[1033] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2010 |
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| 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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[1031] | 19 | #ifndef LEMON_INSERTION_TSP_H |
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| 20 | #define LEMON_INSERTION_TSP_H |
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| 21 | |
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[1033] | 22 | /// \ingroup tsp |
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| 23 | /// \file |
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| 24 | /// \brief Insertion algorithm for symmetric TSP |
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| 25 | |
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| 26 | #include <vector> |
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[1031] | 27 | #include <lemon/full_graph.h> |
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| 28 | #include <lemon/maps.h> |
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| 29 | #include <lemon/random.h> |
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| 30 | |
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| 31 | namespace lemon { |
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| 32 | |
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[1034] | 33 | /// \ingroup tsp |
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| 34 | /// |
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[1033] | 35 | /// \brief Insertion algorithm for symmetric TSP. |
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| 36 | /// |
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| 37 | /// InsertionTsp implements the insertion heuristic for solving |
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| 38 | /// symmetric \ref tsp "TSP". |
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| 39 | /// |
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| 40 | /// This is a basic TSP heuristic that has many variants. |
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| 41 | /// It starts with a subtour containing a few nodes of the graph and it |
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| 42 | /// iteratively inserts the other nodes into this subtour according to a |
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| 43 | /// certain node selection rule. |
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| 44 | /// |
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| 45 | /// This implementation provides four different node selection rules, |
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| 46 | /// from which the most powerful one is used by default. |
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| 47 | /// For more information, see \ref SelectionRule. |
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| 48 | /// |
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| 49 | /// \tparam CM Type of the cost map. |
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| 50 | template <typename CM> |
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| 51 | class InsertionTsp |
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| 52 | { |
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| 53 | public: |
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[1031] | 54 | |
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[1033] | 55 | /// Type of the cost map |
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[1031] | 56 | typedef CM CostMap; |
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[1033] | 57 | /// Type of the edge costs |
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[1031] | 58 | typedef typename CM::Value Cost; |
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| 59 | |
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| 60 | private: |
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| 61 | |
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[1033] | 62 | GRAPH_TYPEDEFS(FullGraph); |
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| 63 | |
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| 64 | const FullGraph &_gr; |
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| 65 | const CostMap &_cost; |
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| 66 | std::vector<Node> _notused; |
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| 67 | std::vector<Node> _path; |
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| 68 | Cost _sum; |
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| 69 | |
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| 70 | public: |
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| 71 | |
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| 72 | /// \brief Constants for specifying the node selection rule. |
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| 73 | /// |
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| 74 | /// Enum type containing constants for specifying the node selection |
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| 75 | /// rule for the \ref run() function. |
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| 76 | /// |
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| 77 | /// During the algorithm, nodes are selected for addition to the current |
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| 78 | /// subtour according to the applied rule. |
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[1034] | 79 | /// In general, the FARTHEST method yields the best tours, thus it is the |
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| 80 | /// default option. The RANDOM rule usually gives somewhat worse results, |
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| 81 | /// but it is much faster than the others and it is the most robust. |
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[1033] | 82 | /// |
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| 83 | /// The desired selection rule can be specified as a parameter of the |
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| 84 | /// \ref run() function. |
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| 85 | enum SelectionRule { |
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| 86 | |
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| 87 | /// An unvisited node having minimum distance from the current |
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| 88 | /// subtour is selected at each step. |
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| 89 | /// The algorithm runs in O(n<sup>3</sup>) time using this |
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| 90 | /// selection rule. |
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| 91 | NEAREST, |
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| 92 | |
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| 93 | /// An unvisited node having maximum distance from the current |
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| 94 | /// subtour is selected at each step. |
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| 95 | /// The algorithm runs in O(n<sup>3</sup>) time using this |
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| 96 | /// selection rule. |
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| 97 | FARTHEST, |
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| 98 | |
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| 99 | /// An unvisited node whose insertion results in the least |
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| 100 | /// increase of the subtour's total cost is selected at each step. |
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| 101 | /// The algorithm runs in O(n<sup>3</sup>) time using this |
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| 102 | /// selection rule. |
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| 103 | CHEAPEST, |
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| 104 | |
