LEMON/LEMON-official Changeset - r1025:140c953ad5d1

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Changeset - r1025:140c953ad5d1

« 1021:4980b0

1026:9312d6 »

r1025:140c953ad5d1

Sat, 08 Jan 2011 16:11:48

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Minor doc improvements

0 5 0

default

5 files changed with 8 insertions and 7 deletions:

lemon/capacity_scaling.h

lemon/cost_scaling.h

lemon/cycle_canceling.h

lemon/kruskal.h

lemon/network_simplex.h

↑ Collapse diff ↑

lemon/capacity_scaling.h

Show inline comments

 		/* -*- 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.
 		  ///
-		  /// \warning Both number types must be signed and all input data must
+		  /// \warning Both \c V and \c C must be signed number types.
 		  /// \warning All input data (capacities, supply values, and costs) must
 		  /// 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
 		    /// @{
 		    template <typename T>
 		    struct SetHeapTraits : public Traits {
 		      typedef T Heap;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c Heap type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c Heap
 		    /// type, which is 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>".
 		    template <typename T>
 		    struct SetHeap
 		      : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {
 		      typedef  CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;
 		    };
 		    /// @}
 		  protected:
 		    CapacityScaling() {}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param graph The digraph the algorithm runs on.
 		    CapacityScaling(const GR& graph) :
 		      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
 		      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 CapacityScaling must be signed");
 		      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
 		        "The cost type of CapacityScaling must be signed");
 		      // Reset data structures
 		      reset();
+		    }
 		    /// \name Parameters
 		    /// The parameters of the algorithm can be specified using these
 		    /// functions.
 		    /// @{
 		    /// \brief Set the lower bounds on the arcs.
 		    ///
 		    /// This function sets the lower bounds on the arcs.
 		    /// If it is not used before calling \ref run(), the lower bounds
 		    /// will be set to zero on all arcs.
 		    ///
 		    /// \param map An arc map storing the lower bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template <typename LowerMap>
 		    CapacityScaling& lowerMap(const LowerMap& map) {
 		      _have_lower = true;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _lower[_arc_idf[a]] = map[a];
 		        _lower[_arc_idb[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the upper bounds (capacities) on the arcs.
 		    ///
 		    /// This function sets the upper bounds (capacities) on the arcs.
 		    /// If it is not used before calling \ref run(), the upper bounds
 		    /// will be set to \ref INF on all arcs (i.e. the flow value will be
 		    /// unbounded from above).
 		    ///
 		    /// \param map An arc map storing the upper bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename UpperMap>
 		    CapacityScaling& upperMap(const UpperMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _upper[_arc_idf[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the costs of the arcs.
 		    ///
 		    /// This function sets the costs of the arcs.
 		    /// If it is not used before calling \ref run(), the costs
 		    /// will be set to \c 1 on all arcs.
 		    ///
 		    /// \param map An arc map storing the costs.
 		    /// Its \c Value type must be convertible to the \c Cost type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename CostMap>
 		    CapacityScaling& costMap(const CostMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _cost[_arc_idf[a]] =  map[a];
 		        _cost[_arc_idb[a]] = -map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the supply values of the nodes.
 		    ///
 		    /// This function sets the supply values of the nodes.
 		    /// If neither this function nor \ref stSupply() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// \param map A node map storing the supply values.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename SupplyMap>
 		    CapacityScaling& supplyMap(const SupplyMap& map) {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        _supply[_node_id[n]] = map[n];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set single source and target nodes and a supply value.
 		    ///
 		    /// This function sets a single source node and a single target node
 		    /// and the required flow value.
 		    /// If neither this function nor \ref supplyMap() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// Using this function has the same effect as using \ref supplyMap()
 		    /// with such a map in which \c k is assigned to \c s, \c -k is
 		    /// assigned to \c t and all other nodes have zero supply value.
 		    ///
 		    /// \param s The source node.
 		    /// \param t The target node.
 		    /// \param k The required amount of flow from node \c s to node \c t
 		    /// (i.e. the supply of \c s and the demand of \c t).
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CapacityScaling& stSupply(const Node& s, const Node& t, Value k) {
 		      for (int i = 0; i != _node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      _supply[_node_id[s]] =  k;
 		      _supply[_node_id[t]] = -k;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Execution control
 		    /// The algorithm can be executed using \ref run().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// The paramters can be specified using functions \ref lowerMap(),
 		    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    /// For example,
 		    /// \code
 		    ///   CapacityScaling<ListDigraph> cs(graph);
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// This function can be called more than once. All the given parameters
 		    /// are kept for the next call, unless \ref resetParams() or \ref reset()
 		    /// is used, thus only the modified parameters have to be set again.
 		    /// If the underlying digraph was also modified after the construction
 		    /// of the class (or the last \ref reset() call), then the \ref reset()
 		    /// function must be called.
 		    ///
 		    /// \param factor The capacity scaling factor. It must be larger than
 		    /// one to use scaling. If it is less or equal to one, then scaling
 		    /// will be disabled.
 		    ///
 		    /// \return \c INFEASIBLE if no feasible flow exists,

