lemon/capacity_scaling.h
author Peter Kovacs <kpeter@inf.elte.hu>
Thu, 04 Mar 2010 10:03:14 +0100
changeset 862 b6f76c95992e
parent 831 cc9e0c15d747
parent 839 f3bc4e9b5f3a
child 863 a93f1a27d831
permissions -rw-r--r--
Clarify type names in NetworkSimplex (#353)

This patch clarifies the misleading effects of the renamings
in [f3bc4e9b5f3a].
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/* -*- C++ -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library
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 *
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 * Copyright (C) 2003-2008
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_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" \ref amo93networkflows,
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  /// \ref edmondskarp72theoretical. It is an efficient dual
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  /// solution method.
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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 number types must be signed and all input data must
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  /// be integer.
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  /// \warning This algorithm does not support negative costs for such
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  /// arcs that have 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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  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
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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 CostMap>
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    CapacityScaling& costMap(const CostMap& map) {
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      for (ArcIt a(_graph); a != INVALID; ++a) {
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        _cost[_arc_idf[a]] =  map[a];
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        _cost[_arc_idb[a]] = -map[a];
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      }
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      return *this;
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    }
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   394
    /// \brief Set the supply values of the nodes.
kpeter@806
   395
    ///
kpeter@806
   396
    /// This function sets the supply values of the nodes.
kpeter@806
   397
    /// If neither this function nor \ref stSupply() is used before
kpeter@806
   398
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@806
   399
    ///
kpeter@806
   400
    /// \param map A node map storing the supply values.
kpeter@806
   401
    /// Its \c Value type must be convertible to the \c Value type
kpeter@806
   402
    /// of the algorithm.
kpeter@806
   403
    ///
kpeter@806
   404
    /// \return <tt>(*this)</tt>
kpeter@806
   405
    template<typename SupplyMap>
kpeter@806
   406
    CapacityScaling& supplyMap(const SupplyMap& map) {
kpeter@806
   407
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@806
   408
        _supply[_node_id[n]] = map[n];
kpeter@806
   409
      }
kpeter@806
   410
      return *this;
kpeter@806
   411
    }
kpeter@806
   412
kpeter@806
   413
    /// \brief Set single source and target nodes and a supply value.
kpeter@806
   414
    ///
kpeter@806
   415
    /// This function sets a single source node and a single target node
kpeter@806
   416
    /// and the required flow value.
kpeter@806
   417
    /// If neither this function nor \ref supplyMap() is used before
kpeter@806
   418
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@806
   419
    ///
kpeter@806
   420
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@806
   421
    /// with such a map in which \c k is assigned to \c s, \c -k is
kpeter@806
   422
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@806
   423
    ///
kpeter@806
   424
    /// \param s The source node.
kpeter@806
   425
    /// \param t The target node.
kpeter@806
   426
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@806
   427
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@806
   428
    ///
kpeter@806
   429
    /// \return <tt>(*this)</tt>
kpeter@806
   430
    CapacityScaling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@806
   431
      for (int i = 0; i != _node_num; ++i) {
kpeter@806
   432
        _supply[i] = 0;
kpeter@806
   433
      }
kpeter@806
   434
      _supply[_node_id[s]] =  k;
kpeter@806
   435
      _supply[_node_id[t]] = -k;
kpeter@806
   436
      return *this;
kpeter@806
   437
    }
kpeter@806
   438
    
kpeter@806
   439
    /// @}
kpeter@806
   440
kpeter@805
   441
    /// \name Execution control
kpeter@807
   442
    /// The algorithm can be executed using \ref run().
kpeter@805
   443
kpeter@805
   444
    /// @{
kpeter@805
   445
kpeter@805
   446
    /// \brief Run the algorithm.
kpeter@805
   447
    ///
kpeter@805
   448
    /// This function runs the algorithm.
kpeter@806
   449
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@806
   450
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@806
   451
    /// For example,
kpeter@806
   452
    /// \code
kpeter@806
   453
    ///   CapacityScaling<ListDigraph> cs(graph);
kpeter@806
   454
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@806
   455
    ///     .supplyMap(sup).run();
kpeter@806
   456
    /// \endcode
kpeter@806
   457
    ///
kpeter@830
   458
    /// This function can be called more than once. All the given parameters
kpeter@830
   459
    /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@830
   460
    /// is used, thus only the modified parameters have to be set again.
