lemon/capacity_scaling.h
author Peter Kovacs <kpeter@inf.elte.hu>
Thu, 28 Feb 2013 18:17:53 +0100
changeset 1057 6a8a688eacf6
parent 1049 7bf489cf624e
child 1071 879fcb781086
permissions -rw-r--r--
Improve and fix API doc of EdmondsKarp according to Preflow (#177)
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2010
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_CAPACITY_SCALING_H
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#define LEMON_CAPACITY_SCALING_H
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/// \ingroup min_cost_flow_algs
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///
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/// \file
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/// \brief Capacity Scaling algorithm for finding a minimum cost flow.
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#include <vector>
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#include <limits>
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#include <lemon/core.h>
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#include <lemon/bin_heap.h>
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namespace lemon {
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  /// \brief Default traits class of CapacityScaling algorithm.
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  ///
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  /// Default traits class of CapacityScaling algorithm.
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  /// \tparam GR Digraph type.
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  /// \tparam V The number type used for flow amounts, capacity bounds
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  /// and supply values. By default it is \c int.
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  /// \tparam C The number type used for costs and potentials.
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  /// By default it is the same as \c V.
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  template <typename GR, typename V = int, typename C = V>
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  struct CapacityScalingDefaultTraits
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  {
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    /// The type of the digraph
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    typedef GR Digraph;
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    /// The type of the flow amounts, capacity bounds and supply values
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    typedef V Value;
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    /// The type of the arc costs
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    typedef C Cost;
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    /// \brief The type of the heap used for internal Dijkstra computations.
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    ///
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    /// The type of the heap used for internal Dijkstra computations.
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    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
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    /// its priority type must be \c Cost and its cross reference type
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    /// must be \ref RangeMap "RangeMap<int>".
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    typedef BinHeap<Cost, RangeMap<int> > Heap;
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  };
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  /// \addtogroup min_cost_flow_algs
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  /// @{
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  /// \brief Implementation of the Capacity Scaling algorithm for
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  /// finding a \ref min_cost_flow "minimum cost flow".
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  ///
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  /// \ref CapacityScaling implements the capacity scaling version
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  /// of the successive shortest path algorithm for finding a
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  /// \ref min_cost_flow "minimum cost flow" \cite amo93networkflows,
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  /// \cite edmondskarp72theoretical. It is an efficient dual
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  /// solution method, which runs in polynomial time
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  /// \f$O(e\log U (n+e)\log n)\f$, where <i>U</i> denotes the maximum
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  /// of node supply and arc capacity values.
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  ///
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  /// This algorithm is typically slower than \ref CostScaling and
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  /// \ref NetworkSimplex, but in special cases, it can be more
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  /// efficient than them.
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  /// (For more information, see \ref min_cost_flow_algs "the module page".)
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  ///
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  /// Most of the parameters of the problem (except for the digraph)
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  /// can be given using separate functions, and the algorithm can be
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  /// executed using the \ref run() function. If some parameters are not
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  /// specified, then default values will be used.
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  ///
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  /// \tparam GR The digraph type the algorithm runs on.
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  /// \tparam V The number type used for flow amounts, capacity bounds
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  /// and supply values in the algorithm. By default, it is \c int.
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  /// \tparam C The number type used for costs and potentials in the
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  /// algorithm. By default, it is the same as \c V.
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  /// \tparam TR The traits class that defines various types used by the
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  /// algorithm. By default, it is \ref CapacityScalingDefaultTraits
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  /// "CapacityScalingDefaultTraits<GR, V, C>".
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  /// In most cases, this parameter should not be set directly,
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  /// consider to use the named template parameters instead.
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  ///
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  /// \warning Both \c V and \c C must be signed number types.
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  /// \warning Capacity bounds and supply values must be integer, but
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  /// arc costs can be arbitrary real numbers.
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  /// \warning This algorithm does not support negative costs for
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  /// arcs having infinite upper bound.
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#ifdef DOXYGEN
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  template <typename GR, typename V, typename C, typename TR>
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#else
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  template < typename GR, typename V = int, typename C = V,
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             typename TR = CapacityScalingDefaultTraits<GR, V, C> >
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#endif
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  class CapacityScaling
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  {
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  public:
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    /// The type of the digraph
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    typedef typename TR::Digraph Digraph;
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    /// The type of the flow amounts, capacity bounds and supply values
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    typedef typename TR::Value Value;
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    /// The type of the arc costs
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    typedef typename TR::Cost Cost;
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    /// The type of the heap used for internal Dijkstra computations
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    typedef typename TR::Heap Heap;
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    /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm
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    typedef TR Traits;
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  public:
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    /// \brief Problem type constants for the \c run() function.
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    ///
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    /// Enum type containing the problem type constants that can be
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    /// returned by the \ref run() function of the algorithm.
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    enum ProblemType {
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      /// The problem has no feasible solution (flow).
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      INFEASIBLE,
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      /// The problem has optimal solution (i.e. it is feasible and
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      /// bounded), and the algorithm has found optimal flow and node
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      /// potentials (primal and dual solutions).
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      OPTIMAL,
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      /// The digraph contains an arc of negative cost and infinite
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      /// upper bound. It means that the objective function is unbounded
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      /// on that arc, however, note that it could actually be bounded
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      /// over the feasible flows, but this algroithm cannot handle
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      /// these cases.
