[877] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[805] | 2 | * |
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[877] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[805] | 4 | * |
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[1092] | 5 | * Copyright (C) 2003-2013 |
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[805] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_CAPACITY_SCALING_H |
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| 20 | #define LEMON_CAPACITY_SCALING_H |
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| 21 | |
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[806] | 22 | /// \ingroup min_cost_flow_algs |
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[805] | 23 | /// |
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| 24 | /// \file |
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[806] | 25 | /// \brief Capacity Scaling algorithm for finding a minimum cost flow. |
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[805] | 26 | |
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| 27 | #include <vector> |
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[806] | 28 | #include <limits> |
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| 29 | #include <lemon/core.h> |
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[1151] | 30 | #include <lemon/maps.h> |
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[805] | 31 | #include <lemon/bin_heap.h> |
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| 32 | |
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| 33 | namespace lemon { |
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| 34 | |
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[807] | 35 | /// \brief Default traits class of CapacityScaling algorithm. |
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| 36 | /// |
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| 37 | /// Default traits class of CapacityScaling algorithm. |
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| 38 | /// \tparam GR Digraph type. |
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[812] | 39 | /// \tparam V The number type used for flow amounts, capacity bounds |
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[807] | 40 | /// and supply values. By default it is \c int. |
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[812] | 41 | /// \tparam C The number type used for costs and potentials. |
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[807] | 42 | /// By default it is the same as \c V. |
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| 43 | template <typename GR, typename V = int, typename C = V> |
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| 44 | struct CapacityScalingDefaultTraits |
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| 45 | { |
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| 46 | /// The type of the digraph |
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| 47 | typedef GR Digraph; |
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| 48 | /// The type of the flow amounts, capacity bounds and supply values |
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| 49 | typedef V Value; |
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| 50 | /// The type of the arc costs |
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| 51 | typedef C Cost; |
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| 52 | |
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| 53 | /// \brief The type of the heap used for internal Dijkstra computations. |
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| 54 | /// |
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| 55 | /// The type of the heap used for internal Dijkstra computations. |
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| 56 | /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, |
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| 57 | /// its priority type must be \c Cost and its cross reference type |
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| 58 | /// must be \ref RangeMap "RangeMap<int>". |
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| 59 | typedef BinHeap<Cost, RangeMap<int> > Heap; |
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| 60 | }; |
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| 61 | |
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[806] | 62 | /// \addtogroup min_cost_flow_algs |
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[805] | 63 | /// @{ |
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| 64 | |
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[806] | 65 | /// \brief Implementation of the Capacity Scaling algorithm for |
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| 66 | /// finding a \ref min_cost_flow "minimum cost flow". |
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[805] | 67 | /// |
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| 68 | /// \ref CapacityScaling implements the capacity scaling version |
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[806] | 69 | /// of the successive shortest path algorithm for finding a |
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[1053] | 70 | /// \ref min_cost_flow "minimum cost flow" \cite amo93networkflows, |
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| 71 | /// \cite edmondskarp72theoretical. It is an efficient dual |
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[1049] | 72 | /// solution method, which runs in polynomial time |
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[1080] | 73 | /// \f$O(m\log U (n+m)\log n)\f$, where <i>U</i> denotes the maximum |
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[1049] | 74 | /// of node supply and arc capacity values. |
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[821] | 75 | /// |
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[1003] | 76 | /// This algorithm is typically slower than \ref CostScaling and |
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| 77 | /// \ref NetworkSimplex, but in special cases, it can be more |
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| 78 | /// efficient than them. |
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| 79 | /// (For more information, see \ref min_cost_flow_algs "the module page".) |
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[805] | 80 | /// |
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[806] | 81 | /// Most of the parameters of the problem (except for the digraph) |
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| 82 | /// can be given using separate functions, and the algorithm can be |
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| 83 | /// executed using the \ref run() function. If some parameters are not |
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| 84 | /// specified, then default values will be used. |
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[805] | 85 | /// |
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[806] | 86 | /// \tparam GR The digraph type the algorithm runs on. |
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[812] | 87 | /// \tparam V The number type used for flow amounts, capacity bounds |
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[825] | 88 | /// and supply values in the algorithm. By default, it is \c int. |
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[812] | 89 | /// \tparam C The number type used for costs and potentials in the |
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[825] | 90 | /// algorithm. By default, it is the same as \c V. |
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| 91 | /// \tparam TR The traits class that defines various types used by the |
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| 92 | /// algorithm. By default, it is \ref CapacityScalingDefaultTraits |
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| 93 | /// "CapacityScalingDefaultTraits<GR, V, C>". |
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| 94 | /// In most cases, this parameter should not be set directly, |
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| 95 | /// consider to use the named template parameters instead. |
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[805] | 96 | /// |
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[921] | 97 | /// \warning Both \c V and \c C must be signed number types. |
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[985] | 98 | /// \warning Capacity bounds and supply values must be integer, but |
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| 99 | /// arc costs can be arbitrary real numbers. |
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[919] | 100 | /// \warning This algorithm does not support negative costs for |
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| 101 | /// arcs having infinite upper bound. |
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[807] | 102 | #ifdef DOXYGEN |
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| 103 | template <typename GR, typename V, typename C, typename TR> |
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| 104 | #else |
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| 105 | template < typename GR, typename V = int, typename C = V, |
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| 106 | typename TR = CapacityScalingDefaultTraits<GR, V, C> > |
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| 107 | #endif |
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[805] | 108 | class CapacityScaling |
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| 109 | { |
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[806] | 110 | public: |
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[805] | 111 | |
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[807] | 112 | /// The type of the digraph |
