[906] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[1956] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[906] | 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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[921] | 19 | #ifndef LEMON_KRUSKAL_H |
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| 20 | #define LEMON_KRUSKAL_H |
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[810] | 21 | |
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| 22 | #include <algorithm> |
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[1942] | 23 | #include <vector> |
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[921] | 24 | #include <lemon/unionfind.h> |
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[1993] | 25 | #include <lemon/bits/utility.h> |
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| 26 | #include <lemon/bits/traits.h> |
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[810] | 27 | |
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| 28 | ///\ingroup spantree |
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| 29 | ///\file |
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| 30 | ///\brief Kruskal's algorithm to compute a minimum cost tree |
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| 31 | /// |
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| 32 | ///Kruskal's algorithm to compute a minimum cost tree. |
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[1557] | 33 | /// |
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[810] | 34 | |
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[921] | 35 | namespace lemon { |
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[810] | 36 | |
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| 37 | /// \addtogroup spantree |
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| 38 | /// @{ |
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| 39 | |
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| 40 | /// Kruskal's algorithm to find a minimum cost tree of a graph. |
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| 41 | |
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| 42 | /// This function runs Kruskal's algorithm to find a minimum cost tree. |
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[1557] | 43 | /// Due to hard C++ hacking, it accepts various input and output types. |
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| 44 | /// |
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[1555] | 45 | /// \param g The graph the algorithm runs on. |
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[2260] | 46 | /// It can be either \ref concepts::Graph "directed" or |
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| 47 | /// \ref concepts::UGraph "undirected". |
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[1555] | 48 | /// If the graph is directed, the algorithm consider it to be |
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| 49 | /// undirected by disregarding the direction of the edges. |
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[810] | 50 | /// |
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[1557] | 51 | /// \param in This object is used to describe the edge costs. It can be one |
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| 52 | /// of the following choices. |
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| 53 | /// - An STL compatible 'Forward Container' |
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[824] | 54 | /// with <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, |
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[1557] | 55 | /// where \c X is the type of the costs. The pairs indicates the edges along |
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| 56 | /// with the assigned cost. <em>They must be in a |
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| 57 | /// cost-ascending order.</em> |
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| 58 | /// - Any readable Edge map. The values of the map indicate the edge costs. |
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[810] | 59 | /// |
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[1557] | 60 | /// \retval out Here we also have a choise. |
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[2259] | 61 | /// - It can be a writable \c bool edge map. |
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[810] | 62 | /// After running the algorithm |
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| 63 | /// this will contain the found minimum cost spanning tree: the value of an |
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| 64 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
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| 65 | /// be set to \c false. The value of each edge will be set exactly once. |
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[1557] | 66 | /// - It can also be an iteraror of an STL Container with |
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| 67 | /// <tt>GR::Edge</tt> as its <tt>value_type</tt>. |
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| 68 | /// The algorithm copies the elements of the found tree into this sequence. |
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| 69 | /// For example, if we know that the spanning tree of the graph \c g has |
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[1603] | 70 | /// say 53 edges, then |
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[2259] | 71 | /// we can put its edges into an STL vector \c tree with a code like this. |
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[1946] | 72 | ///\code |
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[1557] | 73 | /// std::vector<Edge> tree(53); |
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| 74 | /// kruskal(g,cost,tree.begin()); |
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[1946] | 75 | ///\endcode |
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[1557] | 76 | /// Or if we don't know in advance the size of the tree, we can write this. |
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[1946] | 77 | ///\code |
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[1557] | 78 | /// std::vector<Edge> tree; |
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| 79 | /// kruskal(g,cost,std::back_inserter(tree)); |
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[1946] | 80 | ///\endcode |
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[810] | 81 | /// |
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| 82 | /// \return The cost of the found tree. |
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[1449] | 83 | /// |
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[2259] | 84 | /// \warning If kruskal runs on an |
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[2260] | 85 | /// \ref lemon::concepts::UGraph "undirected graph", be sure that the |
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[1603] | 86 | /// map storing the tree is also undirected |
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[1909] | 87 | /// (e.g. ListUGraph::UEdgeMap<bool>, otherwise the values of the |
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[1603] | 88 | /// half of the edges will not be set. |
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| 89 | /// |
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[810] | 90 | |
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[1557] | 91 | #ifdef DOXYGEN |
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[824] | 92 | template <class GR, class IN, class OUT> |
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[2354] | 93 | CostType |
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[1547] | 94 | kruskal(GR const& g, IN const& in, |
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[1557] | 95 | OUT& out) |