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      UNBOUNDED
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    };
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  private:
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    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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    typedef std::vector<int> IntVector;
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    typedef std::vector<Value> ValueVector;
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    typedef std::vector<Cost> CostVector;
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    typedef std::vector<char> BoolVector;
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    // Note: vector<char> is used instead of vector<bool> for efficiency reasons
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  private:
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    // Data related to the underlying digraph
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    const GR &_graph;
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    int _node_num;
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    int _arc_num;
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    int _res_arc_num;
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    int _root;
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    // Parameters of the problem
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    bool _have_lower;
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    Value _sum_supply;
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    // Data structures for storing the digraph
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    IntNodeMap _node_id;
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    IntArcMap _arc_idf;
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    IntArcMap _arc_idb;
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    IntVector _first_out;
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    BoolVector _forward;
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    IntVector _source;
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    IntVector _target;
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    IntVector _reverse;
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    // Node and arc data
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    ValueVector _lower;
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    ValueVector _upper;
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    CostVector _cost;
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    ValueVector _supply;
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    ValueVector _res_cap;
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    CostVector _pi;
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    ValueVector _excess;
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    IntVector _excess_nodes;
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    IntVector _deficit_nodes;
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    Value _delta;
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    int _factor;
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    IntVector _pred;
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  public:
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    /// \brief Constant for infinite upper bounds (capacities).
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    ///
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    /// Constant for infinite upper bounds (capacities).
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    /// It is \c std::numeric_limits<Value>::infinity() if available,
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    /// \c std::numeric_limits<Value>::max() otherwise.
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    const Value INF;
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  private:
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    // Special implementation of the Dijkstra algorithm for finding
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    // shortest paths in the residual network of the digraph with
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    // respect to the reduced arc costs and modifying the node
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    // potentials according to the found distance labels.
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    class ResidualDijkstra
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    {
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    private:
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      int _node_num;
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      bool _geq;
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      const IntVector &_first_out;
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      const IntVector &_target;
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      const CostVector &_cost;
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      const ValueVector &_res_cap;
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      const ValueVector &_excess;
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      CostVector &_pi;
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      IntVector &_pred;
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      IntVector _proc_nodes;
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      CostVector _dist;
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    public:
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      ResidualDijkstra(CapacityScaling& cs) :
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        _node_num(cs._node_num), _geq(cs._sum_supply < 0),
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        _first_out(cs._first_out), _target(cs._target), _cost(cs._cost),
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        _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi),
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        _pred(cs._pred), _dist(cs._node_num)
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      {}
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      int run(int s, Value delta = 1) {
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        RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP);
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        Heap heap(heap_cross_ref);
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        heap.push(s, 0);
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        _pred[s] = -1;
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        _proc_nodes.clear();
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        // Process nodes
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        while (!heap.empty() && _excess[heap.top()] > -delta) {
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          int u = heap.top(), v;
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          Cost d = heap.prio() + _pi[u], dn;
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          _dist[u] = heap.prio();
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          _proc_nodes.push_back(u);
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          heap.pop();
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          // Traverse outgoing residual arcs
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          int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1;
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          for (int a = _first_out[u]; a != last_out; ++a) {
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            if (_res_cap[a] < delta) continue;
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            v = _target[a];
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            switch (heap.state(v)) {
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              case Heap::PRE_HEAP:
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                heap.push(v, d + _cost[a] - _pi[v]);
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                _pred[v] = a;
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                break;
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              case Heap::IN_HEAP:
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                dn = d + _cost[a] - _pi[v];
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                if (dn < heap[v]) {
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                  heap.decrease(v, dn);
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                  _pred[v] = a;
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                }
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                break;
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              case Heap::POST_HEAP:
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                break;
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            }
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          }
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        }
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        if (heap.empty()) return -1;
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        // Update potentials of processed nodes
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        int t = heap.top();
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        Cost dt = heap.prio();
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        for (int i = 0; i < int(_proc_nodes.size()); ++i) {
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          _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt;
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        }
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        return t;
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      }
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    }; //class ResidualDijkstra
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  public:
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    /// \name Named Template Parameters
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    /// @{
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    template <typename T>
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    struct SetHeapTraits : public Traits {
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      typedef T Heap;
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// \c Heap type.
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    ///
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    /// \ref named-templ-param "Named parameter" for setting \c Heap
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    /// type, which is used for internal Dijkstra computations.
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    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
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    /// its priority type must be \c Cost and its cross reference type
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    /// must be \ref RangeMap "RangeMap<int>".
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    template <typename T>
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    struct SetHeap
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      : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {
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      typedef  CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;
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    };
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    /// @}
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  protected:
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    CapacityScaling() {}
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  public:
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    /// \brief Constructor.
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    ///
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    /// The constructor of the class.
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    ///
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    /// \param graph The digraph the algorithm runs on.
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    CapacityScaling(const GR& graph) :
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      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
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      INF(std::numeric_limits<Value>::has_infinity ?
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          std::numeric_limits<Value>::infinity() :
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          std::numeric_limits<Value>::max())
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    {
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      // Check the number types
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      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
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        "The flow type of CapacityScaling must be signed");
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      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
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        "The cost type of CapacityScaling must be signed");
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      // Reset data structures
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      reset();
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    }
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    /// \name Parameters
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    /// The parameters of the algorithm can be specified using these
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    /// functions.
