[956] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[871] | 2 | * |
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[956] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[871] | 4 | * |
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[956] | 5 | * Copyright (C) 2003-2010 |
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[871] | 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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[872] | 22 | /// \ingroup min_cost_flow_algs |
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[871] | 23 | /// |
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| 24 | /// \file |
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[872] | 25 | /// \brief Capacity Scaling algorithm for finding a minimum cost flow. |
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[871] | 26 | |
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| 27 | #include <vector> |
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[872] | 28 | #include <limits> |
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| 29 | #include <lemon/core.h> |
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[871] | 30 | #include <lemon/bin_heap.h> |
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| 31 | |
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| 32 | namespace lemon { |
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| 33 | |
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[873] | 34 | /// \brief Default traits class of CapacityScaling algorithm. |
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| 35 | /// |
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| 36 | /// Default traits class of CapacityScaling algorithm. |
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| 37 | /// \tparam GR Digraph type. |
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[878] | 38 | /// \tparam V The number type used for flow amounts, capacity bounds |
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[873] | 39 | /// and supply values. By default it is \c int. |
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[878] | 40 | /// \tparam C The number type used for costs and potentials. |
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[873] | 41 | /// By default it is the same as \c V. |
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| 42 | template <typename GR, typename V = int, typename C = V> |
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| 43 | struct CapacityScalingDefaultTraits |
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| 44 | { |
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| 45 | /// The type of the digraph |
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| 46 | typedef GR Digraph; |
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| 47 | /// The type of the flow amounts, capacity bounds and supply values |
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| 48 | typedef V Value; |
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| 49 | /// The type of the arc costs |
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| 50 | typedef C Cost; |
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| 51 | |
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| 52 | /// \brief The type of the heap used for internal Dijkstra computations. |
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| 53 | /// |
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| 54 | /// The type of the heap used for internal Dijkstra computations. |
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| 55 | /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, |
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| 56 | /// its priority type must be \c Cost and its cross reference type |
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| 57 | /// must be \ref RangeMap "RangeMap<int>". |
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| 58 | typedef BinHeap<Cost, RangeMap<int> > Heap; |
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| 59 | }; |
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| 60 | |
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[872] | 61 | /// \addtogroup min_cost_flow_algs |
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[871] | 62 | /// @{ |
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| 63 | |
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[872] | 64 | /// \brief Implementation of the Capacity Scaling algorithm for |
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| 65 | /// finding a \ref min_cost_flow "minimum cost flow". |
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[871] | 66 | /// |
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| 67 | /// \ref CapacityScaling implements the capacity scaling version |
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[872] | 68 | /// of the successive shortest path algorithm for finding a |
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[879] | 69 | /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows, |
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| 70 | /// \ref edmondskarp72theoretical. It is an efficient dual |
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[872] | 71 | /// solution method. |
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[871] | 72 | /// |
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[1165] | 73 | /// This algorithm is typically slower than \ref CostScaling and |
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| 74 | /// \ref NetworkSimplex, but in special cases, it can be more |
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| 75 | /// efficient than them. |
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| 76 | /// (For more information, see \ref min_cost_flow_algs "the module page".) |
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| 77 | /// |
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[872] | 78 | /// Most of the parameters of the problem (except for the digraph) |
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| 79 | /// can be given using separate functions, and the algorithm can be |
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| 80 | /// executed using the \ref run() function. If some parameters are not |
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| 81 | /// specified, then default values will be used. |
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[871] | 82 | /// |
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[872] | 83 | /// \tparam GR The digraph type the algorithm runs on. |
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[878] | 84 | /// \tparam V The number type used for flow amounts, capacity bounds |
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[891] | 85 | /// and supply values in the algorithm. By default, it is \c int. |
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[878] | 86 | /// \tparam C The number type used for costs and potentials in the |
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[891] | 87 | /// algorithm. By default, it is the same as \c V. |
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| 88 | /// \tparam TR The traits class that defines various types used by the |
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| 89 | /// algorithm. By default, it is \ref CapacityScalingDefaultTraits |
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| 90 | /// "CapacityScalingDefaultTraits<GR, V, C>". |
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| 91 | /// In most cases, this parameter should not be set directly, |
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| 92 | /// consider to use the named template parameters instead. |
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[871] | 93 | /// |
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[1025] | 94 | /// \warning Both \c V and \c C must be signed number types. |
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[1137] | 95 | /// \warning Capacity bounds and supply values must be integer, but |
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| 96 | /// arc costs can be arbitrary real numbers. |
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[1023] | 97 | /// \warning This algorithm does not support negative costs for |
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| 98 | /// arcs having infinite upper bound. |
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[873] | 99 | #ifdef DOXYGEN |
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| 100 | template <typename GR, typename V, typename C, typename TR> |
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| 101 | #else |