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| 105 | /// An unvisited node is selected randomly without any evaluation |
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| 106 | /// at each step. |
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| 107 | /// The global \ref rnd "random number generator instance" is used. |
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| 108 | /// You can seed it before executing the algorithm, if you |
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| 109 | /// would like to. |
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| 110 | /// The algorithm runs in O(n<sup>2</sup>) time using this |
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| 111 | /// selection rule. |
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| 112 | RANDOM |
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| 113 | }; |
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| 114 | |
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| 115 | public: |
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| 116 | |
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| 117 | /// \brief Constructor |
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| 118 | /// |
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| 119 | /// Constructor. |
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| 120 | /// \param gr The \ref FullGraph "full graph" the algorithm runs on. |
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| 121 | /// \param cost The cost map. |
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| 122 | InsertionTsp(const FullGraph &gr, const CostMap &cost) |
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| 123 | : _gr(gr), _cost(cost) {} |
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| 124 | |
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| 125 | /// \name Execution Control |
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| 126 | /// @{ |
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| 127 | |
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| 128 | /// \brief Runs the algorithm. |
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| 129 | /// |
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| 130 | /// This function runs the algorithm. |
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| 131 | /// |
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| 132 | /// \param rule The node selection rule. For more information, see |
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| 133 | /// \ref SelectionRule. |
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| 134 | /// |
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| 135 | /// \return The total cost of the found tour. |
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| 136 | Cost run(SelectionRule rule = FARTHEST) { |
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| 137 | _path.clear(); |
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| 138 | |
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| 139 | if (_gr.nodeNum() == 0) return _sum = 0; |
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| 140 | else if (_gr.nodeNum() == 1) { |
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| 141 | _path.push_back(_gr(0)); |
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| 142 | return _sum = 0; |
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| 143 | } |
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| 144 | |
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| 145 | switch (rule) { |
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| 146 | case NEAREST: |
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| 147 | init(true); |
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| 148 | start<NearestSelection, DefaultInsertion>(); |
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| 149 | break; |
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| 150 | case FARTHEST: |
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| 151 | init(false); |
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| 152 | start<FarthestSelection, DefaultInsertion>(); |
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| 153 | break; |
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| 154 | case CHEAPEST: |
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| 155 | init(true); |
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| 156 | start<CheapestSelection, CheapestInsertion>(); |
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| 157 | break; |
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| 158 | case RANDOM: |
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| 159 | init(true); |
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| 160 | start<RandomSelection, DefaultInsertion>(); |
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| 161 | break; |
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| 162 | } |
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| 163 | return _sum; |
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| 164 | } |
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| 165 | |
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| 166 | /// @} |
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| 167 | |
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| 168 | /// \name Query Functions |
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| 169 | /// @{ |
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| 170 | |
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| 171 | /// \brief The total cost of the found tour. |
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| 172 | /// |
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| 173 | /// This function returns the total cost of the found tour. |
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| 174 | /// |
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| 175 | /// \pre run() must be called before using this function. |
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| 176 | Cost tourCost() const { |
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| 177 | return _sum; |
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| 178 | } |
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| 179 | |
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| 180 | /// \brief Returns a const reference to the node sequence of the |
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| 181 | /// found tour. |
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| 182 | /// |
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[1034] | 183 | /// This function returns a const reference to a vector |
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[1033] | 184 | /// that stores the node sequence of the found tour. |
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| 185 | /// |
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| 186 | /// \pre run() must be called before using this function. |
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| 187 | const std::vector<Node>& tourNodes() const { |
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| 188 | return _path; |
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| 189 | } |
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| 190 | |
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| 191 | /// \brief Gives back the node sequence of the found tour. |
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| 192 | /// |
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| 193 | /// This function copies the node sequence of the found tour into |
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| 194 | /// the given standard container. |
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| 195 | /// |
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| 196 | /// \pre run() must be called before using this function. |
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| 197 | template <typename Container> |
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| 198 | void tourNodes(Container &container) const { |