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    /// @{
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    /// \brief Set the lower bounds on the arcs.
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    ///
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    /// This function sets the lower bounds on the arcs.
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    /// If it is not used before calling \ref run(), the lower bounds
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    /// will be set to zero on all arcs.
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    ///
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    /// \param map An arc map storing the lower bounds.
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    /// Its \c Value type must be convertible to the \c Value type
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    /// of the algorithm.
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    ///
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    /// \return <tt>(*this)</tt>
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    template <typename LowerMap>
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    CapacityScaling& lowerMap(const LowerMap& map) {
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      _have_lower = true;
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      for (ArcIt a(_graph); a != INVALID; ++a) {
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        _lower[_arc_idf[a]] = map[a];
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        _lower[_arc_idb[a]] = map[a];
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      }
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      return *this;
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    }
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    /// \brief Set the upper bounds (capacities) on the arcs.
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    ///
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    /// This function sets the upper bounds (capacities) on the arcs.
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    /// If it is not used before calling \ref run(), the upper bounds
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    /// will be set to \ref INF on all arcs (i.e. the flow value will be
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    /// unbounded from above).
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    ///
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    /// \param map An arc map storing the upper bounds.
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    /// Its \c Value type must be convertible to the \c Value type
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    /// of the algorithm.
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    ///
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    /// \return <tt>(*this)</tt>
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    template<typename UpperMap>
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    CapacityScaling& upperMap(const UpperMap& map) {
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      for (ArcIt a(_graph); a != INVALID; ++a) {
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        _upper[_arc_idf[a]] = map[a];
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      }
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      return *this;
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    }
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    /// \brief Set the costs of the arcs.
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    ///
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    /// This function sets the costs of the arcs.
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    /// If it is not used before calling \ref run(), the costs
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    /// will be set to \c 1 on all arcs.
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    ///
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    /// \param map An arc map storing the costs.
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    /// Its \c Value type must be convertible to the \c Cost type
kpeter@806
   394
    /// of the algorithm.
kpeter@806
   395
    ///
kpeter@806
   396
    /// \return <tt>(*this)</tt>
kpeter@806
   397
    template<typename CostMap>
kpeter@806
   398
    CapacityScaling& costMap(const CostMap& map) {
kpeter@806
   399
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806
   400
        _cost[_arc_idf[a]] =  map[a];
kpeter@806
   401
        _cost[_arc_idb[a]] = -map[a];
kpeter@806
   402
      }
kpeter@806
   403
      return *this;
kpeter@806
   404
    }
kpeter@806
   405
kpeter@806
   406
    /// \brief Set the supply values of the nodes.
kpeter@806
   407
    ///
kpeter@806
   408
    /// This function sets the supply values of the nodes.
kpeter@806
   409
    /// If neither this function nor \ref stSupply() is used before
kpeter@806
   410
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@806
   411
    ///
kpeter@806
   412
    /// \param map A node map storing the supply values.
kpeter@806
   413
    /// Its \c Value type must be convertible to the \c Value type
kpeter@806
   414
    /// of the algorithm.
kpeter@806
   415
    ///
kpeter@806
   416
    /// \return <tt>(*this)</tt>
kpeter@806
   417
    template<typename SupplyMap>
kpeter@806
   418
    CapacityScaling& supplyMap(const SupplyMap& map) {
kpeter@806
   419
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@806
   420
        _supply[_node_id[n]] = map[n];
kpeter@806
   421
      }
kpeter@806
   422
      return *this;
kpeter@806
   423
    }
kpeter@806
   424
kpeter@806
   425
    /// \brief Set single source and target nodes and a supply value.
kpeter@806
   426
    ///
kpeter@806
   427
    /// This function sets a single source node and a single target node
kpeter@806
   428
    /// and the required flow value.
kpeter@806
   429
    /// If neither this function nor \ref supplyMap() is used before
kpeter@806
   430
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@806
   431
    ///
kpeter@806
   432
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@919
   433
    /// with a map in which \c k is assigned to \c s, \c -k is
kpeter@806
   434
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@806
   435
    ///
kpeter@806
   436
    /// \param s The source node.
kpeter@806
   437
    /// \param t The target node.
kpeter@806
   438
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@806
   439
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@806
   440
    ///
kpeter@806
   441
    /// \return <tt>(*this)</tt>
kpeter@806
   442
    CapacityScaling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@806
   443
      for (int i = 0; i != _node_num; ++i) {
kpeter@806
   444
        _supply[i] = 0;
kpeter@806
   445
      }
kpeter@806
   446
      _supply[_node_id[s]] =  k;
kpeter@806
   447
      _supply[_node_id[t]] = -k;
kpeter@806
   448
      return *this;
kpeter@806
   449
    }
alpar@877
   450
kpeter@806
   451
    /// @}
kpeter@806
   452
kpeter@805
   453
    /// \name Execution control
kpeter@807
   454
    /// The algorithm can be executed using \ref run().
kpeter@805
   455
kpeter@805
   456
    /// @{
kpeter@805
   457
kpeter@805
   458
    /// \brief Run the algorithm.
kpeter@805
   459
    ///
kpeter@805
   460
    /// This function runs the algorithm.