lemon/cost_scaling.h

Show inline comments

 		/* -*- 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.
 		  ///
-		  /// \warning Both number types must be signed and all input data must
+		  /// \warning Both \c V and \c C must be signed number types.
 		  /// \warning All input data (capacities, supply values, and costs) must
 		  /// 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
 		    /// @{
 		    template <typename T>
 		    struct SetLargeCostTraits : public Traits {
 		      typedef T LargeCost;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c LargeCost type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
 		    /// type, which is used for internal computations in the algorithm.
 		    /// \c Cost must be convertible to \c LargeCost.
 		    template <typename T>
 		    struct SetLargeCost
 		      : public CostScaling<GR, V, C, SetLargeCostTraits<T> > {
 		      typedef  CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;
 		    };
 		    /// @}
 		  protected:
 		    CostScaling() {}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param graph The digraph the algorithm runs on.
 		    CostScaling(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 CostScaling must be signed");
 		      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
 		        "The cost type of CostScaling must be signed");
 		      // Reset data structures
 		      reset();
+		    }
 		    /// \name Parameters
 		    /// The parameters of the algorithm can be specified using these
 		    /// functions.
 		    /// @{
 		    /// \brief Set the lower bounds on the arcs.
 		    ///
 		    /// This function sets the lower bounds on the arcs.
 		    /// If it is not used before calling \ref run(), the lower bounds
 		    /// will be set to zero on all arcs.
 		    ///
 		    /// \param map An arc map storing the lower bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template <typename LowerMap>
 		    CostScaling& lowerMap(const LowerMap& map) {
 		      _have_lower = true;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _lower[_arc_idf[a]] = map[a];
 		        _lower[_arc_idb[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the upper bounds (capacities) on the arcs.
 		    ///
 		    /// This function sets the upper bounds (capacities) on the arcs.
 		    /// If it is not used before calling \ref run(), the upper bounds
 		    /// will be set to \ref INF on all arcs (i.e. the flow value will be
 		    /// unbounded from above).
 		    ///
 		    /// \param map An arc map storing the upper bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename UpperMap>
 		    CostScaling& upperMap(const UpperMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _upper[_arc_idf[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the costs of the arcs.
 		    ///
 		    /// This function sets the costs of the arcs.
 		    /// If it is not used before calling \ref run(), the costs
 		    /// will be set to \c 1 on all arcs.
 		    ///
 		    /// \param map An arc map storing the costs.
 		    /// Its \c Value type must be convertible to the \c Cost type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename CostMap>
 		    CostScaling& costMap(const CostMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _scost[_arc_idf[a]] =  map[a];
 		        _scost[_arc_idb[a]] = -map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the supply values of the nodes.
 		    ///
 		    /// This function sets the supply values of the nodes.
 		    /// If neither this function nor \ref stSupply() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// \param map A node map storing the supply values.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename SupplyMap>
 		    CostScaling& supplyMap(const SupplyMap& map) {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        _supply[_node_id[n]] = map[n];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set single source and target nodes and a supply value.
 		    ///
 		    /// This function sets a single source node and a single target node
 		    /// and the required flow value.
 		    /// If neither this function nor \ref supplyMap() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// Using this function has the same effect as using \ref supplyMap()
 		    /// with such a map in which \c k is assigned to \c s, \c -k is
 		    /// assigned to \c t and all other nodes have zero supply value.
 		    ///
 		    /// \param s The source node.
 		    /// \param t The target node.
 		    /// \param k The required amount of flow from node \c s to node \c t
 		    /// (i.e. the supply of \c s and the demand of \c t).
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CostScaling& stSupply(const Node& s, const Node& t, Value k) {
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      _supply[_node_id[s]] =  k;
 		      _supply[_node_id[t]] = -k;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Execution control
 		    /// The algorithm can be executed using \ref run().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// The paramters can be specified using functions \ref lowerMap(),
 		    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    /// For example,
 		    /// \code
 		    ///   CostScaling<ListDigraph> cs(graph);
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// This function can be called more than once. All the given parameters
 		    /// are kept for the next call, unless \ref resetParams() or \ref reset()
 		    /// is used, thus only the modified parameters have to be set again.
 		    /// If the underlying digraph was also modified after the construction
 		    /// of the class (or the last \ref reset() call), then the \ref reset()
 		    /// function must be called.
 		    ///
 		    /// \param method The internal method that will be used in the
 		    /// algorithm. For more information, see \ref Method.
 		    /// \param factor The cost scaling factor. It must be larger than one.
 		    ///
 		    /// \return \c INFEASIBLE if no feasible flow exists,
 		    /// \n \c OPTIMAL if the problem has optimal solution
 		    /// (i.e. it is feasible and bounded), and the algorithm has found