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| 199 | container.assign(_path.begin(), _path.end()); |
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| 200 | } |
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| 201 | |
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| 202 | /// \brief Gives back the found tour as a path. |
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| 203 | /// |
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| 204 | /// This function copies the found tour as a list of arcs/edges into |
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| 205 | /// the given \ref concept::Path "path structure". |
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| 206 | /// |
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| 207 | /// \pre run() must be called before using this function. |
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| 208 | template <typename Path> |
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| 209 | void tour(Path &path) const { |
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| 210 | path.clear(); |
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| 211 | for (int i = 0; i < int(_path.size()) - 1; ++i) { |
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| 212 | path.addBack(_gr.arc(_path[i], _path[i+1])); |
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| 213 | } |
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| 214 | if (int(_path.size()) >= 2) { |
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| 215 | path.addBack(_gr.arc(_path.back(), _path.front())); |
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| 216 | } |
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| 217 | } |
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| 218 | |
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| 219 | /// @} |
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| 220 | |
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| 221 | private: |
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| 222 | |
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| 223 | // Initializes the algorithm |
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| 224 | void init(bool min) { |
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| 225 | Edge min_edge = min ? mapMin(_gr, _cost) : mapMax(_gr, _cost); |
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| 226 | |
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| 227 | _path.clear(); |
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| 228 | _path.push_back(_gr.u(min_edge)); |
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| 229 | _path.push_back(_gr.v(min_edge)); |
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| 230 | |
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| 231 | _notused.clear(); |
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| 232 | for (NodeIt n(_gr); n!=INVALID; ++n) { |
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| 233 | if (n != _gr.u(min_edge) && n != _gr.v(min_edge)) { |
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| 234 | _notused.push_back(n); |
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| 235 | } |
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| 236 | } |
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| 237 | |
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| 238 | _sum = _cost[min_edge] * 2; |
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| 239 | } |
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| 240 | |
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| 241 | // Executes the algorithm |
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| 242 | template <class SelectionFunctor, class InsertionFunctor> |
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| 243 | void start() { |
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| 244 | SelectionFunctor selectNode(_gr, _cost, _path, _notused); |
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| 245 | InsertionFunctor insertNode(_gr, _cost, _path, _sum); |
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| 246 | |
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| 247 | for (int i=0; i<_gr.nodeNum()-2; ++i) { |
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| 248 | insertNode.insert(selectNode.select()); |
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| 249 | } |
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| 250 | |
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| 251 | _sum = _cost[_gr.edge(_path.back(), _path.front())]; |
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| 252 | for (int i = 0; i < int(_path.size())-1; ++i) { |
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| 253 | _sum += _cost[_gr.edge(_path[i], _path[i+1])]; |
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| 254 | } |
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| 255 | } |
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| 256 | |
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| 257 | |
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| 258 | // Implementation of the nearest selection rule |
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| 259 | class NearestSelection { |
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[1031] | 260 | public: |
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[1033] | 261 | NearestSelection(const FullGraph &gr, const CostMap &cost, |
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| 262 | std::vector<Node> &path, std::vector<Node> ¬used) |
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| 263 | : _gr(gr), _cost(cost), _path(path), _notused(notused) {} |
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[1031] | 264 | |
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[1033] | 265 | Node select() const { |
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| 266 | Cost insert_val = 0; |
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| 267 | int insert_node = -1; |
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| 268 | |
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| 269 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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| 270 | Cost min_val = _cost[_gr.edge(_notused[i], _path[0])]; |
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| 271 | int min_node = 0; |
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| 272 | |
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| 273 | for (unsigned int j=1; j<_path.size(); ++j) { |
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| 274 | Cost curr = _cost[_gr.edge(_notused[i], _path[j])]; |
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| 275 | if (min_val > curr) { |
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| 276 | min_val = curr; |
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| 277 | min_node = j; |
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| 278 | } |
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| 279 | } |
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| 280 | |
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| 281 | if (insert_val > min_val || insert_node == -1) { |
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| 282 | insert_val = min_val; |
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| 283 | insert_node = i; |
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[1031] | 284 | } |
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| 285 | } |
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[1033] | 286 | |
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| 287 | Node n = _notused[insert_node]; |
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| 288 | _notused.erase(_notused.begin()+insert_node); |
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| 289 | |
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| 290 | return n; |
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[1031] | 291 | } |
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| 292 | |