kpeter@806
   461
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@806
   462
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@806
   463
    /// For example,
kpeter@806
   464
    /// \code
kpeter@806
   465
    ///   CapacityScaling<ListDigraph> cs(graph);
kpeter@806
   466
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@806
   467
    ///     .supplyMap(sup).run();
kpeter@806
   468
    /// \endcode
kpeter@806
   469
    ///
kpeter@830
   470
    /// This function can be called more than once. All the given parameters
kpeter@830
   471
    /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@830
   472
    /// is used, thus only the modified parameters have to be set again.
kpeter@830
   473
    /// If the underlying digraph was also modified after the construction
kpeter@830
   474
    /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@830
   475
    /// function must be called.
kpeter@805
   476
    ///
kpeter@810
   477
    /// \param factor The capacity scaling factor. It must be larger than
kpeter@810
   478
    /// one to use scaling. If it is less or equal to one, then scaling
kpeter@810
   479
    /// will be disabled.
kpeter@805
   480
    ///
kpeter@806
   481
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@806
   482
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@806
   483
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@806
   484
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@806
   485
    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@806
   486
    /// and infinite upper bound. It means that the objective function
kpeter@812
   487
    /// is unbounded on that arc, however, note that it could actually be
kpeter@806
   488
    /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@806
   489
    /// these cases.
kpeter@806
   490
    ///
kpeter@806
   491
    /// \see ProblemType
kpeter@830
   492
    /// \see resetParams(), reset()
kpeter@810
   493
    ProblemType run(int factor = 4) {
kpeter@810
   494
      _factor = factor;
kpeter@810
   495
      ProblemType pt = init();
kpeter@806
   496
      if (pt != OPTIMAL) return pt;
kpeter@806
   497
      return start();
kpeter@806
   498
    }
kpeter@806
   499
kpeter@806
   500
    /// \brief Reset all the parameters that have been given before.
kpeter@806
   501
    ///
kpeter@806
   502
    /// This function resets all the paramaters that have been given
kpeter@806
   503
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@806
   504
    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@806
   505
    ///
kpeter@830
   506
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   507
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   508
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   509
    /// If the underlying digraph was also modified after the construction
kpeter@830
   510
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   511
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@806
   512
    ///
kpeter@806
   513
    /// For example,
kpeter@806
   514
    /// \code
kpeter@806
   515
    ///   CapacityScaling<ListDigraph> cs(graph);
kpeter@806
   516
    ///
kpeter@806
   517
    ///   // First run
kpeter@806
   518
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@806
   519
    ///     .supplyMap(sup).run();
kpeter@806
   520
    ///
kpeter@830
   521
    ///   // Run again with modified cost map (resetParams() is not called,
kpeter@806
   522
    ///   // so only the cost map have to be set again)
kpeter@806
   523
    ///   cost[e] += 100;
kpeter@806
   524
    ///   cs.costMap(cost).run();
kpeter@806
   525
    ///
kpeter@830
   526
    ///   // Run again from scratch using resetParams()
kpeter@806
   527
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@830
   528
    ///   cs.resetParams();
kpeter@806
   529
    ///   cs.upperMap(capacity).costMap(cost)
kpeter@806
   530
    ///     .supplyMap(sup).run();
kpeter@806
   531
    /// \endcode
kpeter@806
   532
    ///
kpeter@806
   533
    /// \return <tt>(*this)</tt>
kpeter@830
   534
    ///
kpeter@830
   535
    /// \see reset(), run()
kpeter@830
   536
    CapacityScaling& resetParams() {
kpeter@806
   537
      for (int i = 0; i != _node_num; ++i) {
kpeter@806
   538
        _supply[i] = 0;
kpeter@806
   539
      }
kpeter@806
   540
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@806
   541
        _lower[j] = 0;
kpeter@806
   542
        _upper[j] = INF;
kpeter@806
   543
        _cost[j] = _forward[j] ? 1 : -1;
kpeter@806
   544
      }
kpeter@806
   545
      _have_lower = false;
kpeter@806
   546
      return *this;
kpeter@805
   547
    }
kpeter@805
   548
kpeter@830
   549
    /// \brief Reset the internal data structures and all the parameters
kpeter@830
   550
    /// that have been given before.
kpeter@830
   551
    ///
kpeter@830
   552
    /// This function resets the internal data structures and all the
kpeter@830
   553
    /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@830
   554
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@830
   555
    ///
kpeter@830
   556
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   557
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   558
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   559
    /// If the underlying digraph was also modified after the construction
kpeter@830
   560
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   561
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@830
   562
    ///
kpeter@830
   563
    /// See \ref resetParams() for examples.