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| 102 | template < typename GR, typename V = int, typename C = V, |
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| 103 | typename TR = CapacityScalingDefaultTraits<GR, V, C> > |
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| 104 | #endif |
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[871] | 105 | class CapacityScaling |
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| 106 | { |
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[872] | 107 | public: |
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[871] | 108 | |
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[873] | 109 | /// The type of the digraph |
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| 110 | typedef typename TR::Digraph Digraph; |
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[872] | 111 | /// The type of the flow amounts, capacity bounds and supply values |
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[873] | 112 | typedef typename TR::Value Value; |
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[872] | 113 | /// The type of the arc costs |
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[873] | 114 | typedef typename TR::Cost Cost; |
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| 115 | |
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| 116 | /// The type of the heap used for internal Dijkstra computations |
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| 117 | typedef typename TR::Heap Heap; |
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| 118 | |
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| 119 | /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm |
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| 120 | typedef TR Traits; |
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[871] | 121 | |
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| 122 | public: |
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| 123 | |
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[872] | 124 | /// \brief Problem type constants for the \c run() function. |
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| 125 | /// |
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| 126 | /// Enum type containing the problem type constants that can be |
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| 127 | /// returned by the \ref run() function of the algorithm. |
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| 128 | enum ProblemType { |
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| 129 | /// The problem has no feasible solution (flow). |
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| 130 | INFEASIBLE, |
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| 131 | /// The problem has optimal solution (i.e. it is feasible and |
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| 132 | /// bounded), and the algorithm has found optimal flow and node |
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| 133 | /// potentials (primal and dual solutions). |
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| 134 | OPTIMAL, |
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| 135 | /// The digraph contains an arc of negative cost and infinite |
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| 136 | /// upper bound. It means that the objective function is unbounded |
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[878] | 137 | /// on that arc, however, note that it could actually be bounded |
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[872] | 138 | /// over the feasible flows, but this algroithm cannot handle |
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| 139 | /// these cases. |
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| 140 | UNBOUNDED |
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| 141 | }; |
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[956] | 142 | |
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[872] | 143 | private: |
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| 144 | |
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| 145 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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| 146 | |
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| 147 | typedef std::vector<int> IntVector; |
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| 148 | typedef std::vector<Value> ValueVector; |
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| 149 | typedef std::vector<Cost> CostVector; |
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[910] | 150 | typedef std::vector<char> BoolVector; |
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| 151 | // Note: vector<char> is used instead of vector<bool> for efficiency reasons |
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[871] | 152 | |
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| 153 | private: |
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| 154 | |
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[872] | 155 | // Data related to the underlying digraph |
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| 156 | const GR &_graph; |
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| 157 | int _node_num; |
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| 158 | int _arc_num; |
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| 159 | int _res_arc_num; |
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| 160 | int _root; |
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| 161 | |
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| 162 | // Parameters of the problem |
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[1297] | 163 | bool _has_lower; |
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[872] | 164 | Value _sum_supply; |
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| 165 | |
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| 166 | // Data structures for storing the digraph |
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| 167 | IntNodeMap _node_id; |
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| 168 | IntArcMap _arc_idf; |
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| 169 | IntArcMap _arc_idb; |
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| 170 | IntVector _first_out; |
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| 171 | BoolVector _forward; |
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| 172 | IntVector _source; |
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| 173 | IntVector _target; |
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| 174 | IntVector _reverse; |
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| 175 | |
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| 176 | // Node and arc data |
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| 177 | ValueVector _lower; |
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| 178 | ValueVector _upper; |
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| 179 | CostVector _cost; |
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| 180 | ValueVector _supply; |
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| 181 | |
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| 182 | ValueVector _res_cap; |
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| 183 | CostVector _pi; |
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| 184 | ValueVector _excess; |
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| 185 | IntVector _excess_nodes; |
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| 186 | IntVector _deficit_nodes; |
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| 187 | |
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| 188 | Value _delta; |
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[876] | 189 | int _factor; |
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[872] | 190 | IntVector _pred; |
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| 191 | |
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| 192 | public: |
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[956] | 193 | |
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[872] | 194 | /// \brief Constant for infinite upper bounds (capacities). |
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[871] | 195 | /// |
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[872] | 196 | /// Constant for infinite upper bounds (capacities). |
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| 197 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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| 198 | /// \c std::numeric_limits<Value>::max() otherwise. |
