alpar@209: /* -*- mode: C++; indent-tabs-mode: nil; -*-
alpar@103:  *
alpar@209:  * This file is a part of LEMON, a generic C++ optimization library.
alpar@103:  *
alpar@103:  * Copyright (C) 2003-2008
alpar@103:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@103:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@103:  *
alpar@103:  * Permission to use, modify and distribute this software is granted
alpar@103:  * provided that this copyright notice appears in all copies. For
alpar@103:  * precise terms see the accompanying LICENSE file.
alpar@103:  *
alpar@103:  * This software is provided "AS IS" with no warranty of any kind,
alpar@103:  * express or implied, and with no claim as to its suitability for any
alpar@103:  * purpose.
alpar@103:  *
alpar@103:  */
alpar@103: 
alpar@103: #ifndef LEMON_KRUSKAL_H
alpar@103: #define LEMON_KRUSKAL_H
alpar@103: 
alpar@103: #include <algorithm>
alpar@103: #include <vector>
alpar@103: #include <lemon/unionfind.h>
alpar@103: // #include <lemon/graph_utils.h>
alpar@103: #include <lemon/maps.h>
alpar@103: 
alpar@103: // #include <lemon/radix_sort.h>
alpar@103: 
alpar@103: #include <lemon/bits/utility.h>
alpar@103: #include <lemon/bits/traits.h>
alpar@103: 
alpar@103: ///\ingroup spantree
alpar@103: ///\file
kpeter@194: ///\brief Kruskal's algorithm to compute a minimum cost spanning tree
alpar@103: ///
kpeter@194: ///Kruskal's algorithm to compute a minimum cost spanning tree.
alpar@103: ///
alpar@103: 
alpar@103: namespace lemon {
alpar@103: 
alpar@103:   namespace _kruskal_bits {
alpar@103: 
alpar@103:     // Kruskal for directed graphs.
alpar@103: 
alpar@103:     template <typename Digraph, typename In, typename Out>
alpar@103:     typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
alpar@209:                        typename In::value_type::second_type >::type
alpar@103:     kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
alpar@103:       typedef typename In::value_type::second_type Value;
alpar@103:       typedef typename Digraph::template NodeMap<int> IndexMap;
alpar@103:       typedef typename Digraph::Node Node;
alpar@209: 
alpar@103:       IndexMap index(digraph);
alpar@103:       UnionFind<IndexMap> uf(index);
alpar@103:       for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
alpar@103:         uf.insert(it);
alpar@103:       }
alpar@209: 
alpar@103:       Value tree_value = 0;
alpar@103:       for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
alpar@103:         if (uf.join(digraph.target(it->first),digraph.source(it->first))) {
alpar@103:           out.set(it->first, true);
alpar@103:           tree_value += it->second;
alpar@103:         }
alpar@103:         else {
alpar@103:           out.set(it->first, false);
alpar@103:         }
alpar@103:       }
alpar@103:       return tree_value;
alpar@103:     }
alpar@103: 
alpar@103:     // Kruskal for undirected graphs.
alpar@103: 
alpar@103:     template <typename Graph, typename In, typename Out>
alpar@103:     typename enable_if<lemon::UndirectedTagIndicator<Graph>,
alpar@209:                        typename In::value_type::second_type >::type
alpar@103:     kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
alpar@103:       typedef typename In::value_type::second_type Value;
alpar@103:       typedef typename Graph::template NodeMap<int> IndexMap;
alpar@103:       typedef typename Graph::Node Node;
alpar@209: 
alpar@103:       IndexMap index(graph);
alpar@103:       UnionFind<IndexMap> uf(index);
alpar@103:       for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
alpar@103:         uf.insert(it);
alpar@103:       }
alpar@209: 
alpar@103:       Value tree_value = 0;
alpar@103:       for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
alpar@103:         if (uf.join(graph.u(it->first),graph.v(it->first))) {
alpar@103:           out.set(it->first, true);
alpar@103:           tree_value += it->second;
alpar@103:         }
alpar@103:         else {
alpar@103:           out.set(it->first, false);
alpar@103:         }
alpar@103:       }
alpar@103:       return tree_value;
alpar@103:     }
alpar@103: 
alpar@103: 
alpar@103:     template <typename Sequence>
alpar@103:     struct PairComp {
alpar@103:       typedef typename Sequence::value_type Value;
alpar@103:       bool operator()(const Value& left, const Value& right) {
alpar@209:         return left.second < right.second;
alpar@103:       }
alpar@103:     };
alpar@103: 
alpar@103:     template <typename In, typename Enable = void>
alpar@103:     struct SequenceInputIndicator {
alpar@103:       static const bool value = false;
alpar@103:     };
alpar@103: 
alpar@103:     template <typename In>
alpar@209:     struct SequenceInputIndicator<In,
alpar@103:       typename exists<typename In::value_type::first_type>::type> {
alpar@103:       static const bool value = true;
alpar@103:     };
alpar@103: 
alpar@103:     template <typename In, typename Enable = void>
alpar@103:     struct MapInputIndicator {
alpar@103:       static const bool value = false;
alpar@103:     };
alpar@103: 
alpar@103:     template <typename In>
alpar@209:     struct MapInputIndicator<In,
alpar@103:       typename exists<typename In::Value>::type> {