kpeter@830
   564
    ///
kpeter@830
   565
    /// \return <tt>(*this)</tt>
kpeter@830
   566
    ///
kpeter@830
   567
    /// \see resetParams(), run()
kpeter@830
   568
    CapacityScaling& reset() {
kpeter@830
   569
      // Resize vectors
kpeter@830
   570
      _node_num = countNodes(_graph);
kpeter@830
   571
      _arc_num = countArcs(_graph);
kpeter@830
   572
      _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@830
   573
      _root = _node_num;
kpeter@830
   574
      ++_node_num;
kpeter@830
   575
kpeter@830
   576
      _first_out.resize(_node_num + 1);
kpeter@830
   577
      _forward.resize(_res_arc_num);
kpeter@830
   578
      _source.resize(_res_arc_num);
kpeter@830
   579
      _target.resize(_res_arc_num);
kpeter@830
   580
      _reverse.resize(_res_arc_num);
kpeter@830
   581
kpeter@830
   582
      _lower.resize(_res_arc_num);
kpeter@830
   583
      _upper.resize(_res_arc_num);
kpeter@830
   584
      _cost.resize(_res_arc_num);
kpeter@830
   585
      _supply.resize(_node_num);
alpar@877
   586
kpeter@830
   587
      _res_cap.resize(_res_arc_num);
kpeter@830
   588
      _pi.resize(_node_num);
kpeter@830
   589
      _excess.resize(_node_num);
kpeter@830
   590
      _pred.resize(_node_num);
kpeter@830
   591
kpeter@830
   592
      // Copy the graph
kpeter@830
   593
      int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1;
kpeter@830
   594
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   595
        _node_id[n] = i;
kpeter@830
   596
      }
kpeter@830
   597
      i = 0;
kpeter@830
   598
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   599
        _first_out[i] = j;
kpeter@830
   600
        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830
   601
          _arc_idf[a] = j;
kpeter@830
   602
          _forward[j] = true;
kpeter@830
   603
          _source[j] = i;
kpeter@830
   604
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830
   605
        }
kpeter@830
   606
        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830
   607
          _arc_idb[a] = j;
kpeter@830
   608
          _forward[j] = false;
kpeter@830
   609
          _source[j] = i;
kpeter@830
   610
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830
   611
        }
kpeter@830
   612
        _forward[j] = false;
kpeter@830
   613
        _source[j] = i;
kpeter@830
   614
        _target[j] = _root;
kpeter@830
   615
        _reverse[j] = k;
kpeter@830
   616
        _forward[k] = true;
kpeter@830
   617
        _source[k] = _root;
kpeter@830
   618
        _target[k] = i;
kpeter@830
   619
        _reverse[k] = j;
kpeter@830
   620
        ++j; ++k;
kpeter@830
   621
      }
kpeter@830
   622
      _first_out[i] = j;
kpeter@830
   623
      _first_out[_node_num] = k;
kpeter@830
   624
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@830
   625
        int fi = _arc_idf[a];
kpeter@830
   626
        int bi = _arc_idb[a];
kpeter@830
   627
        _reverse[fi] = bi;
kpeter@830
   628
        _reverse[bi] = fi;
kpeter@830
   629
      }
alpar@877
   630
kpeter@830
   631
      // Reset parameters
kpeter@830
   632
      resetParams();
kpeter@830
   633
      return *this;
kpeter@830
   634
    }
kpeter@830
   635
kpeter@805
   636
    /// @}
kpeter@805
   637
kpeter@805
   638
    /// \name Query Functions
kpeter@805
   639
    /// The results of the algorithm can be obtained using these
kpeter@805
   640
    /// functions.\n
kpeter@806
   641
    /// The \ref run() function must be called before using them.
kpeter@805
   642
kpeter@805
   643
    /// @{
kpeter@805
   644
kpeter@806
   645
    /// \brief Return the total cost of the found flow.
kpeter@805
   646
    ///
kpeter@806
   647
    /// This function returns the total cost of the found flow.
kpeter@806
   648
    /// Its complexity is O(e).
kpeter@806
   649
    ///
kpeter@806
   650
    /// \note The return type of the function can be specified as a
kpeter@806
   651
    /// template parameter. For example,
kpeter@806
   652
    /// \code
kpeter@806
   653
    ///   cs.totalCost<double>();
kpeter@806
   654
    /// \endcode
kpeter@806
   655
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@806
   656
    /// type of the algorithm, which is the default return type of the
kpeter@806
   657
    /// function.
kpeter@805
   658
    ///
kpeter@805
   659
    /// \pre \ref run() must be called before using this function.
kpeter@806
   660
    template <typename Number>
kpeter@806
   661
    Number totalCost() const {
kpeter@806
   662
      Number c = 0;
kpeter@806
   663
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806
   664
        int i = _arc_idb[a];
kpeter@806
   665
        c += static_cast<Number>(_res_cap[i]) *
kpeter@806
   666
             (-static_cast<Number>(_cost[i]));
kpeter@806
   667
      }
kpeter@806
   668
      return c;
kpeter@805
   669
    }
kpeter@805
   670
kpeter@806
   671
#ifndef DOXYGEN
kpeter@806
   672
    Cost totalCost() const {
kpeter@806
   673
      return totalCost<Cost>();
kpeter@805
   674
    }
kpeter@806
   675
#endif
kpeter@805
   676
kpeter@805
   677
    /// \brief Return the flow on the given arc.
kpeter@805
   678
    ///
kpeter@806
   679
    /// This function returns the flow on the given arc.
kpeter@805
   680
    ///
kpeter@805
   681
    /// \pre \ref run() must be called before using this function.
kpeter@806
   682
    Value flow(const Arc& a) const {
kpeter@806
   683
      return _res_cap[_arc_idb[a]];
kpeter@805
   684
    }
kpeter@805
   685
kpeter@1003
   686
    /// \brief Copy the flow values (the primal solution) into the
kpeter@1003
   687
    /// given map.
kpeter@805
   688
    ///
kpeter@806
   689
    /// This function copies the flow value on each arc into the given
kpeter@806
   690
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@806
   691
    /// the \c Value type of the map.
kpeter@805
   692
    ///
kpeter@805
   693
    /// \pre \ref run() must be called before using this function.
