[1201] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
---|
| 2 | * |
---|
| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
---|
| 4 | * |
---|
[1270] | 5 | * Copyright (C) 2003-2013 |
---|
[1201] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
| 8 | * |
---|
| 9 | * Permission to use, modify and distribute this software is granted |
---|
| 10 | * provided that this copyright notice appears in all copies. For |
---|
| 11 | * precise terms see the accompanying LICENSE file. |
---|
| 12 | * |
---|
| 13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
| 14 | * express or implied, and with no claim as to its suitability for any |
---|
| 15 | * purpose. |
---|
| 16 | * |
---|
| 17 | */ |
---|
| 18 | |
---|
[1199] | 19 | #ifndef LEMON_GREEDY_TSP_H |
---|
| 20 | #define LEMON_GREEDY_TSP_H |
---|
| 21 | |
---|
[1201] | 22 | /// \ingroup tsp |
---|
| 23 | /// \file |
---|
| 24 | /// \brief Greedy algorithm for symmetric TSP |
---|
| 25 | |
---|
| 26 | #include <vector> |
---|
| 27 | #include <algorithm> |
---|
[1199] | 28 | #include <lemon/full_graph.h> |
---|
| 29 | #include <lemon/unionfind.h> |
---|
| 30 | |
---|
| 31 | namespace lemon { |
---|
| 32 | |
---|
[1202] | 33 | /// \ingroup tsp |
---|
| 34 | /// |
---|
[1201] | 35 | /// \brief Greedy algorithm for symmetric TSP. |
---|
| 36 | /// |
---|
| 37 | /// GreedyTsp implements the greedy heuristic for solving |
---|
| 38 | /// symmetric \ref tsp "TSP". |
---|
| 39 | /// |
---|
| 40 | /// This algorithm is quite similar to the \ref NearestNeighborTsp |
---|
| 41 | /// "nearest neighbor" heuristic, but it maintains a set of disjoint paths. |
---|
| 42 | /// At each step, the shortest possible edge is added to these paths |
---|
| 43 | /// as long as it does not create a cycle of less than n edges and it does |
---|
| 44 | /// not increase the degree of any node above two. |
---|
| 45 | /// |
---|
[1204] | 46 | /// This method runs in O(n<sup>2</sup>) time. |
---|
| 47 | /// It quickly finds a relatively short tour for most TSP instances, |
---|
| 48 | /// but it could also yield a really bad (or even the worst) solution |
---|
| 49 | /// in special cases. |
---|
[1201] | 50 | /// |
---|
| 51 | /// \tparam CM Type of the cost map. |
---|
| 52 | template <typename CM> |
---|
| 53 | class GreedyTsp |
---|
| 54 | { |
---|
| 55 | public: |
---|
[1199] | 56 | |
---|
[1201] | 57 | /// Type of the cost map |
---|
| 58 | typedef CM CostMap; |
---|
| 59 | /// Type of the edge costs |
---|
| 60 | typedef typename CM::Value Cost; |
---|
| 61 | |
---|
| 62 | private: |
---|
| 63 | |
---|
| 64 | GRAPH_TYPEDEFS(FullGraph); |
---|
| 65 | |
---|
| 66 | const FullGraph &_gr; |
---|
| 67 | const CostMap &_cost; |
---|
| 68 | Cost _sum; |
---|
| 69 | std::vector<Node> _path; |
---|
[1270] | 70 | |
---|
[1201] | 71 | private: |
---|
[1270] | 72 | |
---|
[1201] | 73 | // Functor class to compare edges by their costs |
---|
| 74 | class EdgeComp { |
---|
| 75 | private: |
---|
| 76 | const CostMap &_cost; |
---|
| 77 | |
---|
[1199] | 78 | public: |
---|
[1201] | 79 | EdgeComp(const CostMap &cost) : _cost(cost) {} |
---|
| 80 | |
---|
| 81 | bool operator()(const Edge &a, const Edge &b) const { |
---|
| 82 | return _cost[a] < _cost[b]; |
---|