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| 113 | typedef typename TR::Digraph Digraph; |
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[806] | 114 | /// The type of the flow amounts, capacity bounds and supply values |
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[807] | 115 | typedef typename TR::Value Value; |
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[806] | 116 | /// The type of the arc costs |
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[807] | 117 | typedef typename TR::Cost Cost; |
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| 118 | |
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| 119 | /// The type of the heap used for internal Dijkstra computations |
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| 120 | typedef typename TR::Heap Heap; |
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| 121 | |
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[1074] | 122 | /// \brief The \ref lemon::CapacityScalingDefaultTraits "traits class" |
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| 123 | /// of the algorithm |
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[807] | 124 | typedef TR Traits; |
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[805] | 125 | |
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| 126 | public: |
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| 127 | |
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[806] | 128 | /// \brief Problem type constants for the \c run() function. |
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| 129 | /// |
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| 130 | /// Enum type containing the problem type constants that can be |
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| 131 | /// returned by the \ref run() function of the algorithm. |
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| 132 | enum ProblemType { |
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| 133 | /// The problem has no feasible solution (flow). |
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| 134 | INFEASIBLE, |
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| 135 | /// The problem has optimal solution (i.e. it is feasible and |
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| 136 | /// bounded), and the algorithm has found optimal flow and node |
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| 137 | /// potentials (primal and dual solutions). |
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| 138 | OPTIMAL, |
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| 139 | /// The digraph contains an arc of negative cost and infinite |
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| 140 | /// upper bound. It means that the objective function is unbounded |
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[812] | 141 | /// on that arc, however, note that it could actually be bounded |
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[806] | 142 | /// over the feasible flows, but this algroithm cannot handle |
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| 143 | /// these cases. |
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| 144 | UNBOUNDED |
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| 145 | }; |
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[877] | 146 | |
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[806] | 147 | private: |
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| 148 | |
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| 149 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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| 150 | |
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| 151 | typedef std::vector<int> IntVector; |
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| 152 | typedef std::vector<Value> ValueVector; |
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| 153 | typedef std::vector<Cost> CostVector; |
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[839] | 154 | typedef std::vector<char> BoolVector; |
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| 155 | // Note: vector<char> is used instead of vector<bool> for efficiency reasons |
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[805] | 156 | |
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| 157 | private: |
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| 158 | |
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[806] | 159 | // Data related to the underlying digraph |
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| 160 | const GR &_graph; |
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| 161 | int _node_num; |
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| 162 | int _arc_num; |
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| 163 | int _res_arc_num; |
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| 164 | int _root; |
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| 165 | |
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| 166 | // Parameters of the problem |
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[1103] | 167 | bool _has_lower; |
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[806] | 168 | Value _sum_supply; |
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| 169 | |
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| 170 | // Data structures for storing the digraph |
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| 171 | IntNodeMap _node_id; |
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| 172 | IntArcMap _arc_idf; |
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| 173 | IntArcMap _arc_idb; |
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| 174 | IntVector _first_out; |
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| 175 | BoolVector _forward; |
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| 176 | IntVector _source; |
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| 177 | IntVector _target; |
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| 178 | IntVector _reverse; |
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| 179 | |
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| 180 | // Node and arc data |
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| 181 | ValueVector _lower; |
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| 182 | ValueVector _upper; |
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| 183 | CostVector _cost; |
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| 184 | ValueVector _supply; |
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| 185 | |
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| 186 | ValueVector _res_cap; |
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| 187 | CostVector _pi; |
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| 188 | ValueVector _excess; |
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| 189 | IntVector _excess_nodes; |
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| 190 | IntVector _deficit_nodes; |
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| 191 | |
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| 192 | Value _delta; |
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[810] | 193 | int _factor; |
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[806] | 194 | IntVector _pred; |
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| 195 | |
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| 196 | public: |
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[877] | 197 | |
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[806] | 198 | /// \brief Constant for infinite upper bounds (capacities). |
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[805] | 199 | /// |
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[806] | 200 | /// Constant for infinite upper bounds (capacities). |
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| 201 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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| 202 | /// \c std::numeric_limits<Value>::max() otherwise. |
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| 203 | const Value INF; |
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| 204 | |
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| 205 | private: |
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| 206 | |
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| 207 | // Special implementation of the Dijkstra algorithm for finding |
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| 208 | // shortest paths in the residual network of the digraph with |
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| 209 | // respect to the reduced arc costs and modifying the node |
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| 210 | // potentials according to the found distance labels. |
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[805] | 211 | class ResidualDijkstra |
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| 212 | { |
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| 213 | private: |
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| 214 | |
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[806] | 215 | int _node_num; |
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[811] | 216 | bool _geq; |
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[806] | 217 | const IntVector &_first_out; |
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| 218 | const IntVector &_target; |
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| 219 | const CostVector &_cost; |
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| 220 | const ValueVector &_res_cap; |
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| 221 | const ValueVector &_excess; |
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| 222 | CostVector &_pi; |
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| 223 | IntVector &_pred; |
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[877] | 224 | |