kpeter@806
   694
    template <typename FlowMap>
kpeter@806
   695
    void flowMap(FlowMap &map) const {
kpeter@806
   696
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806
   697
        map.set(a, _res_cap[_arc_idb[a]]);
kpeter@806
   698
      }
kpeter@805
   699
    }
kpeter@805
   700
kpeter@806
   701
    /// \brief Return the potential (dual value) of the given node.
kpeter@805
   702
    ///
kpeter@806
   703
    /// This function returns the potential (dual value) of the
kpeter@806
   704
    /// given node.
kpeter@805
   705
    ///
kpeter@805
   706
    /// \pre \ref run() must be called before using this function.
kpeter@806
   707
    Cost potential(const Node& n) const {
kpeter@806
   708
      return _pi[_node_id[n]];
kpeter@806
   709
    }
kpeter@806
   710
kpeter@1003
   711
    /// \brief Copy the potential values (the dual solution) into the
kpeter@1003
   712
    /// given map.
kpeter@806
   713
    ///
kpeter@806
   714
    /// This function copies the potential (dual value) of each node
kpeter@806
   715
    /// into the given map.
kpeter@806
   716
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@806
   717
    /// \c Value type of the map.
kpeter@806
   718
    ///
kpeter@806
   719
    /// \pre \ref run() must be called before using this function.
kpeter@806
   720
    template <typename PotentialMap>
kpeter@806
   721
    void potentialMap(PotentialMap &map) const {
kpeter@806
   722
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@806
   723
        map.set(n, _pi[_node_id[n]]);
kpeter@806
   724
      }
kpeter@805
   725
    }
kpeter@805
   726
kpeter@805
   727
    /// @}
kpeter@805
   728
kpeter@805
   729
  private:
kpeter@805
   730
kpeter@806
   731
    // Initialize the algorithm
kpeter@810
   732
    ProblemType init() {
kpeter@821
   733
      if (_node_num <= 1) return INFEASIBLE;
kpeter@805
   734
kpeter@806
   735
      // Check the sum of supply values
kpeter@806
   736
      _sum_supply = 0;
kpeter@806
   737
      for (int i = 0; i != _root; ++i) {
kpeter@806
   738
        _sum_supply += _supply[i];
kpeter@805
   739
      }
kpeter@806
   740
      if (_sum_supply > 0) return INFEASIBLE;
alpar@877
   741
kpeter@811
   742
      // Initialize vectors
kpeter@806
   743
      for (int i = 0; i != _root; ++i) {
kpeter@806
   744
        _pi[i] = 0;
kpeter@806
   745
        _excess[i] = _supply[i];
kpeter@805
   746
      }
kpeter@805
   747
kpeter@806
   748
      // Remove non-zero lower bounds
kpeter@811
   749
      const Value MAX = std::numeric_limits<Value>::max();
kpeter@811
   750
      int last_out;
kpeter@806
   751
      if (_have_lower) {
kpeter@806
   752
        for (int i = 0; i != _root; ++i) {
kpeter@811
   753
          last_out = _first_out[i+1];
kpeter@811
   754
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@806
   755
            if (_forward[j]) {
kpeter@806
   756
              Value c = _lower[j];
kpeter@806
   757
              if (c >= 0) {
kpeter@811
   758
                _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;
kpeter@806
   759
              } else {
kpeter@811
   760
                _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;
kpeter@806
   761
              }
kpeter@806
   762
              _excess[i] -= c;
kpeter@806
   763
              _excess[_target[j]] += c;
kpeter@806
   764
            } else {
kpeter@806
   765
              _res_cap[j] = 0;
kpeter@806
   766
            }
kpeter@806
   767
          }
kpeter@806
   768
        }
kpeter@806
   769
      } else {
kpeter@806
   770
        for (int j = 0; j != _res_arc_num; ++j) {
kpeter@806
   771
          _res_cap[j] = _forward[j] ? _upper[j] : 0;
kpeter@806
   772
        }
kpeter@806
   773
      }
kpeter@805
   774
kpeter@806
   775
      // Handle negative costs
kpeter@811
   776
      for (int i = 0; i != _root; ++i) {
kpeter@811
   777
        last_out = _first_out[i+1] - 1;
kpeter@811
   778
        for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@811
   779
          Value rc = _res_cap[j];
kpeter@811
   780
          if (_cost[j] < 0 && rc > 0) {
kpeter@811
   781
