RhodeCode

/* -*- 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_CAPACITY_SCALING_H

#define LEMON_CAPACITY_SCALING_H

/// \ingroup min_cost_flow_algs

///

/// \file

/// \brief Capacity Scaling algorithm for finding a minimum cost flow.

#include <vector>

#include <limits>

#include <lemon/core.h>

#include <lemon/bin_heap.h>

namespace lemon {

  /// \brief Default traits class of CapacityScaling algorithm.

  ///

  /// Default traits class of CapacityScaling algorithm.

  /// \tparam GR Digraph type.

  /// \tparam V The number type used for flow amounts, capacity bounds

  /// and supply values. By default it is \c int.

  /// \tparam C The number type used for costs and potentials.

  /// By default it is the same as \c V.

  template <typename GR, typename V = int, typename C = V>

  struct CapacityScalingDefaultTraits

  {

    /// The type of the digraph

    typedef GR Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef V Value;

    /// The type of the arc costs

    typedef C Cost;

    /// \brief The type of the heap used for internal Dijkstra computations.

    ///

    /// The type of the heap used for internal Dijkstra computations.

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

    /// its priority type must be \c Cost and its cross reference type

    /// must be \ref RangeMap "RangeMap<int>".

    typedef BinHeap<Cost, RangeMap<int> > Heap;

  };

  /// \addtogroup min_cost_flow_algs

  /// @{

  /// \brief Implementation of the Capacity Scaling algorithm for

  /// finding a \ref min_cost_flow "minimum cost flow".

  ///

  /// \ref CapacityScaling implements the capacity scaling version

  /// of the successive shortest path algorithm for finding a

  /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows,

  /// \ref edmondskarp72theoretical. It is an efficient dual

  /// solution method.

  ///

  /// Most of the parameters of the problem (except for the digraph)

  /// can be given using separate functions, and the algorithm can be

  /// executed using the \ref run() function. If some parameters are not

  /// specified, then default values will be used.

  ///

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

  /// \tparam V The number type used for flow amounts, capacity bounds

  /// and supply values in the algorithm. By default, it is \c int.

  /// \tparam C The number type used for costs and potentials in the

  /// algorithm. By default, it is the same as \c V.

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

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

  /// "CapacityScalingDefaultTraits<GR, V, C>".

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

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

  ///

  /// be integer.

  /// \warning This algorithm does not support negative costs for such

  /// arcs that have infinite upper bound.

#ifdef DOXYGEN

  template <typename GR, typename V, typename C, typename TR>

#else

  template < typename GR, typename V = int, typename C = V,

             typename TR = CapacityScalingDefaultTraits<GR, V, C> >

#endif

  class CapacityScaling

  {

  public:

    /// The type of the digraph

    typedef typename TR::Digraph Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef typename TR::Value Value;

    /// The type of the arc costs

    typedef typename TR::Cost Cost;

    /// The type of the heap used for internal Dijkstra computations

    typedef typename TR::Heap Heap;

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

    typedef TR Traits;

  public:

    /// \brief Problem type constants for the \c run() function.

    ///

    /// Enum type containing the problem type constants that can be

    /// returned by the \ref run() function of the algorithm.

    enum ProblemType {

      /// The problem has no feasible solution (flow).

      INFEASIBLE,

      /// The problem has optimal solution (i.e. it is feasible and

      /// bounded), and the algorithm has found optimal flow and node

      /// potentials (primal and dual solutions).

      OPTIMAL,

      /// The digraph contains an arc of negative cost and infinite

      /// upper bound. It means that the objective function is unbounded

      /// on that arc, however, note that it could actually be bounded

      /// over the feasible flows, but this algroithm cannot handle

      /// these cases.