lemon/cycle_canceling.h

Show inline comments

 		/* -*- 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.
 		  ///
-		  /// \warning Both number types must be signed and all input data must
+		  /// \warning Both \c V and \c C must be signed number types.
 		  /// \warning All input data (capacities, supply values, and costs) must
 		  /// 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.
 		    /// @{
 		    /// \brief Set the lower bounds on the arcs.
 		    ///
 		    /// This function sets the lower bounds on the arcs.
 		    /// If it is not used before calling \ref run(), the lower bounds
 		    /// will be set to zero on all arcs.
 		    ///
 		    /// \param map An arc map storing the lower bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template <typename LowerMap>
 		    CycleCanceling& lowerMap(const LowerMap& map) {
 		      _have_lower = true;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _lower[_arc_idf[a]] = map[a];
 		        _lower[_arc_idb[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the upper bounds (capacities) on the arcs.
 		    ///
 		    /// This function sets the upper bounds (capacities) on the arcs.
 		    /// If it is not used before calling \ref run(), the upper bounds
 		    /// will be set to \ref INF on all arcs (i.e. the flow value will be
 		    /// unbounded from above).
 		    ///
 		    /// \param map An arc map storing the upper bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename UpperMap>
 		    CycleCanceling& upperMap(const UpperMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _upper[_arc_idf[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the costs of the arcs.
 		    ///
 		    /// This function sets the costs of the arcs.
 		    /// If it is not used before calling \ref run(), the costs
 		    /// will be set to \c 1 on all arcs.
 		    ///
 		    /// \param map An arc map storing the costs.
 		    /// Its \c Value type must be convertible to the \c Cost type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename CostMap>
 		    CycleCanceling& costMap(const CostMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _cost[_arc_idf[a]] =  map[a];
 		        _cost[_arc_idb[a]] = -map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the supply values of the nodes.
 		    ///
 		    /// This function sets the supply values of the nodes.
 		    /// If neither this function nor \ref stSupply() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// \param map A node map storing the supply values.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename SupplyMap>
 		    CycleCanceling& supplyMap(const SupplyMap& map) {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        _supply[_node_id[n]] = map[n];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set single source and target nodes and a supply value.
 		    ///
 		    /// This function sets a single source node and a single target node
 		    /// and the required flow value.
 		    /// If neither this function nor \ref supplyMap() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// Using this function has the same effect as using \ref supplyMap()
 		    /// with such a map in which \c k is assigned to \c s, \c -k is
 		    /// assigned to \c t and all other nodes have zero supply value.
 		    ///
 		    /// \param s The source node.
