle_path;
kpeter@812
   438
    }
kpeter@812
   439
kpeter@812
   440
    ///@}
kpeter@812
   441
kpeter@812
   442
  private:
kpeter@812
   443
kpeter@812
   444
    // Initialization
kpeter@812
   445
    void init() {
kpeter@812
   446
      if (!_cycle_path) {
kpeter@812
   447
        _local_path = true;
kpeter@812
   448
        _cycle_path = new Path;
kpeter@812
   449
      }
kpeter@812
   450
      _cycle_path->clear();
kpeter@812
   451
      _cycle_length = 0;
kpeter@812
   452
      _cycle_size = 1;
kpeter@812
   453
      _cycle_node = INVALID;
kpeter@812
   454
      for (NodeIt u(_gr); u != INVALID; ++u)
kpeter@812
   455
        _data[u].clear();
kpeter@812
   456
    }
kpeter@812
   457
kpeter@812
   458
    // Find strongly connected components and initialize _comp_nodes
kpeter@812
   459
    // and _out_arcs
kpeter@812
   460
    void findComponents() {
kpeter@812
   461
      _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@812
   462
      _comp_nodes.resize(_comp_num);
kpeter@812
   463
      if (_comp_num == 1) {
kpeter@812
   464
        _comp_nodes[0].clear();
kpeter@812
   465
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@812
   466
          _comp_nodes[0].push_back(n);
kpeter@812
   467
          _out_arcs[n].clear();
kpeter@812
   468
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@812
   469
            _out_arcs[n].push_back(a);
kpeter@812
   470
          }
kpeter@812
   471
        }
kpeter@812
   472
      } else {
kpeter@812
   473
        for (int i = 0; i < _comp_num; ++i)
kpeter@812
   474
          _comp_nodes[i].clear();
kpeter@812
   475
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@812
   476
          int k = _comp[n];
kpeter@812
   477
          _comp_nodes[k].push_back(n);
kpeter@812
   478
          _out_arcs[n].clear();
kpeter@812
   479
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@812
   480
            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
kpeter@812
   481
          }
kpeter@812
   482
        }
kpeter@812
   483
      }
kpeter@812
   484
    }
kpeter@812
   485
kpeter@812
   486
    // Initialize path data for the current component
kpeter@812
   487
    bool initComponent(int comp) {
kpeter@812
   488
      _nodes = &(_comp_nodes[comp]);
kpeter@812
   489
      int n = _nodes->size();
kpeter@812
   490
      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@812
   491
        return false;
kpeter@812
   492
      }      
kpeter@812
   493
      for (int i = 0; i < n; ++i) {
kpeter@814
   494
        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
kpeter@812
   495
      }
kpeter@812
   496
      return true;
kpeter@812
   497
    }
kpeter@812
   498
kpeter@812
   499
    // Process all rounds of computing path data for the current component.
kpeter@812
   500
    // _data[v][k] is the length of a shortest directed walk from the root
kpeter@812
   501
    // node to node v containing exactly k arcs.
kpeter@812
   502
    void processRounds() {
kpeter@812
   503
      Node start = (*_nodes)[0];
kpeter@814
   504
      _data[start][0] = PathData(0);
kpeter@812
   505
      _process.clear();
kpeter@812
   506
      _process.push_back(start);
kpeter@812
   507
kpeter@812
   508
      int k, n = _nodes->size();
kpeter@812
   509
      for (k = 1; k <= n && int(_process.size()) < n; ++k) {
kpeter@812
   510
        processNextBuildRound(k);
kpeter@812
   511
      }
kpeter@812
   512
      for ( ; k <= n; ++k) {
kpeter@812
   513
        processNextFullRound(k);
kpeter@812
   514
      }
kpeter@812
   515
    }
kpeter@812
   516
kpeter@812
   517
    // Process one round and rebuild _process
kpeter@812
   518
    void processNextBuildRound(int k) {
kpeter@812
   519
      std::vector<Node> next;
kpeter@812
   520
      Node u, v;
kpeter@812
   521
      Arc e;
kpeter@812
   522
      LargeValue d;
kpeter@812
   523
      for (int i = 0; i < int(_process.size()); ++i) {
kpeter@812
   524
        u = _process[i];
kpeter@812
   525
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@812
   526
          e = _out_arcs[u][j];
kpeter@812
   527
          v = _gr.target(e);
kpeter@812
   528
          d = _data[u][k-1].dist + _length[e];
kpeter@814
   529
          if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@814
   530
            if (_data[v][k].dist == INF) next.push_back(v);
kpeter@814
   531
            _data[v][k] = PathData(d, e);
kpeter@812
   532
          }
kpeter@812
   533
        }
kpeter@812
   534
      }
kpeter@812
   535
      _process.swap(next);
kpeter@812
   536
    }
kpeter@812
   537
kpeter@812
   538
    // Process one round using _nodes instead of _process
kpeter@812
   539
    void processNextFullRound(int k) {
kpeter@812
   540
      Node u, v;
kpeter@812
   541
      Arc e;
kpeter@812
   542
      LargeValue d;
kpeter@812
   543
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@812
   544
        u = (*_nodes)[i];
kpeter@812
   545
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@812
   546
          e = _out_arcs[u][j];
kpeter@812
   547
          v = _gr.target(e);
kpeter@812
   548
          d = _data[u][k-1].dist + _length[e];
kpeter@814
   549
          if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@814
   550
            _data[v][k] = PathData(d, e);
kpeter@812
   551
          }
kpeter@812
   552
        }
kpeter@812
   553
      }
kpeter@812
   554
    }
kpeter@812
   555
kpeter@812
   556
    // Update the minimum cycle mean
kpeter@812
   557
    void updateMinMean() {
kpeter@812
   558
      int n = _nodes->size();
kpeter@812
   559
      for (int i = 0; i < n; ++i) {
kpeter@812
   560
        Node u = (*_nodes)[i];
kpeter@814
   561
        if (_data[u][n].dist == INF) continue;
kpeter@812
   562
        LargeValue length, max_length = 0;
kpeter@812
   563
        int size, max_size = 1;
kpeter@812
   564
        bool found_curr = false;
kpeter@812
   565
        for (int k = 0; k < n; ++k) {
kpeter@814
   566
          if (_data[u][k].dist == INF) continue;
kpeter@812
   567
          length = _data[u][n].dist - _data[u][k].dist;
kpeter@812
   568
          size = n - k;
kpeter@812
   569
          if (!found_curr || length * max_size > max_length * size) {
kpeter@812
   570
            found_curr = true;
kpeter@812
   571
            max_length = length;
kpeter@812
   572
            max_size = size;
kpeter@812
   573
          }
kpeter@812
   574
        }
kpeter@812
   575
        if ( found_curr && (_cycle_node == INVALID ||
kpeter@812
   576
             max_length * _cycle_size < _cycle_length * max_size) ) {
kpeter@812
   577
          _cycle_length = max_length;
kpeter@812
   578
          _cycle_size = max_size;
kpeter@812
   579
          _cycle_node = u;
kpeter@812
   580
        }
kpeter@812
   581
      }
kpeter@812
   582
    }
kpeter@812
   583
kpeter@812
   584
  }; //class Karp
kpeter@812
   585
kpeter@812
   586
  ///@}
kpeter@812
   587
kpeter@812
   588
} //namespace lemon
kpeter@812
   589
kpeter@812
   590
#endif //LEMON_KARP_H