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[806] | 225 | IntVector _proc_nodes; |
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| 226 | CostVector _dist; |
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[877] | 227 | |
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[805] | 228 | public: |
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| 229 | |
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[806] | 230 | ResidualDijkstra(CapacityScaling& cs) : |
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[811] | 231 | _node_num(cs._node_num), _geq(cs._sum_supply < 0), |
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| 232 | _first_out(cs._first_out), _target(cs._target), _cost(cs._cost), |
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| 233 | _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi), |
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| 234 | _pred(cs._pred), _dist(cs._node_num) |
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[805] | 235 | {} |
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| 236 | |
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[806] | 237 | int run(int s, Value delta = 1) { |
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[807] | 238 | RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP); |
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[805] | 239 | Heap heap(heap_cross_ref); |
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| 240 | heap.push(s, 0); |
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[806] | 241 | _pred[s] = -1; |
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[805] | 242 | _proc_nodes.clear(); |
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| 243 | |
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[806] | 244 | // Process nodes |
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[805] | 245 | while (!heap.empty() && _excess[heap.top()] > -delta) { |
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[806] | 246 | int u = heap.top(), v; |
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| 247 | Cost d = heap.prio() + _pi[u], dn; |
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[805] | 248 | _dist[u] = heap.prio(); |
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[806] | 249 | _proc_nodes.push_back(u); |
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[805] | 250 | heap.pop(); |
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| 251 | |
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[806] | 252 | // Traverse outgoing residual arcs |
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[811] | 253 | int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1; |
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| 254 | for (int a = _first_out[u]; a != last_out; ++a) { |
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[806] | 255 | if (_res_cap[a] < delta) continue; |
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| 256 | v = _target[a]; |
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| 257 | switch (heap.state(v)) { |
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[805] | 258 | case Heap::PRE_HEAP: |
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[806] | 259 | heap.push(v, d + _cost[a] - _pi[v]); |
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| 260 | _pred[v] = a; |
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[805] | 261 | break; |
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| 262 | case Heap::IN_HEAP: |
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[806] | 263 | dn = d + _cost[a] - _pi[v]; |
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| 264 | if (dn < heap[v]) { |
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| 265 | heap.decrease(v, dn); |
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| 266 | _pred[v] = a; |
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[805] | 267 | } |
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| 268 | break; |
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| 269 | case Heap::POST_HEAP: |
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| 270 | break; |
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| 271 | } |
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| 272 | } |
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| 273 | } |
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[806] | 274 | if (heap.empty()) return -1; |
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[805] | 275 | |
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[806] | 276 | // Update potentials of processed nodes |
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| 277 | int t = heap.top(); |
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| 278 | Cost dt = heap.prio(); |
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| 279 | for (int i = 0; i < int(_proc_nodes.size()); ++i) { |
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| 280 | _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt; |
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| 281 | } |
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[805] | 282 | |
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| 283 | return t; |
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| 284 | } |
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| 285 | |
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| 286 | }; //class ResidualDijkstra |
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| 287 | |
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| 288 | public: |
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| 289 | |
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[807] | 290 | /// \name Named Template Parameters |
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| 291 | /// @{ |
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| 292 | |
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| 293 | template <typename T> |
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| 294 | struct SetHeapTraits : public Traits { |
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| 295 | typedef T Heap; |
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| 296 | }; |
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| 297 | |
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| 298 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 299 | /// \c Heap type. |
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| 300 | /// |
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| 301 | /// \ref named-templ-param "Named parameter" for setting \c Heap |
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| 302 | /// type, which is used for internal Dijkstra computations. |
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| 303 | /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, |
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| 304 | /// its priority type must be \c Cost and its cross reference type |
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| 305 | /// must be \ref RangeMap "RangeMap<int>". |
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| 306 | template <typename T> |
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| 307 | struct SetHeap |
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| 308 | : public CapacityScaling<GR, V, C, SetHeapTraits<T> > { |
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| 309 | typedef CapacityScaling<GR, V, C, SetHeapTraits<T> > Create; |
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| 310 | }; |
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| 311 | |
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| 312 | /// @} |
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| 313 | |
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[863] | 314 | protected: |
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| 315 | |
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| 316 | CapacityScaling() {} |
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| 317 | |
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[807] | 318 | public: |
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| 319 | |
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[806] | 320 | /// \brief Constructor. |
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[805] | 321 | /// |
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[806] | 322 | /// The constructor of the class. |
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[805] | 323 | /// |
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[806] | 324 | /// \param graph The digraph the algorithm runs on. |
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| 325 | CapacityScaling(const GR& graph) : |
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| 326 | _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), |
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| 327 | INF(std::numeric_limits<Value>::has_infinity ? |
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| 328 | std::numeric_limits<Value>::infinity() : |
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| 329 | std::numeric_limits<Value>::max()) |
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[805] | 330 | { |
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[812] | 331 | // Check the number types |
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[806] | 332 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
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| 333 | "The flow type of CapacityScaling must be signed"); |
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| 334 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
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| 335 | "The cost type of CapacityScaling must be signed"); |
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| 336 | |
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[830] | 337 | // Reset data structures |
