[906] | 1 | /* -*- C++ -*- |
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[921] | 2 | * src/lemon/kruskal.h - Part of LEMON, a generic C++ optimization library |
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[906] | 3 | * |
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| 4 | * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 5 | * (Egervary Combinatorial Optimization Research Group, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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[921] | 17 | #ifndef LEMON_KRUSKAL_H |
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| 18 | #define LEMON_KRUSKAL_H |
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[810] | 19 | |
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| 20 | #include <algorithm> |
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[921] | 21 | #include <lemon/unionfind.h> |
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[810] | 22 | |
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| 23 | /** |
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| 24 | @defgroup spantree Minimum Cost Spanning Tree Algorithms |
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| 25 | @ingroup galgs |
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| 26 | \brief This group containes the algorithms for finding a minimum cost spanning |
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| 27 | tree in a graph |
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| 28 | |
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| 29 | This group containes the algorithms for finding a minimum cost spanning |
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| 30 | tree in a graph |
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| 31 | */ |
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| 32 | |
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| 33 | ///\ingroup spantree |
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| 34 | ///\file |
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| 35 | ///\brief Kruskal's algorithm to compute a minimum cost tree |
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| 36 | /// |
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| 37 | ///Kruskal's algorithm to compute a minimum cost tree. |
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| 38 | |
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[921] | 39 | namespace lemon { |
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[810] | 40 | |
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| 41 | /// \addtogroup spantree |
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| 42 | /// @{ |
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| 43 | |
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| 44 | /// Kruskal's algorithm to find a minimum cost tree of a graph. |
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| 45 | |
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| 46 | /// This function runs Kruskal's algorithm to find a minimum cost tree. |
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| 47 | /// \param G The graph the algorithm runs on. The algorithm considers the |
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| 48 | /// graph to be undirected, the direction of the edges are not used. |
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| 49 | /// |
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| 50 | /// \param in This object is used to describe the edge costs. It must |
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| 51 | /// be an STL compatible 'Forward Container' |
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[824] | 52 | /// with <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, |
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[810] | 53 | /// where X is the type of the costs. It must contain every edge in |
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| 54 | /// cost-ascending order. |
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| 55 | ///\par |
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| 56 | /// For the sake of simplicity, there is a helper class KruskalMapInput, |
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| 57 | /// which converts a |
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| 58 | /// simple edge map to an input of this form. Alternatively, you can use |
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| 59 | /// the function \ref kruskalEdgeMap to compute the minimum cost tree if |
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| 60 | /// the edge costs are given by an edge map. |
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| 61 | /// |
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| 62 | /// \retval out This must be a writable \c bool edge map. |
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| 63 | /// After running the algorithm |
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| 64 | /// this will contain the found minimum cost spanning tree: the value of an |
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| 65 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
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| 66 | /// be set to \c false. The value of each edge will be set exactly once. |
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| 67 | /// |
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| 68 | /// \return The cost of the found tree. |
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| 69 | |
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[824] | 70 | template <class GR, class IN, class OUT> |
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| 71 | typename IN::value_type::second_type |
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| 72 | kruskal(GR const& G, IN const& in, |
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| 73 | OUT& out) |
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[810] | 74 | { |
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[824] | 75 | typedef typename IN::value_type::second_type EdgeCost; |
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| 76 | typedef typename GR::template NodeMap<int> NodeIntMap; |
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| 77 | typedef typename GR::Node Node; |
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[810] | 78 | |
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| 79 | NodeIntMap comp(G, -1); |
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| 80 | UnionFind<Node,NodeIntMap> uf(comp); |
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| 81 | |
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| 82 | EdgeCost tot_cost = 0; |
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[824] | 83 | for (typename IN::const_iterator p = in.begin(); |
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[810] | 84 | p!=in.end(); ++p ) { |
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| 85 | if ( uf.join(G.head((*p).first), |
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| 86 | G.tail((*p).first)) ) { |
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| 87 | out.set((*p).first, true); |
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| 88 | tot_cost += (*p).second; |
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| 89 | } |
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| 90 | else { |
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| 91 | out.set((*p).first, false); |
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| 92 | } |
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| 93 | } |
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| 94 | return tot_cost; |
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| 95 | } |
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| 96 | |
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| 97 | /* A work-around for running Kruskal with const-reference bool maps... */ |
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| 98 | |
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[885] | 99 | /// Helper class for calling kruskal with "constant" output map. |
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| 100 | |
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| 101 | /// Helper class for calling kruskal with output maps constructed |
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| 102 | /// on-the-fly. |
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[810] | 103 | /// |
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[885] | 104 | /// A typical examle is the following call: |
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| 105 | /// <tt>kruskal(G, some_input, makeSequenceOutput(iterator))</tt>. |