kpeter@830
   461
    /// If the underlying digraph was also modified after the construction
kpeter@830
   462
    /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@830
   463
    /// function must be called.
kpeter@805
   464
    ///
kpeter@810
   465
    /// \param factor The capacity scaling factor. It must be larger than
kpeter@810
   466
    /// one to use scaling. If it is less or equal to one, then scaling
kpeter@810
   467
    /// will be disabled.
kpeter@805
   468
    ///
kpeter@806
   469
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@806
   470
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@806
   471
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@806
   472
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@806
   473
    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@806
   474
    /// and infinite upper bound. It means that the objective function
kpeter@812
   475
    /// is unbounded on that arc, however, note that it could actually be
kpeter@806
   476
    /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@806
   477
    /// these cases.
kpeter@806
   478
    ///
kpeter@806
   479
    /// \see ProblemType
kpeter@830
   480
    /// \see resetParams(), reset()
kpeter@810
   481
    ProblemType run(int factor = 4) {
kpeter@810
   482
      _factor = factor;
kpeter@810
   483
      ProblemType pt = init();
kpeter@806
   484
      if (pt != OPTIMAL) return pt;
kpeter@806
   485
      return start();
kpeter@806
   486
    }
kpeter@806
   487
kpeter@806
   488
    /// \brief Reset all the parameters that have been given before.
kpeter@806
   489
    ///
kpeter@806
   490
    /// This function resets all the paramaters that have been given
kpeter@806
   491
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@806
   492
    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@806
   493
    ///
kpeter@830
   494
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   495
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   496
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   497
    /// If the underlying digraph was also modified after the construction
kpeter@830
   498
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   499
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@806
   500
    ///
kpeter@806
   501
    /// For example,
kpeter@806
   502
    /// \code
kpeter@806
   503
    ///   CapacityScaling<ListDigraph> cs(graph);
kpeter@806
   504
    ///
kpeter@806
   505
    ///   // First run
kpeter@806
   506
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@806
   507
    ///     .supplyMap(sup).run();
kpeter@806
   508
    ///
kpeter@830
   509
    ///   // Run again with modified cost map (resetParams() is not called,
kpeter@806
   510
    ///   // so only the cost map have to be set again)
kpeter@806
   511
    ///   cost[e] += 100;
kpeter@806
   512
    ///   cs.costMap(cost).run();
kpeter@806
   513
    ///
kpeter@830
   514
    ///   // Run again from scratch using resetParams()
kpeter@806
   515
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@830
   516
    ///   cs.resetParams();
kpeter@806
   517
    ///   cs.upperMap(capacity).costMap(cost)
kpeter@806
   518
    ///     .supplyMap(sup).run();
kpeter@806
   519
    /// \endcode
kpeter@806
   520
    ///
kpeter@806
   521
    /// \return <tt>(*this)</tt>
kpeter@830
   522
    ///
kpeter@830
   523
    /// \see reset(), run()
kpeter@830
   524
    CapacityScaling& resetParams() {
kpeter@806
   525
      for (int i = 0; i != _node_num; ++i) {
kpeter@806
   526
        _supply[i] = 0;
kpeter@806
   527
      }
kpeter@806
   528
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@806
   529
        _lower[j] = 0;
kpeter@806
   530
        _upper[j] = INF;
kpeter@806
   531
        _cost[j] = _forward[j] ? 1 : -1;
kpeter@806
   532
      }
kpeter@806
   533
      _have_lower = false;
kpeter@806
   534
      return *this;
kpeter@805
   535
    }
kpeter@805
   536
kpeter@830
   537
    /// \brief Reset the internal data structures and all the parameters
kpeter@830
   538
    /// that have been given before.
kpeter@830
   539
    ///
kpeter@830
   540
    /// This function resets the internal data structures and all the
kpeter@830
   541
    /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@830
   542
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@830
   543
    ///
kpeter@830
   544
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   545
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   546
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   547
    /// If the underlying digraph was also modified after the construction
kpeter@830
   548
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   549
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@830
   550
    ///
kpeter@830
   551
    /// See \ref resetParams() for examples.