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[806] | 338 | reset(); |
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[805] | 339 | } |
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| 340 | |
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[806] | 341 | /// \name Parameters |
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| 342 | /// The parameters of the algorithm can be specified using these |
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| 343 | /// functions. |
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| 344 | |
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| 345 | /// @{ |
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| 346 | |
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| 347 | /// \brief Set the lower bounds on the arcs. |
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[805] | 348 | /// |
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[806] | 349 | /// This function sets the lower bounds on the arcs. |
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| 350 | /// If it is not used before calling \ref run(), the lower bounds |
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| 351 | /// will be set to zero on all arcs. |
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[805] | 352 | /// |
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[806] | 353 | /// \param map An arc map storing the lower bounds. |
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| 354 | /// Its \c Value type must be convertible to the \c Value type |
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| 355 | /// of the algorithm. |
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| 356 | /// |
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| 357 | /// \return <tt>(*this)</tt> |
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| 358 | template <typename LowerMap> |
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| 359 | CapacityScaling& lowerMap(const LowerMap& map) { |
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[1103] | 360 | _has_lower = true; |
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[806] | 361 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 362 | _lower[_arc_idf[a]] = map[a]; |
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[805] | 363 | } |
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| 364 | return *this; |
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| 365 | } |
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| 366 | |
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[806] | 367 | /// \brief Set the upper bounds (capacities) on the arcs. |
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[805] | 368 | /// |
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[806] | 369 | /// This function sets the upper bounds (capacities) on the arcs. |
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| 370 | /// If it is not used before calling \ref run(), the upper bounds |
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| 371 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
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[812] | 372 | /// unbounded from above). |
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[805] | 373 | /// |
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[806] | 374 | /// \param map An arc map storing the upper bounds. |
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| 375 | /// Its \c Value type must be convertible to the \c Value type |
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| 376 | /// of the algorithm. |
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| 377 | /// |
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| 378 | /// \return <tt>(*this)</tt> |
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| 379 | template<typename UpperMap> |
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| 380 | CapacityScaling& upperMap(const UpperMap& map) { |
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| 381 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 382 | _upper[_arc_idf[a]] = map[a]; |
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[805] | 383 | } |
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| 384 | return *this; |
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| 385 | } |
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| 386 | |
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[806] | 387 | /// \brief Set the costs of the arcs. |
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| 388 | /// |
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| 389 | /// This function sets the costs of the arcs. |
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| 390 | /// If it is not used before calling \ref run(), the costs |
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| 391 | /// will be set to \c 1 on all arcs. |
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| 392 | /// |
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| 393 | /// \param map An arc map storing the costs. |
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| 394 | /// Its \c Value type must be convertible to the \c Cost type |
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| 395 | /// of the algorithm. |
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| 396 | /// |
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| 397 | /// \return <tt>(*this)</tt> |
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| 398 | template<typename CostMap> |
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| 399 | CapacityScaling& costMap(const CostMap& map) { |
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| 400 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 401 | _cost[_arc_idf[a]] = map[a]; |
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| 402 | _cost[_arc_idb[a]] = -map[a]; |
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| 403 | } |
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| 404 | return *this; |
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| 405 | } |
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| 406 | |
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| 407 | /// \brief Set the supply values of the nodes. |
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| 408 | /// |
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| 409 | /// This function sets the supply values of the nodes. |
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| 410 | /// If neither this function nor \ref stSupply() is used before |
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| 411 | /// calling \ref run(), the supply of each node will be set to zero. |
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| 412 | /// |
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| 413 | /// \param map A node map storing the supply values. |
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| 414 | /// Its \c Value type must be convertible to the \c Value type |
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| 415 | /// of the algorithm. |
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| 416 | /// |
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| 417 | /// \return <tt>(*this)</tt> |
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| 418 | template<typename SupplyMap> |
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| 419 | CapacityScaling& supplyMap(const SupplyMap& map) { |
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| 420 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 421 | _supply[_node_id[n]] = map[n]; |
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| 422 | } |
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| 423 | return *this; |
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| 424 | } |
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| 425 | |
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| 426 | /// \brief Set single source and target nodes and a supply value. |
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| 427 | /// |
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| 428 | /// This function sets a single source node and a single target node |
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| 429 | /// and the required flow value. |
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| 430 | /// If neither this function nor \ref supplyMap() is used before |
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| 431 | /// calling \ref run(), the supply of each node will be set to zero. |
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| 432 | /// |
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| 433 | /// Using this function has the same effect as using \ref supplyMap() |
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[919] | 434 | /// with a map in which \c k is assigned to \c s, \c -k is |
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[806] | 435 | /// assigned to \c t and all other nodes have zero supply value. |
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| 436 | /// |
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| 437 | /// \param s The source node. |
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| 438 | /// \param t The target node. |
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| 439 | /// \param k The required amount of flow from node \c s to node \c t |
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| 440 | /// (i.e. the supply of \c s and the demand of \c t). |
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| 441 | /// |
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| 442 | /// \return <tt>(*this)</tt> |
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| 443 | CapacityScaling& stSupply(const Node& s, const Node& t, Value k) { |
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| 444 | for (int i = 0; i != _node_num; ++i) { |
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| 445 | _supply[i] = 0; |
