[209] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[103] | 2 | * |
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[209] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[103] | 4 | * |
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| 5 | * Copyright (C) 2003-2008 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_KRUSKAL_H |
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| 20 | #define LEMON_KRUSKAL_H |
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| 21 | |
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| 22 | #include <algorithm> |
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| 23 | #include <vector> |
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| 24 | #include <lemon/unionfind.h> |
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| 25 | #include <lemon/maps.h> |
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| 26 | |
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[220] | 27 | #include <lemon/core.h> |
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[103] | 28 | #include <lemon/bits/traits.h> |
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| 29 | |
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| 30 | ///\ingroup spantree |
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| 31 | ///\file |
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[194] | 32 | ///\brief Kruskal's algorithm to compute a minimum cost spanning tree |
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[103] | 33 | /// |
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[194] | 34 | ///Kruskal's algorithm to compute a minimum cost spanning tree. |
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[103] | 35 | /// |
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| 36 | |
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| 37 | namespace lemon { |
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| 38 | |
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| 39 | namespace _kruskal_bits { |
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| 40 | |
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| 41 | // Kruskal for directed graphs. |
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| 42 | |
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| 43 | template <typename Digraph, typename In, typename Out> |
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| 44 | typename disable_if<lemon::UndirectedTagIndicator<Digraph>, |
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[209] | 45 | typename In::value_type::second_type >::type |
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[103] | 46 | kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) { |
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| 47 | typedef typename In::value_type::second_type Value; |
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| 48 | typedef typename Digraph::template NodeMap<int> IndexMap; |
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| 49 | typedef typename Digraph::Node Node; |
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[209] | 50 | |
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[103] | 51 | IndexMap index(digraph); |
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| 52 | UnionFind<IndexMap> uf(index); |
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| 53 | for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) { |
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| 54 | uf.insert(it); |
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| 55 | } |
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[209] | 56 | |
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[103] | 57 | Value tree_value = 0; |
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| 58 | for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { |
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| 59 | if (uf.join(digraph.target(it->first),digraph.source(it->first))) { |
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| 60 | out.set(it->first, true); |
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| 61 | tree_value += it->second; |
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| 62 | } |
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| 63 | else { |
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| 64 | out.set(it->first, false); |
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| 65 | } |
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| 66 | } |
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| 67 | return tree_value; |
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| 68 | } |
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| 69 | |
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| 70 | // Kruskal for undirected graphs. |
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| 71 | |
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| 72 | template <typename Graph, typename In, typename Out> |
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| 73 | typename enable_if<lemon::UndirectedTagIndicator<Graph>, |
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[209] | 74 | typename In::value_type::second_type >::type |
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[103] | 75 | kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) { |
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| 76 | typedef typename In::value_type::second_type Value; |
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| 77 | typedef typename Graph::template NodeMap<int> IndexMap; |
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| 78 | typedef typename Graph::Node Node; |
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[209] | 79 | |
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[103] | 80 | IndexMap index(graph); |
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| 81 | UnionFind<IndexMap> uf(index); |
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| 82 | for (typename Graph::NodeIt it(graph); it != INVALID; ++it) { |
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| 83 | uf.insert(it); |
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| 84 | } |
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[209] | 85 | |
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[103] | 86 | Value tree_value = 0; |
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| 87 | for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { |
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| 88 | if (uf.join(graph.u(it->first),graph.v(it->first))) { |
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| 89 | out.set(it->first, true); |
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| 90 | tree_value += it->second; |
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| 91 | } |
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| 92 | else { |
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| 93 | out.set(it->first, false); |
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| 94 | } |
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| 95 | } |
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| 96 | return tree_value; |
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| 97 | } |
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| 98 | |
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| 99 | |
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| 100 | template <typename Sequence> |
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| 101 | struct PairComp { |
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| 102 | typedef typename Sequence::value_type Value; |
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| 103 | bool operator()(const Value& left, const Value& right) { |
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[209] | 104 | return left.second < right.second; |
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[103] | 105 | } |
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| 106 | }; |
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| 107 | |
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| 108 | template <typename In, typename Enable = void> |
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| 109 | struct SequenceInputIndicator { |
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| 110 | static const bool value = false; |
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| 111 | }; |
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| 112 | |
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| 113 | template <typename In> |
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[209] | 114 | struct SequenceInputIndicator<In, |
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[103] | 115 | typename exists<typename In::value_type::first_type>::type> { |
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| 116 | static const bool value = true; |
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| 117 | }; |
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| 118 | |
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| 119 | template <typename In, typename Enable = void> |
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| 120 | struct MapInputIndicator { |
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| 121 | static const bool value = false; |
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| 122 | }; |
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| 123 | |
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| 124 | template <typename In> |
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[209] | 125 | struct MapInputIndicator<In, |