alpar@103:       static const bool value = true;
alpar@103:     };
alpar@103: 
alpar@103:     template <typename In, typename Enable = void>
alpar@103:     struct SequenceOutputIndicator {
alpar@103:       static const bool value = false;
alpar@103:     };
alpar@209: 
alpar@103:     template <typename Out>
alpar@209:     struct SequenceOutputIndicator<Out,
alpar@103:       typename exists<typename Out::value_type>::type> {
alpar@103:       static const bool value = true;
alpar@103:     };
alpar@103: 
alpar@103:     template <typename Out, typename Enable = void>
alpar@103:     struct MapOutputIndicator {
alpar@103:       static const bool value = false;
alpar@103:     };
alpar@103: 
alpar@103:     template <typename Out>
alpar@209:     struct MapOutputIndicator<Out,
alpar@103:       typename exists<typename Out::Value>::type> {
alpar@103:       static const bool value = true;
alpar@103:     };
alpar@103: 
alpar@103:     template <typename In, typename InEnable = void>
alpar@103:     struct KruskalValueSelector {};
alpar@103: 
alpar@103:     template <typename In>
alpar@103:     struct KruskalValueSelector<In,
alpar@209:       typename enable_if<SequenceInputIndicator<In>, void>::type>
alpar@103:     {
alpar@103:       typedef typename In::value_type::second_type Value;
alpar@209:     };
alpar@103: 
alpar@103:     template <typename In>
alpar@103:     struct KruskalValueSelector<In,
alpar@209:       typename enable_if<MapInputIndicator<In>, void>::type>
alpar@103:     {
alpar@103:       typedef typename In::Value Value;
alpar@209:     };
alpar@209: 
alpar@103:     template <typename Graph, typename In, typename Out,
alpar@103:               typename InEnable = void>
alpar@103:     struct KruskalInputSelector {};
alpar@103: 
alpar@103:     template <typename Graph, typename In, typename Out,
alpar@103:               typename InEnable = void>
alpar@103:     struct KruskalOutputSelector {};
alpar@209: 
alpar@103:     template <typename Graph, typename In, typename Out>
alpar@103:     struct KruskalInputSelector<Graph, In, Out,
alpar@209:       typename enable_if<SequenceInputIndicator<In>, void>::type >
alpar@103:     {
alpar@103:       typedef typename In::value_type::second_type Value;
alpar@103: 
alpar@103:       static Value kruskal(const Graph& graph, const In& in, Out& out) {
alpar@103:         return KruskalOutputSelector<Graph, In, Out>::
alpar@103:           kruskal(graph, in, out);
alpar@103:       }
alpar@103: 
alpar@103:     };
alpar@103: 
alpar@103:     template <typename Graph, typename In, typename Out>
alpar@103:     struct KruskalInputSelector<Graph, In, Out,
alpar@209:       typename enable_if<MapInputIndicator<In>, void>::type >
alpar@103:     {
alpar@103:       typedef typename In::Value Value;
alpar@103:       static Value kruskal(const Graph& graph, const In& in, Out& out) {
alpar@103:         typedef typename In::Key MapArc;
alpar@103:         typedef typename In::Value Value;
alpar@103:         typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
alpar@103:         typedef std::vector<std::pair<MapArc, Value> > Sequence;
alpar@103:         Sequence seq;
alpar@209: 
alpar@103:         for (MapArcIt it(graph); it != INVALID; ++it) {
alpar@103:           seq.push_back(std::make_pair(it, in[it]));
alpar@103:         }
alpar@103: 
alpar@103:         std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
alpar@103:         return KruskalOutputSelector<Graph, Sequence, Out>::
alpar@103:           kruskal(graph, seq, out);
alpar@103:       }
alpar@103:     };
alpar@103: 
deba@136:     template <typename T>
deba@136:     struct RemoveConst {
deba@136:       typedef T type;
deba@136:     };
deba@136: 
deba@136:     template <typename T>
deba@136:     struct RemoveConst<const T> {
deba@136:       typedef T type;
deba@136:     };
deba@136: 
alpar@103:     template <typename Graph, typename In, typename Out>
alpar@103:     struct KruskalOutputSelector<Graph, In, Out,
alpar@209:       typename enable_if<SequenceOutputIndicator<Out>, void>::type >
alpar@103:     {
alpar@103:       typedef typename In::value_type::second_type Value;
alpar@103: 
alpar@103:       static Value kruskal(const Graph& graph, const In& in, Out& out) {
kpeter@167:         typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map;
alpar@103:         Map map(out);
alpar@103:         return _kruskal_bits::kruskal(graph, in, map);
alpar@103:       }
alpar@103: 
alpar@103:     };
alpar@103: 
alpar@103:     template <typename Graph, typename In, typename Out>
alpar@103:     struct KruskalOutputSelector<Graph, In, Out,
alpar@209:       typename enable_if<MapOutputIndicator<Out>, void>::type >
alpar@103:     {
alpar@103:       typedef typename In::value_type::second_type Value;
alpar@103: 
alpar@103:       static Value kruskal(const Graph& graph, const In& in, Out& out) {
alpar@103:         return _kruskal_bits::kruskal(graph, in, out);
alpar@103:       }
alpar@103:     };
alpar@103: 
alpar@103:   }
alpar@103: 
alpar@103:   /// \ingroup spantree
alpar@103:   ///
kpeter@194:   /// \brief Kruskal algorithm to find a minimum cost spanning tree of
kpeter@194:   /// a graph.