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| 199 | const Value INF; |
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| 200 | |
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| 201 | private: |
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| 202 | |
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| 203 | // Special implementation of the Dijkstra algorithm for finding |
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| 204 | // shortest paths in the residual network of the digraph with |
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| 205 | // respect to the reduced arc costs and modifying the node |
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| 206 | // potentials according to the found distance labels. |
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[871] | 207 | class ResidualDijkstra |
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| 208 | { |
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| 209 | private: |
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| 210 | |
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[872] | 211 | int _node_num; |
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[877] | 212 | bool _geq; |
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[872] | 213 | const IntVector &_first_out; |
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| 214 | const IntVector &_target; |
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| 215 | const CostVector &_cost; |
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| 216 | const ValueVector &_res_cap; |
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| 217 | const ValueVector &_excess; |
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| 218 | CostVector &_pi; |
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| 219 | IntVector &_pred; |
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[956] | 220 | |
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[872] | 221 | IntVector _proc_nodes; |
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| 222 | CostVector _dist; |
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[956] | 223 | |
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[871] | 224 | public: |
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| 225 | |
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[872] | 226 | ResidualDijkstra(CapacityScaling& cs) : |
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[877] | 227 | _node_num(cs._node_num), _geq(cs._sum_supply < 0), |
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| 228 | _first_out(cs._first_out), _target(cs._target), _cost(cs._cost), |
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| 229 | _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi), |
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| 230 | _pred(cs._pred), _dist(cs._node_num) |
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[871] | 231 | {} |
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| 232 | |
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[872] | 233 | int run(int s, Value delta = 1) { |
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[873] | 234 | RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP); |
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[871] | 235 | Heap heap(heap_cross_ref); |
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| 236 | heap.push(s, 0); |
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[872] | 237 | _pred[s] = -1; |
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[871] | 238 | _proc_nodes.clear(); |
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| 239 | |
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[872] | 240 | // Process nodes |
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[871] | 241 | while (!heap.empty() && _excess[heap.top()] > -delta) { |
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[872] | 242 | int u = heap.top(), v; |
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| 243 | Cost d = heap.prio() + _pi[u], dn; |
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[871] | 244 | _dist[u] = heap.prio(); |
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[872] | 245 | _proc_nodes.push_back(u); |
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[871] | 246 | heap.pop(); |
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| 247 | |
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[872] | 248 | // Traverse outgoing residual arcs |
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[877] | 249 | int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1; |
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| 250 | for (int a = _first_out[u]; a != last_out; ++a) { |
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[872] | 251 | if (_res_cap[a] < delta) continue; |
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| 252 | v = _target[a]; |
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| 253 | switch (heap.state(v)) { |
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[871] | 254 | case Heap::PRE_HEAP: |
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[872] | 255 | heap.push(v, d + _cost[a] - _pi[v]); |
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| 256 | _pred[v] = a; |
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[871] | 257 | break; |
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| 258 | case Heap::IN_HEAP: |
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[872] | 259 | dn = d + _cost[a] - _pi[v]; |
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| 260 | if (dn < heap[v]) { |
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| 261 | heap.decrease(v, dn); |
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| 262 | _pred[v] = a; |
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[871] | 263 | } |
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| 264 | break; |
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| 265 | case Heap::POST_HEAP: |
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| 266 | break; |
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| 267 | } |
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| 268 | } |
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| 269 | } |
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[872] | 270 | if (heap.empty()) return -1; |
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[871] | 271 | |
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[872] | 272 | // Update potentials of processed nodes |
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| 273 | int t = heap.top(); |
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| 274 | Cost dt = heap.prio(); |
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| 275 | for (int i = 0; i < int(_proc_nodes.size()); ++i) { |
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| 276 | _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt; |
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| 277 | } |
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[871] | 278 | |
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| 279 | return t; |
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| 280 | } |
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| 281 | |
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| 282 | }; //class ResidualDijkstra |
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| 283 | |
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| 284 | public: |
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| 285 | |
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[873] | 286 | /// \name Named Template Parameters |
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| 287 | /// @{ |
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| 288 | |
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| 289 | template <typename T> |
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| 290 | struct SetHeapTraits : public Traits { |
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| 291 | typedef T Heap; |
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| 292 | }; |
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| 293 | |
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| 294 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 295 | /// \c Heap type. |
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| 296 | /// |
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| 297 | /// \ref named-templ-param "Named parameter" for setting \c Heap |
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| 298 | /// type, which is used for internal Dijkstra computations. |
