[1201] | 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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[1199] | 19 | #ifndef LEMON_OPT2_TSP_H |
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| 20 | #define LEMON_OPT2_TSP_H |
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| 21 | |
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[1201] | 22 | /// \ingroup tsp |
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| 23 | /// \file |
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| 24 | /// \brief 2-opt algorithm for symmetric TSP |
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| 25 | |
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[1199] | 26 | #include <vector> |
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| 27 | #include <lemon/full_graph.h> |
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| 28 | |
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| 29 | namespace lemon { |
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[1201] | 30 | |
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| 31 | /// \brief 2-opt algorithm for symmetric TSP. |
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| 32 | /// |
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| 33 | /// Opt2Tsp implements the 2-opt heuristic for solving |
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| 34 | /// symmetric \ref tsp "TSP". |
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| 35 | /// |
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| 36 | /// This algorithm starts with an initial tour and iteratively improves it. |
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| 37 | /// At each step, it removes two edges and the reconnects the created two |
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| 38 | /// paths in the other way if the resulting tour is shorter. |
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| 39 | /// The algorithm finishes when no such 2-opt move can be applied, and so |
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| 40 | /// the tour is 2-optimal. |
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| 41 | /// |
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| 42 | /// If no starting tour is given to the \ref run() function, then the |
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| 43 | /// algorithm uses the node sequence determined by the node IDs. |
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| 44 | /// Oherwise, it starts with the given tour. |
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| 45 | /// |
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| 46 | /// This is a relatively slow but powerful method. |
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| 47 | /// A typical usage of it is the improvement of a solution that is resulted |
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| 48 | /// by a fast tour construction heuristic (e.g. the InsertionTsp algorithm). |
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| 49 | /// |
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| 50 | /// \tparam CM Type of the cost map. |
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[1199] | 51 | template <typename CM> |
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[1201] | 52 | class Opt2Tsp |
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| 53 | { |
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| 54 | public: |
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| 55 | |
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| 56 | /// Type of the cost map |
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| 57 | typedef CM CostMap; |
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| 58 | /// Type of the edge costs |
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| 59 | typedef typename CM::Value Cost; |
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| 60 | |
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[1199] | 61 | private: |
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[1201] | 62 | |
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[1199] | 63 | GRAPH_TYPEDEFS(FullGraph); |
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| 64 | |
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[1201] | 65 | const FullGraph &_gr; |
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| 66 | const CostMap &_cost; |
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| 67 | Cost _sum; |
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| 68 | std::vector<int> _plist; |
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| 69 | std::vector<Node> _path; |
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| 70 | |
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[1199] | 71 | public: |
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[1201] | 72 | |
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| 73 | /// \brief Constructor |
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| 74 | /// |
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| 75 | /// Constructor. |
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| 76 | /// \param gr The \ref FullGraph "full graph" the algorithm runs on. |
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| 77 | /// \param cost The cost map. |
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| 78 | Opt2Tsp(const FullGraph &gr, const CostMap &cost) |
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| 79 | : _gr(gr), _cost(cost) {} |
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| 80 | |
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| 81 | /// \name Execution Control |
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| 82 | /// @{ |
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| 83 | |
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| 84 | /// \brief Runs the algorithm from scratch. |
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| 85 | /// |
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| 86 | /// This function runs the algorithm starting from the tour that is |
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| 87 | /// determined by the node ID sequence. |
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| 88 | /// |
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| 89 | /// \return The total cost of the found tour. |
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| 90 | Cost run() { |
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| 91 | _path.clear(); |
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| 92 | |
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| 93 | if (_gr.nodeNum() == 0) return _sum = 0; |
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| 94 | else if (_gr.nodeNum() == 1) { |
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| 95 | _path.push_back(_gr(0)); |
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| 96 | return _sum = 0; |
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[1199] | 97 | } |
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[1201] | 98 | else if (_gr.nodeNum() == 2) { |
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| 99 | _path.push_back(_gr(0)); |
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| 100 | _path.push_back(_gr(1)); |