 		    /// \param t The target node.
 		    /// \param k The required amount of flow from node \c s to node \c t
 		    /// (i.e. the supply of \c s and the demand of \c t).
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CycleCanceling& stSupply(const Node& s, const Node& t, Value k) {
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      _supply[_node_id[s]] =  k;
 		      _supply[_node_id[t]] = -k;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Execution control
 		    /// The algorithm can be executed using \ref run().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// The paramters can be specified using functions \ref lowerMap(),
 		    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    /// For example,
 		    /// \code
 		    ///   CycleCanceling<ListDigraph> cc(graph);
 		    ///   cc.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// This function can be called more than once. All the given parameters
 		    /// are kept for the next call, unless \ref resetParams() or \ref reset()
 		    /// is used, thus only the modified parameters have to be set again.
 		    /// If the underlying digraph was also modified after the construction
 		    /// of the class (or the last \ref reset() call), then the \ref reset()
 		    /// function must be called.
 		    ///
 		    /// \param method The cycle-canceling method that will be used.
 		    /// For more information, see \ref Method.
 		    ///
 		    /// \return \c INFEASIBLE if no feasible flow exists,
 		    /// \n \c OPTIMAL if 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),
 		    /// \n \c UNBOUNDED if 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.
 		    ///
 		    /// \see ProblemType, Method
 		    /// \see resetParams(), reset()
 		    ProblemType run(Method method = CANCEL_AND_TIGHTEN) {
 		      ProblemType pt = init();
 		      if (pt != OPTIMAL) return pt;
 		      start(method);
 		      return OPTIMAL;
+		    }
 		    /// \brief Reset all the parameters that have been given before.
 		    ///
 		    /// This function resets all the paramaters that have been given
 		    /// before using functions \ref lowerMap(), \ref upperMap(),
 		    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    ///
 		    /// It is useful for multiple \ref run() calls. Basically, all the given
 		    /// parameters are kept for the next \ref run() call, unless
 		    /// \ref resetParams() or \ref reset() is used.
 		    /// If the underlying digraph was also modified after the construction
 		    /// of the class or the last \ref reset() call, then the \ref reset()
 		    /// function must be used, otherwise \ref resetParams() is sufficient.
 		    ///
 		    /// For example,
 		    /// \code
 		    ///   CycleCanceling<ListDigraph> cs(graph);
 		    ///
 		    ///   // First run
 		    ///   cc.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    ///
 		    ///   // Run again with modified cost map (resetParams() is not called,
 		    ///   // so only the cost map have to be set again)
 		    ///   cost[e] += 100;
 		    ///   cc.costMap(cost).run();
 		    ///
 		    ///   // Run again from scratch using resetParams()
 		    ///   // (the lower bounds will be set to zero on all arcs)
 		    ///   cc.resetParams();
 		    ///   cc.upperMap(capacity).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    ///