      UNBOUNDED

    };

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(GR);

    typedef std::vector<int> IntVector;

    typedef std::vector<Value> ValueVector;

    typedef std::vector<Cost> CostVector;

    typedef std::vector<char> BoolVector;

    // Note: vector<char> is used instead of vector<bool> for efficiency reasons

  private:

    // Data related to the underlying digraph

    const GR &_graph;

    int _node_num;

    int _arc_num;

    int _res_arc_num;

    int _root;

    // Parameters of the problem

    bool _have_lower;

    Value _sum_supply;

    // Data structures for storing the digraph

    IntNodeMap _node_id;

    IntArcMap _arc_idf;

    IntArcMap _arc_idb;

    IntVector _first_out;

    BoolVector _forward;

    IntVector _source;

    IntVector _target;

    IntVector _reverse;

    // Node and arc data

    ValueVector _lower;

    ValueVector _upper;

    CostVector _cost;

    ValueVector _supply;

    ValueVector _res_cap;

    CostVector _pi;

    ValueVector _excess;

    IntVector _excess_nodes;

    IntVector _deficit_nodes;

    Value _delta;

    int _factor;

    IntVector _pred;

  public:

    /// \brief Constant for infinite upper bounds (capacities).

    ///

    /// Constant for infinite upper bounds (capacities).

    /// It is \c std::numeric_limits<Value>::infinity() if available,

    /// \c std::numeric_limits<Value>::max() otherwise.

    const Value INF;

  private:

    // Special implementation of the Dijkstra algorithm for finding

    // shortest paths in the residual network of the digraph with

    // respect to the reduced arc costs and modifying the node

    // potentials according to the found distance labels.

    class ResidualDijkstra

    {

    private:

      int _node_num;

      bool _geq;

      const IntVector &_first_out;

      const IntVector &_target;

      const CostVector &_cost;

      const ValueVector &_res_cap;

      const ValueVector &_excess;

      CostVector &_pi;

      IntVector &_pred;

      IntVector _proc_nodes;

      CostVector _dist;

    public:

      ResidualDijkstra(CapacityScaling& cs) :

        _node_num(cs._node_num), _geq(cs._sum_supply < 0),

        _first_out(cs._first_out), _target(cs._target), _cost(cs._cost),

        _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi),

        _pred(cs._pred), _dist(cs._node_num)

      {}

      int run(int s, Value delta = 1) {

        RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP);

        Heap heap(heap_cross_ref);

        heap.push(s, 0);

        _pred[s] = -1;

        _proc_nodes.clear();

        // Process nodes

        while (!heap.empty() && _excess[heap.top()] > -delta) {

          int u = heap.top(), v;

          Cost d = heap.prio() + _pi[u], dn;

          _dist[u] = heap.prio();

          _proc_nodes.push_back(u);

          heap.pop();

          // Traverse outgoing residual arcs

          int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1;

          for (int a = _first_out[u]; a != last_out; ++a) {

            if (_res_cap[a] < delta) continue;

            v = _target[a];

            switch (heap.state(v)) {

              case Heap::PRE_HEAP:

                heap.push(v, d + _cost[a] - _pi[v]);

                _pred[v] = a;

                break;

              case Heap::IN_HEAP:

                dn = d + _cost[a] - _pi[v];

                if (dn < heap[v]) {

                  heap.decrease(v, dn);

                  _pred[v] = a;

                }

                break;

              case Heap::POST_HEAP:

                break;

            }

          }

        }

        if (heap.empty()) return -1;

        // Update potentials of processed nodes

        int t = heap.top();

        Cost dt = heap.prio();

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

          _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt;

        }

        return t;

      }

    }; //class ResidualDijkstra

  public:

    /// \name Named Template Parameters

    /// @{

/* -*- 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_COST_SCALING_H

#define LEMON_COST_SCALING_H

/// \ingroup min_cost_flow_algs

/// \file

/// \brief Cost scaling algorithm for finding a minimum cost flow.

#include <vector>

#include <deque>

#include <limits>

#include <lemon/core.h>

#include <lemon/maps.h>

#include <lemon/math.h>

#include <lemon/static_graph.h>

#include <lemon/circulation.h>

#include <lemon/bellman_ford.h>

namespace lemon {

  /// \brief Default traits class of CostScaling algorithm.

  ///

  /// Default traits class of CostScaling algorithm.

  /// \tparam GR Digraph type.

  /// \tparam V The number type used for flow amounts, capacity bounds

  /// and supply values. By default it is \c int.