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| 299 | /// It must conform to the \ref lemon::concepts::Heap "Heap" concept, |
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| 300 | /// its priority type must be \c Cost and its cross reference type |
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| 301 | /// must be \ref RangeMap "RangeMap<int>". |
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| 302 | template <typename T> |
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| 303 | struct SetHeap |
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| 304 | : public CapacityScaling<GR, V, C, SetHeapTraits<T> > { |
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| 305 | typedef CapacityScaling<GR, V, C, SetHeapTraits<T> > Create; |
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| 306 | }; |
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| 307 | |
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| 308 | /// @} |
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| 309 | |
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[941] | 310 | protected: |
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| 311 | |
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| 312 | CapacityScaling() {} |
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| 313 | |
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[873] | 314 | public: |
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| 315 | |
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[872] | 316 | /// \brief Constructor. |
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[871] | 317 | /// |
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[872] | 318 | /// The constructor of the class. |
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[871] | 319 | /// |
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[872] | 320 | /// \param graph The digraph the algorithm runs on. |
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| 321 | CapacityScaling(const GR& graph) : |
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| 322 | _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), |
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| 323 | INF(std::numeric_limits<Value>::has_infinity ? |
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| 324 | std::numeric_limits<Value>::infinity() : |
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| 325 | std::numeric_limits<Value>::max()) |
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[871] | 326 | { |
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[878] | 327 | // Check the number types |
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[872] | 328 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
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| 329 | "The flow type of CapacityScaling must be signed"); |
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| 330 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
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| 331 | "The cost type of CapacityScaling must be signed"); |
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| 332 | |
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[898] | 333 | // Reset data structures |
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[872] | 334 | reset(); |
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[871] | 335 | } |
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| 336 | |
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[872] | 337 | /// \name Parameters |
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| 338 | /// The parameters of the algorithm can be specified using these |
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| 339 | /// functions. |
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| 340 | |
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| 341 | /// @{ |
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| 342 | |
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| 343 | /// \brief Set the lower bounds on the arcs. |
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[871] | 344 | /// |
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[872] | 345 | /// This function sets the lower bounds on the arcs. |
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| 346 | /// If it is not used before calling \ref run(), the lower bounds |
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| 347 | /// will be set to zero on all arcs. |
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[871] | 348 | /// |
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[872] | 349 | /// \param map An arc map storing the lower bounds. |
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| 350 | /// Its \c Value type must be convertible to the \c Value type |
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| 351 | /// of the algorithm. |
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| 352 | /// |
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| 353 | /// \return <tt>(*this)</tt> |
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| 354 | template <typename LowerMap> |
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| 355 | CapacityScaling& lowerMap(const LowerMap& map) { |
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[1297] | 356 | _has_lower = true; |
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[872] | 357 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 358 | _lower[_arc_idf[a]] = map[a]; |
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[871] | 359 | } |
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| 360 | return *this; |
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| 361 | } |
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| 362 | |
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[872] | 363 | /// \brief Set the upper bounds (capacities) on the arcs. |
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[871] | 364 | /// |
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[872] | 365 | /// This function sets the upper bounds (capacities) on the arcs. |
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| 366 | /// If it is not used before calling \ref run(), the upper bounds |
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| 367 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
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[878] | 368 | /// unbounded from above). |
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[871] | 369 | /// |
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[872] | 370 | /// \param map An arc map storing the upper bounds. |
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| 371 | /// Its \c Value type must be convertible to the \c Value type |
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| 372 | /// of the algorithm. |
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| 373 | /// |
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| 374 | /// \return <tt>(*this)</tt> |
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| 375 | template<typename UpperMap> |
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| 376 | CapacityScaling& upperMap(const UpperMap& map) { |
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| 377 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 378 | _upper[_arc_idf[a]] = map[a]; |
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[871] | 379 | } |
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| 380 | return *this; |
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| 381 | } |
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| 382 | |
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[872] | 383 | /// \brief Set the costs of the arcs. |
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| 384 | /// |
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| 385 | /// This function sets the costs of the arcs. |
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| 386 | /// If it is not used before calling \ref run(), the costs |
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| 387 | /// will be set to \c 1 on all arcs. |
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| 388 | /// |
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| 389 | /// \param map An arc map storing the costs. |
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| 390 | /// Its \c Value type must be convertible to the \c Cost type |
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| 391 | /// of the algorithm. |
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| 392 | /// |
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| 393 | /// \return <tt>(*this)</tt> |