            if (rc >= MAX) return UNBOUNDED;
kpeter@811
   782
            _excess[i] -= rc;
kpeter@811
   783
            _excess[_target[j]] += rc;
kpeter@811
   784
            _res_cap[j] = 0;
kpeter@811
   785
            _res_cap[_reverse[j]] += rc;
kpeter@806
   786
          }
kpeter@806
   787
        }
kpeter@806
   788
      }
alpar@877
   789
kpeter@806
   790
      // Handle GEQ supply type
kpeter@806
   791
      if (_sum_supply < 0) {
kpeter@806
   792
        _pi[_root] = 0;
kpeter@806
   793
        _excess[_root] = -_sum_supply;
kpeter@806
   794
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@811
   795
          int ra = _reverse[a];
kpeter@811
   796
          _res_cap[a] = -_sum_supply + 1;
kpeter@811
   797
          _res_cap[ra] = 0;
kpeter@806
   798
          _cost[a] = 0;
kpeter@811
   799
          _cost[ra] = 0;
kpeter@806
   800
        }
kpeter@806
   801
      } else {
kpeter@806
   802
        _pi[_root] = 0;
kpeter@806
   803
        _excess[_root] = 0;
kpeter@806
   804
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@811
   805
          int ra = _reverse[a];
kpeter@806
   806
          _res_cap[a] = 1;
kpeter@811
   807
          _res_cap[ra] = 0;
kpeter@806
   808
          _cost[a] = 0;
kpeter@811
   809
          _cost[ra] = 0;
kpeter@806
   810
        }
kpeter@806
   811
      }
kpeter@806
   812
kpeter@806
   813
      // Initialize delta value
kpeter@810
   814
      if (_factor > 1) {
kpeter@805
   815
        // With scaling
kpeter@839
   816
        Value max_sup = 0, max_dem = 0, max_cap = 0;
kpeter@839
   817
        for (int i = 0; i != _root; ++i) {
kpeter@811
   818
          Value ex = _excess[i];
kpeter@811
   819
          if ( ex > max_sup) max_sup =  ex;
kpeter@811
   820
          if (-ex > max_dem) max_dem = -ex;
kpeter@839
   821
          int last_out = _first_out[i+1] - 1;
kpeter@839
   822
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@839
   823
            if (_res_cap[j] > max_cap) max_cap = _res_cap[j];
kpeter@839
   824
          }
kpeter@805
   825
        }
kpeter@805
   826
        max_sup = std::min(std::min(max_sup, max_dem), max_cap);
kpeter@810
   827
        for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;
kpeter@805
   828
      } else {
kpeter@805
   829
        // Without scaling
kpeter@805
   830
        _delta = 1;
kpeter@805
   831
      }
kpeter@805
   832
kpeter@806
   833
      return OPTIMAL;
kpeter@805
   834
    }
kpeter@805
   835
kpeter@806
   836
    ProblemType start() {
kpeter@806
   837
      // Execute the algorithm
kpeter@806
   838
      ProblemType pt;
kpeter@805
   839
      if (_delta > 1)
kpeter@806
   840
        pt = startWithScaling();
kpeter@805
   841
      else
kpeter@806
   842
        pt = startWithoutScaling();
kpeter@806
   843
kpeter@806
   844
      // Handle non-zero lower bounds
kpeter@806
   845
      if (_have_lower) {
kpeter@811
   846
        int limit = _first_out[_root];
kpeter@811
   847
        for (int j = 0; j != limit; ++j) {
kpeter@806
   848
          if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@806
   849
        }
kpeter@806
   850
      }
kpeter@806
   851
kpeter@806
   852
      // Shift potentials if necessary
kpeter@806
   853
      Cost pr = _pi[_root];
kpeter@806
   854
      if (_sum_supply < 0 || pr > 0) {
kpeter@806
   855
        for (int i = 0; i != _node_num; ++i) {
kpeter@806
   856
          _pi[i] -= pr;
alpar@877
   857
        }
kpeter@806
   858
      }
alpar@877
   859
kpeter@806
   860
      return pt;
kpeter@805
   861
    }
kpeter@805
   862
kpeter@806
   863
    // Execute the capacity scaling algorithm
kpeter@806
   864
    ProblemType startWithScaling() {
kpeter@807
   865
      // Perform capacity scaling phases
kpeter@806
   866
      int s, t;
kpeter@806
   867
      ResidualDijkstra _dijkstra(*this);
kpeter@805
   868
      while (true) {
kpeter@806
   869
        // Saturate all arcs not satisfying the optimality condition
kpeter@811
   870
        int last_out;
kpeter@806
   871
        for (int u = 0; u != _node_num; ++u) {
kpeter@811
   872
          last_out = _sum_supply < 0 ?