lemon/kruskal.h

Show inline comments

 		/* -*- 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
 		///
 		///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;
 		      static Value kruskal(const Graph& graph, const In& in, Out& out) {
 		        typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map;
 		        Map map(out);
 		        return _kruskal_bits::kruskal(graph, in, map);
+		      }
 		    };
 		    template <typename Graph, typename In, typename Out>
 		    struct KruskalOutputSelector<Graph, In, Out,
 		      typename enable_if<MapOutputIndicator<Out>, void>::type >
+		    {
 		      typedef typename In::value_type::second_type Value;
 		      static Value kruskal(const Graph& graph, const In& in, Out& out) {
 		        return _kruskal_bits::kruskal(graph, in, out);
+		      }
 		    };
+		  }
 		  /// \ingroup spantree
 		  ///
 		  /// \brief Kruskal's algorithm for finding a minimum cost spanning tree of
 		  /// a graph.
 		  ///
 		  /// This function runs Kruskal's algorithm to find a minimum cost
 		  /// spanning tree of a graph.
 		  /// Due to some C++ hacking, it accepts various input and output types.
 		  ///
 		  /// \param g The graph the algorithm runs on.
 		  /// It can be either \ref concepts::Digraph "directed" or
 		  /// \ref concepts::Graph "undirected".
 		  /// If the graph is directed, the algorithm consider it to be
 		  /// undirected by disregarding the direction of the arcs.
 		  ///
 		  /// \param in This object is used to describe the arc/edge costs.
 		  /// It can be one of the following choices.
 		  /// - An STL compatible 'Forward Container' with
 		  /// <tt>std::pair<GR::Arc,C></tt> or
 		  /// <tt>std::pair<GR::Edge,C></tt> as its <tt>value_type</tt>, where
 		  /// \c C is the type of the costs. The pairs indicates the arcs/edges
 		  /// along with the assigned cost. <em>They must be in a
 		  /// cost-ascending order.</em>
 		  /// - Any readable arc/edge map. The values of the map indicate the
 		  /// arc/edge costs.
 		  ///
 		  /// \retval out Here we also have a choice.
 		  /// - It can be a writable arc/edge map with \c bool value type. After
 		  /// running the algorithm it will contain the found minimum cost spanning
 		  /// tree: the value of an arc/edge will be set to \c true if it belongs
 		  /// to the tree, otherwise it will be set to \c false. The value of
 		  /// each arc/edge will be set exactly once.
 		  /// - It can also be an iteraror of an STL Container with
 		  /// <tt>GR::Arc</tt> or <tt>GR::Edge</tt> as its
 		  /// <tt>value_type</tt>.  The algorithm copies the elements of the
 		  /// found tree into this sequence.  For example, if we know that the
 		  /// spanning tree of the graph \c g has say 53 arcs, then we can
 		  /// put its arcs into an STL vector \c tree with a code like this.
 		  ///\code
 		  /// std::vector<Arc> tree(53);
 		  /// kruskal(g,cost,tree.begin());
 		  ///\endcode
 		  /// Or if we don't know in advance the size of the tree, we can
 		  /// write this.
 		  ///\code
 		  /// std::vector<Arc> tree;
 		  /// kruskal(g,cost,std::back_inserter(tree));
 		  ///\endcode
 		  ///
 		  /// \return The total cost of the found spanning tree.
 		  ///
 		  /// \note If the input graph is not (weakly) connected, a spanning
 		  /// forest is calculated instead of a spanning tree.
 		#ifdef DOXYGEN
 		  template <typename Graph, typename In, typename Out>
 		  Value kruskal(const Graph& g, const In& in, Out& out)
 		#else
 		  template <class Graph, class In, class Out>
 		  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
 		  kruskal(const Graph& graph, const In& in, Out& out)
 		#endif
+		  {
 		    return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
 		      kruskal(graph, in, out);
+		  }
 		  template <class Graph, class In, class Out>
 		  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
 		  kruskal(const Graph& graph, const In& in, const Out& out)
+		  {
 		    return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
 		      kruskal(graph, in, out);
+		  }
 		} //namespace lemon
 		#endif //LEMON_KRUSKAL_H

