lemon/kruskal.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 19 Sep 2017 15:19:48 +0200
branch1.2
changeset 1007 00769a5f0f5d
parent 440 88ed40ad0d4f
permissions -rw-r--r--
Merge bugfix #607 to branch 1.2
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_KRUSKAL_H
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#define LEMON_KRUSKAL_H
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#include <algorithm>
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#include <vector>
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#include <lemon/unionfind.h>
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#include <lemon/maps.h>
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#include <lemon/core.h>
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#include <lemon/bits/traits.h>
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///\ingroup spantree
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///\file
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///\brief Kruskal's algorithm to compute a minimum cost spanning tree
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///
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///Kruskal's algorithm to compute a minimum cost spanning tree.
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///
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namespace lemon {
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  namespace _kruskal_bits {
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    // Kruskal for directed graphs.
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    template <typename Digraph, typename In, typename Out>
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    typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
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                       typename In::value_type::second_type >::type
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    kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
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      typedef typename In::value_type::second_type Value;
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      typedef typename Digraph::template NodeMap<int> IndexMap;
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      typedef typename Digraph::Node Node;
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      IndexMap index(digraph);
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      UnionFind<IndexMap> uf(index);
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      for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
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        uf.insert(it);
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      }
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      Value tree_value = 0;
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      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
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        if (uf.join(digraph.target(it->first),digraph.source(it->first))) {
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          out.set(it->first, true);
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          tree_value += it->second;
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        }
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        else {
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          out.set(it->first, false);
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        }
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      }
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      return tree_value;
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    }
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    // Kruskal for undirected graphs.
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    template <typename Graph, typename In, typename Out>
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    typename enable_if<lemon::UndirectedTagIndicator<Graph>,
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                       typename In::value_type::second_type >::type
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    kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
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      typedef typename In::value_type::second_type Value;
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      typedef typename Graph::template NodeMap<int> IndexMap;
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      typedef typename Graph::Node Node;
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      IndexMap index(graph);
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      UnionFind<IndexMap> uf(index);
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      for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
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        uf.insert(it);
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      }
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      Value tree_value = 0;
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      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
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        if (uf.join(graph.u(it->first),graph.v(it->first))) {
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          out.set(it->first, true);
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          tree_value += it->second;
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        }
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        else {
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          out.set(it->first, false);
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        }
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      }
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      return tree_value;
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    }
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    template <typename Sequence>
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    struct PairComp {
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      typedef typename Sequence::value_type Value;
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      bool operator()(const Value& left, const Value& right) {
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        return left.second < right.second;
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      }
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    };
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    template <typename In, typename Enable = void>
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    struct SequenceInputIndicator {
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      static const bool value = false;
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    };
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    template <typename In>
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    struct SequenceInputIndicator<In,
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      typename exists<typename In::value_type::first_type>::type> {
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      static const bool value = true;
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    };
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    template <typename In, typename Enable = void>
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    struct MapInputIndicator {
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      static const bool value = false;
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    };
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    template <typename In>
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    struct MapInputIndicator<In,
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      typename exists<typename In::Value>::type> {
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      static const bool value = true;
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    };
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    template <typename In, typename Enable = void>
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    struct SequenceOutputIndicator {
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      static const bool value = false;
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    };
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    template <typename Out>
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    struct SequenceOutputIndicator<Out,
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      typename exists<typename Out::value_type>::type> {
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      static const bool value = true;
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    };
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    template <typename Out, typename Enable = void>
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    struct MapOutputIndicator {
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      static const bool value = false;
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    };
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    template <typename Out>
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    struct MapOutputIndicator<Out,
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      typename exists<typename Out::Value>::type> {
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      static const bool value = true;
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    };
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    template <typename In, typename InEnable = void>
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    struct KruskalValueSelector {};
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    template <typename In>
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    struct KruskalValueSelector<In,
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      typename enable_if<SequenceInputIndicator<In>, void>::type>
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    {
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      typedef typename In::value_type::second_type Value;
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    };
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    template <typename In>
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    struct KruskalValueSelector<In,
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      typename enable_if<MapInputIndicator<In>, void>::type>
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    {
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      typedef typename In::Value Value;
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    };
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    template <typename Graph, typename In, typename Out,
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              typename InEnable = void>
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    struct KruskalInputSelector {};
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    template <typename Graph, typename In, typename Out,
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              typename InEnable = void>
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    struct KruskalOutputSelector {};
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    template <typename Graph, typename In, typename Out>
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    struct KruskalInputSelector<Graph, In, Out,
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      typename enable_if<SequenceInputIndicator<In>, void>::type >
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    {