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| 96 | #else |
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| 97 | template <class GR, class IN, class OUT> |
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| 98 | typename IN::value_type::second_type |
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| 99 | kruskal(GR const& g, IN const& in, |
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| 100 | OUT& out, |
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| 101 | // typename IN::value_type::first_type = typename GR::Edge() |
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| 102 | // ,typename OUT::Key = OUT::Key() |
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| 103 | // //,typename OUT::Key = typename GR::Edge() |
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| 104 | const typename IN::value_type::first_type * = |
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| 105 | (const typename IN::value_type::first_type *)(0), |
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| 106 | const typename OUT::Key * = (const typename OUT::Key *)(0) |
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| 107 | ) |
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| 108 | #endif |
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[810] | 109 | { |
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[824] | 110 | typedef typename IN::value_type::second_type EdgeCost; |
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| 111 | typedef typename GR::template NodeMap<int> NodeIntMap; |
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| 112 | typedef typename GR::Node Node; |
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[810] | 113 | |
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[2205] | 114 | NodeIntMap comp(g); |
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[2308] | 115 | UnionFind<NodeIntMap> uf(comp); |
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[2205] | 116 | for (typename GR::NodeIt it(g); it != INVALID; ++it) { |
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| 117 | uf.insert(it); |
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| 118 | } |
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[810] | 119 | |
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| 120 | EdgeCost tot_cost = 0; |
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[824] | 121 | for (typename IN::const_iterator p = in.begin(); |
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[810] | 122 | p!=in.end(); ++p ) { |
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[1547] | 123 | if ( uf.join(g.target((*p).first), |
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| 124 | g.source((*p).first)) ) { |
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[810] | 125 | out.set((*p).first, true); |
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| 126 | tot_cost += (*p).second; |
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| 127 | } |
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| 128 | else { |
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| 129 | out.set((*p).first, false); |
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| 130 | } |
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| 131 | } |
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| 132 | return tot_cost; |
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| 133 | } |
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| 134 | |
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[1557] | 135 | |
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| 136 | /// @} |
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| 137 | |
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| 138 | |
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[810] | 139 | /* A work-around for running Kruskal with const-reference bool maps... */ |
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| 140 | |
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[885] | 141 | /// Helper class for calling kruskal with "constant" output map. |
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| 142 | |
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| 143 | /// Helper class for calling kruskal with output maps constructed |
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| 144 | /// on-the-fly. |
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[810] | 145 | /// |
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[885] | 146 | /// A typical examle is the following call: |
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[1547] | 147 | /// <tt>kruskal(g, some_input, makeSequenceOutput(iterator))</tt>. |
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[885] | 148 | /// Here, the third argument is a temporary object (which wraps around an |
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| 149 | /// iterator with a writable bool map interface), and thus by rules of C++ |
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| 150 | /// is a \c const object. To enable call like this exist this class and |
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| 151 | /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt> |
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| 152 | /// third argument. |
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[824] | 153 | template<class Map> |
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[810] | 154 | class NonConstMapWr { |
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| 155 | const Map &m; |
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| 156 | public: |
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[1557] | 157 | typedef typename Map::Key Key; |
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[987] | 158 | typedef typename Map::Value Value; |
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[810] | 159 | |
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| 160 | NonConstMapWr(const Map &_m) : m(_m) {} |
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| 161 | |
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[987] | 162 | template<class Key> |
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| 163 | void set(Key const& k, Value const &v) const { m.set(k,v); } |
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[810] | 164 | }; |
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| 165 | |
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[824] | 166 | template <class GR, class IN, class OUT> |
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[810] | 167 | inline |
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[885] | 168 | typename IN::value_type::second_type |
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[1557] | 169 | kruskal(GR const& g, IN const& edges, OUT const& out_map, |
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| 170 | // typename IN::value_type::first_type = typename GR::Edge(), |
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| 171 | // typename OUT::Key = GR::Edge() |
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| 172 | const typename IN::value_type::first_type * = |
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| 173 | (const typename IN::value_type::first_type *)(0), |
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| 174 | const typename OUT::Key * = (const typename OUT::Key *)(0) |
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| 175 | ) |
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[810] | 176 | { |
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[824] | 177 | NonConstMapWr<OUT> map_wr(out_map); |
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[1547] | 178 | return kruskal(g, edges, map_wr); |
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[810] | 179 | } |