lemon/network_simplex.h

Show inline comments

 		/* -*- 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_NETWORK_SIMPLEX_H
 		#define LEMON_NETWORK_SIMPLEX_H
 		/// \ingroup min_cost_flow_algs
 		///
 		/// \file
 		/// \brief Network Simplex algorithm for finding a minimum cost flow.
 		#include <vector>
 		#include <limits>
 		#include <algorithm>
 		#include <lemon/core.h>
 		#include <lemon/math.h>
 		namespace lemon {
 		  /// \addtogroup min_cost_flow_algs
 		  /// @{
 		  /// \brief Implementation of the primal Network Simplex algorithm
 		  /// for finding a \ref min_cost_flow "minimum cost flow".
 		  ///
 		  /// \ref NetworkSimplex implements the primal Network Simplex algorithm
 		  /// for finding a \ref min_cost_flow "minimum cost flow"
 		  /// \ref amo93networkflows, \ref dantzig63linearprog,
 		  /// \ref kellyoneill91netsimplex.
 		  /// This algorithm is a highly efficient specialized version of the
 		  /// linear programming simplex method directly for the minimum cost
 		  /// flow problem.
 		  ///
 		  /// In general, %NetworkSimplex is the fastest implementation available
 		  /// in LEMON for this problem.
 		  /// Moreover, it supports both directions of the supply/demand inequality
 		  /// constraints. For more information, see \ref SupplyType.
 		  ///
 		  /// 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.
 		  ///
-		  /// \warning Both number types must be signed and all input data must
+		  /// \warning Both \c V and \c C must be signed number types.
 		  /// \warning All input data (capacities, supply values, and costs) must
 		  /// be integer.
 		  ///
 		  /// \note %NetworkSimplex provides five different pivot rule
 		  /// implementations, from which the most efficient one is used
 		  /// by default. For more information, see \ref PivotRule.
 		  template <typename GR, typename V = int, typename C = V>
 		  class NetworkSimplex
+		  {
 		  public:
 		    /// 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 objective function of the problem is unbounded, i.e.
 		      /// there is a directed cycle having negative total cost and
 		      /// infinite upper bound.
 		      UNBOUNDED
 		    };
 		    /// \brief Constants for selecting the type of the supply constraints.
 		    ///
 		    /// Enum type containing constants for selecting the supply type,
 		    /// i.e. the direction of the inequalities in the supply/demand
 		    /// constraints of the \ref min_cost_flow "minimum cost flow problem".
 		    ///
 		    /// The default supply type is \c GEQ, the \c LEQ type can be
 		    /// selected using \ref supplyType().
 		    /// The equality form is a special case of both supply types.
 		    enum SupplyType {
 		      /// This option means that there are <em>"greater or equal"</em>
 		      /// supply/demand constraints in the definition of the problem.
 		      GEQ,
 		      /// This option means that there are <em>"less or equal"</em>
 		      /// supply/demand constraints in the definition of the problem.
 		      LEQ
 		    };
 		    /// \brief Constants for selecting the pivot rule.
 		    ///
 		    /// Enum type containing constants for selecting the pivot rule for
 		    /// the \ref run() function.
 		    ///
 		    /// \ref NetworkSimplex provides five different pivot rule
 		    /// implementations that significantly affect the running time
 		    /// of the algorithm.
 		    /// By default, \ref BLOCK_SEARCH "Block Search" is used, which
 		    /// proved to be the most efficient and the most robust on various
 		    /// test inputs.
 		    /// However, another pivot rule can be selected using the \ref run()
 		    /// function with the proper parameter.
 		    enum PivotRule {
 		      /// The \e First \e Eligible pivot rule.
 		      /// The next eligible arc is selected in a wraparound fashion
 		      /// in every iteration.
 		      FIRST_ELIGIBLE,
 		      /// The \e Best \e Eligible pivot rule.
 		      /// The best eligible arc is selected in every iteration.
 		      BEST_ELIGIBLE,
 		      /// The \e Block \e Search pivot rule.
 		      /// A specified number of arcs are examined in every iteration
 		      /// in a wraparound fashion and the best eligible arc is selected
 		      /// from this block.
 		      BLOCK_SEARCH,
 		      /// The \e Candidate \e List pivot rule.