  /// \tparam C The number type used for costs and potentials.

  /// By default it is the same as \c V.

#ifdef DOXYGEN

  template <typename GR, typename V = int, typename C = V>

#else

  template < typename GR, typename V = int, typename C = V,

             bool integer = std::numeric_limits<C>::is_integer >

#endif

  struct CostScalingDefaultTraits

  {

    /// The type of the digraph

    typedef GR Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef V Value;

    /// The type of the arc costs

    typedef C 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;

  };

  // Default traits class for integer cost types

  template <typename GR, typename V, typename C>

  struct CostScalingDefaultTraits<GR, V, C, true>

  {

    typedef GR Digraph;

    typedef V Value;

    typedef C Cost;

#ifdef LEMON_HAVE_LONG_LONG

    typedef long long LargeCost;

#else

    typedef long LargeCost;

#endif

  };

  /// \addtogroup min_cost_flow_algs

  /// @{

  /// \brief Implementation of the Cost Scaling algorithm for

  /// finding a \ref min_cost_flow "minimum cost flow".

  ///

  /// \ref CostScaling implements a cost scaling algorithm that performs

  /// push/augment and relabel operations for finding a \ref min_cost_flow

  /// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation,

  /// \ref goldberg97efficient, \ref bunnagel98efficient.

  /// It is a highly efficient primal-dual solution method, which

  /// can be viewed as the generalization of the \ref Preflow

  /// "preflow push-relabel" algorithm for the maximum flow problem.

  ///

  /// Most of the parameters of the problem (except for the digraph)

  /// can be given using separate functions, and the algorithm can be

  /// executed using the \ref run() function. If some parameters are not

  /// specified, then default values will be used.

  ///

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

  /// \tparam V The number type used for flow amounts, capacity bounds

  /// and supply values in the algorithm. By default, it is \c int.

  /// \tparam C The number type used for costs and potentials in the

  /// algorithm. By default, it is the same as \c V.

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

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

  /// "CostScalingDefaultTraits<GR, V, C>".

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

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

  ///

  /// be integer.

  /// \warning This algorithm does not support negative costs for such

  /// arcs that have infinite upper bound.

  ///

  /// \note %CostScaling provides three different internal methods,

  /// from which the most efficient one is used by default.

  /// For more information, see \ref Method.

#ifdef DOXYGEN

  template <typename GR, typename V, typename C, typename TR>

#else

  template < typename GR, typename V = int, typename C = V,

             typename TR = CostScalingDefaultTraits<GR, V, C> >

#endif

  class CostScaling

  {

  public:

    /// The type of the digraph

    typedef typename TR::Digraph Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef typename TR::Value Value;

    /// 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 \ref CostScalingDefaultTraits "traits class" of the algorithm

    typedef TR Traits;

  public:

    /// \brief Problem type constants for the \c run() function.

    ///

    /// Enum type containing the problem type constants that can be

    /// returned by the \ref run() function of the algorithm.

    enum ProblemType {

      /// The problem has no feasible solution (flow).

      INFEASIBLE,

      /// The problem has optimal solution (i.e. it is feasible and

      /// bounded), and the algorithm has found optimal flow and node

      /// potentials (primal and dual solutions).

      OPTIMAL,

      /// The digraph contains an arc of negative cost and infinite

      /// upper bound. It means that the objective function is unbounded

      /// on that arc, however, note that it could actually be bounded

      /// over the feasible flows, but this algroithm cannot handle

      /// these cases.

      UNBOUNDED

    };

    /// \brief Constants for selecting the internal method.

    ///

    /// Enum type containing constants for selecting the internal method

    /// for the \ref run() function.

    ///

    /// \ref CostScaling provides three internal methods that differ mainly

    /// in their base operations, which are used in conjunction with the

    /// relabel operation.

    /// By default, the so called \ref PARTIAL_AUGMENT

    /// "Partial Augment-Relabel" method is used, which proved to be

    /// the most efficient and the most robust on various test inputs.