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| 101 | return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))]; |
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| 102 | } |
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[1199] | 103 | |
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[1201] | 104 | _plist.resize(2*_gr.nodeNum()); |
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| 105 | for (int i = 1; i < _gr.nodeNum()-1; ++i) { |
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| 106 | _plist[2*i] = i-1; |
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| 107 | _plist[2*i+1] = i+1; |
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[1199] | 108 | } |
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[1201] | 109 | _plist[0] = _gr.nodeNum()-1; |
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| 110 | _plist[1] = 1; |
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| 111 | _plist[2*_gr.nodeNum()-2] = _gr.nodeNum()-2; |
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| 112 | _plist[2*_gr.nodeNum()-1] = 0; |
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| 113 | |
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| 114 | return start(); |
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[1199] | 115 | } |
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| 116 | |
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[1201] | 117 | /// \brief Runs the algorithm from the given tour. |
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| 118 | /// |
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| 119 | /// This function runs the algorithm starting from the given tour. |
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| 120 | /// |
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| 121 | /// \param tour The tour as a path structure. It must be a |
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| 122 | /// \ref checkPath() "valid path" containing excactly n arcs. |
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| 123 | /// |
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| 124 | /// \return The total cost of the found tour. |
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| 125 | template <typename Path> |
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| 126 | Cost run(const Path& tour) { |
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| 127 | _path.clear(); |
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| 128 | |
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| 129 | if (_gr.nodeNum() == 0) return _sum = 0; |
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| 130 | else if (_gr.nodeNum() == 1) { |
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| 131 | _path.push_back(_gr(0)); |
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| 132 | return _sum = 0; |
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| 133 | } |
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| 134 | else if (_gr.nodeNum() == 2) { |
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| 135 | _path.push_back(_gr(0)); |
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| 136 | _path.push_back(_gr(1)); |
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| 137 | return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))]; |
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| 138 | } |
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| 139 | |
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| 140 | _plist.resize(2*_gr.nodeNum()); |
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| 141 | typename Path::ArcIt it(tour); |
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| 142 | int first = _gr.id(_gr.source(it)), |
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| 143 | prev = first, |
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| 144 | curr = _gr.id(_gr.target(it)), |
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| 145 | next = -1; |
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| 146 | _plist[2*first+1] = curr; |
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| 147 | for (++it; it != INVALID; ++it) { |
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| 148 | next = _gr.id(_gr.target(it)); |
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| 149 | _plist[2*curr] = prev; |
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| 150 | _plist[2*curr+1] = next; |
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| 151 | prev = curr; |
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| 152 | curr = next; |
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| 153 | } |
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| 154 | _plist[2*first] = prev; |
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| 155 | |
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| 156 | return start(); |
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| 157 | } |
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| 158 | |
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| 159 | /// \brief Runs the algorithm from the given tour. |
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| 160 | /// |
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| 161 | /// This function runs the algorithm starting from the given tour. |
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| 162 | /// |
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| 163 | /// \param tour The tour as a node sequence. It must be a standard |
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| 164 | /// sequence container storing all <tt>Node</tt>s in the desired order. |
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| 165 | /// |
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| 166 | /// \return The total cost of the found tour. |
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| 167 | template <template <typename> class Container> |
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| 168 | Cost run(const Container<Node>& tour) { |
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| 169 | _path.clear(); |
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| 170 | |
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| 171 | if (_gr.nodeNum() == 0) return _sum = 0; |
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| 172 | else if (_gr.nodeNum() == 1) { |
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| 173 | _path.push_back(_gr(0)); |
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| 174 | return _sum = 0; |
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| 175 | } |
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| 176 | else if (_gr.nodeNum() == 2) { |
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| 177 | _path.push_back(_gr(0)); |
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| 178 | _path.push_back(_gr(1)); |
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| 179 | return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))]; |
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| 180 | } |
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| 181 | |
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| 182 | _plist.resize(2*_gr.nodeNum()); |
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| 183 | typename Container<Node>::const_iterator it = tour.begin(); |