 		      /// In a major iteration a candidate list is built from eligible arcs
 		      /// in a wraparound fashion and in the following minor iterations
 		      /// the best eligible arc is selected from this list.
 		      CANDIDATE_LIST,
 		      /// The \e Altering \e Candidate \e List pivot rule.
 		      /// It is a modified version of the Candidate List method.
 		      /// It keeps only the several best eligible arcs from the former
 		      /// candidate list and extends this list in every iteration.
 		      ALTERING_LIST
 		    };
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
 		    typedef std::vector<int> IntVector;
 		    typedef std::vector<Value> ValueVector;
 		    typedef std::vector<Cost> CostVector;
 		    typedef std::vector<signed char> CharVector;
 		    // Note: vector<signed char> is used instead of vector<ArcState> and
 		    // vector<ArcDirection> for efficiency reasons
 		    // State constants for arcs
 		    enum ArcState {
 		      STATE_UPPER = -1,
 		      STATE_TREE  =  0,
 		      STATE_LOWER =  1
 		    };
 		    // Direction constants for tree arcs
 		    enum ArcDirection {
 		      DIR_DOWN = -1,
 		      DIR_UP   =  1
 		    };
 		  private:
 		    // Data related to the underlying digraph
 		    const GR &_graph;
 		    int _node_num;
 		    int _arc_num;
 		    int _all_arc_num;
 		    int _search_arc_num;
 		    // Parameters of the problem
 		    bool _have_lower;
 		    SupplyType _stype;
 		    Value _sum_supply;
 		    // Data structures for storing the digraph
 		    IntNodeMap _node_id;
 		    IntArcMap _arc_id;
 		    IntVector _source;
 		    IntVector _target;
 		    bool _arc_mixing;
 		    // Node and arc data
 		    ValueVector _lower;
 		    ValueVector _upper;
 		    ValueVector _cap;
 		    CostVector _cost;
 		    ValueVector _supply;
 		    ValueVector _flow;
 		    CostVector _pi;
 		    // Data for storing the spanning tree structure
 		    IntVector _parent;
 		    IntVector _pred;
 		    IntVector _thread;
 		    IntVector _rev_thread;
 		    IntVector _succ_num;
 		    IntVector _last_succ;
 		    CharVector _pred_dir;
 		    CharVector _state;
 		    IntVector _dirty_revs;
 		    int _root;
 		    // Temporary data used in the current pivot iteration
 		    int in_arc, join, u_in, v_in, u_out, v_out;
 		    Value delta;
 		    const Value MAX;
 		  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:
 		    // Implementation of the First Eligible pivot rule
 		    class FirstEligiblePivotRule
+		    {
 		    private:
 		      // References to the NetworkSimplex class
 		      const IntVector  &_source;
 		      const IntVector  &_target;
 		      const CostVector &_cost;
 		      const CharVector &_state;
 		      const CostVector &_pi;
 		      int &_in_arc;
 		      int _search_arc_num;
 		      // Pivot rule data
 		      int _next_arc;
 		    public:
 		      // Constructor
 		      FirstEligiblePivotRule(NetworkSimplex &ns) :
 		        _source(ns._source), _target(ns._target),
 		        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
 		        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
 		        _next_arc(0)
 		      {}
 		      // Find next entering arc
 		      bool findEnteringArc() {
 		        Cost c;
 		        for (int e = _next_arc; e != _search_arc_num; ++e) {
 		          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
 		          if (c < 0) {
 		            _in_arc = e;
 		            _next_arc = e + 1;
 		            return true;
+		          }
+		        }
 		        for (int e = 0; e != _next_arc; ++e) {
 		          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
 		          if (c < 0) {
 		            _in_arc = e;
 		            _next_arc = e + 1;
 		            return true;
+		          }
+		        }
 		        return false;
+		      }
 		    }; //class FirstEligiblePivotRule
 		    // Implementation of the Best Eligible pivot rule
 		    class BestEligiblePivotRule
+		    {
 		    private:
 		      // References to the NetworkSimplex class
 		      const IntVector  &_source;
 		      const IntVector  &_target;
 		      const CostVector &_cost;
 		      const CharVector &_state;
 		      const CostVector &_pi;
 		      int &_in_arc;
 		      int _search_arc_num;
 		    public:
 		      // Constructor
 		      BestEligiblePivotRule(NetworkSimplex &ns) :