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| 106 | /// Here, the third argument is a temporary object (which wraps around an |
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| 107 | /// iterator with a writable bool map interface), and thus by rules of C++ |
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| 108 | /// is a \c const object. To enable call like this exist this class and |
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| 109 | /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt> |
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| 110 | /// third argument. |
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[824] | 111 | template<class Map> |
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[810] | 112 | class NonConstMapWr { |
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| 113 | const Map &m; |
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| 114 | public: |
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| 115 | typedef typename Map::ValueType ValueType; |
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| 116 | |
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| 117 | NonConstMapWr(const Map &_m) : m(_m) {} |
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| 118 | |
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[824] | 119 | template<class KeyType> |
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[810] | 120 | void set(KeyType const& k, ValueType const &v) const { m.set(k,v); } |
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| 121 | }; |
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| 122 | |
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[824] | 123 | template <class GR, class IN, class OUT> |
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[810] | 124 | inline |
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[885] | 125 | typename IN::value_type::second_type |
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| 126 | kruskal(GR const& G, IN const& edges, OUT const& out_map) |
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[810] | 127 | { |
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[824] | 128 | NonConstMapWr<OUT> map_wr(out_map); |
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[810] | 129 | return kruskal(G, edges, map_wr); |
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| 130 | } |
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| 131 | |
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| 132 | /* ** ** Input-objects ** ** */ |
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| 133 | |
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| 134 | /// Kruskal input source. |
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| 135 | |
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| 136 | /// Kruskal input source. |
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| 137 | /// |
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| 138 | /// In most cases you possibly want to use the \ref kruskalEdgeMap() instead. |
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| 139 | /// |
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| 140 | /// \sa makeKruskalMapInput() |
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| 141 | /// |
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[824] | 142 | ///\param GR The type of the graph the algorithm runs on. |
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[810] | 143 | ///\param Map An edge map containing the cost of the edges. |
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| 144 | ///\par |
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| 145 | ///The cost type can be any type satisfying |
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| 146 | ///the STL 'LessThan comparable' |
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| 147 | ///concept if it also has an operator+() implemented. (It is necessary for |
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| 148 | ///computing the total cost of the tree). |
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| 149 | /// |
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[824] | 150 | template<class GR, class Map> |
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[810] | 151 | class KruskalMapInput |
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[824] | 152 | : public std::vector< std::pair<typename GR::Edge, |
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[810] | 153 | typename Map::ValueType> > { |
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| 154 | |
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| 155 | public: |
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[824] | 156 | typedef std::vector< std::pair<typename GR::Edge, |
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[810] | 157 | typename Map::ValueType> > Parent; |
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| 158 | typedef typename Parent::value_type value_type; |
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| 159 | |
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| 160 | private: |
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| 161 | class comparePair { |
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| 162 | public: |
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| 163 | bool operator()(const value_type& a, |
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| 164 | const value_type& b) { |
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| 165 | return a.second < b.second; |
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| 166 | } |
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| 167 | }; |
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| 168 | |
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| 169 | public: |
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| 170 | |
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| 171 | void sort() { |
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| 172 | std::sort(this->begin(), this->end(), comparePair()); |
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| 173 | } |
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| 174 | |
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[824] | 175 | KruskalMapInput(GR const& G, Map const& m) { |
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| 176 | typedef typename GR::EdgeIt EdgeIt; |
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[810] | 177 | |
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[885] | 178 | for(EdgeIt e(G);e!=INVALID;++e) push_back(value_type(e, m[e])); |
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[810] | 179 | sort(); |
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| 180 | } |
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| 181 | }; |
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| 182 | |
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| 183 | /// Creates a KruskalMapInput object for \ref kruskal() |
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| 184 | |
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| 185 | /// It makes is easier to use |
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| 186 | /// \ref KruskalMapInput by making it unnecessary |
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| 187 | /// to explicitly give the type of the parameters. |
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| 188 | /// |
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| 189 | /// In most cases you possibly |
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| 190 | /// want to use the function kruskalEdgeMap() instead. |
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| 191 | /// |
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| 192 | ///\param G The type of the graph the algorithm runs on. |
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| 193 | ///\param m An edge map containing the cost of the edges. |
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| 194 | ///\par |
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| 195 | ///The cost type can be any type satisfying the |
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| 196 | ///STL 'LessThan Comparable' |
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| 197 | ///concept if it also has an operator+() implemented. (It is necessary for |
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| 198 | ///computing the total cost of the tree). |
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| 199 | /// |
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| 200 | ///\return An appropriate input source for \ref kruskal(). |