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[103] | 126 | typename exists<typename In::Value>::type> { |
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| 127 | static const bool value = true; |
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| 128 | }; |
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| 129 | |
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| 130 | template <typename In, typename Enable = void> |
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| 131 | struct SequenceOutputIndicator { |
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| 132 | static const bool value = false; |
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| 133 | }; |
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[209] | 134 | |
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[103] | 135 | template <typename Out> |
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[209] | 136 | struct SequenceOutputIndicator<Out, |
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[103] | 137 | typename exists<typename Out::value_type>::type> { |
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| 138 | static const bool value = true; |
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| 139 | }; |
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| 140 | |
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| 141 | template <typename Out, typename Enable = void> |
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| 142 | struct MapOutputIndicator { |
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| 143 | static const bool value = false; |
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| 144 | }; |
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| 145 | |
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| 146 | template <typename Out> |
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[209] | 147 | struct MapOutputIndicator<Out, |
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[103] | 148 | typename exists<typename Out::Value>::type> { |
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| 149 | static const bool value = true; |
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| 150 | }; |
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| 151 | |
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| 152 | template <typename In, typename InEnable = void> |
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| 153 | struct KruskalValueSelector {}; |
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| 154 | |
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| 155 | template <typename In> |
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| 156 | struct KruskalValueSelector<In, |
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[209] | 157 | typename enable_if<SequenceInputIndicator<In>, void>::type> |
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[103] | 158 | { |
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| 159 | typedef typename In::value_type::second_type Value; |
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[209] | 160 | }; |
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[103] | 161 | |
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| 162 | template <typename In> |
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| 163 | struct KruskalValueSelector<In, |
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[209] | 164 | typename enable_if<MapInputIndicator<In>, void>::type> |
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[103] | 165 | { |
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| 166 | typedef typename In::Value Value; |
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[209] | 167 | }; |
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| 168 | |
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[103] | 169 | template <typename Graph, typename In, typename Out, |
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| 170 | typename InEnable = void> |
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| 171 | struct KruskalInputSelector {}; |
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| 172 | |
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| 173 | template <typename Graph, typename In, typename Out, |
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| 174 | typename InEnable = void> |
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| 175 | struct KruskalOutputSelector {}; |
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[209] | 176 | |
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[103] | 177 | template <typename Graph, typename In, typename Out> |
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| 178 | struct KruskalInputSelector<Graph, In, Out, |
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[209] | 179 | typename enable_if<SequenceInputIndicator<In>, void>::type > |
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[103] | 180 | { |
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| 181 | typedef typename In::value_type::second_type Value; |
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| 182 | |
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| 183 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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| 184 | return KruskalOutputSelector<Graph, In, Out>:: |
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| 185 | kruskal(graph, in, out); |
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| 186 | } |
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| 187 | |
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| 188 | }; |
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| 189 | |
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| 190 | template <typename Graph, typename In, typename Out> |
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| 191 | struct KruskalInputSelector<Graph, In, Out, |
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[209] | 192 | typename enable_if<MapInputIndicator<In>, void>::type > |
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[103] | 193 | { |
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| 194 | typedef typename In::Value Value; |
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| 195 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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| 196 | typedef typename In::Key MapArc; |
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| 197 | typedef typename In::Value Value; |
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| 198 | typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt; |
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| 199 | typedef std::vector<std::pair<MapArc, Value> > Sequence; |
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| 200 | Sequence seq; |
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[209] | 201 | |
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[103] | 202 | for (MapArcIt it(graph); it != INVALID; ++it) { |
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| 203 | seq.push_back(std::make_pair(it, in[it])); |
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| 204 | } |
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| 205 | |
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| 206 | std::sort(seq.begin(), seq.end(), PairComp<Sequence>()); |
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| 207 | return KruskalOutputSelector<Graph, Sequence, Out>:: |
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| 208 | kruskal(graph, seq, out); |
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| 209 | } |
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| 210 | }; |
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| 211 | |
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[136] | 212 | template <typename T> |
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| 213 | struct RemoveConst { |
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| 214 | typedef T type; |
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| 215 | }; |
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| 216 | |
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| 217 | template <typename T> |
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| 218 | struct RemoveConst<const T> { |
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| 219 | typedef T type; |
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| 220 | }; |
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| 221 | |
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[103] | 222 | template <typename Graph, typename In, typename Out> |
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| 223 | struct KruskalOutputSelector<Graph, In, Out, |
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[209] | 224 | typename enable_if<SequenceOutputIndicator<Out>, void>::type > |
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[103] | 225 | { |
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| 226 | typedef typename In::value_type::second_type Value; |
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| 227 | |
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| 228 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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[167] | 229 | typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map; |
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[103] | 230 | Map map(out); |
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| 231 | return _kruskal_bits::kruskal(graph, in, map); |