 		        _source(ns._source), _target(ns._target),
 		        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
 		        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num)
 		      {}
 		      // Find next entering arc
 		      bool findEnteringArc() {
 		        Cost c, min = 0;
 		        for (int e = 0; e != _search_arc_num; ++e) {
 		          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
 		          if (c < min) {
 		            min = c;
 		            _in_arc = e;
+		          }
+		        }
 		        return min < 0;
+		      }
 		    }; //class BestEligiblePivotRule
 		    // Implementation of the Block Search pivot rule
 		    class BlockSearchPivotRule
+		    {
 		    private:
 		      // References to the NetworkSimplex class
 		      const IntVector  &_source;
 		      const IntVector  &_target;
 		      const CostVector &_cost;
 		      const CharVector &_state;
 		      const CostVector &_pi;
 		      int &_in_arc;
 		      int _search_arc_num;
 		      // Pivot rule data
 		      int _block_size;
 		      int _next_arc;
 		    public:
 		      // Constructor
 		      BlockSearchPivotRule(NetworkSimplex &ns) :
 		        _source(ns._source), _target(ns._target),
 		        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
 		        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
 		        _next_arc(0)
+		      {
 		        // The main parameters of the pivot rule
 		        const double BLOCK_SIZE_FACTOR = 1.0;
 		        const int MIN_BLOCK_SIZE = 10;
 		        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
 		                                    std::sqrt(double(_search_arc_num))),
 		                                MIN_BLOCK_SIZE );
+		      }
 		      // Find next entering arc
 		      bool findEnteringArc() {
 		        Cost c, min = 0;
 		        int cnt = _block_size;
 		        int e;
 		        for (e = _next_arc; e != _search_arc_num; ++e) {
 		          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
 		          if (c < min) {
 		            min = c;
 		            _in_arc = e;
+		          }
 		          if (--cnt == 0) {
 		            if (min < 0) goto search_end;
 		            cnt = _block_size;
+		          }
+		        }
 		        for (e = 0; e != _next_arc; ++e) {
 		          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
 		          if (c < min) {
 		            min = c;
 		            _in_arc = e;
+		          }
 		          if (--cnt == 0) {
 		            if (min < 0) goto search_end;
 		            cnt = _block_size;
+		          }
+		        }
 		        if (min >= 0) return false;
 		      search_end:
 		        _next_arc = e;
 		        return true;
+		      }
 		    }; //class BlockSearchPivotRule
 		    // Implementation of the Candidate List pivot rule
 		    class CandidateListPivotRule
+		    {
 		    private:
 		      // References to the NetworkSimplex class
 		      const IntVector  &_source;
 		      const IntVector  &_target;
 		      const CostVector &_cost;
 		      const CharVector &_state;
 		      const CostVector &_pi;
 		      int &_in_arc;
 		      int _search_arc_num;
 		      // Pivot rule data
 		      IntVector _candidates;
 		      int _list_length, _minor_limit;
 		      int _curr_length, _minor_count;
 		      int _next_arc;
 		    public:
 		      /// Constructor
 		      CandidateListPivotRule(NetworkSimplex &ns) :
 		        _source(ns._source), _target(ns._target),
 		        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
 		        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
 		        _next_arc(0)
+		      {
 		        // The main parameters of the pivot rule
 		        const double LIST_LENGTH_FACTOR = 0.25;
 		        const int MIN_LIST_LENGTH = 10;
 		        const double MINOR_LIMIT_FACTOR = 0.1;
 		        const int MIN_MINOR_LIMIT = 3;
 		        _list_length = std::max( int(LIST_LENGTH_FACTOR *
 		                                     std::sqrt(double(_search_arc_num))),
 		                                 MIN_LIST_LENGTH );
 		        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
 		                                 MIN_MINOR_LIMIT );
 		        _curr_length = _minor_count = 0;
 		        _candidates.resize(_list_length);

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