kpeter@830
   552
    ///
kpeter@830
   553
    /// \return <tt>(*this)</tt>
kpeter@830
   554
    ///
kpeter@830
   555
    /// \see resetParams(), run()
kpeter@830
   556
    CapacityScaling& reset() {
kpeter@830
   557
      // Resize vectors
kpeter@830
   558
      _node_num = countNodes(_graph);
kpeter@830
   559
      _arc_num = countArcs(_graph);
kpeter@830
   560
      _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@830
   561
      _root = _node_num;
kpeter@830
   562
      ++_node_num;
kpeter@830
   563
kpeter@830
   564
      _first_out.resize(_node_num + 1);
kpeter@830
   565
      _forward.resize(_res_arc_num);
kpeter@830
   566
      _source.resize(_res_arc_num);
kpeter@830
   567
      _target.resize(_res_arc_num);
kpeter@830
   568
      _reverse.resize(_res_arc_num);
kpeter@830
   569
kpeter@830
   570
      _lower.resize(_res_arc_num);
kpeter@830
   571
      _upper.resize(_res_arc_num);
kpeter@830
   572
      _cost.resize(_res_arc_num);
kpeter@830
   573
      _supply.resize(_node_num);
kpeter@830
   574
      
kpeter@830
   575
      _res_cap.resize(_res_arc_num);
kpeter@830
   576
      _pi.resize(_node_num);
kpeter@830
   577
      _excess.resize(_node_num);
kpeter@830
   578
      _pred.resize(_node_num);
kpeter@830
   579
kpeter@830
   580
      // Copy the graph
kpeter@830
   581
      int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1;
kpeter@830
   582
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   583
        _node_id[n] = i;
kpeter@830
   584
      }
kpeter@830
   585
      i = 0;
kpeter@830
   586
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   587
        _first_out[i] = j;
kpeter@830
   588
        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830
   589
          _arc_idf[a] = j;
kpeter@830
   590
          _forward[j] = true;
kpeter@830
   591
          _source[j] = i;
kpeter@830
   592
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830
   593
        }
kpeter@830
   594
        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830
   595
          _arc_idb[a] = j;
kpeter@830
   596
          _forward[j] = false;
kpeter@830
   597
          _source[j] = i;
kpeter@830
   598
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830
   599
        }
kpeter@830
   600
        _forward[j] = false;
kpeter@830
   601
        _source[j] = i;
kpeter@830
   602
        _target[j] = _root;
kpeter@830
   603
        _reverse[j] = k;
kpeter@830
   604
        _forward[k] = true;
kpeter@830
   605
        _source[k] = _root;
kpeter@830
   606
        _target[k] = i;
kpeter@830
   607
        _reverse[k] = j;
kpeter@830
   608
        ++j; ++k;
kpeter@830
   609
      }
kpeter@830
   610
      _first_out[i] = j;
kpeter@830
   611
      _first_out[_node_num] = k;
kpeter@830
   612
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@830
   613
        int fi = _arc_idf[a];
kpeter@830
   614
        int bi = _arc_idb[a];
kpeter@830
   615
        _reverse[fi] = bi;
kpeter@830
   616
        _reverse[bi] = fi;
kpeter@830
   617
      }
kpeter@830
   618
      
kpeter@830
   619
      // Reset parameters
kpeter@830
   620
      resetParams();
kpeter@830
   621
      return *this;
kpeter@830
   622
    }
kpeter@830
   623
kpeter@805
   624
    /// @}
kpeter@805
   625
kpeter@805
   626
    /// \name Query Functions
kpeter@805
   627
    /// The results of the algorithm can be obtained using these
kpeter@805
   628
    /// functions.\n
kpeter@806
   629
    /// The \ref run() function must be called before using them.
kpeter@805
   630
kpeter@805
   631
    /// @{
kpeter@805
   632
kpeter@806
   633
    /// \brief Return the total cost of the found flow.
kpeter@805
   634
    ///
kpeter@806
   635
    /// This function returns the total cost of the found flow.
kpeter@806
   636
    /// Its complexity is O(e).
kpeter@806
   637
    ///
kpeter@806
   638
    /// \note The return type of the function can be specified as a
kpeter@806
   639
    /// template parameter. For example,
kpeter@806
   640
    /// \code
kpeter@806
   641
    ///   cs.totalCost<double>();
kpeter@806
   642
    /// \endcode
kpeter@806
   643
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@806
   644
    /// type of the algorithm, which is the default return type of the
kpeter@806
   645
    /// function.
kpeter@805
   646
    ///
kpeter@805
   647
    /// \pre \ref run() must be called before using this function.