[1199] | 83 | } |
---|
[1201] | 84 | }; |
---|
[1199] | 85 | |
---|
[1201] | 86 | public: |
---|
[1199] | 87 | |
---|
[1201] | 88 | /// \brief Constructor |
---|
| 89 | /// |
---|
| 90 | /// Constructor. |
---|
| 91 | /// \param gr The \ref FullGraph "full graph" the algorithm runs on. |
---|
| 92 | /// \param cost The cost map. |
---|
| 93 | GreedyTsp(const FullGraph &gr, const CostMap &cost) |
---|
| 94 | : _gr(gr), _cost(cost) {} |
---|
[1199] | 95 | |
---|
[1201] | 96 | /// \name Execution Control |
---|
| 97 | /// @{ |
---|
[1199] | 98 | |
---|
[1201] | 99 | /// \brief Runs the algorithm. |
---|
| 100 | /// |
---|
| 101 | /// This function runs the algorithm. |
---|
| 102 | /// |
---|
| 103 | /// \return The total cost of the found tour. |
---|
[1199] | 104 | Cost run() { |
---|
[1201] | 105 | _path.clear(); |
---|
| 106 | |
---|
| 107 | if (_gr.nodeNum() == 0) return _sum = 0; |
---|
| 108 | else if (_gr.nodeNum() == 1) { |
---|
| 109 | _path.push_back(_gr(0)); |
---|
| 110 | return _sum = 0; |
---|
| 111 | } |
---|
| 112 | |
---|
| 113 | std::vector<int> plist; |
---|
| 114 | plist.resize(_gr.nodeNum()*2, -1); |
---|
| 115 | |
---|
| 116 | std::vector<Edge> sorted_edges; |
---|
[1199] | 117 | sorted_edges.reserve(_gr.edgeNum()); |
---|
[1201] | 118 | for (EdgeIt e(_gr); e != INVALID; ++e) |
---|
| 119 | sorted_edges.push_back(e); |
---|
| 120 | std::sort(sorted_edges.begin(), sorted_edges.end(), EdgeComp(_cost)); |
---|
[1199] | 121 | |
---|
[1201] | 122 | FullGraph::NodeMap<int> item_int_map(_gr); |
---|
| 123 | UnionFind<FullGraph::NodeMap<int> > union_find(item_int_map); |
---|
| 124 | for (NodeIt n(_gr); n != INVALID; ++n) |
---|
| 125 | union_find.insert(n); |
---|
[1199] | 126 | |
---|
| 127 | FullGraph::NodeMap<int> degree(_gr, 0); |
---|
| 128 | |
---|
| 129 | int nodesNum = 0, i = 0; |
---|
[1201] | 130 | while (nodesNum != _gr.nodeNum()-1) { |
---|
| 131 | Edge e = sorted_edges[i++]; |
---|
| 132 | Node u = _gr.u(e), |
---|
| 133 | v = _gr.v(e); |
---|
[1199] | 134 | |
---|
[1201] | 135 | if (degree[u] <= 1 && degree[v] <= 1) { |
---|
| 136 | if (union_find.join(u, v)) { |
---|
| 137 | const int uid = _gr.id(u), |
---|
| 138 | vid = _gr.id(v); |
---|
| 139 | |
---|
| 140 | plist[uid*2 + degree[u]] = vid; |
---|
| 141 | plist[vid*2 + degree[v]] = uid; |
---|
| 142 | |
---|
[1199] | 143 | ++degree[u]; |
---|
| 144 | ++degree[v]; |
---|
| 145 | ++nodesNum; |
---|
| 146 | } |
---|
| 147 | } |
---|
| 148 | } |
---|
| 149 | |
---|
| 150 | for (int i=0, n=-1; i<_gr.nodeNum()*2; ++i) { |
---|
[1201] | 151 | if (plist[i] == -1) { |
---|
[1199] | 152 | if (n==-1) { |
---|
| 153 | n = i; |
---|
| 154 | } else { |
---|
[1201] | 155 | plist[n] = i/2; |
---|
| 156 | plist[i] = n/2; |
---|
[1199] | 157 | break; |
---|
| 158 | } |
---|
| 159 | } |
---|
| 160 | } |
---|
| 161 | |
---|
[1201] | 162 | for (int i=0, next=0, last=-1; i!=_gr.nodeNum(); ++i) { |
---|
| 163 | _path.push_back(_gr.nodeFromId(next)); |
---|
| 164 | if (plist[2*next] != last) { |
---|
| 165 | last = next; |
---|
| 166 | next = plist[2*next]; |
---|
[1199] | 167 | } else { |
---|
[1201] | 168 | last = next; |
---|
| 169 | next = plist[2*next+1]; |
---|
[1199] | 170 | } |
---|
| 171 | } |
---|
| 172 | |
---|