alpar@103:   ///
alpar@209:   /// This function runs Kruskal's algorithm to find a minimum cost
kpeter@194:   /// spanning tree.
alpar@103:   /// Due to some C++ hacking, it accepts various input and output types.
alpar@103:   ///
alpar@103:   /// \param g The graph the algorithm runs on.
alpar@209:   /// It can be either \ref concepts::Digraph "directed" or
alpar@103:   /// \ref concepts::Graph "undirected".
alpar@209:   /// If the graph is directed, the algorithm consider it to be
alpar@103:   /// undirected by disregarding the direction of the arcs.
alpar@103:   ///
alpar@209:   /// \param in This object is used to describe the arc/edge costs.
kpeter@194:   /// It can be one of the following choices.
alpar@103:   /// - An STL compatible 'Forward Container' with
kpeter@194:   /// <tt>std::pair<GR::Arc,X></tt> or
kpeter@194:   /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where
kpeter@194:   /// \c X is the type of the costs. The pairs indicates the arcs/edges
alpar@103:   /// along with the assigned cost. <em>They must be in a
alpar@103:   /// cost-ascending order.</em>
alpar@209:   /// - Any readable arc/edge map. The values of the map indicate the
kpeter@194:   /// arc/edge costs.
alpar@103:   ///
kpeter@194:   /// \retval out Here we also have a choice.
kpeter@194:   /// - It can be a writable \c bool arc/edge map. After running the
kpeter@194:   /// algorithm it will contain the found minimum cost spanning
kpeter@194:   /// tree: the value of an arc/edge will be set to \c true if it belongs
alpar@103:   /// to the tree, otherwise it will be set to \c false. The value of
kpeter@194:   /// each arc/edge will be set exactly once.
alpar@103:   /// - It can also be an iteraror of an STL Container with
kpeter@194:   /// <tt>GR::Arc</tt> or <tt>GR::Edge</tt> as its
alpar@103:   /// <tt>value_type</tt>.  The algorithm copies the elements of the
alpar@103:   /// found tree into this sequence.  For example, if we know that the
alpar@103:   /// spanning tree of the graph \c g has say 53 arcs, then we can
alpar@103:   /// put its arcs into an STL vector \c tree with a code like this.
alpar@103:   ///\code
alpar@103:   /// std::vector<Arc> tree(53);
alpar@103:   /// kruskal(g,cost,tree.begin());
alpar@103:   ///\endcode
alpar@103:   /// Or if we don't know in advance the size of the tree, we can
alpar@209:   /// write this.
kpeter@194:   ///\code
kpeter@194:   /// std::vector<Arc> tree;
alpar@209:   /// kruskal(g,cost,std::back_inserter(tree));
alpar@103:   ///\endcode
alpar@103:   ///
kpeter@194:   /// \return The total cost of the found spanning tree.
alpar@103:   ///
kpeter@194:   /// \warning If Kruskal runs on an be consistent of using the same
alpar@103:   /// Arc type for input and output.
alpar@103:   ///
alpar@103: 
alpar@103: #ifdef DOXYGEN
alpar@103:   template <class Graph, class In, class Out>
alpar@103:   Value kruskal(GR const& g, const In& in, Out& out)
alpar@209: #else
alpar@103:   template <class Graph, class In, class Out>
alpar@209:   inline typename _kruskal_bits::KruskalValueSelector<In>::Value
alpar@209:   kruskal(const Graph& graph, const In& in, Out& out)
alpar@103: #endif
alpar@103:   {
alpar@103:     return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
alpar@103:       kruskal(graph, in, out);
alpar@103:   }
alpar@103: 
alpar@209: 
alpar@209: 
alpar@103: 
alpar@103:   template <class Graph, class In, class Out>
alpar@103:   inline typename _kruskal_bits::KruskalValueSelector<In>::Value
alpar@103:   kruskal(const Graph& graph, const In& in, const Out& out)
alpar@103:   {
alpar@103:     return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
alpar@103:       kruskal(graph, in, out);
alpar@209:   }
alpar@103: 
alpar@103: } //namespace lemon
alpar@103: 
alpar@103: #endif //LEMON_KRUSKAL_H