kpeter@806
   648
    template <typename Number>
kpeter@806
   649
    Number totalCost() const {
kpeter@806
   650
      Number c = 0;
kpeter@806
   651
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806
   652
        int i = _arc_idb[a];
kpeter@806
   653
        c += static_cast<Number>(_res_cap[i]) *
kpeter@806
   654
             (-static_cast<Number>(_cost[i]));
kpeter@806
   655
      }
kpeter@806
   656
      return c;
kpeter@805
   657
    }
kpeter@805
   658
kpeter@806
   659
#ifndef DOXYGEN
kpeter@806
   660
    Cost totalCost() const {
kpeter@806
   661
      return totalCost<Cost>();
kpeter@805
   662
    }
kpeter@806
   663
#endif
kpeter@805
   664
kpeter@805
   665
    /// \brief Return the flow on the given arc.
kpeter@805
   666
    ///
kpeter@806
   667
    /// This function returns the flow on the given arc.
kpeter@805
   668
    ///
kpeter@805
   669
    /// \pre \ref run() must be called before using this function.
kpeter@806
   670
    Value flow(const Arc& a) const {
kpeter@806
   671
      return _res_cap[_arc_idb[a]];
kpeter@805
   672
    }
kpeter@805
   673
kpeter@806
   674
    /// \brief Return the flow map (the primal solution).
kpeter@805
   675
    ///
kpeter@806
   676
    /// This function copies the flow value on each arc into the given
kpeter@806
   677
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@806
   678
    /// the \c Value type of the map.
kpeter@805
   679
    ///
kpeter@805
   680
    /// \pre \ref run() must be called before using this function.
kpeter@806
   681
    template <typename FlowMap>
kpeter@806
   682
    void flowMap(FlowMap &map) const {
kpeter@806
   683
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806
   684
        map.set(a, _res_cap[_arc_idb[a]]);
kpeter@806
   685
      }
kpeter@805
   686
    }
kpeter@805
   687
kpeter@806
   688
    /// \brief Return the potential (dual value) of the given node.
kpeter@805
   689
    ///
kpeter@806
   690
    /// This function returns the potential (dual value) of the
kpeter@806
   691
    /// given node.
kpeter@805
   692
    ///
kpeter@805
   693
    /// \pre \ref run() must be called before using this function.
kpeter@806
   694
    Cost potential(const Node& n) const {
kpeter@806
   695
      return _pi[_node_id[n]];
kpeter@806
   696
    }
kpeter@806
   697
kpeter@806
   698
    /// \brief Return the potential map (the dual solution).
kpeter@806
   699
    ///
kpeter@806
   700
    /// This function copies the potential (dual value) of each node
kpeter@806
   701
    /// into the given map.
kpeter@806
   702
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@806
   703
    /// \c Value type of the map.
kpeter@806
   704
    ///
kpeter@806
   705
    /// \pre \ref run() must be called before using this function.
kpeter@806
   706
    template <typename PotentialMap>
kpeter@806
   707
    void potentialMap(PotentialMap &map) const {
kpeter@806
   708
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@806
   709
        map.set(n, _pi[_node_id[n]]);
kpeter@806
   710
      }
kpeter@805
   711
    }
kpeter@805
   712
kpeter@805
   713
    /// @}
kpeter@805
   714
kpeter@805
   715
  private:
kpeter@805
   716
kpeter@806
   717
    // Initialize the algorithm
kpeter@810
   718
    ProblemType init() {
kpeter@821
   719
      if (_node_num <= 1) return INFEASIBLE;
kpeter@805
   720
kpeter@806
   721
      // Check the sum of supply values
kpeter@806
   722
      _sum_supply = 0;
kpeter@806
   723
      for (int i = 0; i != _root; ++i) {
kpeter@806
   724
        _sum_supply += _supply[i];
kpeter@805
   725
      }
kpeter@806
   726
      if (_sum_supply > 0) return INFEASIBLE;
kpeter@806
   727
      
kpeter@811
   728
      // Initialize vectors
kpeter@806
   729
      for (int i = 0; i != _root; ++i) {
kpeter@806
   730
        _pi[i] = 0;
kpeter@806
   731
        _excess[i] = _supply[i];
kpeter@805
   732
      }
kpeter@805
   733
kpeter@806