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| 184 | int first = _gr.id(*it), |
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| 185 | prev = first, |
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| 186 | curr = _gr.id(*(++it)), |
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| 187 | next = -1; |
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| 188 | _plist[2*first+1] = curr; |
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| 189 | for (++it; it != tour.end(); ++it) { |
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| 190 | next = _gr.id(*it); |
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| 191 | _plist[2*curr] = prev; |
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| 192 | _plist[2*curr+1] = next; |
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| 193 | prev = curr; |
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| 194 | curr = next; |
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| 195 | } |
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| 196 | _plist[2*first] = curr; |
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| 197 | _plist[2*curr] = prev; |
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| 198 | _plist[2*curr+1] = first; |
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| 199 | |
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| 200 | return start(); |
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| 201 | } |
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| 202 | |
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| 203 | /// @} |
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| 204 | |
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| 205 | /// \name Query Functions |
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| 206 | /// @{ |
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| 207 | |
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| 208 | /// \brief The total cost of the found tour. |
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| 209 | /// |
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| 210 | /// This function returns the total cost of the found tour. |
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| 211 | /// |
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| 212 | /// \pre run() must be called before using this function. |
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| 213 | Cost tourCost() const { |
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| 214 | return _sum; |
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| 215 | } |
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| 216 | |
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| 217 | /// \brief Returns a const reference to the node sequence of the |
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| 218 | /// found tour. |
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| 219 | /// |
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| 220 | /// This function returns a const reference to the internal structure |
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| 221 | /// that stores the node sequence of the found tour. |
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| 222 | /// |
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| 223 | /// \pre run() must be called before using this function. |
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| 224 | const std::vector<Node>& tourNodes() const { |
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| 225 | return _path; |
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| 226 | } |
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| 227 | |
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| 228 | /// \brief Gives back the node sequence of the found tour. |
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| 229 | /// |
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| 230 | /// This function copies the node sequence of the found tour into |
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| 231 | /// the given standard container. |
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| 232 | /// |
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| 233 | /// \pre run() must be called before using this function. |
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| 234 | template <typename Container> |
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| 235 | void tourNodes(Container &container) const { |
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| 236 | container.assign(_path.begin(), _path.end()); |
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| 237 | } |
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| 238 | |
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| 239 | /// \brief Gives back the found tour as a path. |
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| 240 | /// |
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| 241 | /// This function copies the found tour as a list of arcs/edges into |
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| 242 | /// the given \ref concept::Path "path structure". |
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| 243 | /// |
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| 244 | /// \pre run() must be called before using this function. |
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| 245 | template <typename Path> |
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| 246 | void tour(Path &path) const { |
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| 247 | path.clear(); |
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| 248 | for (int i = 0; i < int(_path.size()) - 1; ++i) { |
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| 249 | path.addBack(_gr.arc(_path[i], _path[i+1])); |
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| 250 | } |
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| 251 | if (int(_path.size()) >= 2) { |
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| 252 | path.addBack(_gr.arc(_path.back(), _path.front())); |
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| 253 | } |
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| 254 | } |
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| 255 | |
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| 256 | /// @} |
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| 257 | |
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[1199] | 258 | private: |
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[1201] | 259 | |
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| 260 | // Iterator class for the linked list storage of the tour |
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| 261 | class PathListIt { |
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[1199] | 262 | public: |
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[1201] | 263 | PathListIt(const std::vector<int> &pl, int i=0) |
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| 264 | : plist(&pl), act(i), last(pl[2*act]) {} |
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| 265 | PathListIt(const std::vector<int> &pl, int i, int l) |
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| 266 | : plist(&pl), act(i), last(l) {} |
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[1199] | 267 | |