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| 446 | } |
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| 447 | _supply[_node_id[s]] = k; |
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| 448 | _supply[_node_id[t]] = -k; |
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| 449 | return *this; |
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| 450 | } |
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[877] | 451 | |
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[806] | 452 | /// @} |
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| 453 | |
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[805] | 454 | /// \name Execution control |
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[807] | 455 | /// The algorithm can be executed using \ref run(). |
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[805] | 456 | |
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| 457 | /// @{ |
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| 458 | |
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| 459 | /// \brief Run the algorithm. |
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| 460 | /// |
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| 461 | /// This function runs the algorithm. |
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[806] | 462 | /// The paramters can be specified using functions \ref lowerMap(), |
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| 463 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 464 | /// For example, |
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| 465 | /// \code |
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| 466 | /// CapacityScaling<ListDigraph> cs(graph); |
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| 467 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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| 468 | /// .supplyMap(sup).run(); |
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| 469 | /// \endcode |
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| 470 | /// |
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[830] | 471 | /// This function can be called more than once. All the given parameters |
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| 472 | /// are kept for the next call, unless \ref resetParams() or \ref reset() |
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| 473 | /// is used, thus only the modified parameters have to be set again. |
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| 474 | /// If the underlying digraph was also modified after the construction |
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| 475 | /// of the class (or the last \ref reset() call), then the \ref reset() |
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| 476 | /// function must be called. |
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[805] | 477 | /// |
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[810] | 478 | /// \param factor The capacity scaling factor. It must be larger than |
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| 479 | /// one to use scaling. If it is less or equal to one, then scaling |
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| 480 | /// will be disabled. |
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[805] | 481 | /// |
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[806] | 482 | /// \return \c INFEASIBLE if no feasible flow exists, |
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| 483 | /// \n \c OPTIMAL if the problem has optimal solution |
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| 484 | /// (i.e. it is feasible and bounded), and the algorithm has found |
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| 485 | /// optimal flow and node potentials (primal and dual solutions), |
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| 486 | /// \n \c UNBOUNDED if the digraph contains an arc of negative cost |
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| 487 | /// and infinite upper bound. It means that the objective function |
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[812] | 488 | /// is unbounded on that arc, however, note that it could actually be |
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[806] | 489 | /// bounded over the feasible flows, but this algroithm cannot handle |
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| 490 | /// these cases. |
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| 491 | /// |
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| 492 | /// \see ProblemType |
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[830] | 493 | /// \see resetParams(), reset() |
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[810] | 494 | ProblemType run(int factor = 4) { |
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| 495 | _factor = factor; |
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| 496 | ProblemType pt = init(); |
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[806] | 497 | if (pt != OPTIMAL) return pt; |
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| 498 | return start(); |
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| 499 | } |
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| 500 | |
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| 501 | /// \brief Reset all the parameters that have been given before. |
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| 502 | /// |
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| 503 | /// This function resets all the paramaters that have been given |
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| 504 | /// before using functions \ref lowerMap(), \ref upperMap(), |
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| 505 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 506 | /// |
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[830] | 507 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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| 508 | /// parameters are kept for the next \ref run() call, unless |
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| 509 | /// \ref resetParams() or \ref reset() is used. |
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| 510 | /// If the underlying digraph was also modified after the construction |
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| 511 | /// of the class or the last \ref reset() call, then the \ref reset() |
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| 512 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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[806] | 513 | /// |
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| 514 | /// For example, |
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| 515 | /// \code |
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| 516 | /// CapacityScaling<ListDigraph> cs(graph); |
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| 517 | /// |
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| 518 | /// // First run |
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| 519 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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| 520 | /// .supplyMap(sup).run(); |
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| 521 | /// |
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[830] | 522 | /// // Run again with modified cost map (resetParams() is not called, |
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[806] | 523 | /// // so only the cost map have to be set again) |
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| 524 | /// cost[e] += 100; |
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| 525 | /// cs.costMap(cost).run(); |
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| 526 | /// |
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[830] | 527 | /// // Run again from scratch using resetParams() |
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[806] | 528 | /// // (the lower bounds will be set to zero on all arcs) |
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[830] | 529 | /// cs.resetParams(); |
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[806] | 530 | /// cs.upperMap(capacity).costMap(cost) |
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| 531 | /// .supplyMap(sup).run(); |
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| 532 | /// \endcode |
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| 533 | /// |
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| 534 | /// \return <tt>(*this)</tt> |
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[830] | 535 | /// |
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| 536 | /// \see reset(), run() |
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| 537 | CapacityScaling& resetParams() { |
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[806] | 538 | for (int i = 0; i != _node_num; ++i) { |
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| 539 | _supply[i] = 0; |
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| 540 | } |
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| 541 | for (int j = 0; j != _res_arc_num; ++j) { |
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| 542 | _lower[j] = 0; |
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| 543 | _upper[j] = INF; |
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| 544 | _cost[j] = _forward[j] ? 1 : -1; |
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| 545 | } |
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[1103] | 546 | _has_lower = false; |
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[821] | 547 | return *this; |
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| 548 | } |
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| 549 | |
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[830] | 550 | /// \brief Reset the internal data structures and all the parameters |