    /// However, the other methods can be selected using the \ref run()

    /// function with the proper parameter.

    enum Method {

      /// Local push operations are used, i.e. flow is moved only on one

      /// admissible arc at once.

      PUSH,

      /// Augment operations are used, i.e. flow is moved on admissible

      /// paths from a node with excess to a node with deficit.

      AUGMENT,

      /// Partial augment operations are used, i.e. flow is moved on

      /// admissible paths started from a node with excess, but the

      /// lengths of these paths are limited. This method can be viewed

      /// as a combined version of the previous two operations.

      PARTIAL_AUGMENT

    };

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(GR);

    typedef std::vector<int> IntVector;

    typedef std::vector<Value> ValueVector;

    typedef std::vector<Cost> CostVector;

    typedef std::vector<LargeCost> LargeCostVector;

    typedef std::vector<char> BoolVector;

    // Note: vector<char> is used instead of vector<bool> for efficiency reasons

  private:

    template <typename KT, typename VT>

    class StaticVectorMap {

    public:

      typedef KT Key;

      typedef VT Value;

      StaticVectorMap(std::vector<Value>& v) : _v(v) {}

      const Value& operator[](const Key& key) const {

        return _v[StaticDigraph::id(key)];

      }

      Value& operator[](const Key& key) {

        return _v[StaticDigraph::id(key)];

      }

      void set(const Key& key, const Value& val) {

        _v[StaticDigraph::id(key)] = val;

      }

    private:

      std::vector<Value>& _v;

    };

    typedef StaticVectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap;

    typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;

  private:

    // Data related to the underlying digraph

    const GR &_graph;

    int _node_num;

    int _arc_num;

    int _res_node_num;

    int _res_arc_num;

    int _root;

    // Parameters of the problem

    bool _have_lower;

    Value _sum_supply;

    int _sup_node_num;

    // Data structures for storing the digraph

    IntNodeMap _node_id;

    IntArcMap _arc_idf;

    IntArcMap _arc_idb;

    IntVector _first_out;

    BoolVector _forward;

    IntVector _source;

    IntVector _target;

    IntVector _reverse;

    // Node and arc data

    ValueVector _lower;

    ValueVector _upper;

    CostVector _scost;

    ValueVector _supply;

    ValueVector _res_cap;

    LargeCostVector _cost;

    LargeCostVector _pi;

    ValueVector _excess;

    IntVector _next_out;

    std::deque<int> _active_nodes;

    // Data for scaling

    LargeCost _epsilon;

    int _alpha;

    IntVector _buckets;

    IntVector _bucket_next;

    IntVector _bucket_prev;

    IntVector _rank;

    int _max_rank;

    // Data for a StaticDigraph structure

    typedef std::pair<int, int> IntPair;

    StaticDigraph _sgr;

    std::vector<IntPair> _arc_vec;

    std::vector<LargeCost> _cost_vec;

    LargeCostArcMap _cost_map;

    LargeCostNodeMap _pi_map;

  public:

    /// \brief Constant for infinite upper bounds (capacities).

    ///

    /// Constant for infinite upper bounds (capacities).

    /// It is \c std::numeric_limits<Value>::infinity() if available,

    /// \c std::numeric_limits<Value>::max() otherwise.

    const Value INF;

  public:

    /// \name Named Template Parameters

    /// @{

/* -*- 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_CYCLE_CANCELING_H

#define LEMON_CYCLE_CANCELING_H

/// \ingroup min_cost_flow_algs

/// \file

/// \brief Cycle-canceling algorithms for finding a minimum cost flow.

#include <vector>

#include <limits>

#include <lemon/core.h>

#include <lemon/maps.h>

#include <lemon/path.h>

#include <lemon/math.h>

#include <lemon/static_graph.h>

#include <lemon/adaptors.h>

#include <lemon/circulation.h>

#include <lemon/bellman_ford.h>

#include <lemon/howard_mmc.h>

namespace lemon {

  /// \addtogroup min_cost_flow_algs

  /// @{

  /// \brief Implementation of cycle-canceling algorithms for

  /// finding a \ref min_cost_flow "minimum cost flow".

