kpeter@1033: /* -*- mode: C++; indent-tabs-mode: nil; -*- kpeter@1033: * kpeter@1033: * This file is a part of LEMON, a generic C++ optimization library. kpeter@1033: * kpeter@1033: * Copyright (C) 2003-2010 kpeter@1033: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport kpeter@1033: * (Egervary Research Group on Combinatorial Optimization, EGRES). kpeter@1033: * kpeter@1033: * Permission to use, modify and distribute this software is granted kpeter@1033: * provided that this copyright notice appears in all copies. For kpeter@1033: * precise terms see the accompanying LICENSE file. kpeter@1033: * kpeter@1033: * This software is provided "AS IS" with no warranty of any kind, kpeter@1033: * express or implied, and with no claim as to its suitability for any kpeter@1033: * purpose. kpeter@1033: * kpeter@1033: */ kpeter@1033: f4c3@1031: #ifndef LEMON_GREEDY_TSP_H f4c3@1031: #define LEMON_GREEDY_TSP_H f4c3@1031: kpeter@1033: /// \ingroup tsp kpeter@1033: /// \file kpeter@1033: /// \brief Greedy algorithm for symmetric TSP kpeter@1033: kpeter@1033: #include kpeter@1033: #include f4c3@1031: #include f4c3@1031: #include f4c3@1031: f4c3@1031: namespace lemon { f4c3@1031: kpeter@1034: /// \ingroup tsp kpeter@1034: /// kpeter@1033: /// \brief Greedy algorithm for symmetric TSP. kpeter@1033: /// kpeter@1033: /// GreedyTsp implements the greedy heuristic for solving kpeter@1033: /// symmetric \ref tsp "TSP". kpeter@1033: /// kpeter@1033: /// This algorithm is quite similar to the \ref NearestNeighborTsp kpeter@1033: /// "nearest neighbor" heuristic, but it maintains a set of disjoint paths. kpeter@1033: /// At each step, the shortest possible edge is added to these paths kpeter@1033: /// as long as it does not create a cycle of less than n edges and it does kpeter@1033: /// not increase the degree of any node above two. kpeter@1033: /// kpeter@1036: /// This method runs in O(n2) time. kpeter@1036: /// It quickly finds a relatively short tour for most TSP instances, kpeter@1036: /// but it could also yield a really bad (or even the worst) solution kpeter@1036: /// in special cases. kpeter@1033: /// kpeter@1033: /// \tparam CM Type of the cost map. kpeter@1033: template kpeter@1033: class GreedyTsp kpeter@1033: { kpeter@1033: public: f4c3@1031: kpeter@1033: /// Type of the cost map kpeter@1033: typedef CM CostMap; kpeter@1033: /// Type of the edge costs kpeter@1033: typedef typename CM::Value Cost; kpeter@1033: kpeter@1033: private: kpeter@1033: kpeter@1033: GRAPH_TYPEDEFS(FullGraph); kpeter@1033: kpeter@1033: const FullGraph &_gr; kpeter@1033: const CostMap &_cost; kpeter@1033: Cost _sum; kpeter@1033: std::vector _path; f4c3@1031: kpeter@1033: private: kpeter@1033: kpeter@1033: // Functor class to compare edges by their costs kpeter@1033: class EdgeComp { kpeter@1033: private: kpeter@1033: const CostMap &_cost; kpeter@1033: f4c3@1031: public: kpeter@1033: EdgeComp(const CostMap &cost) : _cost(cost) {} kpeter@1033: kpeter@1033: bool operator()(const Edge &a, const Edge &b) const { kpeter@1033: return _cost[a] < _cost[b]; f4c3@1031: } kpeter@1033: }; f4c3@1031: kpeter@1033: public: f4c3@1031: kpeter@1033: /// \brief Constructor kpeter@1033: /// kpeter@1033: /// Constructor. kpeter@1033: /// \param gr The \ref FullGraph "full graph" the algorithm runs on. kpeter@1033: /// \param cost The cost map. kpeter@1033: GreedyTsp(const FullGraph &gr, const CostMap &cost) kpeter@1033: : _gr(gr), _cost(cost) {} f4c3@1031: kpeter@1033: /// \name Execution Control kpeter@1033: /// @{ f4c3@1031: kpeter@1033: /// \brief Runs the algorithm. kpeter@1033: /// kpeter@1033: /// This function runs the algorithm. kpeter@1033: /// kpeter@1033: /// \return The total cost of the found tour. f4c3@1031: Cost run() { kpeter@1033: _path.clear(); kpeter@1033: kpeter@1033: if (_gr.nodeNum() == 0) return _sum = 0; kpeter@1033: else if (_gr.nodeNum() == 1) { kpeter@1033: _path.push_back(_gr(0)); kpeter@1033: return _sum = 0; kpeter@1033: } kpeter@1033: kpeter@1033: std::vector plist; kpeter@1033: plist.resize(_gr.nodeNum()*2, -1); kpeter@1033: kpeter@1033: std::vector sorted_edges; f4c3@1031: sorted_edges.reserve(_gr.edgeNum()); kpeter@1033: for (EdgeIt e(_gr); e != INVALID; ++e) kpeter@1033: sorted_edges.push_back(e); kpeter@1033: std::sort(sorted_edges.begin(), sorted_edges.end(), EdgeComp(_cost)); f4c3@1031: kpeter@1033: FullGraph::NodeMap item_int_map(_gr); kpeter@1033: UnionFind > union_find(item_int_map); kpeter@1033: for (NodeIt n(_gr); n != INVALID; ++n) kpeter@1033: union_find.insert(n); f4c3@1031: f4c3@1031: FullGraph::NodeMap degree(_gr, 0); f4c3@1031: f4c3@1031: int nodesNum = 0, i = 0; kpeter@1033: while (nodesNum != _gr.nodeNum()-1) { kpeter@1033: Edge e = sorted_edges[i++]; kpeter@1033: Node u = _gr.u(e), kpeter@1033: v = _gr.v(e); f4c3@1031: kpeter@1033: if (degree[u] <= 1 && degree[v] <= 1) { kpeter@1033: if (union_find.join(u, v)) { kpeter@1033: const int uid = _gr.id(u), kpeter@1033: vid = _gr.id(v); kpeter@1033: kpeter@1033: plist[uid*2 + degree[u]] = vid; kpeter@1033: plist[vid*2 + degree[v]] = uid; kpeter@1033: f4c3@1031: ++degree[u]; f4c3@1031: ++degree[v]; f4c3@1031: ++nodesNum; f4c3@1031: } f4c3@1031: } f4c3@1031: } f4c3@1031: f4c3@1031: for (int i=0, n=-1; i<_gr.nodeNum()*2; ++i) { kpeter@1033: if (plist[i] == -1) { f4c3@1031: if (n==-1) { f4c3@1031: n = i; f4c3@1031: } else { kpeter@1033: plist[n] = i/2; kpeter@1033: plist[i] = n/2; f4c3@1031: break; f4c3@1031: } f4c3@1031: } f4c3@1031: } f4c3@1031: kpeter@1033: for (int i=0, next=0, last=-1; i!=_gr.nodeNum(); ++i) { kpeter@1033: _path.push_back(_gr.nodeFromId(next)); kpeter@1033: if (plist[2*next] != last) { kpeter@1033: last = next; kpeter@1033: next = plist[2*next]; f4c3@1031: } else { kpeter@1033: last = next; kpeter@1033: next = plist[2*next+1]; f4c3@1031: } f4c3@1031: } f4c3@1031: kpeter@1033: _sum = _cost[_gr.edge(_path.back(), _path.front())]; kpeter@1033: for (int i = 0; i < int(_path.size())-1; ++i) { kpeter@1033: _sum += _cost[_gr.edge(_path[i], _path[i+1])]; kpeter@1033: } f4c3@1031: f4c3@1031: return _sum; f4c3@1031: } f4c3@1031: kpeter@1033: /// @} f4c3@1031: kpeter@1033: /// \name Query Functions kpeter@1033: /// @{ f4c3@1031: kpeter@1033: /// \brief The total cost of the found tour. kpeter@1033: /// kpeter@1033: /// This function returns the total cost of the found tour. kpeter@1033: /// kpeter@1033: /// \pre run() must be called before using this function. kpeter@1033: Cost tourCost() const { f4c3@1031: return _sum; f4c3@1031: } f4c3@1031: kpeter@1033: /// \brief Returns a const reference to the node sequence of the kpeter@1033: /// found tour. kpeter@1033: /// kpeter@1034: /// This function returns a const reference to a vector kpeter@1033: /// that stores the node sequence of the found tour. kpeter@1033: /// kpeter@1033: /// \pre run() must be called before using this function. kpeter@1033: const std::vector& tourNodes() const { kpeter@1033: return _path; kpeter@1033: } kpeter@1033: kpeter@1033: /// \brief Gives back the node sequence of the found tour. kpeter@1033: /// kpeter@1033: /// This function copies the node sequence of the found tour into kpeter@1037: /// an STL container through the given output iterator. The kpeter@1037: /// value_type of the container must be FullGraph::Node. kpeter@1037: /// For example, kpeter@1037: /// \code kpeter@1037: /// std::vector nodes(countNodes(graph)); kpeter@1037: /// tsp.tourNodes(nodes.begin()); kpeter@1037: /// \endcode kpeter@1037: /// or kpeter@1037: /// \code kpeter@1037: /// std::list nodes; kpeter@1037: /// tsp.tourNodes(std::back_inserter(nodes)); kpeter@1037: /// \endcode kpeter@1033: /// kpeter@1033: /// \pre run() must be called before using this function. kpeter@1037: template kpeter@1037: void tourNodes(Iterator out) const { kpeter@1037: std::copy(_path.begin(), _path.end(), out); kpeter@1033: } kpeter@1033: kpeter@1033: /// \brief Gives back the found tour as a path. kpeter@1033: /// kpeter@1033: /// This function copies the found tour as a list of arcs/edges into kpeter@1033: /// the given \ref concept::Path "path structure". kpeter@1033: /// kpeter@1033: /// \pre run() must be called before using this function. kpeter@1033: template kpeter@1033: void tour(Path &path) const { kpeter@1033: path.clear(); kpeter@1033: for (int i = 0; i < int(_path.size()) - 1; ++i) { kpeter@1033: path.addBack(_gr.arc(_path[i], _path[i+1])); kpeter@1033: } kpeter@1033: if (int(_path.size()) >= 2) { kpeter@1033: path.addBack(_gr.arc(_path.back(), _path.front())); kpeter@1033: } kpeter@1033: } kpeter@1033: kpeter@1033: /// @} kpeter@1033: f4c3@1031: }; f4c3@1031: f4c3@1031: }; // namespace lemon f4c3@1031: f4c3@1031: #endif