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| 551 | /// that have been given before. |
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| 552 | /// |
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| 553 | /// This function resets the internal data structures and all the |
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| 554 | /// paramaters that have been given before using functions \ref lowerMap(), |
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| 555 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 556 | /// |
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| 557 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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| 558 | /// parameters are kept for the next \ref run() call, unless |
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| 559 | /// \ref resetParams() or \ref reset() is used. |
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| 560 | /// If the underlying digraph was also modified after the construction |
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| 561 | /// of the class or the last \ref reset() call, then the \ref reset() |
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| 562 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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| 563 | /// |
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| 564 | /// See \ref resetParams() for examples. |
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| 565 | /// |
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| 566 | /// \return <tt>(*this)</tt> |
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| 567 | /// |
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| 568 | /// \see resetParams(), run() |
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| 569 | CapacityScaling& reset() { |
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| 570 | // Resize vectors |
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| 571 | _node_num = countNodes(_graph); |
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| 572 | _arc_num = countArcs(_graph); |
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| 573 | _res_arc_num = 2 * (_arc_num + _node_num); |
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| 574 | _root = _node_num; |
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| 575 | ++_node_num; |
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| 576 | |
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| 577 | _first_out.resize(_node_num + 1); |
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| 578 | _forward.resize(_res_arc_num); |
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| 579 | _source.resize(_res_arc_num); |
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| 580 | _target.resize(_res_arc_num); |
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| 581 | _reverse.resize(_res_arc_num); |
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| 582 | |
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| 583 | _lower.resize(_res_arc_num); |
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| 584 | _upper.resize(_res_arc_num); |
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| 585 | _cost.resize(_res_arc_num); |
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| 586 | _supply.resize(_node_num); |
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[877] | 587 | |
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[830] | 588 | _res_cap.resize(_res_arc_num); |
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| 589 | _pi.resize(_node_num); |
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| 590 | _excess.resize(_node_num); |
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| 591 | _pred.resize(_node_num); |
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| 592 | |
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| 593 | // Copy the graph |
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| 594 | int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1; |
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| 595 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
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| 596 | _node_id[n] = i; |
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| 597 | } |
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| 598 | i = 0; |
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| 599 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
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| 600 | _first_out[i] = j; |
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| 601 | for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
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| 602 | _arc_idf[a] = j; |
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| 603 | _forward[j] = true; |
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| 604 | _source[j] = i; |
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| 605 | _target[j] = _node_id[_graph.runningNode(a)]; |
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| 606 | } |
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| 607 | for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
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| 608 | _arc_idb[a] = j; |
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| 609 | _forward[j] = false; |
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| 610 | _source[j] = i; |
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| 611 | _target[j] = _node_id[_graph.runningNode(a)]; |
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| 612 | } |
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| 613 | _forward[j] = false; |
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| 614 | _source[j] = i; |
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| 615 | _target[j] = _root; |
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| 616 | _reverse[j] = k; |
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| 617 | _forward[k] = true; |
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| 618 | _source[k] = _root; |
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| 619 | _target[k] = i; |
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| 620 | _reverse[k] = j; |
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| 621 | ++j; ++k; |
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| 622 | } |
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| 623 | _first_out[i] = j; |
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| 624 | _first_out[_node_num] = k; |
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| 625 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 626 | int fi = _arc_idf[a]; |
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| 627 | int bi = _arc_idb[a]; |
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| 628 | _reverse[fi] = bi; |
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| 629 | _reverse[bi] = fi; |
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| 630 | } |
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[877] | 631 | |
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[830] | 632 | // Reset parameters |
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| 633 | resetParams(); |
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[806] | 634 | return *this; |
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[805] | 635 | } |
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| 636 | |
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| 637 | /// @} |
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| 638 | |
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| 639 | /// \name Query Functions |
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| 640 | /// The results of the algorithm can be obtained using these |
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| 641 | /// functions.\n |
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[806] | 642 | /// The \ref run() function must be called before using them. |
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[805] | 643 | |
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| 644 | /// @{ |
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| 645 | |
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[806] | 646 | /// \brief Return the total cost of the found flow. |
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[805] | 647 | /// |
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[806] | 648 | /// This function returns the total cost of the found flow. |
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[1080] | 649 | /// Its complexity is O(m). |
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[806] | 650 | /// |
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| 651 | /// \note The return type of the function can be specified as a |
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| 652 | /// template parameter. For example, |
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| 653 | /// \code |
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| 654 | /// cs.totalCost<double>(); |
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| 655 | /// \endcode |
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| 656 | /// It is useful if the total cost cannot be stored in the \c Cost |
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| 657 | /// type of the algorithm, which is the default return type of the |
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| 658 | /// function. |
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[805] | 659 | /// |
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| 660 | /// \pre \ref run() must be called before using this function. |
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[806] | 661 | template <typename Number> |
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| 662 | Number totalCost() const { |