  ///

  /// \ref CycleCanceling implements three different cycle-canceling

  /// algorithms for finding a \ref min_cost_flow "minimum cost flow"

  /// \ref amo93networkflows, \ref klein67primal,

  /// \ref goldberg89cyclecanceling.

  /// The most efficent one (both theoretically and practically)

  /// is the \ref CANCEL_AND_TIGHTEN "Cancel and Tighten" algorithm,

  /// thus it is the default method.

  /// It is strongly polynomial, but in practice, it is typically much

  /// slower than the scaling algorithms and NetworkSimplex.

  ///

  /// Most of the parameters of the problem (except for the digraph)

  /// can be given using separate functions, and the algorithm can be

  /// executed using the \ref run() function. If some parameters are not

  /// specified, then default values will be used.

  ///

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

  /// \tparam V The number type used for flow amounts, capacity bounds

  /// and supply values in the algorithm. By default, it is \c int.

  /// \tparam C The number type used for costs and potentials in the

  /// algorithm. By default, it is the same as \c V.

  ///

  /// be integer.

  /// \warning This algorithm does not support negative costs for such

  /// arcs that have infinite upper bound.

  ///

  /// \note For more information about the three available methods,

  /// see \ref Method.

#ifdef DOXYGEN

  template <typename GR, typename V, typename C>

#else

  template <typename GR, typename V = int, typename C = V>

#endif

  class CycleCanceling

  {

  public:

    /// The type of the digraph

    typedef GR Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef V Value;

    /// The type of the arc costs

    typedef C Cost;

  public:

    /// \brief Problem type constants for the \c run() function.

    ///

    /// Enum type containing the problem type constants that can be

    /// returned by the \ref run() function of the algorithm.

    enum ProblemType {

      /// The problem has no feasible solution (flow).

      INFEASIBLE,

      /// The problem has optimal solution (i.e. it is feasible and

      /// bounded), and the algorithm has found optimal flow and node

      /// potentials (primal and dual solutions).

      OPTIMAL,

      /// The digraph contains an arc of negative cost and infinite

      /// upper bound. It means that the objective function is unbounded

      /// on that arc, however, note that it could actually be bounded

      /// over the feasible flows, but this algroithm cannot handle

      /// these cases.

      UNBOUNDED

    };

    /// \brief Constants for selecting the used method.

    ///

    /// Enum type containing constants for selecting the used method

    /// for the \ref run() function.

    ///

    /// \ref CycleCanceling provides three different cycle-canceling

    /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel and Tighten"

    /// is used, which proved to be the most efficient and the most robust

    /// on various test inputs.

    /// However, the other methods can be selected using the \ref run()

    /// function with the proper parameter.

    enum Method {

      /// A simple cycle-canceling method, which uses the

      /// \ref BellmanFord "Bellman-Ford" algorithm with limited iteration

      /// number for detecting negative cycles in the residual network.

      SIMPLE_CYCLE_CANCELING,

      /// The "Minimum Mean Cycle-Canceling" algorithm, which is a

      /// well-known strongly polynomial method

      /// \ref goldberg89cyclecanceling. It improves along a

      /// \ref min_mean_cycle "minimum mean cycle" in each iteration.

      /// Its running time complexity is O(n<sup>2</sup>m<sup>3</sup>log(n)).

      MINIMUM_MEAN_CYCLE_CANCELING,

      /// The "Cancel And Tighten" algorithm, which can be viewed as an

      /// improved version of the previous method

      /// \ref goldberg89cyclecanceling.

      /// It is faster both in theory and in practice, its running time

      /// complexity is O(n<sup>2</sup>m<sup>2</sup>log(n)).

