/* -*- C++ -*- * * This file is a part of LEMON, a generic C++ optimization library * * Copyright (C) 2003-2008 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport * (Egervary Research Group on Combinatorial Optimization, EGRES). * * Permission to use, modify and distribute this software is granted * provided that this copyright notice appears in all copies. For * precise terms see the accompanying LICENSE file. * * This software is provided "AS IS" with no warranty of any kind, * express or implied, and with no claim as to its suitability for any * purpose. * */ #ifndef LEMON_KRUSKAL_H #define LEMON_KRUSKAL_H #include #include #include // #include #include // #include #include #include ///\ingroup spantree ///\file ///\brief Kruskal's algorithm to compute a minimum cost tree /// ///Kruskal's algorithm to compute a minimum cost tree. /// namespace lemon { namespace _kruskal_bits { // Kruskal for directed graphs. template typename disable_if, typename In::value_type::second_type >::type kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) { typedef typename In::value_type::second_type Value; typedef typename Digraph::template NodeMap IndexMap; typedef typename Digraph::Node Node; IndexMap index(digraph); UnionFind uf(index); for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) { uf.insert(it); } Value tree_value = 0; for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { if (uf.join(digraph.target(it->first),digraph.source(it->first))) { out.set(it->first, true); tree_value += it->second; } else { out.set(it->first, false); } } return tree_value; } // Kruskal for undirected graphs. template typename enable_if, typename In::value_type::second_type >::type kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) { typedef typename In::value_type::second_type Value; typedef typename Graph::template NodeMap IndexMap; typedef typename Graph::Node Node; IndexMap index(graph); UnionFind uf(index); for (typename Graph::NodeIt it(graph); it != INVALID; ++it) { uf.insert(it); } Value tree_value = 0; for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { if (uf.join(graph.u(it->first),graph.v(it->first))) { out.set(it->first, true); tree_value += it->second; } else { out.set(it->first, false); } } return tree_value; } template struct PairComp { typedef typename Sequence::value_type Value; bool operator()(const Value& left, const Value& right) { return left.second < right.second; } }; template struct SequenceInputIndicator { static const bool value = false; }; template struct SequenceInputIndicator::type> { static const bool value = true; }; template struct MapInputIndicator { static const bool value = false; }; template struct MapInputIndicator::type> { static const bool value = true; }; template struct SequenceOutputIndicator { static const bool value = false; }; template struct SequenceOutputIndicator::type> { static const bool value = true; }; template struct MapOutputIndicator { static const bool value = false; }; template struct MapOutputIndicator::type> { static const bool value = true; }; template struct KruskalValueSelector {}; template struct KruskalValueSelector, void>::type> { typedef typename In::value_type::second_type Value; }; template struct KruskalValueSelector, void>::type> { typedef typename In::Value Value; }; template struct KruskalInputSelector {}; template struct KruskalOutputSelector {}; template struct KruskalInputSelector, void>::type > { typedef typename In::value_type::second_type Value; static Value kruskal(const Graph& graph, const In& in, Out& out) { return KruskalOutputSelector:: kruskal(graph, in, out); } }; template struct KruskalInputSelector, void>::type > { typedef typename In::Value Value; static Value kruskal(const Graph& graph, const In& in, Out& out) { typedef typename In::Key MapArc; typedef typename In::Value Value; typedef typename ItemSetTraits::ItemIt MapArcIt; typedef std::vector > Sequence; Sequence seq; for (MapArcIt it(graph); it != INVALID; ++it) { seq.push_back(std::make_pair(it, in[it])); } std::sort(seq.begin(), seq.end(), PairComp()); return KruskalOutputSelector:: kruskal(graph, seq, out); } }; template struct KruskalOutputSelector, void>::type > { typedef typename In::value_type::second_type Value; static Value kruskal(const Graph& graph, const In& in, Out& out) { typedef StoreBoolMap Map; Map map(out); return _kruskal_bits::kruskal(graph, in, map); } }; template struct KruskalOutputSelector, void>::type > { typedef typename In::value_type::second_type Value; static Value kruskal(const Graph& graph, const In& in, Out& out) { return _kruskal_bits::kruskal(graph, in, out); } }; } /// \ingroup spantree /// /// \brief Kruskal's algorithm to find a minimum cost tree of a graph. /// /// This function runs Kruskal's algorithm to find a minimum cost tree. /// Due to some C++ hacking, it accepts various input and output types. /// /// \param g The graph the algorithm runs on. /// It can be either \ref concepts::Digraph "directed" or /// \ref concepts::Graph "undirected". /// If the graph is directed, the algorithm consider it to be /// undirected by disregarding the direction of the arcs. /// /// \param in This object is used to describe the arc costs. It can be one /// of the following choices. /// - An STL compatible 'Forward Container' with /// std::pair or /// std::pair as its value_type, where /// \c X is the type of the costs. The pairs indicates the arcs /// along with the assigned cost. They must be in a /// cost-ascending order. /// - Any readable Arc map. The values of the map indicate the arc costs. /// /// \retval out Here we also have a choise. /// - It can be a writable \c bool arc map. After running the /// algorithm this will contain the found minimum cost spanning /// tree: the value of an arc will be set to \c true if it belongs /// to the tree, otherwise it will be set to \c false. The value of /// each arc will be set exactly once. /// - It can also be an iteraror of an STL Container with /// GR::Edge or GR::Arc as its /// value_type. The algorithm copies the elements of the /// found tree into this sequence. For example, if we know that the /// spanning tree of the graph \c g has say 53 arcs, then we can /// put its arcs into an STL vector \c tree with a code like this. ///\code /// std::vector tree(53); /// kruskal(g,cost,tree.begin()); ///\endcode /// Or if we don't know in advance the size of the tree, we can /// write this. ///\code std::vector tree; /// kruskal(g,cost,std::back_inserter(tree)); ///\endcode /// /// \return The total cost of the found tree. /// /// \warning If kruskal runs on an be consistent of using the same /// Arc type for input and output. /// #ifdef DOXYGEN template Value kruskal(GR const& g, const In& in, Out& out) #else template inline typename _kruskal_bits::KruskalValueSelector::Value kruskal(const Graph& graph, const In& in, Out& out) #endif { return _kruskal_bits::KruskalInputSelector:: kruskal(graph, in, out); } template inline typename _kruskal_bits::KruskalValueSelector::Value kruskal(const Graph& graph, const In& in, const Out& out) { return _kruskal_bits::KruskalInputSelector:: kruskal(graph, in, out); } } //namespace lemon #endif //LEMON_KRUSKAL_H