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| 663 | Number c = 0; |
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| 664 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 665 | int i = _arc_idb[a]; |
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| 666 | c += static_cast<Number>(_res_cap[i]) * |
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| 667 | (-static_cast<Number>(_cost[i])); |
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| 668 | } |
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| 669 | return c; |
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[805] | 670 | } |
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| 671 | |
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[806] | 672 | #ifndef DOXYGEN |
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| 673 | Cost totalCost() const { |
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| 674 | return totalCost<Cost>(); |
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[805] | 675 | } |
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[806] | 676 | #endif |
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[805] | 677 | |
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| 678 | /// \brief Return the flow on the given arc. |
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| 679 | /// |
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[806] | 680 | /// This function returns the flow on the given arc. |
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[805] | 681 | /// |
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| 682 | /// \pre \ref run() must be called before using this function. |
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[806] | 683 | Value flow(const Arc& a) const { |
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| 684 | return _res_cap[_arc_idb[a]]; |
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[805] | 685 | } |
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| 686 | |
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[1003] | 687 | /// \brief Copy the flow values (the primal solution) into the |
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| 688 | /// given map. |
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[805] | 689 | /// |
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[806] | 690 | /// This function copies the flow value on each arc into the given |
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| 691 | /// map. The \c Value type of the algorithm must be convertible to |
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| 692 | /// the \c Value type of the map. |
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[805] | 693 | /// |
---|
| 694 | /// \pre \ref run() must be called before using this function. |
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[806] | 695 | template <typename FlowMap> |
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| 696 | void flowMap(FlowMap &map) const { |
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| 697 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 698 | map.set(a, _res_cap[_arc_idb[a]]); |
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| 699 | } |
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[805] | 700 | } |
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| 701 | |
---|
[806] | 702 | /// \brief Return the potential (dual value) of the given node. |
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[805] | 703 | /// |
---|
[806] | 704 | /// This function returns the potential (dual value) of the |
---|
| 705 | /// given node. |
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[805] | 706 | /// |
---|
| 707 | /// \pre \ref run() must be called before using this function. |
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[806] | 708 | Cost potential(const Node& n) const { |
---|
| 709 | return _pi[_node_id[n]]; |
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| 710 | } |
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| 711 | |
---|
[1003] | 712 | /// \brief Copy the potential values (the dual solution) into the |
---|
| 713 | /// given map. |
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[806] | 714 | /// |
---|
| 715 | /// This function copies the potential (dual value) of each node |
---|
| 716 | /// into the given map. |
---|
| 717 | /// The \c Cost type of the algorithm must be convertible to the |
---|
| 718 | /// \c Value type of the map. |
---|
| 719 | /// |
---|
| 720 | /// \pre \ref run() must be called before using this function. |
---|
| 721 | template <typename PotentialMap> |
---|
| 722 | void potentialMap(PotentialMap &map) const { |
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| 723 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 724 | map.set(n, _pi[_node_id[n]]); |
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| 725 | } |
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[805] | 726 | } |
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| 727 | |
---|
| 728 | /// @} |
---|
| 729 | |
---|
| 730 | private: |
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| 731 | |
---|
[806] | 732 | // Initialize the algorithm |
---|
[810] | 733 | ProblemType init() { |
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[821] | 734 | if (_node_num <= 1) return INFEASIBLE; |
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[805] | 735 | |
---|
[806] | 736 | // Check the sum of supply values |
---|
| 737 | _sum_supply = 0; |
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| 738 | for (int i = 0; i != _root; ++i) { |
---|
| 739 | _sum_supply += _supply[i]; |
---|
[805] | 740 | } |
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[806] | 741 | if (_sum_supply > 0) return INFEASIBLE; |
---|
[877] | 742 | |
---|
[1070] | 743 | // Check lower and upper bounds |
---|
| 744 | LEMON_DEBUG(checkBoundMaps(), |
---|
| 745 | "Upper bounds must be greater or equal to the lower bounds"); |
---|
| 746 | |
---|
| 747 | |
---|
[811] | 748 | // Initialize vectors |
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[806] | 749 | for (int i = 0; i != _root; ++i) { |
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| 750 | _pi[i] = 0; |
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| 751 | _excess[i] = _supply[i]; |
---|
[805] | 752 | } |
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| 753 | |
---|
[806] | 754 | // Remove non-zero lower bounds |
---|
[811] | 755 | const Value MAX = std::numeric_limits<Value>::max(); |
---|
| 756 | int last_out; |
---|
[1103] | 757 | if (_has_lower) { |
---|
[806] | 758 | for (int i = 0; i != _root; ++i) { |
---|
[811] | 759 | last_out = _first_out[i+1]; |
---|
| 760 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
[806] | 761 | if (_forward[j]) { |
---|
| 762 | Value c = _lower[j]; |
---|
| 763 | if (c >= 0) { |
---|
[811] | 764 | _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF; |
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[806] | 765 | } else { |
---|
[811] | 766 | _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF; |
---|
[806] | 767 | } |
---|
| 768 | _excess[i] -= c; |
---|
| 769 | _excess[_target[j]] += c; |
---|
| 770 | } else { |
---|
| 771 | _res_cap[j] = 0; |
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| 772 | } |
---|
| 773 | } |
---|
| 774 | } |
---|
| 775 | } else { |
---|
| 776 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 777 | _res_cap[j] = _forward[j] ? _upper[j] : 0; |
---|
| 778 | } |
---|
| 779 | } |
---|
[805] | 780 | |
---|
[806] | 781 | // Handle negative costs |
---|
[811] | 782 | for (int i = 0; i != _root; ++i) { |
---|
| 783 | last_out = _first_out[i+1] - 1; |
---|
| 784 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 785 | Value rc = _res_cap[j]; |
---|
| 786 | if (_cost[j] < 0 && rc > 0) { |
---|
| 787 | if (rc >= MAX) return UNBOUNDED; |
---|
| 788 | _excess[i] -= rc; |
---|
| 789 | _excess[_target[j]] += rc; |
---|
| 790 | _res_cap[j] = 0; |
---|
| 791 | _res_cap[_reverse[j]] += rc; |
---|
[806] | 792 | } |
---|
| 793 | } |
---|
| 794 | } |
---|
[877] | 795 | |
---|
[806] | 796 | // Handle GEQ supply type |
---|
| 797 | if (_sum_supply < 0) { |
---|
| 798 | _pi[_root] = 0; |
---|
| 799 | _excess[_root] = -_sum_supply; |
---|
| 800 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
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[811] | 801 | int ra = _reverse[a]; |
---|
| 802 | _res_cap[a] = -_sum_supply + 1; |
---|
| 803 | _res_cap[ra] = 0; |
---|
[806] | 804 | _cost[a] = 0; |
---|
[811] | 805 | _cost[ra] = 0; |
---|
[806] | 806 | } |
---|
| 807 | } else { |
---|
| 808 | _pi[_root] = 0; |
---|
| 809 | _excess[_root] = 0; |
---|
| 810 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
[811] | 811 | int ra = _reverse[a]; |
---|
[806] | 812 | _res_cap[a] = 1; |
---|
[811] | 813 | _res_cap[ra] = 0; |
---|
[806] | 814 | _cost[a] = 0; |
---|
[811] | 815 | _cost[ra] = 0; |
---|
[806] | 816 | } |
---|
| 817 | } |
---|
| 818 | |
---|
| 819 | // Initialize delta value |
---|
[810] | 820 | if (_factor > 1) { |
---|
[805] | 821 | // With scaling |
---|
[839] | 822 | Value max_sup = 0, max_dem = 0, max_cap = 0; |
---|
| 823 | for (int i = 0; i != _root; ++i) { |
---|
[811] | 824 | Value ex = _excess[i]; |
---|
| 825 | if ( ex > max_sup) max_sup = ex; |
---|
| 826 | if (-ex > max_dem) max_dem = -ex; |
---|
[839] | 827 | int last_out = _first_out[i+1] - 1; |
---|
| 828 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 829 | if (_res_cap[j] > max_cap) max_cap = _res_cap[j]; |
---|
| 830 | } |
---|
[805] | 831 | } |
---|
| 832 | max_sup = std::min(std::min(max_sup, max_dem), max_cap); |
---|
[810] | 833 | for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ; |
---|
[805] | 834 | } else { |
---|
| 835 | // Without scaling |
---|
| 836 | _delta = 1; |
---|
| 837 | } |
---|
| 838 | |
---|
[806] | 839 | return OPTIMAL; |
---|
[805] | 840 | } |
---|
| 841 | |
---|