[1201] | 173 | _sum = _cost[_gr.edge(_path.back(), _path.front())]; |
---|
| 174 | for (int i = 0; i < int(_path.size())-1; ++i) { |
---|
| 175 | _sum += _cost[_gr.edge(_path[i], _path[i+1])]; |
---|
| 176 | } |
---|
[1199] | 177 | |
---|
| 178 | return _sum; |
---|
| 179 | } |
---|
| 180 | |
---|
[1201] | 181 | /// @} |
---|
[1199] | 182 | |
---|
[1201] | 183 | /// \name Query Functions |
---|
| 184 | /// @{ |
---|
[1199] | 185 | |
---|
[1201] | 186 | /// \brief The total cost of the found tour. |
---|
| 187 | /// |
---|
| 188 | /// This function returns the total cost of the found tour. |
---|
| 189 | /// |
---|
| 190 | /// \pre run() must be called before using this function. |
---|
| 191 | Cost tourCost() const { |
---|
[1199] | 192 | return _sum; |
---|
| 193 | } |
---|
| 194 | |
---|
[1201] | 195 | /// \brief Returns a const reference to the node sequence of the |
---|
| 196 | /// found tour. |
---|
| 197 | /// |
---|
[1202] | 198 | /// This function returns a const reference to a vector |
---|
[1201] | 199 | /// that stores the node sequence of the found tour. |
---|
| 200 | /// |
---|
| 201 | /// \pre run() must be called before using this function. |
---|
| 202 | const std::vector<Node>& tourNodes() const { |
---|
| 203 | return _path; |
---|
| 204 | } |
---|
| 205 | |
---|
| 206 | /// \brief Gives back the node sequence of the found tour. |
---|
| 207 | /// |
---|
| 208 | /// This function copies the node sequence of the found tour into |
---|
[1205] | 209 | /// an STL container through the given output iterator. The |
---|
| 210 | /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>. |
---|
| 211 | /// For example, |
---|
| 212 | /// \code |
---|
| 213 | /// std::vector<FullGraph::Node> nodes(countNodes(graph)); |
---|
| 214 | /// tsp.tourNodes(nodes.begin()); |
---|
| 215 | /// \endcode |
---|
| 216 | /// or |
---|
| 217 | /// \code |
---|
| 218 | /// std::list<FullGraph::Node> nodes; |
---|
| 219 | /// tsp.tourNodes(std::back_inserter(nodes)); |
---|
| 220 | /// \endcode |
---|
[1201] | 221 | /// |
---|
| 222 | /// \pre run() must be called before using this function. |
---|
[1205] | 223 | template <typename Iterator> |
---|
| 224 | void tourNodes(Iterator out) const { |
---|
| 225 | std::copy(_path.begin(), _path.end(), out); |
---|
[1201] | 226 | } |
---|
| 227 | |
---|
| 228 | /// \brief Gives back the found tour as a path. |
---|
| 229 | /// |
---|
| 230 | /// This function copies the found tour as a list of arcs/edges into |
---|
[1250] | 231 | /// the given \ref lemon::concepts::Path "path structure". |
---|
[1201] | 232 | /// |
---|
| 233 | /// \pre run() must be called before using this function. |
---|
| 234 | template <typename Path> |
---|
| 235 | void tour(Path &path) const { |
---|
| 236 | path.clear(); |
---|
| 237 | for (int i = 0; i < int(_path.size()) - 1; ++i) { |
---|
| 238 | path.addBack(_gr.arc(_path[i], _path[i+1])); |
---|
| 239 | } |
---|
| 240 | if (int(_path.size()) >= 2) { |
---|
| 241 | path.addBack(_gr.arc(_path.back(), _path.front())); |
---|
| 242 | } |
---|
| 243 | } |
---|
| 244 | |
---|
| 245 | /// @} |
---|
| 246 | |
---|
[1199] | 247 | }; |
---|
| 248 | |
---|
| 249 | }; // namespace lemon |
---|
| 250 | |
---|
| 251 | #endif |
---|