   734
      // Remove non-zero lower bounds
kpeter@811
   735
      const Value MAX = std::numeric_limits<Value>::max();
kpeter@811
   736
      int last_out;
kpeter@806
   737
      if (_have_lower) {
kpeter@806
   738
        for (int i = 0; i != _root; ++i) {
kpeter@811
   739
          last_out = _first_out[i+1];
kpeter@811
   740
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@806
   741
            if (_forward[j]) {
kpeter@806
   742
              Value c = _lower[j];
kpeter@806
   743
              if (c >= 0) {
kpeter@811
   744
                _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;
kpeter@806
   745
              } else {
kpeter@811
   746
                _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;
kpeter@806
   747
              }
kpeter@806
   748
              _excess[i] -= c;
kpeter@806
   749
              _excess[_target[j]] += c;
kpeter@806
   750
            } else {
kpeter@806
   751
              _res_cap[j] = 0;
kpeter@806
   752
            }
kpeter@806
   753
          }
kpeter@806
   754
        }
kpeter@806
   755
      } else {
kpeter@806
   756
        for (int j = 0; j != _res_arc_num; ++j) {
kpeter@806
   757
          _res_cap[j] = _forward[j] ? _upper[j] : 0;
kpeter@806
   758
        }
kpeter@806
   759
      }
kpeter@805
   760
kpeter@806
   761
      // Handle negative costs
kpeter@811
   762
      for (int i = 0; i != _root; ++i) {
kpeter@811
   763
        last_out = _first_out[i+1] - 1;
kpeter@811
   764
        for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@811
   765
          Value rc = _res_cap[j];
kpeter@811
   766
          if (_cost[j] < 0 && rc > 0) {
kpeter@811
   767
            if (rc >= MAX) return UNBOUNDED;
kpeter@811
   768
            _excess[i] -= rc;
kpeter@811
   769
            _excess[_target[j]] += rc;
kpeter@811
   770
            _res_cap[j] = 0;
kpeter@811
   771
            _res_cap[_reverse[j]] += rc;
kpeter@806
   772
          }
kpeter@806
   773
        }
kpeter@806
   774
      }
kpeter@806
   775
      
kpeter@806
   776
      // Handle GEQ supply type
kpeter@806
   777
      if (_sum_supply < 0) {
kpeter@806
   778
        _pi[_root] = 0;
kpeter@806
   779
        _excess[_root] = -_sum_supply;
kpeter@806
   780
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@811
   781
          int ra = _reverse[a];
kpeter@811
   782
          _res_cap[a] = -_sum_supply + 1;
kpeter@811
   783
          _res_cap[ra] = 0;
kpeter@806
   784
          _cost[a] = 0;
kpeter@811
   785
          _cost[ra] = 0;
kpeter@806
   786
        }
kpeter@806
   787
      } else {
kpeter@806
   788
        _pi[_root] = 0;
kpeter@806
   789
        _excess[_root] = 0;
kpeter@806
   790
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@811
   791
          int ra = _reverse[a];
kpeter@806
   792
          _res_cap[a] = 1;
kpeter@811
   793
          _res_cap[ra] = 0;
kpeter@806
   794
          _cost[a] = 0;
kpeter@811
   795
          _cost[ra] = 0;
kpeter@806
   796
        }
kpeter@806
   797
      }
kpeter@806
   798
kpeter@806
   799
      // Initialize delta value
kpeter@810
   800
      if (_factor > 1) {
kpeter@805
   801
        // With scaling
kpeter@839
   802
        Value max_sup = 0, max_dem = 0, max_cap = 0;
kpeter@839
   803
        for (int i = 0; i != _root; ++i) {
kpeter@811
   804
          Value ex = _excess[i];
kpeter@811
   805
          if ( ex > max_sup) max_sup =  ex;
kpeter@811
   806
          if (-ex > max_dem) max_dem = -ex;
kpeter@839
   807
          int last_out = _first_out[i+1] - 1;
kpeter@839
   808
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@839
   809
            if (_res_cap[j] > max_cap) max_cap = _res_cap[j];
kpeter@839
   810
          }
kpeter@805
   811
        }
kpeter@805
   812
        max_sup = std::min(std::min(max_sup, max_dem), max_cap);
kpeter@810
   813
        for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;