      CANCEL_AND_TIGHTEN

    };

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(GR);

    typedef std::vector<int> IntVector;

    typedef std::vector<double> DoubleVector;

    typedef std::vector<Value> ValueVector;

    typedef std::vector<Cost> CostVector;

    typedef std::vector<char> BoolVector;

    // Note: vector<char> is used instead of vector<bool> for efficiency reasons

  private:

    template <typename KT, typename VT>

    class StaticVectorMap {

    public:

      typedef KT Key;

      typedef VT Value;

      StaticVectorMap(std::vector<Value>& v) : _v(v) {}

      const Value& operator[](const Key& key) const {

        return _v[StaticDigraph::id(key)];

      }

      Value& operator[](const Key& key) {

        return _v[StaticDigraph::id(key)];

      }

      void set(const Key& key, const Value& val) {

        _v[StaticDigraph::id(key)] = val;

      }

    private:

      std::vector<Value>& _v;

    };

    typedef StaticVectorMap<StaticDigraph::Node, Cost> CostNodeMap;

    typedef StaticVectorMap<StaticDigraph::Arc, Cost> CostArcMap;

  private:

    // Data related to the underlying digraph

    const GR &_graph;

    int _node_num;

    int _arc_num;

    int _res_node_num;

    int _res_arc_num;

    int _root;

    // Parameters of the problem

    bool _have_lower;

    Value _sum_supply;

    // Data structures for storing the digraph

    IntNodeMap _node_id;

    IntArcMap _arc_idf;

    IntArcMap _arc_idb;

    IntVector _first_out;

    BoolVector _forward;

    IntVector _source;

    IntVector _target;

    IntVector _reverse;

    // Node and arc data

    ValueVector _lower;

    ValueVector _upper;

    CostVector _cost;

    ValueVector _supply;

    ValueVector _res_cap;

    CostVector _pi;

    // Data for a StaticDigraph structure

    typedef std::pair<int, int> IntPair;

    StaticDigraph _sgr;

    std::vector<IntPair> _arc_vec;

    std::vector<Cost> _cost_vec;

    IntVector _id_vec;

    CostArcMap _cost_map;

    CostNodeMap _pi_map;

  public:

    /// \brief Constant for infinite upper bounds (capacities).

    ///

    /// Constant for infinite upper bounds (capacities).

    /// It is \c std::numeric_limits<Value>::infinity() if available,

    /// \c std::numeric_limits<Value>::max() otherwise.

    const Value INF;

  public:

    /// \brief Constructor.

    ///

    /// The constructor of the class.

    ///

    /// \param graph The digraph the algorithm runs on.

    CycleCanceling(const GR& graph) :

      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),

      _cost_map(_cost_vec), _pi_map(_pi),

      INF(std::numeric_limits<Value>::has_infinity ?

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

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

    {

      // Check the number types

      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,

        "The flow type of CycleCanceling must be signed");

      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,

        "The cost type of CycleCanceling must be signed");

      // Reset data structures

      reset();

    }

    /// \name Parameters

    /// The parameters of the algorithm can be specified using these

    /// functions.

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

 *

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

 *

 * Copyright (C) 2003-2009

 * 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_KRUSKAL_H

#define LEMON_KRUSKAL_H

#include <algorithm>

#include <vector>

#include <lemon/unionfind.h>

#include <lemon/maps.h>

#include <lemon/core.h>

#include <lemon/bits/traits.h>

///\ingroup spantree

///\file

///\brief Kruskal's algorithm to compute a minimum cost spanning tree

namespace lemon {

  namespace _kruskal_bits {

    // Kruskal for directed graphs.

    template <typename Digraph, typename In, typename Out>

    typename disable_if<lemon::UndirectedTagIndicator<Digraph>,

                       typename In::value_type::second_type >::type

    kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {

      typedef typename In::value_type::second_type Value;

      typedef typename Digraph::template NodeMap<int> IndexMap;

      typedef typename Digraph::Node Node;

      IndexMap index(digraph);

      UnionFind<IndexMap> uf(index);

      for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {

        uf.insert(it);

      }

      Value tree_value = 0;

      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {

        if (uf.join(digraph.target(it->first),digraph.source(it->first))) {

          out.set(it->first, true);

          tree_value += it->second;

        }

        else {

          out.set(it->first, false);

        }

      }

      return tree_value;

    }

    // Kruskal for undirected graphs.

    template <typename Graph, typename In, typename Out>

    typename enable_if<lemon::UndirectedTagIndicator<Graph>,

                       typename In::value_type::second_type >::type

    kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {

      typedef typename In::value_type::second_type Value;

      typedef typename Graph::template NodeMap<int> IndexMap;

      typedef typename Graph::Node Node;