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| 180 | |
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| 181 | /* ** ** Input-objects ** ** */ |
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| 182 | |
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[1274] | 183 | /// Kruskal's input source. |
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[1557] | 184 | |
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[1274] | 185 | /// Kruskal's input source. |
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[810] | 186 | /// |
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[1570] | 187 | /// In most cases you possibly want to use the \ref kruskal() instead. |
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[810] | 188 | /// |
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| 189 | /// \sa makeKruskalMapInput() |
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| 190 | /// |
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[824] | 191 | ///\param GR The type of the graph the algorithm runs on. |
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[810] | 192 | ///\param Map An edge map containing the cost of the edges. |
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| 193 | ///\par |
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| 194 | ///The cost type can be any type satisfying |
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| 195 | ///the STL 'LessThan comparable' |
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| 196 | ///concept if it also has an operator+() implemented. (It is necessary for |
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| 197 | ///computing the total cost of the tree). |
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| 198 | /// |
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[824] | 199 | template<class GR, class Map> |
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[810] | 200 | class KruskalMapInput |
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[824] | 201 | : public std::vector< std::pair<typename GR::Edge, |
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[987] | 202 | typename Map::Value> > { |
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[810] | 203 | |
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| 204 | public: |
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[824] | 205 | typedef std::vector< std::pair<typename GR::Edge, |
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[987] | 206 | typename Map::Value> > Parent; |
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[810] | 207 | typedef typename Parent::value_type value_type; |
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| 208 | |
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| 209 | private: |
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| 210 | class comparePair { |
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| 211 | public: |
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| 212 | bool operator()(const value_type& a, |
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| 213 | const value_type& b) { |
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| 214 | return a.second < b.second; |
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| 215 | } |
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| 216 | }; |
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| 217 | |
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[1449] | 218 | template<class _GR> |
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[1979] | 219 | typename enable_if<UndirectedTagIndicator<_GR>,void>::type |
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[1547] | 220 | fillWithEdges(const _GR& g, const Map& m,dummy<0> = 0) |
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[1449] | 221 | { |
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[1909] | 222 | for(typename GR::UEdgeIt e(g);e!=INVALID;++e) |
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[1679] | 223 | push_back(value_type(g.direct(e, true), m[e])); |
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[1449] | 224 | } |
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| 225 | |
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| 226 | template<class _GR> |
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[1979] | 227 | typename disable_if<UndirectedTagIndicator<_GR>,void>::type |
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[1547] | 228 | fillWithEdges(const _GR& g, const Map& m,dummy<1> = 1) |
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[1449] | 229 | { |
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[1547] | 230 | for(typename GR::EdgeIt e(g);e!=INVALID;++e) |
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[1449] | 231 | push_back(value_type(e, m[e])); |
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| 232 | } |
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| 233 | |
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| 234 | |
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[810] | 235 | public: |
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| 236 | |
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| 237 | void sort() { |
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| 238 | std::sort(this->begin(), this->end(), comparePair()); |
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| 239 | } |
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| 240 | |
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[1547] | 241 | KruskalMapInput(GR const& g, Map const& m) { |
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| 242 | fillWithEdges(g,m); |
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[810] | 243 | sort(); |
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| 244 | } |
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| 245 | }; |
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| 246 | |
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| 247 | /// Creates a KruskalMapInput object for \ref kruskal() |
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| 248 | |
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[1274] | 249 | /// It makes easier to use |
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[810] | 250 | /// \ref KruskalMapInput by making it unnecessary |
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| 251 | /// to explicitly give the type of the parameters. |
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| 252 | /// |
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| 253 | /// In most cases you possibly |
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[1570] | 254 | /// want to use \ref kruskal() instead. |
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[810] | 255 | /// |
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[1547] | 256 | ///\param g The type of the graph the algorithm runs on. |
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[810] | 257 | ///\param m An edge map containing the cost of the edges. |
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| 258 | ///\par |
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| 259 | ///The cost type can be any type satisfying the |
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| 260 | ///STL 'LessThan Comparable' |
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| 261 | ///concept if it also has an operator+() implemented. (It is necessary for |
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| 262 | ///computing the total cost of the tree). |
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| 263 | /// |
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| 264 | ///\return An appropriate input source for \ref kruskal(). |
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| 265 | /// |
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[824] | 266 | template<class GR, class Map> |