kpeter@805
   814
      } else {
kpeter@805
   815
        // Without scaling
kpeter@805
   816
        _delta = 1;
kpeter@805
   817
      }
kpeter@805
   818
kpeter@806
   819
      return OPTIMAL;
kpeter@805
   820
    }
kpeter@805
   821
kpeter@806
   822
    ProblemType start() {
kpeter@806
   823
      // Execute the algorithm
kpeter@806
   824
      ProblemType pt;
kpeter@805
   825
      if (_delta > 1)
kpeter@806
   826
        pt = startWithScaling();
kpeter@805
   827
      else
kpeter@806
   828
        pt = startWithoutScaling();
kpeter@806
   829
kpeter@806
   830
      // Handle non-zero lower bounds
kpeter@806
   831
      if (_have_lower) {
kpeter@811
   832
        int limit = _first_out[_root];
kpeter@811
   833
        for (int j = 0; j != limit; ++j) {
kpeter@806
   834
          if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@806
   835
        }
kpeter@806
   836
      }
kpeter@806
   837
kpeter@806
   838
      // Shift potentials if necessary
kpeter@806
   839
      Cost pr = _pi[_root];
kpeter@806
   840
      if (_sum_supply < 0 || pr > 0) {
kpeter@806
   841
        for (int i = 0; i != _node_num; ++i) {
kpeter@806
   842
          _pi[i] -= pr;
kpeter@806
   843
        }        
kpeter@806
   844
      }
kpeter@806
   845
      
kpeter@806
   846
      return pt;
kpeter@805
   847
    }
kpeter@805
   848
kpeter@806
   849
    // Execute the capacity scaling algorithm
kpeter@806
   850
    ProblemType startWithScaling() {
kpeter@807
   851
      // Perform capacity scaling phases
kpeter@806
   852
      int s, t;
kpeter@806
   853
      ResidualDijkstra _dijkstra(*this);
kpeter@805
   854
      while (true) {
kpeter@806
   855
        // Saturate all arcs not satisfying the optimality condition
kpeter@811
   856
        int last_out;
kpeter@806
   857
        for (int u = 0; u != _node_num; ++u) {
kpeter@811
   858
          last_out = _sum_supply < 0 ?
kpeter@811
   859
            _first_out[u+1] : _first_out[u+1] - 1;
kpeter@811
   860
          for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@806
   861
            int v = _target[a];
kpeter@806
   862
            Cost c = _cost[a] + _pi[u] - _pi[v];
kpeter@806
   863
            Value rc = _res_cap[a];
kpeter@806
   864
            if (c < 0 && rc >= _delta) {
kpeter@806
   865
              _excess[u] -= rc;
kpeter@806
   866
              _excess[v] += rc;
kpeter@806
   867
              _res_cap[a] = 0;
kpeter@806
   868
              _res_cap[_reverse[a]] += rc;
kpeter@806
   869
            }
kpeter@805
   870
          }
kpeter@805
   871
        }
kpeter@805
   872
kpeter@806
   873
        // Find excess nodes and deficit nodes
kpeter@805
   874
        _excess_nodes.clear();
kpeter@805
   875
        _deficit_nodes.clear();
kpeter@806
   876
        for (int u = 0; u != _node_num; ++u) {
kpeter@811
   877
          Value ex = _excess[u];
kpeter@811
   878
          if (ex >=  _delta) _excess_nodes.push_back(u);
kpeter@811
   879
          if (ex <= -_delta) _deficit_nodes.push_back(u);
kpeter@805
   880
        }
kpeter@805
   881
        int next_node = 0, next_def_node = 0;
kpeter@805
   882
kpeter@806
   883
        // Find augmenting shortest paths
kpeter@805
   884
        while (next_node < int(_excess_nodes.size())) {
kpeter@806
   885
          // Check deficit nodes
kpeter@805
   886
          if (_delta > 1) {
kpeter@805
   887
            bool delta_deficit = false;
kpeter@805
   888
            for ( ; next_def_node < int(_deficit_nodes.size());
kpeter@805
   889
                    ++next_def_node ) {
kpeter@805
   890
              if (_excess[_deficit_nodes[next_def_node]] <= -_delta) {
kpeter@805
   891
                delta_deficit = true;
kpeter@805
   892
                break;
kpeter@805
   893
              }
kpeter@805
   894
            }
kpeter@805
   895
            if (!delta_deficit) break;
kpeter@805
   896
          }
kpeter@805
   897