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| 394 | template<typename CostMap> |
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| 395 | CapacityScaling& costMap(const CostMap& map) { |
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| 396 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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| 397 | _cost[_arc_idf[a]] = map[a]; |
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| 398 | _cost[_arc_idb[a]] = -map[a]; |
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| 399 | } |
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| 400 | return *this; |
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| 401 | } |
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| 402 | |
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| 403 | /// \brief Set the supply values of the nodes. |
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| 404 | /// |
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| 405 | /// This function sets the supply values of the nodes. |
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| 406 | /// If neither this function nor \ref stSupply() is used before |
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| 407 | /// calling \ref run(), the supply of each node will be set to zero. |
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| 408 | /// |
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| 409 | /// \param map A node map storing the supply values. |
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| 410 | /// Its \c Value type must be convertible to the \c Value type |
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| 411 | /// of the algorithm. |
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| 412 | /// |
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| 413 | /// \return <tt>(*this)</tt> |
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| 414 | template<typename SupplyMap> |
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| 415 | CapacityScaling& supplyMap(const SupplyMap& map) { |
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| 416 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 417 | _supply[_node_id[n]] = map[n]; |
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| 418 | } |
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| 419 | return *this; |
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| 420 | } |
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| 421 | |
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| 422 | /// \brief Set single source and target nodes and a supply value. |
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| 423 | /// |
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| 424 | /// This function sets a single source node and a single target node |
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| 425 | /// and the required flow value. |
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| 426 | /// If neither this function nor \ref supplyMap() is used before |
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| 427 | /// calling \ref run(), the supply of each node will be set to zero. |
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| 428 | /// |
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| 429 | /// Using this function has the same effect as using \ref supplyMap() |
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[1023] | 430 | /// with a map in which \c k is assigned to \c s, \c -k is |
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[872] | 431 | /// assigned to \c t and all other nodes have zero supply value. |
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| 432 | /// |
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| 433 | /// \param s The source node. |
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| 434 | /// \param t The target node. |
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| 435 | /// \param k The required amount of flow from node \c s to node \c t |
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| 436 | /// (i.e. the supply of \c s and the demand of \c t). |
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| 437 | /// |
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| 438 | /// \return <tt>(*this)</tt> |
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| 439 | CapacityScaling& stSupply(const Node& s, const Node& t, Value k) { |
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| 440 | for (int i = 0; i != _node_num; ++i) { |
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| 441 | _supply[i] = 0; |
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| 442 | } |
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| 443 | _supply[_node_id[s]] = k; |
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| 444 | _supply[_node_id[t]] = -k; |
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| 445 | return *this; |
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| 446 | } |
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[956] | 447 | |
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[872] | 448 | /// @} |
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| 449 | |
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[871] | 450 | /// \name Execution control |
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[873] | 451 | /// The algorithm can be executed using \ref run(). |
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[871] | 452 | |
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| 453 | /// @{ |
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| 454 | |
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| 455 | /// \brief Run the algorithm. |
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| 456 | /// |
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| 457 | /// This function runs the algorithm. |
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[872] | 458 | /// The paramters can be specified using functions \ref lowerMap(), |
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| 459 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 460 | /// For example, |
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| 461 | /// \code |
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| 462 | /// CapacityScaling<ListDigraph> cs(graph); |
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| 463 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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| 464 | /// .supplyMap(sup).run(); |
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| 465 | /// \endcode |
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| 466 | /// |
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[898] | 467 | /// This function can be called more than once. All the given parameters |
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| 468 | /// are kept for the next call, unless \ref resetParams() or \ref reset() |
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| 469 | /// is used, thus only the modified parameters have to be set again. |
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| 470 | /// If the underlying digraph was also modified after the construction |
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| 471 | /// of the class (or the last \ref reset() call), then the \ref reset() |
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| 472 | /// function must be called. |
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[871] | 473 | /// |
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[876] | 474 | /// \param factor The capacity scaling factor. It must be larger than |
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| 475 | /// one to use scaling. If it is less or equal to one, then scaling |
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| 476 | /// will be disabled. |
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[871] | 477 | /// |
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[872] | 478 | /// \return \c INFEASIBLE if no feasible flow exists, |
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| 479 | /// \n \c OPTIMAL if the problem has optimal solution |
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| 480 | /// (i.e. it is feasible and bounded), and the algorithm has found |
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| 481 | /// optimal flow and node potentials (primal and dual solutions), |
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| 482 | /// \n \c UNBOUNDED if the digraph contains an arc of negative cost |