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[810] | 267 | inline |
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[1547] | 268 | KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &g,const Map &m) |
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[810] | 269 | { |
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[1547] | 270 | return KruskalMapInput<GR,Map>(g,m); |
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[810] | 271 | } |
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| 272 | |
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| 273 | |
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[885] | 274 | |
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| 275 | /* ** ** Output-objects: simple writable bool maps ** ** */ |
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[810] | 276 | |
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[885] | 277 | |
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| 278 | |
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[810] | 279 | /// A writable bool-map that makes a sequence of "true" keys |
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| 280 | |
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| 281 | /// A writable bool-map that creates a sequence out of keys that receives |
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| 282 | /// the value "true". |
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[885] | 283 | /// |
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| 284 | /// \sa makeKruskalSequenceOutput() |
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| 285 | /// |
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| 286 | /// Very often, when looking for a min cost spanning tree, we want as |
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| 287 | /// output a container containing the edges of the found tree. For this |
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| 288 | /// purpose exist this class that wraps around an STL iterator with a |
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| 289 | /// writable bool map interface. When a key gets value "true" this key |
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| 290 | /// is added to sequence pointed by the iterator. |
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| 291 | /// |
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| 292 | /// A typical usage: |
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[1946] | 293 | ///\code |
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[885] | 294 | /// std::vector<Graph::Edge> v; |
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| 295 | /// kruskal(g, input, makeKruskalSequenceOutput(back_inserter(v))); |
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[1946] | 296 | ///\endcode |
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[885] | 297 | /// |
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| 298 | /// For the most common case, when the input is given by a simple edge |
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| 299 | /// map and the output is a sequence of the tree edges, a special |
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| 300 | /// wrapper function exists: \ref kruskalEdgeMap_IteratorOut(). |
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| 301 | /// |
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[987] | 302 | /// \warning Not a regular property map, as it doesn't know its Key |
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[885] | 303 | |
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[824] | 304 | template<class Iterator> |
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[885] | 305 | class KruskalSequenceOutput { |
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[810] | 306 | mutable Iterator it; |
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| 307 | |
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| 308 | public: |
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[1942] | 309 | typedef typename std::iterator_traits<Iterator>::value_type Key; |
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[987] | 310 | typedef bool Value; |
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[810] | 311 | |
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[885] | 312 | KruskalSequenceOutput(Iterator const &_it) : it(_it) {} |
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[810] | 313 | |
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[987] | 314 | template<typename Key> |
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| 315 | void set(Key const& k, bool v) const { if(v) {*it=k; ++it;} } |
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[810] | 316 | }; |
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| 317 | |
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[824] | 318 | template<class Iterator> |
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[810] | 319 | inline |
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[885] | 320 | KruskalSequenceOutput<Iterator> |
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| 321 | makeKruskalSequenceOutput(Iterator it) { |
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| 322 | return KruskalSequenceOutput<Iterator>(it); |
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[810] | 323 | } |
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| 324 | |
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[885] | 325 | |
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| 326 | |
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[810] | 327 | /* ** ** Wrapper funtions ** ** */ |
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| 328 | |
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[1557] | 329 | // \brief Wrapper function to kruskal(). |
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| 330 | // Input is from an edge map, output is a plain bool map. |
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| 331 | // |
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| 332 | // Wrapper function to kruskal(). |
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| 333 | // Input is from an edge map, output is a plain bool map. |
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| 334 | // |
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| 335 | // \param g The type of the graph the algorithm runs on. |
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| 336 | // \param in An edge map containing the cost of the edges. |
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| 337 | // \par |
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| 338 | // The cost type can be any type satisfying the |
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| 339 | // STL 'LessThan Comparable' |
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| 340 | // concept if it also has an operator+() implemented. (It is necessary for |
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| 341 | // computing the total cost of the tree). |
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| 342 | // |
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| 343 | // \retval out This must be a writable \c bool edge map. |
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| 344 | // After running the algorithm |
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| 345 | // this will contain the found minimum cost spanning tree: the value of an |
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| 346 | // edge will be set to \c true if it belongs to the tree, otherwise it will |
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| 347 | // be set to \c false. The value of each edge will be set exactly once. |
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| 348 | // |