      IndexMap index(graph);

      UnionFind<IndexMap> uf(index);

      for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {

        uf.insert(it);

      }

      Value tree_value = 0;

      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {

        if (uf.join(graph.u(it->first),graph.v(it->first))) {

          out.set(it->first, true);

          tree_value += it->second;

        }

        else {

          out.set(it->first, false);

        }

      }

      return tree_value;

    }

    template <typename Sequence>

    struct PairComp {

      typedef typename Sequence::value_type Value;

      bool operator()(const Value& left, const Value& right) {

        return left.second < right.second;

      }

    };

    template <typename In, typename Enable = void>

    struct SequenceInputIndicator {

      static const bool value = false;

    };

    template <typename In>

    struct SequenceInputIndicator<In,

      typename exists<typename In::value_type::first_type>::type> {

      static const bool value = true;

    };

    template <typename In, typename Enable = void>

    struct MapInputIndicator {

      static const bool value = false;

    };

    template <typename In>

    struct MapInputIndicator<In,

      typename exists<typename In::Value>::type> {

      static const bool value = true;

    };

    template <typename In, typename Enable = void>

    struct SequenceOutputIndicator {

      static const bool value = false;

    };

    template <typename Out>

    struct SequenceOutputIndicator<Out,

      typename exists<typename Out::value_type>::type> {

      static const bool value = true;

    };

    template <typename Out, typename Enable = void>

    struct MapOutputIndicator {

      static const bool value = false;

    };

    template <typename Out>

    struct MapOutputIndicator<Out,

      typename exists<typename Out::Value>::type> {

      static const bool value = true;

    };

    template <typename In, typename InEnable = void>

    struct KruskalValueSelector {};

    template <typename In>

    struct KruskalValueSelector<In,

      typename enable_if<SequenceInputIndicator<In>, void>::type>

    {

      typedef typename In::value_type::second_type Value;

    };

    template <typename In>

    struct KruskalValueSelector<In,

      typename enable_if<MapInputIndicator<In>, void>::type>

    {

      typedef typename In::Value Value;

    };

    template <typename Graph, typename In, typename Out,

              typename InEnable = void>

    struct KruskalInputSelector {};

    template <typename Graph, typename In, typename Out,

              typename InEnable = void>

    struct KruskalOutputSelector {};

    template <typename Graph, typename In, typename Out>

    struct KruskalInputSelector<Graph, In, Out,

      typename enable_if<SequenceInputIndicator<In>, void>::type >

    {

      typedef typename In::value_type::second_type Value;

      static Value kruskal(const Graph& graph, const In& in, Out& out) {

        return KruskalOutputSelector<Graph, In, Out>::

          kruskal(graph, in, out);

      }

    };

    template <typename Graph, typename In, typename Out>

    struct KruskalInputSelector<Graph, In, Out,

      typename enable_if<MapInputIndicator<In>, void>::type >

    {

      typedef typename In::Value Value;

      static Value kruskal(const Graph& graph, const In& in, Out& out) {

        typedef typename In::Key MapArc;

        typedef typename In::Value Value;

        typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;

        typedef std::vector<std::pair<MapArc, Value> > Sequence;

        Sequence seq;

        for (MapArcIt it(graph); it != INVALID; ++it) {

          seq.push_back(std::make_pair(it, in[it]));

        }

        std::sort(seq.begin(), seq.end(), PairComp<Sequence>());

        return KruskalOutputSelector<Graph, Sequence, Out>::

          kruskal(graph, seq, out);

      }

    };

    template <typename T>

    struct RemoveConst {

      typedef T type;

    };

    template <typename T>

    struct RemoveConst<const T> {

      typedef T type;

    };

    template <typename Graph, typename In, typename Out>

    struct KruskalOutputSelector<Graph, In, Out,

      typename enable_if<SequenceOutputIndicator<Out>, void>::type >

    {

      typedef typename In::value_type::second_type Value;

/* -*- 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.