[1102] | 842 | // Check if the upper bound is greater than or equal to the lower bound |
---|
| 843 | // on each forward arc. |
---|
[1070] | 844 | bool checkBoundMaps() { |
---|
| 845 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
[1102] | 846 | if (_forward[j] && _upper[j] < _lower[j]) return false; |
---|
[1070] | 847 | } |
---|
| 848 | return true; |
---|
| 849 | } |
---|
[821] | 850 | |
---|
[806] | 851 | ProblemType start() { |
---|
| 852 | // Execute the algorithm |
---|
| 853 | ProblemType pt; |
---|
[805] | 854 | if (_delta > 1) |
---|
[806] | 855 | pt = startWithScaling(); |
---|
[805] | 856 | else |
---|
[806] | 857 | pt = startWithoutScaling(); |
---|
| 858 | |
---|
| 859 | // Handle non-zero lower bounds |
---|
[1103] | 860 | if (_has_lower) { |
---|
[811] | 861 | int limit = _first_out[_root]; |
---|
| 862 | for (int j = 0; j != limit; ++j) { |
---|
[1102] | 863 | if (_forward[j]) _res_cap[_reverse[j]] += _lower[j]; |
---|
[806] | 864 | } |
---|
| 865 | } |
---|
| 866 | |
---|
| 867 | // Shift potentials if necessary |
---|
| 868 | Cost pr = _pi[_root]; |
---|
| 869 | if (_sum_supply < 0 || pr > 0) { |
---|
| 870 | for (int i = 0; i != _node_num; ++i) { |
---|
| 871 | _pi[i] -= pr; |
---|
[877] | 872 | } |
---|
[806] | 873 | } |
---|
[877] | 874 | |
---|
[806] | 875 | return pt; |
---|
[805] | 876 | } |
---|
| 877 | |
---|
[806] | 878 | // Execute the capacity scaling algorithm |
---|
| 879 | ProblemType startWithScaling() { |
---|
[807] | 880 | // Perform capacity scaling phases |
---|
[806] | 881 | int s, t; |
---|
| 882 | ResidualDijkstra _dijkstra(*this); |
---|
[805] | 883 | while (true) { |
---|
[806] | 884 | // Saturate all arcs not satisfying the optimality condition |
---|
[811] | 885 | int last_out; |
---|
[806] | 886 | for (int u = 0; u != _node_num; ++u) { |
---|
[811] | 887 | last_out = _sum_supply < 0 ? |
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| 888 | _first_out[u+1] : _first_out[u+1] - 1; |
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| 889 | for (int a = _first_out[u]; a != last_out; ++a) { |
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[806] | 890 | int v = _target[a]; |
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| 891 | Cost c = _cost[a] + _pi[u] - _pi[v]; |
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| 892 | Value rc = _res_cap[a]; |
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| 893 | if (c < 0 && rc >= _delta) { |
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| 894 | _excess[u] -= rc; |
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| 895 | _excess[v] += rc; |
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| 896 | _res_cap[a] = 0; |
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| 897 | _res_cap[_reverse[a]] += rc; |
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| 898 | } |
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[805] | 899 | } |
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| 900 | } |
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| 901 | |
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[806] | 902 | // Find excess nodes and deficit nodes |
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[805] | 903 | _excess_nodes.clear(); |
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| 904 | _deficit_nodes.clear(); |
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[806] | 905 | for (int u = 0; u != _node_num; ++u) { |
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[811] | 906 | Value ex = _excess[u]; |
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| 907 | if (ex >= _delta) _excess_nodes.push_back(u); |
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| 908 | if (ex <= -_delta) _deficit_nodes.push_back(u); |
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[805] | 909 | } |
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| 910 | int next_node = 0, next_def_node = 0; |
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| 911 | |
---|
[806] | 912 | // Find augmenting shortest paths |
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[805] | 913 | while (next_node < int(_excess_nodes.size())) { |
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[806] | 914 | // Check deficit nodes |
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[805] | 915 | if (_delta > 1) { |
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| 916 | bool delta_deficit = false; |
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| 917 | for ( ; next_def_node < int(_deficit_nodes.size()); |
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| 918 | ++next_def_node ) { |
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| 919 | if (_excess[_deficit_nodes[next_def_node]] <= -_delta) { |
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| 920 | delta_deficit = true; |
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| 921 | break; |
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| 922 | } |
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| 923 | } |
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| 924 | if (!delta_deficit) break; |
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| 925 | } |
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| 926 | |
---|
[806] | 927 | // Run Dijkstra in the residual network |
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[805] | 928 | s = _excess_nodes[next_node]; |
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[806] | 929 | if ((t = _dijkstra.run(s, _delta)) == -1) { |
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[805] | 930 | if (_delta > 1) { |
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| 931 | ++next_node; |
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| 932 | continue; |
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| 933 | } |
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[806] | 934 | return INFEASIBLE; |
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[805] | 935 | } |
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| 936 | |
---|
[806] | 937 | // Augment along a shortest path from s to t |
---|
| 938 | Value d = std::min(_excess[s], -_excess[t]); |
---|
| 939 | int u = t; |
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| 940 | int a; |
---|
[805] | 941 | if (d > _delta) { |
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[806] | 942 | while ((a = _pred[u]) != -1) { |
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| 943 | if (_res_cap[a] < d) d = _res_cap[a]; |
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| 944 | u = _source[a]; |
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[805] | 945 | } |
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| 946 | } |
---|
| 947 | u = t; |
---|
[806] | 948 | while ((a = _pred[u]) != -1) { |
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| 949 | _res_cap[a] -= d; |
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| 950 | _res_cap[_reverse[a]] += d; |
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| 951 | u = _source[a]; |
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[805] | 952 | } |
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| 953 | _excess[s] -= d; |
---|
| 954 | _excess[t] += d; |
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| 955 | |
---|
| 956 | if (_excess[s] < _delta) ++next_node; |
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| 957 | } |
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| 958 | |
---|
| 959 | if (_delta == 1) break; |
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[810] | 960 | _delta = _delta <= _factor ? 1 : _delta / _factor; |
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[805] | 961 | } |
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| 962 | |
---|
[806] | 963 | return OPTIMAL; |
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[805] | 964 | } |
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| 965 | |
---|
[806] | 966 | // Execute the successive shortest path algorithm |
---|
| 967 | ProblemType startWithoutScaling() { |
---|
| 968 | // Find excess nodes |
---|
| 969 | _excess_nodes.clear(); |
---|
| 970 | for (int i = 0; i != _node_num; ++i) { |
---|
| 971 | if (_excess[i] > 0) _excess_nodes.push_back(i); |
---|
| 972 | } |
---|
| 973 | if (_excess_nodes.size() == 0) return OPTIMAL; |
---|
[805] | 974 | int next_node = 0; |
---|
| 975 | |
---|
[806] | 976 | // Find shortest paths |
---|
| 977 | int s, t; |
---|
| 978 | ResidualDijkstra _dijkstra(*this); |
---|
[805] | 979 | while ( _excess[_excess_nodes[next_node]] > 0 || |
---|
| 980 | ++next_node < int(_excess_nodes.size()) ) |
---|
| 981 | { |
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[806] | 982 | // Run Dijkstra in the residual network |
---|
[805] | 983 | s = _excess_nodes[next_node]; |
---|
[806] | 984 | if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE; |
---|
[805] | 985 | |
---|
[806] | 986 | // Augment along a shortest path from s to t |
---|
| 987 | Value d = std::min(_excess[s], -_excess[t]); |
---|
| 988 | int u = t; |
---|
| 989 | int a; |
---|
[805] | 990 | if (d > 1) { |
---|
[806] | 991 | while ((a = _pred[u]) != -1) { |
---|
| 992 | if (_res_cap[a] < d) d = _res_cap[a]; |
---|
| 993 | u = _source[a]; |
---|
[805] | 994 | } |
---|
| 995 | } |
---|
| 996 | u = t; |
---|
[806] | 997 | while ((a = _pred[u]) != -1) { |
---|
| 998 | _res_cap[a] -= d; |
---|
| 999 | _res_cap[_reverse[a]] += d; |
---|
| 1000 | u = _source[a]; |
---|
[805] | 1001 | } |
---|
| 1002 | _excess[s] -= d; |
---|
| 1003 | _excess[t] += d; |
---|
| 1004 | } |
---|
| 1005 | |
---|
[806] | 1006 | return OPTIMAL; |
---|
[805] | 1007 | } |
---|
| 1008 | |
---|
| 1009 | }; //class CapacityScaling |
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| 1010 | |
---|
| 1011 | ///@} |
---|
| 1012 | |
---|
| 1013 | } //namespace lemon |
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| 1014 | |
---|
| 1015 | #endif //LEMON_CAPACITY_SCALING_H |
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