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| 293 | private: |
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| 294 | const FullGraph &_gr; |
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| 295 | const CostMap &_cost; |
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[1033] | 296 | std::vector<Node> &_path; |
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[1031] | 297 | std::vector<Node> &_notused; |
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| 298 | }; |
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| 299 | |
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[1033] | 300 | |
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| 301 | // Implementation of the farthest selection rule |
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[1031] | 302 | class FarthestSelection { |
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| 303 | public: |
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| 304 | FarthestSelection(const FullGraph &gr, const CostMap &cost, |
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[1033] | 305 | std::vector<Node> &path, std::vector<Node> ¬used) |
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| 306 | : _gr(gr), _cost(cost), _path(path), _notused(notused) {} |
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| 307 | |
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[1031] | 308 | Node select() const { |
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[1033] | 309 | Cost insert_val = 0; |
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| 310 | int insert_node = -1; |
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[1031] | 311 | |
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| 312 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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[1033] | 313 | Cost min_val = _cost[_gr.edge(_notused[i], _path[0])]; |
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[1031] | 314 | int min_node = 0; |
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[1033] | 315 | |
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| 316 | for (unsigned int j=1; j<_path.size(); ++j) { |
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| 317 | Cost curr = _cost[_gr.edge(_notused[i], _path[j])]; |
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| 318 | if (min_val > curr) { |
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| 319 | min_val = curr; |
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[1031] | 320 | min_node = j; |
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| 321 | } |
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| 322 | } |
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[1033] | 323 | |
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[1031] | 324 | if (insert_val < min_val || insert_node == -1) { |
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| 325 | insert_val = min_val; |
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| 326 | insert_node = i; |
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| 327 | } |
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| 328 | } |
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[1033] | 329 | |
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[1031] | 330 | Node n = _notused[insert_node]; |
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| 331 | _notused.erase(_notused.begin()+insert_node); |
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[1033] | 332 | |
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[1031] | 333 | return n; |
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| 334 | } |
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[1033] | 335 | |
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[1031] | 336 | private: |
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| 337 | const FullGraph &_gr; |
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| 338 | const CostMap &_cost; |
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[1033] | 339 | std::vector<Node> &_path; |
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[1031] | 340 | std::vector<Node> &_notused; |
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| 341 | }; |
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| 342 | |
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| 343 | |
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[1033] | 344 | // Implementation of the cheapest selection rule |
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[1031] | 345 | class CheapestSelection { |
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| 346 | private: |
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| 347 | Cost costDiff(Node u, Node v, Node w) const { |
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[1033] | 348 | return |
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[1031] | 349 | _cost[_gr.edge(u, w)] + |
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| 350 | _cost[_gr.edge(v, w)] - |
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| 351 | _cost[_gr.edge(u, v)]; |
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| 352 | } |
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| 353 | |
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| 354 | public: |
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| 355 | CheapestSelection(const FullGraph &gr, const CostMap &cost, |
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[1033] | 356 | std::vector<Node> &path, std::vector<Node> ¬used) |
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| 357 | : _gr(gr), _cost(cost), _path(path), _notused(notused) {} |
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| 358 | |
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[1031] | 359 | Cost select() const { |
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| 360 | int insert_notused = -1; |
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| 361 | int best_insert_index = -1; |
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[1033] | 362 | Cost insert_val = 0; |
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| 363 | |
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[1031] | 364 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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| 365 | int min = i; |
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| 366 | int best_insert_tmp = 0; |
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| 367 | Cost min_val = |
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[1033] | 368 | costDiff(_path.front(), _path.back(), _notused[i]); |
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| 369 | |
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| 370 | for (unsigned int j=1; j<_path.size(); ++j) { |
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[1031] | 371 | Cost tmp = |
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[1033] | 372 | costDiff(_path[j-1], _path[j], _notused[i]); |
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[1031] | 373 | |
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| 374 | if (min_val > tmp) { |
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| 375 | min = i; |
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| 376 | min_val = tmp; |
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| 377 | best_insert_tmp = j; |
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| 378 | } |
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| 379 | } |
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| 380 | |
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[1033] | 381 | if (insert_val > min_val || insert_notused == -1) { |
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[1031] | 382 | insert_notused = min; |
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| 383 | insert_val = min_val; |
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| 384 | best_insert_index = best_insert_tmp; |
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| 385 | } |