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[1201] | 268 | int nextIndex() const { |
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| 269 | return (*plist)[2*act] == last ? 2*act+1 : 2*act; |
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[1199] | 270 | } |
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[1201] | 271 | |
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| 272 | int prevIndex() const { |
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| 273 | return (*plist)[2*act] == last ? 2*act : 2*act+1; |
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[1199] | 274 | } |
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[1201] | 275 | |
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[1199] | 276 | int next() const { |
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[1201] | 277 | int x = (*plist)[2*act]; |
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| 278 | return x == last ? (*plist)[2*act+1] : x; |
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[1199] | 279 | } |
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| 280 | |
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| 281 | int prev() const { |
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[1201] | 282 | return last; |
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[1199] | 283 | } |
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[1201] | 284 | |
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| 285 | PathListIt& operator++() { |
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[1199] | 286 | int tmp = act; |
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| 287 | act = next(); |
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| 288 | last = tmp; |
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| 289 | return *this; |
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| 290 | } |
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[1201] | 291 | |
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[1199] | 292 | operator int() const { |
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| 293 | return act; |
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| 294 | } |
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[1201] | 295 | |
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[1199] | 296 | private: |
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[1201] | 297 | const std::vector<int> *plist; |
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[1199] | 298 | int act; |
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| 299 | int last; |
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| 300 | }; |
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| 301 | |
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[1201] | 302 | // Checks and applies 2-opt move (if it improves the tour) |
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| 303 | bool checkOpt2(const PathListIt& i, const PathListIt& j) { |
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| 304 | Node u = _gr.nodeFromId(i), |
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| 305 | un = _gr.nodeFromId(i.next()), |
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| 306 | v = _gr.nodeFromId(j), |
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| 307 | vn = _gr.nodeFromId(j.next()); |
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[1199] | 308 | |
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[1201] | 309 | if (_cost[_gr.edge(u, un)] + _cost[_gr.edge(v, vn)] > |
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| 310 | _cost[_gr.edge(u, v)] + _cost[_gr.edge(un, vn)]) |
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| 311 | { |
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| 312 | _plist[PathListIt(_plist, i.next(), i).prevIndex()] = j.next(); |
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| 313 | _plist[PathListIt(_plist, j.next(), j).prevIndex()] = i.next(); |
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[1199] | 314 | |
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[1201] | 315 | _plist[i.nextIndex()] = j; |
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| 316 | _plist[j.nextIndex()] = i; |
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[1199] | 317 | |
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[1201] | 318 | return true; |
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[1199] | 319 | } |
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[1201] | 320 | |
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[1199] | 321 | return false; |
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[1201] | 322 | } |
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[1199] | 323 | |
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[1201] | 324 | // Executes the algorithm from the initial tour |
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| 325 | Cost start() { |
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[1199] | 326 | |
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[1201] | 327 | restart_search: |
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| 328 | for (PathListIt i(_plist); true; ++i) { |
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| 329 | PathListIt j = i; |
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| 330 | if (++j == 0 || ++j == 0) break; |
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| 331 | for (; j != 0 && j != i.prev(); ++j) { |
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| 332 | if (checkOpt2(i, j)) |
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| 333 | goto restart_search; |
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[1199] | 334 | } |
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| 335 | } |
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| 336 | |
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[1201] | 337 | PathListIt i(_plist); |
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| 338 | _path.push_back(_gr.nodeFromId(i)); |
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| 339 | for (++i; i != 0; ++i) |
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| 340 | _path.push_back(_gr.nodeFromId(i)); |
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[1199] | 341 | |
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[1201] | 342 | _sum = _cost[_gr.edge(_path.back(), _path.front())]; |
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| 343 | for (int i = 0; i < int(_path.size())-1; ++i) { |
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| 344 | _sum += _cost[_gr.edge(_path[i], _path[i+1])]; |
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| 345 | } |
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[1199] | 346 | |
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| 347 | return _sum; |
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| 348 | } |
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| 349 | |
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| 350 | }; |
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| 351 | |
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| 352 | }; // namespace lemon |
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| 353 | |
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| 354 | #endif |
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