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| 483 | /// and infinite upper bound. It means that the objective function |
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[878] | 484 | /// is unbounded on that arc, however, note that it could actually be |
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[872] | 485 | /// bounded over the feasible flows, but this algroithm cannot handle |
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| 486 | /// these cases. |
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| 487 | /// |
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| 488 | /// \see ProblemType |
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[898] | 489 | /// \see resetParams(), reset() |
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[876] | 490 | ProblemType run(int factor = 4) { |
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| 491 | _factor = factor; |
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| 492 | ProblemType pt = init(); |
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[872] | 493 | if (pt != OPTIMAL) return pt; |
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| 494 | return start(); |
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| 495 | } |
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| 496 | |
---|
| 497 | /// \brief Reset all the parameters that have been given before. |
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| 498 | /// |
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| 499 | /// This function resets all the paramaters that have been given |
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| 500 | /// before using functions \ref lowerMap(), \ref upperMap(), |
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| 501 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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| 502 | /// |
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[898] | 503 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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| 504 | /// parameters are kept for the next \ref run() call, unless |
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| 505 | /// \ref resetParams() or \ref reset() is used. |
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| 506 | /// If the underlying digraph was also modified after the construction |
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| 507 | /// of the class or the last \ref reset() call, then the \ref reset() |
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| 508 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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[872] | 509 | /// |
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| 510 | /// For example, |
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| 511 | /// \code |
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| 512 | /// CapacityScaling<ListDigraph> cs(graph); |
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| 513 | /// |
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| 514 | /// // First run |
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| 515 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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| 516 | /// .supplyMap(sup).run(); |
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| 517 | /// |
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[898] | 518 | /// // Run again with modified cost map (resetParams() is not called, |
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[872] | 519 | /// // so only the cost map have to be set again) |
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| 520 | /// cost[e] += 100; |
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| 521 | /// cs.costMap(cost).run(); |
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| 522 | /// |
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[898] | 523 | /// // Run again from scratch using resetParams() |
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[872] | 524 | /// // (the lower bounds will be set to zero on all arcs) |
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[898] | 525 | /// cs.resetParams(); |
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[872] | 526 | /// cs.upperMap(capacity).costMap(cost) |
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| 527 | /// .supplyMap(sup).run(); |
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| 528 | /// \endcode |
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| 529 | /// |
---|
| 530 | /// \return <tt>(*this)</tt> |
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[898] | 531 | /// |
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| 532 | /// \see reset(), run() |
---|
| 533 | CapacityScaling& resetParams() { |
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[872] | 534 | for (int i = 0; i != _node_num; ++i) { |
---|
| 535 | _supply[i] = 0; |
---|
| 536 | } |
---|
| 537 | for (int j = 0; j != _res_arc_num; ++j) { |
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| 538 | _lower[j] = 0; |
---|
| 539 | _upper[j] = INF; |
---|
| 540 | _cost[j] = _forward[j] ? 1 : -1; |
---|
| 541 | } |
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[1297] | 542 | _has_lower = false; |
---|
[872] | 543 | return *this; |
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[871] | 544 | } |
---|
| 545 | |
---|
[898] | 546 | /// \brief Reset the internal data structures and all the parameters |
---|
| 547 | /// that have been given before. |
---|
| 548 | /// |
---|
| 549 | /// This function resets the internal data structures and all the |
---|
| 550 | /// paramaters that have been given before using functions \ref lowerMap(), |
---|
| 551 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
---|
| 552 | /// |
---|
| 553 | /// It is useful for multiple \ref run() calls. Basically, all the given |
---|
| 554 | /// parameters are kept for the next \ref run() call, unless |
---|
| 555 | /// \ref resetParams() or \ref reset() is used. |
---|
| 556 | /// If the underlying digraph was also modified after the construction |
---|
| 557 | /// of the class or the last \ref reset() call, then the \ref reset() |
---|
| 558 | /// function must be used, otherwise \ref resetParams() is sufficient. |
---|
| 559 | /// |
---|
| 560 | /// See \ref resetParams() for examples. |
---|
| 561 | /// |
---|
| 562 | /// \return <tt>(*this)</tt> |
---|
| 563 | /// |
---|
| 564 | /// \see resetParams(), run() |
---|
| 565 | CapacityScaling& reset() { |
---|
| 566 | // Resize vectors |
---|
| 567 | _node_num = countNodes(_graph); |
---|
| 568 | _arc_num = countArcs(_graph); |
---|
| 569 | _res_arc_num = 2 * (_arc_num + _node_num); |
---|
| 570 | _root = _node_num; |
---|
| 571 | ++_node_num; |
---|
| 572 | |
---|
| 573 | _first_out.resize(_node_num + 1); |
---|
| 574 | _forward.resize(_res_arc_num); |
---|
| 575 | _source.resize(_res_arc_num); |
---|
| 576 | _target.resize(_res_arc_num); |
---|
| 577 | _reverse.resize(_res_arc_num); |
---|
| 578 | |
---|
| 579 | _lower.resize(_res_arc_num); |
---|
| 580 | _upper.resize(_res_arc_num); |
---|
| 581 | _cost.resize(_res_arc_num); |
---|
| 582 | _supply.resize(_node_num); |
---|
[956] | 583 | |
---|
[898] | 584 | _res_cap.resize(_res_arc_num); |
---|
| 585 | _pi.resize(_node_num); |
---|
| 586 | _excess.resize(_node_num); |
---|
| 587 | _pred.resize(_node_num); |
---|
| 588 | |
---|
| 589 | // Copy the graph |
---|
| 590 | int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1; |
---|
| 591 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
| 592 | _node_id[n] = i; |
---|
| 593 | } |
---|
| 594 | i = 0; |
---|
| 595 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
| 596 | _first_out[i] = j; |
---|
| 597 | for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
| 598 | _arc_idf[a] = j; |
---|
| 599 | _forward[j] = true; |
---|
| 600 | _source[j] = i; |
---|
| 601 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
| 602 | } |
---|
| 603 | for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
| 604 | _arc_idb[a] = j; |
---|
| 605 | _forward[j] = false; |
---|
| 606 | _source[j] = i; |
---|
| 607 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
| 608 | } |
---|
| 609 | _forward[j] = false; |
---|
| 610 | _source[j] = i; |
---|
| 611 | _target[j] = _root; |
---|
| 612 | _reverse[j] = k; |
---|
| 613 | _forward[k] = true; |
---|
| 614 | _source[k] = _root; |
---|
| 615 | _target[k] = i; |
---|
| 616 | _reverse[k] = j; |
---|
| 617 | ++j; ++k; |
---|
| 618 | } |
---|
| 619 | _first_out[i] = j; |
---|
| 620 | _first_out[_node_num] = k; |
---|
| 621 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 622 | int fi = _arc_idf[a]; |