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| 386 | } |
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| 387 | |
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[1033] | 388 | _path.insert(_path.begin()+best_insert_index, |
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| 389 | _notused[insert_notused]); |
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[1031] | 390 | _notused.erase(_notused.begin()+insert_notused); |
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| 391 | |
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| 392 | return insert_val; |
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| 393 | } |
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[1033] | 394 | |
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[1031] | 395 | private: |
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| 396 | const FullGraph &_gr; |
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| 397 | const CostMap &_cost; |
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[1033] | 398 | std::vector<Node> &_path; |
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[1031] | 399 | std::vector<Node> &_notused; |
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| 400 | }; |
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| 401 | |
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[1033] | 402 | // Implementation of the random selection rule |
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[1031] | 403 | class RandomSelection { |
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| 404 | public: |
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| 405 | RandomSelection(const FullGraph &, const CostMap &, |
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[1033] | 406 | std::vector<Node> &, std::vector<Node> ¬used) |
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| 407 | : _notused(notused) {} |
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| 408 | |
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[1031] | 409 | Node select() const { |
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| 410 | const int index = rnd[_notused.size()]; |
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| 411 | Node n = _notused[index]; |
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| 412 | _notused.erase(_notused.begin()+index); |
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| 413 | return n; |
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| 414 | } |
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| 415 | private: |
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| 416 | std::vector<Node> &_notused; |
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| 417 | }; |
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| 418 | |
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| 419 | |
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[1033] | 420 | // Implementation of the default insertion method |
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| 421 | class DefaultInsertion { |
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[1031] | 422 | private: |
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| 423 | Cost costDiff(Node u, Node v, Node w) const { |
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[1033] | 424 | return |
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[1031] | 425 | _cost[_gr.edge(u, w)] + |
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| 426 | _cost[_gr.edge(v, w)] - |
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| 427 | _cost[_gr.edge(u, v)]; |
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| 428 | } |
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[1033] | 429 | |
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[1031] | 430 | public: |
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[1033] | 431 | DefaultInsertion(const FullGraph &gr, const CostMap &cost, |
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| 432 | std::vector<Node> &path, Cost &total_cost) : |
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| 433 | _gr(gr), _cost(cost), _path(path), _total(total_cost) {} |
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| 434 | |
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[1031] | 435 | void insert(Node n) const { |
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| 436 | int min = 0; |
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| 437 | Cost min_val = |
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| 438 | costDiff(_path.front(), _path.back(), n); |
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[1033] | 439 | |
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[1031] | 440 | for (unsigned int i=1; i<_path.size(); ++i) { |
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| 441 | Cost tmp = costDiff(_path[i-1], _path[i], n); |
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| 442 | if (tmp < min_val) { |
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| 443 | min = i; |
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| 444 | min_val = tmp; |
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| 445 | } |
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| 446 | } |
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[1033] | 447 | |
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[1031] | 448 | _path.insert(_path.begin()+min, n); |
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[1033] | 449 | _total += min_val; |
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[1031] | 450 | } |
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[1033] | 451 | |
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[1031] | 452 | private: |
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| 453 | const FullGraph &_gr; |
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| 454 | const CostMap &_cost; |
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| 455 | std::vector<Node> &_path; |
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[1033] | 456 | Cost &_total; |
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[1031] | 457 | }; |
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[1033] | 458 | |
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| 459 | // Implementation of a special insertion method for the cheapest |
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| 460 | // selection rule |
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| 461 | class CheapestInsertion { |
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[1031] | 462 | TEMPLATE_GRAPH_TYPEDEFS(FullGraph); |
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| 463 | public: |
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[1033] | 464 | CheapestInsertion(const FullGraph &, const CostMap &, |
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| 465 | std::vector<Node> &, Cost &total_cost) : |
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| 466 | _total(total_cost) {} |
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| 467 | |
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[1031] | 468 | void insert(Cost diff) const { |
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[1033] | 469 | _total += diff; |
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[1031] | 470 | } |
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| 471 | |
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| 472 | private: |
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[1033] | 473 | Cost &_total; |
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| 474 | }; |
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| 475 | |
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[1031] | 476 | }; |
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[1033] | 477 | |
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[1031] | 478 | }; // namespace lemon |
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| 479 | |
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| 480 | #endif |
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