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      typedef typename In::value_type::second_type Value;
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      static Value kruskal(const Graph& graph, const In& in, Out& out) {
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        return KruskalOutputSelector<Graph, In, Out>::
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          kruskal(graph, in, out);
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      }
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    };
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    template <typename Graph, typename In, typename Out>
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    struct KruskalInputSelector<Graph, In, Out,
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      typename enable_if<MapInputIndicator<In>, void>::type >
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    {
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      typedef typename In::Value Value;
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      static Value kruskal(const Graph& graph, const In& in, Out& out) {
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        typedef typename In::Key MapArc;
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        typedef typename In::Value Value;
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        typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
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        typedef std::vector<std::pair<MapArc, Value> > Sequence;
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        Sequence seq;
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        for (MapArcIt it(graph); it != INVALID; ++it) {
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          seq.push_back(std::make_pair(it, in[it]));
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        }
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        std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
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        return KruskalOutputSelector<Graph, Sequence, Out>::
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          kruskal(graph, seq, out);
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      }
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    };
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    template <typename T>
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    struct RemoveConst {
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      typedef T type;
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    };
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    template <typename T>
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    struct RemoveConst<const T> {
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      typedef T type;
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    };
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    template <typename Graph, typename In, typename Out>
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    struct KruskalOutputSelector<Graph, In, Out,
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      typename enable_if<SequenceOutputIndicator<Out>, void>::type >
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    {
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      typedef typename In::value_type::second_type Value;
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      static Value kruskal(const Graph& graph, const In& in, Out& out) {
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        typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map;
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        Map map(out);
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        return _kruskal_bits::kruskal(graph, in, map);
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      }
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    };
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    template <typename Graph, typename In, typename Out>
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    struct KruskalOutputSelector<Graph, In, Out,
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      typename enable_if<MapOutputIndicator<Out>, void>::type >
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    {
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      typedef typename In::value_type::second_type Value;
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      static Value kruskal(const Graph& graph, const In& in, Out& out) {
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        return _kruskal_bits::kruskal(graph, in, out);
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      }
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    };
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  }
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  /// \ingroup spantree
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  ///
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  /// \brief Kruskal's algorithm for finding a minimum cost spanning tree of
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  /// a graph.
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  ///
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  /// This function runs Kruskal's algorithm to find a minimum cost
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  /// spanning tree of a graph.
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  /// Due to some C++ hacking, it accepts various input and output types.
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  ///
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  /// \param g The graph the algorithm runs on.
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  /// It can be either \ref concepts::Digraph "directed" or
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  /// \ref concepts::Graph "undirected".
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  /// If the graph is directed, the algorithm consider it to be
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  /// undirected by disregarding the direction of the arcs.
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  ///
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  /// \param in This object is used to describe the arc/edge costs.
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  /// It can be one of the following choices.
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  /// - An STL compatible 'Forward Container' with
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  /// <tt>std::pair<GR::Arc,C></tt> or
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  /// <tt>std::pair<GR::Edge,C></tt> as its <tt>value_type</tt>, where
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  /// \c C is the type of the costs. The pairs indicates the arcs/edges
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  /// along with the assigned cost. <em>They must be in a
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  /// cost-ascending order.</em>
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  /// - Any readable arc/edge map. The values of the map indicate the
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  /// arc/edge costs.
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  ///
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  /// \retval out Here we also have a choice.
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  /// - It can be a writable arc/edge map with \c bool value type. After
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  /// running the algorithm it will contain the found minimum cost spanning
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  /// tree: the value of an arc/edge will be set to \c true if it belongs
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  /// to the tree, otherwise it will be set to \c false. The value of
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  /// each arc/edge will be set exactly once.
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  /// - It can also be an iteraror of an STL Container with
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  /// <tt>GR::Arc</tt> or <tt>GR::Edge</tt> as its
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  /// <tt>value_type</tt>.  The algorithm copies the elements of the
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  /// found tree into this sequence.  For example, if we know that the
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  /// spanning tree of the graph \c g has say 53 arcs, then we can
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  /// put its arcs into an STL vector \c tree with a code like this.
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  ///\code
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  /// std::vector<Arc> tree(53);
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  /// kruskal(g,cost,tree.begin());
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  ///\endcode
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  /// Or if we don't know in advance the size of the tree, we can
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  /// write this.
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  ///\code
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  /// std::vector<Arc> tree;
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  /// kruskal(g,cost,std::back_inserter(tree));
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  ///\endcode
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  ///
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  /// \return The total cost of the found spanning tree.
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  ///
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  /// \note If the input graph is not (weakly) connected, a spanning
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  /// forest is calculated instead of a spanning tree.
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#ifdef DOXYGEN
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  template <typename Graph, typename In, typename Out>
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  Value kruskal(const Graph& g, const In& in, Out& out)
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#else
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  template <class Graph, class In, class Out>
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  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
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  kruskal(const Graph& graph, const In& in, Out& out)
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#endif
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  {
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    return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
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      kruskal(graph, in, out);
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  }
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  template <class Graph, class In, class Out>
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  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
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  kruskal(const Graph& graph, const In& in, const Out& out)
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  {
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    return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
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      kruskal(graph, in, out);
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  }
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} //namespace lemon
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#endif //LEMON_KRUSKAL_H