kpeter@806
   898
          // Run Dijkstra in the residual network
kpeter@805
   899
          s = _excess_nodes[next_node];
kpeter@806
   900
          if ((t = _dijkstra.run(s, _delta)) == -1) {
kpeter@805
   901
            if (_delta > 1) {
kpeter@805
   902
              ++next_node;
kpeter@805
   903
              continue;
kpeter@805
   904
            }
kpeter@806
   905
            return INFEASIBLE;
kpeter@805
   906
          }
kpeter@805
   907
kpeter@806
   908
          // Augment along a shortest path from s to t
kpeter@806
   909
          Value d = std::min(_excess[s], -_excess[t]);
kpeter@806
   910
          int u = t;
kpeter@806
   911
          int a;
kpeter@805
   912
          if (d > _delta) {
kpeter@806
   913
            while ((a = _pred[u]) != -1) {
kpeter@806
   914
              if (_res_cap[a] < d) d = _res_cap[a];
kpeter@806
   915
              u = _source[a];
kpeter@805
   916
            }
kpeter@805
   917
          }
kpeter@805
   918
          u = t;
kpeter@806
   919
          while ((a = _pred[u]) != -1) {
kpeter@806
   920
            _res_cap[a] -= d;
kpeter@806
   921
            _res_cap[_reverse[a]] += d;
kpeter@806
   922
            u = _source[a];
kpeter@805
   923
          }
kpeter@805
   924
          _excess[s] -= d;
kpeter@805
   925
          _excess[t] += d;
kpeter@805
   926
kpeter@805
   927
          if (_excess[s] < _delta) ++next_node;
kpeter@805
   928
        }
kpeter@805
   929
kpeter@805
   930
        if (_delta == 1) break;
kpeter@810
   931
        _delta = _delta <= _factor ? 1 : _delta / _factor;
kpeter@805
   932
      }
kpeter@805
   933
kpeter@806
   934
      return OPTIMAL;
kpeter@805
   935
    }
kpeter@805
   936
kpeter@806
   937
    // Execute the successive shortest path algorithm
kpeter@806
   938
    ProblemType startWithoutScaling() {
kpeter@806
   939
      // Find excess nodes
kpeter@806
   940
      _excess_nodes.clear();
kpeter@806
   941
      for (int i = 0; i != _node_num; ++i) {
kpeter@806
   942
        if (_excess[i] > 0) _excess_nodes.push_back(i);
kpeter@806
   943
      }
kpeter@806
   944
      if (_excess_nodes.size() == 0) return OPTIMAL;
kpeter@805
   945
      int next_node = 0;
kpeter@805
   946
kpeter@806
   947
      // Find shortest paths
kpeter@806
   948
      int s, t;
kpeter@806
   949
      ResidualDijkstra _dijkstra(*this);
kpeter@805
   950
      while ( _excess[_excess_nodes[next_node]] > 0 ||
kpeter@805
   951
              ++next_node < int(_excess_nodes.size()) )
kpeter@805
   952
      {
kpeter@806
   953
        // Run Dijkstra in the residual network
kpeter@805
   954
        s = _excess_nodes[next_node];
kpeter@806
   955
        if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE;
kpeter@805
   956
kpeter@806
   957
        // Augment along a shortest path from s to t
kpeter@806
   958
        Value d = std::min(_excess[s], -_excess[t]);
kpeter@806
   959
        int u = t;
kpeter@806
   960
        int a;
kpeter@805
   961
        if (d > 1) {
kpeter@806
   962
          while ((a = _pred[u]) != -1) {
kpeter@806
   963
            if (_res_cap[a] < d) d = _res_cap[a];
kpeter@806
   964
            u = _source[a];
kpeter@805
   965
          }
kpeter@805
   966
        }
kpeter@805
   967
        u = t;
kpeter@806
   968
        while ((a = _pred[u]) != -1) {
kpeter@806
   969
          _res_cap[a] -= d;
kpeter@806
   970
          _res_cap[_reverse[a]] += d;
kpeter@806
   971
          u = _source[a];
kpeter@805
   972
        }
kpeter@805
   973
        _excess[s] -= d;
kpeter@805
   974
        _excess[t] += d;
kpeter@805
   975
      }
kpeter@805
   976
kpeter@806
   977
      return OPTIMAL;
kpeter@805
   978
    }
kpeter@805
   979
kpeter@805
   980
  }; //class CapacityScaling
kpeter@805
   981
kpeter@805
   982
  ///@}
kpeter@805
   983
kpeter@805
   984
} //namespace lemon
kpeter@805
   985
kpeter@805
   986
#endif //LEMON_CAPACITY_SCALING_H