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| 349 | // \return The cost of the found tree. |
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[810] | 350 | |
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[824] | 351 | template <class GR, class IN, class RET> |
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[810] | 352 | inline |
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[987] | 353 | typename IN::Value |
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[1557] | 354 | kruskal(GR const& g, |
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| 355 | IN const& in, |
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| 356 | RET &out, |
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| 357 | // typename IN::Key = typename GR::Edge(), |
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| 358 | //typename IN::Key = typename IN::Key (), |
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| 359 | // typename RET::Key = typename GR::Edge() |
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| 360 | const typename IN::Key * = (const typename IN::Key *)(0), |
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| 361 | const typename RET::Key * = (const typename RET::Key *)(0) |
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| 362 | ) |
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| 363 | { |
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[1547] | 364 | return kruskal(g, |
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| 365 | KruskalMapInput<GR,IN>(g,in), |
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[810] | 366 | out); |
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| 367 | } |
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| 368 | |
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[1557] | 369 | // \brief Wrapper function to kruskal(). |
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| 370 | // Input is from an edge map, output is an STL Sequence. |
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| 371 | // |
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| 372 | // Wrapper function to kruskal(). |
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| 373 | // Input is from an edge map, output is an STL Sequence. |
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| 374 | // |
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| 375 | // \param g The type of the graph the algorithm runs on. |
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| 376 | // \param in An edge map containing the cost of the edges. |
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| 377 | // \par |
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| 378 | // The cost type can be any type satisfying the |
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| 379 | // STL 'LessThan Comparable' |
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| 380 | // concept if it also has an operator+() implemented. (It is necessary for |
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| 381 | // computing the total cost of the tree). |
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| 382 | // |
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| 383 | // \retval out This must be an iteraror of an STL Container with |
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| 384 | // <tt>GR::Edge</tt> as its <tt>value_type</tt>. |
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| 385 | // The algorithm copies the elements of the found tree into this sequence. |
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| 386 | // For example, if we know that the spanning tree of the graph \c g has |
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[1603] | 387 | // say 53 edges, then |
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[2259] | 388 | // we can put its edges into an STL vector \c tree with a code like this. |
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[1946] | 389 | //\code |
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[1557] | 390 | // std::vector<Edge> tree(53); |
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[1570] | 391 | // kruskal(g,cost,tree.begin()); |
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[1946] | 392 | //\endcode |
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[1557] | 393 | // Or if we don't know in advance the size of the tree, we can write this. |
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[1946] | 394 | //\code |
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[1557] | 395 | // std::vector<Edge> tree; |
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[1570] | 396 | // kruskal(g,cost,std::back_inserter(tree)); |
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[1946] | 397 | //\endcode |
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[1557] | 398 | // |
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| 399 | // \return The cost of the found tree. |
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| 400 | // |
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| 401 | // \bug its name does not follow the coding style. |
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[885] | 402 | |
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[824] | 403 | template <class GR, class IN, class RET> |
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[810] | 404 | inline |
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[987] | 405 | typename IN::Value |
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[1557] | 406 | kruskal(const GR& g, |
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| 407 | const IN& in, |
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| 408 | RET out, |
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| 409 | const typename RET::value_type * = |
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| 410 | (const typename RET::value_type *)(0) |
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| 411 | ) |
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[810] | 412 | { |
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[885] | 413 | KruskalSequenceOutput<RET> _out(out); |
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[1547] | 414 | return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out); |
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[810] | 415 | } |
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[1557] | 416 | |
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[1942] | 417 | template <class GR, class IN, class RET> |
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| 418 | inline |
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| 419 | typename IN::Value |
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| 420 | kruskal(const GR& g, |
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| 421 | const IN& in, |
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| 422 | RET *out |
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| 423 | ) |
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| 424 | { |
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| 425 | KruskalSequenceOutput<RET*> _out(out); |
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| 426 | return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out); |
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| 427 | } |
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| 428 | |
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[810] | 429 | /// @} |
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| 430 | |
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[921] | 431 | } //namespace lemon |
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[810] | 432 | |
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[921] | 433 | #endif //LEMON_KRUSKAL_H |
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