kpeter@811
   873
            _first_out[u+1] : _first_out[u+1] - 1;
kpeter@811
   874
          for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@806
   875
            int v = _target[a];
kpeter@806
   876
            Cost c = _cost[a] + _pi[u] - _pi[v];
kpeter@806
   877
            Value rc = _res_cap[a];
kpeter@806
   878
            if (c < 0 && rc >= _delta) {
kpeter@806
   879
              _excess[u] -= rc;
kpeter@806
   880
              _excess[v] += rc;
kpeter@806
   881
              _res_cap[a] = 0;
kpeter@806
   882
              _res_cap[_reverse[a]] += rc;
kpeter@806
   883
            }
kpeter@805
   884
          }
kpeter@805
   885
        }
kpeter@805
   886
kpeter@806
   887
        // Find excess nodes and deficit nodes
kpeter@805
   888
        _excess_nodes.clear();
kpeter@805
   889
        _deficit_nodes.clear();
kpeter@806
   890
        for (int u = 0; u != _node_num; ++u) {
kpeter@811
   891
          Value ex = _excess[u];
kpeter@811
   892
          if (ex >=  _delta) _excess_nodes.push_back(u);
kpeter@811
   893
          if (ex <= -_delta) _deficit_nodes.push_back(u);
kpeter@805
   894
        }
kpeter@805
   895
        int next_node = 0, next_def_node = 0;
kpeter@805
   896
kpeter@806
   897
        // Find augmenting shortest paths
kpeter@805
   898
        while (next_node < int(_excess_nodes.size())) {
kpeter@806
   899
          // Check deficit nodes
kpeter@805
   900
          if (_delta > 1) {
kpeter@805
   901
            bool delta_deficit = false;
kpeter@805
   902
            for ( ; next_def_node < int(_deficit_nodes.size());
kpeter@805
   903
                    ++next_def_node ) {
kpeter@805
   904
              if (_excess[_deficit_nodes[next_def_node]] <= -_delta) {
kpeter@805
   905
                delta_deficit = true;
kpeter@805
   906
                break;
kpeter@805
   907
              }
kpeter@805
   908
            }
kpeter@805
   909
            if (!delta_deficit) break;
kpeter@805
   910
          }
kpeter@805
   911
kpeter@806
   912
          // Run Dijkstra in the residual network
kpeter@805
   913
          s = _excess_nodes[next_node];
kpeter@806
   914
          if ((t = _dijkstra.run(s, _delta)) == -1) {
kpeter@805
   915
            if (_delta > 1) {
kpeter@805
   916
              ++next_node;
kpeter@805
   917
              continue;
kpeter@805
   918
            }
kpeter@806
   919
            return INFEASIBLE;
kpeter@805
   920
          }
kpeter@805
   921
kpeter@806
   922
          // Augment along a shortest path from s to t
kpeter@806
   923
          Value d = std::min(_excess[s], -_excess[t]);
kpeter@806
   924
          int u = t;
kpeter@806
   925
          int a;
kpeter@805
   926
          if (d > _delta) {
kpeter@806
   927
            while ((a = _pred[u]) != -1) {
kpeter@806
   928
              if (_res_cap[a] < d) d = _res_cap[a];
kpeter@806
   929
              u = _source[a];
kpeter@805
   930
            }
kpeter@805
   931
          }
kpeter@805
   932
          u = t;
kpeter@806
   933
          while ((a = _pred[u]) != -1) {
kpeter@806
   934
            _res_cap[a] -= d;
kpeter@806
   935
            _res_cap[_reverse[a]] += d;
kpeter@806
   936
            u = _source[a];
kpeter@805
   937
          }
kpeter@805
   938
          _excess[s] -= d;
kpeter@805
   939
          _excess[t] += d;
kpeter@805
   940
kpeter@805
   941
          if (_excess[s] < _delta) ++next_node;
kpeter@805
   942
        }
kpeter@805
   943
kpeter@805
   944
        if (_delta == 1) break;
kpeter@810
   945
        _delta = _delta <= _factor ? 1 : _delta / _factor;
kpeter@805
   946
      }
kpeter@805
   947
kpeter@806
   948
      return OPTIMAL;
kpeter@805
   949
    }
kpeter@805
   950
kpeter@806
   951
    // Execute the successive shortest path algorithm
kpeter@806
   952
    ProblemType startWithoutScaling() {
kpeter@806
   953
      // Find excess nodes
kpeter@806
   954
      _excess_nodes.clear();
kpeter@806
   955
      for (int i = 0; i != _node_num; ++i) {
kpeter@806
   956
        if (_excess[i] > 0) _excess_nodes.push_back(i);
kpeter@806
   957
      }
kpeter@806
   958
      if (_excess_nodes.size() == 0) return OPTIMAL;
kpeter@805
   959
      int next_node = 0;
kpeter@805
   960
kpeter@806
   961
      // Find shortest paths
kpeter@806
   962
      int s, t;
kpeter@806
   963
      ResidualDijkstra _dijkstra(*this);
kpeter@805
   964
      while ( _excess[_excess_nodes[next_node]] > 0 ||
kpeter@805
   965
              ++next_node < int(_excess_nodes.size()) )
kpeter@805
   966
      {
kpeter@806
   967
        // Run Dijkstra in the residual network
kpeter@805
   968
        s = _excess_nodes[next_node];
kpeter@806
   969
        if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE;
kpeter@805
   970
kpeter@806
   971
        // Augment along a shortest path from s to t
kpeter@806
   972
        Value d = std::min(_excess[s], -_excess[t]);
kpeter@806
   973
        int u = t;
kpeter@806
   974
        int a;
kpeter@805
   975
        if (d > 1) {
kpeter@806
   976
          while ((a = _pred[u]) != -1) {
kpeter@806
   977
            if (_res_cap[a] < d) d = _res_cap[a];
kpeter@806
   978
            u = _source[a];
kpeter@805
   979
          }
kpeter@805
   980
        }
kpeter@805
   981
        u = t;
kpeter@806
   982
        while ((a = _pred[u]) != -1) {
kpeter@806
   983
          _res_cap[a] -= d;
kpeter@806
   984
          _res_cap[_reverse[a]] += d;
kpeter@806
   985
          u = _source[a];
kpeter@805
   986
        }
kpeter@805
   987
        _excess[s] -= d;
kpeter@805
   988
        _excess[t] += d;
kpeter@805
   989
      }
kpeter@805
   990
kpeter@806
   991
      return OPTIMAL;
kpeter@805
   992
    }
kpeter@805
   993
kpeter@805
   994
  }; //class CapacityScaling
kpeter@805
   995
kpeter@805
   996
  ///@}
kpeter@805
   997
kpeter@805
   998
} //namespace lemon
kpeter@805
   999
kpeter@805
  1000
#endif //LEMON_CAPACITY_SCALING_H