---|
| 623 | int bi = _arc_idb[a]; |
---|
| 624 | _reverse[fi] = bi; |
---|
| 625 | _reverse[bi] = fi; |
---|
| 626 | } |
---|
[956] | 627 | |
---|
[898] | 628 | // Reset parameters |
---|
| 629 | resetParams(); |
---|
| 630 | return *this; |
---|
| 631 | } |
---|
| 632 | |
---|
[871] | 633 | /// @} |
---|
| 634 | |
---|
| 635 | /// \name Query Functions |
---|
| 636 | /// The results of the algorithm can be obtained using these |
---|
| 637 | /// functions.\n |
---|
[872] | 638 | /// The \ref run() function must be called before using them. |
---|
[871] | 639 | |
---|
| 640 | /// @{ |
---|
| 641 | |
---|
[872] | 642 | /// \brief Return the total cost of the found flow. |
---|
[871] | 643 | /// |
---|
[872] | 644 | /// This function returns the total cost of the found flow. |
---|
| 645 | /// Its complexity is O(e). |
---|
| 646 | /// |
---|
| 647 | /// \note The return type of the function can be specified as a |
---|
| 648 | /// template parameter. For example, |
---|
| 649 | /// \code |
---|
| 650 | /// cs.totalCost<double>(); |
---|
| 651 | /// \endcode |
---|
| 652 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
| 653 | /// type of the algorithm, which is the default return type of the |
---|
| 654 | /// function. |
---|
[871] | 655 | /// |
---|
| 656 | /// \pre \ref run() must be called before using this function. |
---|
[872] | 657 | template <typename Number> |
---|
| 658 | Number totalCost() const { |
---|
| 659 | Number c = 0; |
---|
| 660 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 661 | int i = _arc_idb[a]; |
---|
| 662 | c += static_cast<Number>(_res_cap[i]) * |
---|
| 663 | (-static_cast<Number>(_cost[i])); |
---|
| 664 | } |
---|
| 665 | return c; |
---|
[871] | 666 | } |
---|
| 667 | |
---|
[872] | 668 | #ifndef DOXYGEN |
---|
| 669 | Cost totalCost() const { |
---|
| 670 | return totalCost<Cost>(); |
---|
[871] | 671 | } |
---|
[872] | 672 | #endif |
---|
[871] | 673 | |
---|
| 674 | /// \brief Return the flow on the given arc. |
---|
| 675 | /// |
---|
[872] | 676 | /// This function returns the flow on the given arc. |
---|
[871] | 677 | /// |
---|
| 678 | /// \pre \ref run() must be called before using this function. |
---|
[872] | 679 | Value flow(const Arc& a) const { |
---|
| 680 | return _res_cap[_arc_idb[a]]; |
---|
[871] | 681 | } |
---|
| 682 | |
---|
[1165] | 683 | /// \brief Copy the flow values (the primal solution) into the |
---|
| 684 | /// given map. |
---|
[871] | 685 | /// |
---|
[872] | 686 | /// This function copies the flow value on each arc into the given |
---|
| 687 | /// map. The \c Value type of the algorithm must be convertible to |
---|
| 688 | /// the \c Value type of the map. |
---|
[871] | 689 | /// |
---|
| 690 | /// \pre \ref run() must be called before using this function. |
---|
[872] | 691 | template <typename FlowMap> |
---|
| 692 | void flowMap(FlowMap &map) const { |
---|
| 693 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
| 694 | map.set(a, _res_cap[_arc_idb[a]]); |
---|
| 695 | } |
---|
[871] | 696 | } |
---|
| 697 | |
---|
[872] | 698 | /// \brief Return the potential (dual value) of the given node. |
---|
[871] | 699 | /// |
---|
[872] | 700 | /// This function returns the potential (dual value) of the |
---|
| 701 | /// given node. |
---|
[871] | 702 | /// |
---|
| 703 | /// \pre \ref run() must be called before using this function. |
---|
[872] | 704 | Cost potential(const Node& n) const { |
---|
| 705 | return _pi[_node_id[n]]; |
---|
| 706 | } |
---|
| 707 | |
---|
[1165] | 708 | /// \brief Copy the potential values (the dual solution) into the |
---|
| 709 | /// given map. |
---|
[872] | 710 | /// |
---|
| 711 | /// This function copies the potential (dual value) of each node |
---|
| 712 | /// into the given map. |
---|
| 713 | /// The \c Cost type of the algorithm must be convertible to the |
---|
| 714 | /// \c Value type of the map. |
---|
| 715 | /// |
---|
| 716 | /// \pre \ref run() must be called before using this function. |
---|
| 717 | template <typename PotentialMap> |
---|
| 718 | void potentialMap(PotentialMap &map) const { |
---|
| 719 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 720 | map.set(n, _pi[_node_id[n]]); |
---|
| 721 | } |
---|
[871] | 722 | } |
---|
| 723 | |
---|
| 724 | /// @} |
---|
| 725 | |
---|
| 726 | private: |
---|
| 727 | |
---|
[872] | 728 | // Initialize the algorithm |
---|
[876] | 729 | ProblemType init() { |
---|
[887] | 730 | if (_node_num <= 1) return INFEASIBLE; |
---|
[871] | 731 | |
---|
[872] | 732 | // Check the sum of supply values |
---|
| 733 | _sum_supply = 0; |
---|
| 734 | for (int i = 0; i != _root; ++i) { |
---|
| 735 | _sum_supply += _supply[i]; |
---|
[871] | 736 | } |
---|
[872] | 737 | if (_sum_supply > 0) return INFEASIBLE; |
---|
[956] | 738 | |
---|
[1240] | 739 | // Check lower and upper bounds |
---|
| 740 | LEMON_DEBUG(checkBoundMaps(), |
---|
| 741 | "Upper bounds must be greater or equal to the lower bounds"); |
---|
| 742 | |
---|
| 743 | |
---|
[877] | 744 | // Initialize vectors |
---|
[872] | 745 | for (int i = 0; i != _root; ++i) { |
---|
| 746 | _pi[i] = 0; |
---|
| 747 | _excess[i] = _supply[i]; |
---|
[871] | 748 | } |
---|
| 749 | |
---|
[872] | 750 | // Remove non-zero lower bounds |
---|
[877] | 751 | const Value MAX = std::numeric_limits<Value>::max(); |
---|
| 752 | int last_out; |
---|
[1297] | 753 | if (_has_lower) { |
---|
[872] | 754 | for (int i = 0; i != _root; ++i) { |
---|
[877] | 755 | last_out = _first_out[i+1]; |
---|
| 756 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
[872] | 757 | if (_forward[j]) { |
---|
| 758 | Value c = _lower[j]; |
---|
| 759 | if (c >= 0) { |
---|
[877] | 760 | _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF; |
---|
[872] | 761 | } else { |
---|
[877] | 762 | _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF; |
---|
[872] | 763 | } |
---|
| 764 | _excess[i] -= c; |
---|
| 765 | _excess[_target[j]] += c; |
---|
| 766 | } else { |
---|
| 767 | _res_cap[j] = 0; |
---|
| 768 | } |
---|
| 769 | } |
---|
| 770 | } |
---|
| 771 | } else { |
---|
| 772 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
| 773 | _res_cap[j] = _forward[j] ? _upper[j] : 0; |
---|
| 774 | } |
---|
| 775 | } |
---|
[871] | 776 | |
---|
[872] | 777 | // Handle negative costs |
---|
[877] | 778 | for (int i = 0; i != _root; ++i) { |
---|
| 779 | last_out = _first_out[i+1] - 1; |
---|
| 780 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 781 | Value rc = _res_cap[j]; |
---|
| 782 | if (_cost[j] < 0 && rc > 0) { |
---|
| 783 | if (rc >= MAX) return UNBOUNDED; |
---|
| 784 | _excess[i] -= rc; |
---|
| 785 | _excess[_target[j]] += rc; |
---|
| 786 | _res_cap[j] = 0; |
---|
| 787 | _res_cap[_reverse[j]] += rc; |
---|
[872] | 788 | } |
---|
| 789 | } |
---|
| 790 | } |
---|
[956] | 791 | |
---|
[872] | 792 | // Handle GEQ supply type |
---|
| 793 | if (_sum_supply < 0) { |
---|
| 794 | _pi[_root] = 0; |
---|
| 795 | _excess[_root] = -_sum_supply; |
---|
| 796 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
[877] | 797 | int ra = _reverse[a]; |
---|
| 798 | _res_cap[a] = -_sum_supply + 1; |
---|
| 799 | _res_cap[ra] = 0; |
---|
[872] | 800 | _cost[a] = 0; |
---|
[877] | 801 | _cost[ra] = 0; |
---|
[872] | 802 | } |
---|
| 803 | } else { |
---|
| 804 | _pi[_root] = 0; |
---|
| 805 | _excess[_root] = 0; |
---|
| 806 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
[877] | 807 | int ra = _reverse[a]; |
---|
[872] | 808 | _res_cap[a] = 1; |
---|
[877] | 809 | _res_cap[ra] = 0; |
---|
[872] | 810 | _cost[a] = 0; |
---|
[877] | 811 | _cost[ra] = 0; |
---|
[872] | 812 | } |
---|
| 813 | } |
---|
| 814 | |
---|
| 815 | // Initialize delta value |
---|
[876] | 816 | if (_factor > 1) { |
---|
[871] | 817 | // With scaling |
---|
[910] | 818 | Value max_sup = 0, max_dem = 0, max_cap = 0; |
---|
| 819 | for (int i = 0; i != _root; ++i) { |
---|
[877] | 820 | Value ex = _excess[i]; |
---|
| 821 | if ( ex > max_sup) max_sup = ex; |
---|
| 822 | if (-ex > max_dem) max_dem = -ex; |
---|
[910] | 823 | int last_out = _first_out[i+1] - 1; |
---|
| 824 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
| 825 | if (_res_cap[j] > max_cap) max_cap = _res_cap[j]; |
---|
| 826 | } |
---|
[871] | 827 | } |
---|
| 828 | max_sup = std::min(std::min(max_sup, max_dem), max_cap); |
---|
[876] | 829 | for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ; |
---|
[871] | 830 | } else { |
---|
| 831 | // Without scaling |
---|
| 832 | _delta = 1; |
---|
| 833 | } |
---|
| 834 | |
---|
[872] | 835 | return OPTIMAL; |
---|
[871] | 836 | } |
---|
[1240] | 837 | |
---|
[1296] | 838 | // Check if the upper bound is greater than or equal to the lower bound |