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| 232 | } |
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| 233 | |
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| 234 | }; |
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| 235 | |
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| 236 | template <typename Graph, typename In, typename Out> |
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| 237 | struct KruskalOutputSelector<Graph, In, Out, |
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[209] | 238 | typename enable_if<MapOutputIndicator<Out>, void>::type > |
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[103] | 239 | { |
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| 240 | typedef typename In::value_type::second_type Value; |
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| 241 | |
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| 242 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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| 243 | return _kruskal_bits::kruskal(graph, in, out); |
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| 244 | } |
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| 245 | }; |
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| 246 | |
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| 247 | } |
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| 248 | |
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| 249 | /// \ingroup spantree |
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| 250 | /// |
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[194] | 251 | /// \brief Kruskal algorithm to find a minimum cost spanning tree of |
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| 252 | /// a graph. |
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[103] | 253 | /// |
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[209] | 254 | /// This function runs Kruskal's algorithm to find a minimum cost |
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[194] | 255 | /// spanning tree. |
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[103] | 256 | /// Due to some C++ hacking, it accepts various input and output types. |
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| 257 | /// |
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| 258 | /// \param g The graph the algorithm runs on. |
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[209] | 259 | /// It can be either \ref concepts::Digraph "directed" or |
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[103] | 260 | /// \ref concepts::Graph "undirected". |
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[209] | 261 | /// If the graph is directed, the algorithm consider it to be |
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[103] | 262 | /// undirected by disregarding the direction of the arcs. |
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| 263 | /// |
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[209] | 264 | /// \param in This object is used to describe the arc/edge costs. |
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[194] | 265 | /// It can be one of the following choices. |
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[103] | 266 | /// - An STL compatible 'Forward Container' with |
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[194] | 267 | /// <tt>std::pair<GR::Arc,X></tt> or |
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| 268 | /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where |
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| 269 | /// \c X is the type of the costs. The pairs indicates the arcs/edges |
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[103] | 270 | /// along with the assigned cost. <em>They must be in a |
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| 271 | /// cost-ascending order.</em> |
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[209] | 272 | /// - Any readable arc/edge map. The values of the map indicate the |
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[194] | 273 | /// arc/edge costs. |
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[103] | 274 | /// |
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[194] | 275 | /// \retval out Here we also have a choice. |
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| 276 | /// - It can be a writable \c bool arc/edge map. After running the |
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| 277 | /// algorithm it will contain the found minimum cost spanning |
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| 278 | /// tree: the value of an arc/edge will be set to \c true if it belongs |
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[103] | 279 | /// to the tree, otherwise it will be set to \c false. The value of |
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[194] | 280 | /// each arc/edge will be set exactly once. |
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[103] | 281 | /// - It can also be an iteraror of an STL Container with |
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[194] | 282 | /// <tt>GR::Arc</tt> or <tt>GR::Edge</tt> as its |
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[103] | 283 | /// <tt>value_type</tt>. The algorithm copies the elements of the |
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| 284 | /// found tree into this sequence. For example, if we know that the |
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| 285 | /// spanning tree of the graph \c g has say 53 arcs, then we can |
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| 286 | /// put its arcs into an STL vector \c tree with a code like this. |
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| 287 | ///\code |
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| 288 | /// std::vector<Arc> tree(53); |
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| 289 | /// kruskal(g,cost,tree.begin()); |
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| 290 | ///\endcode |
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| 291 | /// Or if we don't know in advance the size of the tree, we can |
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[209] | 292 | /// write this. |
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[194] | 293 | ///\code |
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| 294 | /// std::vector<Arc> tree; |
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[209] | 295 | /// kruskal(g,cost,std::back_inserter(tree)); |
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[103] | 296 | ///\endcode |
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| 297 | /// |
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[194] | 298 | /// \return The total cost of the found spanning tree. |
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[103] | 299 | /// |
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[220] | 300 | /// \note If the input graph is not (weakly) connected, a spanning |
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[216] | 301 | /// forest is calculated instead of a spanning tree. |
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[103] | 302 | |
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| 303 | #ifdef DOXYGEN |
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| 304 | template <class Graph, class In, class Out> |
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| 305 | Value kruskal(GR const& g, const In& in, Out& out) |
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[209] | 306 | #else |
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[103] | 307 | template <class Graph, class In, class Out> |
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[209] | 308 | inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
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| 309 | kruskal(const Graph& graph, const In& in, Out& out) |
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[103] | 310 | #endif |
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| 311 | { |
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| 312 | return _kruskal_bits::KruskalInputSelector<Graph, In, Out>:: |
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| 313 | kruskal(graph, in, out); |
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| 314 | } |
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| 315 | |
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[209] | 316 | |
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| 317 | |
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[103] | 318 | |
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| 319 | template <class Graph, class In, class Out> |
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| 320 | inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
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| 321 | kruskal(const Graph& graph, const In& in, const Out& out) |
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| 322 | { |
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| 323 | return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>:: |
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| 324 | kruskal(graph, in, out); |
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[209] | 325 | } |
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[103] | 326 | |
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| 327 | } //namespace lemon |
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| 328 | |
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| 329 | #endif //LEMON_KRUSKAL_H |
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