---|
| 839 | // on each forward arc. |
---|
[1240] | 840 | bool checkBoundMaps() { |
---|
| 841 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
[1296] | 842 | if (_forward[j] && _upper[j] < _lower[j]) return false; |
---|
[1240] | 843 | } |
---|
| 844 | return true; |
---|
| 845 | } |
---|
[871] | 846 | |
---|
[872] | 847 | ProblemType start() { |
---|
| 848 | // Execute the algorithm |
---|
| 849 | ProblemType pt; |
---|
[871] | 850 | if (_delta > 1) |
---|
[872] | 851 | pt = startWithScaling(); |
---|
[871] | 852 | else |
---|
[872] | 853 | pt = startWithoutScaling(); |
---|
| 854 | |
---|
| 855 | // Handle non-zero lower bounds |
---|
[1297] | 856 | if (_has_lower) { |
---|
[877] | 857 | int limit = _first_out[_root]; |
---|
| 858 | for (int j = 0; j != limit; ++j) { |
---|
[1296] | 859 | if (_forward[j]) _res_cap[_reverse[j]] += _lower[j]; |
---|
[872] | 860 | } |
---|
| 861 | } |
---|
| 862 | |
---|
| 863 | // Shift potentials if necessary |
---|
| 864 | Cost pr = _pi[_root]; |
---|
| 865 | if (_sum_supply < 0 || pr > 0) { |
---|
| 866 | for (int i = 0; i != _node_num; ++i) { |
---|
| 867 | _pi[i] -= pr; |
---|
[956] | 868 | } |
---|
[872] | 869 | } |
---|
[956] | 870 | |
---|
[872] | 871 | return pt; |
---|
[871] | 872 | } |
---|
| 873 | |
---|
[872] | 874 | // Execute the capacity scaling algorithm |
---|
| 875 | ProblemType startWithScaling() { |
---|
[873] | 876 | // Perform capacity scaling phases |
---|
[872] | 877 | int s, t; |
---|
| 878 | ResidualDijkstra _dijkstra(*this); |
---|
[871] | 879 | while (true) { |
---|
[872] | 880 | // Saturate all arcs not satisfying the optimality condition |
---|
[877] | 881 | int last_out; |
---|
[872] | 882 | for (int u = 0; u != _node_num; ++u) { |
---|
[877] | 883 | last_out = _sum_supply < 0 ? |
---|
| 884 | _first_out[u+1] : _first_out[u+1] - 1; |
---|
| 885 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
[872] | 886 | int v = _target[a]; |
---|
| 887 | Cost c = _cost[a] + _pi[u] - _pi[v]; |
---|
| 888 | Value rc = _res_cap[a]; |
---|
| 889 | if (c < 0 && rc >= _delta) { |
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| 890 | _excess[u] -= rc; |
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| 891 | _excess[v] += rc; |
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| 892 | _res_cap[a] = 0; |
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| 893 | _res_cap[_reverse[a]] += rc; |
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| 894 | } |
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[871] | 895 | } |
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| 896 | } |
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| 897 | |
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[872] | 898 | // Find excess nodes and deficit nodes |
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[871] | 899 | _excess_nodes.clear(); |
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| 900 | _deficit_nodes.clear(); |
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[872] | 901 | for (int u = 0; u != _node_num; ++u) { |
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[877] | 902 | Value ex = _excess[u]; |
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| 903 | if (ex >= _delta) _excess_nodes.push_back(u); |
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| 904 | if (ex <= -_delta) _deficit_nodes.push_back(u); |
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[871] | 905 | } |
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| 906 | int next_node = 0, next_def_node = 0; |
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| 907 | |
---|
[872] | 908 | // Find augmenting shortest paths |
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[871] | 909 | while (next_node < int(_excess_nodes.size())) { |
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[872] | 910 | // Check deficit nodes |
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[871] | 911 | if (_delta > 1) { |
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| 912 | bool delta_deficit = false; |
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| 913 | for ( ; next_def_node < int(_deficit_nodes.size()); |
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| 914 | ++next_def_node ) { |
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| 915 | if (_excess[_deficit_nodes[next_def_node]] <= -_delta) { |
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| 916 | delta_deficit = true; |
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| 917 | break; |
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| 918 | } |
---|
| 919 | } |
---|
| 920 | if (!delta_deficit) break; |
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| 921 | } |
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| 922 | |
---|
[872] | 923 | // Run Dijkstra in the residual network |
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[871] | 924 | s = _excess_nodes[next_node]; |
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[872] | 925 | if ((t = _dijkstra.run(s, _delta)) == -1) { |
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[871] | 926 | if (_delta > 1) { |
---|
| 927 | ++next_node; |
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| 928 | continue; |
---|
| 929 | } |
---|
[872] | 930 | return INFEASIBLE; |
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[871] | 931 | } |
---|
| 932 | |
---|
[872] | 933 | // Augment along a shortest path from s to t |
---|
| 934 | Value d = std::min(_excess[s], -_excess[t]); |
---|
| 935 | int u = t; |
---|
| 936 | int a; |
---|
[871] | 937 | if (d > _delta) { |
---|
[872] | 938 | while ((a = _pred[u]) != -1) { |
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| 939 | if (_res_cap[a] < d) d = _res_cap[a]; |
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| 940 | u = _source[a]; |
---|
[871] | 941 | } |
---|
| 942 | } |
---|
| 943 | u = t; |
---|
[872] | 944 | while ((a = _pred[u]) != -1) { |
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| 945 | _res_cap[a] -= d; |
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| 946 | _res_cap[_reverse[a]] += d; |
---|
| 947 | u = _source[a]; |
---|
[871] | 948 | } |
---|
| 949 | _excess[s] -= d; |
---|
| 950 | _excess[t] += d; |
---|
| 951 | |
---|
| 952 | if (_excess[s] < _delta) ++next_node; |
---|
| 953 | } |
---|
| 954 | |
---|
| 955 | if (_delta == 1) break; |
---|
[876] | 956 | _delta = _delta <= _factor ? 1 : _delta / _factor; |
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[871] | 957 | } |
---|
| 958 | |
---|
[872] | 959 | return OPTIMAL; |
---|
[871] | 960 | } |
---|
| 961 | |
---|
[872] | 962 | // Execute the successive shortest path algorithm |
---|
| 963 | ProblemType startWithoutScaling() { |
---|
| 964 | // Find excess nodes |
---|
| 965 | _excess_nodes.clear(); |
---|
| 966 | for (int i = 0; i != _node_num; ++i) { |
---|
| 967 | if (_excess[i] > 0) _excess_nodes.push_back(i); |
---|
| 968 | } |
---|
| 969 | if (_excess_nodes.size() == 0) return OPTIMAL; |
---|
[871] | 970 | int next_node = 0; |
---|
| 971 | |
---|
[872] | 972 | // Find shortest paths |
---|
| 973 | int s, t; |
---|
| 974 | ResidualDijkstra _dijkstra(*this); |
---|
[871] | 975 | while ( _excess[_excess_nodes[next_node]] > 0 || |
---|
| 976 | ++next_node < int(_excess_nodes.size()) ) |
---|
| 977 | { |
---|
[872] | 978 | // Run Dijkstra in the residual network |
---|
[871] | 979 | s = _excess_nodes[next_node]; |
---|
[872] | 980 | if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE; |
---|
[871] | 981 | |
---|
[872] | 982 | // Augment along a shortest path from s to t |
---|
| 983 | Value d = std::min(_excess[s], -_excess[t]); |
---|
| 984 | int u = t; |
---|
| 985 | int a; |
---|
[871] | 986 | if (d > 1) { |
---|
[872] | 987 | while ((a = _pred[u]) != -1) { |
---|
| 988 | if (_res_cap[a] < d) d = _res_cap[a]; |
---|
| 989 | u = _source[a]; |
---|
[871] | 990 | } |
---|
| 991 | } |
---|
| 992 | u = t; |
---|
[872] | 993 | while ((a = _pred[u]) != -1) { |
---|
| 994 | _res_cap[a] -= d; |
---|
| 995 | _res_cap[_reverse[a]] += d; |
---|
| 996 | u = _source[a]; |
---|
[871] | 997 | } |
---|
| 998 | _excess[s] -= d; |
---|
| 999 | _excess[t] += d; |
---|
| 1000 | } |
---|
| 1001 | |
---|
[872] | 1002 | return OPTIMAL; |
---|
[871] | 1003 | } |
---|
| 1004 | |
---|
| 1005 | }; //class CapacityScaling |
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| 1006 | |
---|
| 1007 | ///@} |
---|
| 1008 | |
---|
| 1009 | } //namespace lemon |
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| 1010 | |
---|
| 1011 | #endif //LEMON_CAPACITY_SCALING_H |
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