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| 201 | /// |
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[824] | 202 | template<class GR, class Map> |
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[810] | 203 | inline |
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[824] | 204 | KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &G,const Map &m) |
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[810] | 205 | { |
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[824] | 206 | return KruskalMapInput<GR,Map>(G,m); |
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[810] | 207 | } |
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| 208 | |
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| 209 | |
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[885] | 210 | |
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| 211 | /* ** ** Output-objects: simple writable bool maps ** ** */ |
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[810] | 212 | |
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[885] | 213 | |
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| 214 | |
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[810] | 215 | /// A writable bool-map that makes a sequence of "true" keys |
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| 216 | |
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| 217 | /// A writable bool-map that creates a sequence out of keys that receives |
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| 218 | /// the value "true". |
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[885] | 219 | /// |
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| 220 | /// \sa makeKruskalSequenceOutput() |
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| 221 | /// |
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| 222 | /// Very often, when looking for a min cost spanning tree, we want as |
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| 223 | /// output a container containing the edges of the found tree. For this |
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| 224 | /// purpose exist this class that wraps around an STL iterator with a |
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| 225 | /// writable bool map interface. When a key gets value "true" this key |
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| 226 | /// is added to sequence pointed by the iterator. |
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| 227 | /// |
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| 228 | /// A typical usage: |
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| 229 | /// \code |
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| 230 | /// std::vector<Graph::Edge> v; |
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| 231 | /// kruskal(g, input, makeKruskalSequenceOutput(back_inserter(v))); |
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| 232 | /// \endcode |
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| 233 | /// |
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| 234 | /// For the most common case, when the input is given by a simple edge |
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| 235 | /// map and the output is a sequence of the tree edges, a special |
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| 236 | /// wrapper function exists: \ref kruskalEdgeMap_IteratorOut(). |
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| 237 | /// |
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[810] | 238 | /// \warning Not a regular property map, as it doesn't know its KeyType |
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[885] | 239 | |
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[824] | 240 | template<class Iterator> |
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[885] | 241 | class KruskalSequenceOutput { |
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[810] | 242 | mutable Iterator it; |
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| 243 | |
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| 244 | public: |
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| 245 | typedef bool ValueType; |
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| 246 | |
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[885] | 247 | KruskalSequenceOutput(Iterator const &_it) : it(_it) {} |
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[810] | 248 | |
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| 249 | template<typename KeyType> |
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| 250 | void set(KeyType const& k, bool v) const { if(v) {*it=k; ++it;} } |
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| 251 | }; |
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| 252 | |
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[824] | 253 | template<class Iterator> |
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[810] | 254 | inline |
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[885] | 255 | KruskalSequenceOutput<Iterator> |
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| 256 | makeKruskalSequenceOutput(Iterator it) { |
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| 257 | return KruskalSequenceOutput<Iterator>(it); |
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[810] | 258 | } |
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| 259 | |
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[885] | 260 | |
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| 261 | |
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[810] | 262 | /* ** ** Wrapper funtions ** ** */ |
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| 263 | |
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| 264 | |
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[885] | 265 | |
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[810] | 266 | /// \brief Wrapper function to kruskal(). |
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| 267 | /// Input is from an edge map, output is a plain bool map. |
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| 268 | /// |
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| 269 | /// Wrapper function to kruskal(). |
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| 270 | /// Input is from an edge map, output is a plain bool map. |
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| 271 | /// |
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| 272 | ///\param G The type of the graph the algorithm runs on. |
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| 273 | ///\param in An edge map containing the cost of the edges. |
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| 274 | ///\par |
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| 275 | ///The cost type can be any type satisfying the |
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| 276 | ///STL 'LessThan Comparable' |
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| 277 | ///concept if it also has an operator+() implemented. (It is necessary for |
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| 278 | ///computing the total cost of the tree). |
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| 279 | /// |
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| 280 | /// \retval out This must be a writable \c bool edge map. |
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| 281 | /// After running the algorithm |
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| 282 | /// this will contain the found minimum cost spanning tree: the value of an |
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| 283 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
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| 284 | /// be set to \c false. The value of each edge will be set exactly once. |
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| 285 | /// |
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| 286 | /// \return The cost of the found tree. |
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| 287 | |
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[824] | 288 | template <class GR, class IN, class RET> |
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[810] | 289 | inline |
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[824] | 290 | typename IN::ValueType |
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| 291 | kruskalEdgeMap(GR const& G, |
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| 292 | IN const& in, |
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| 293 | RET &out) { |
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[810] | 294 | return kruskal(G, |
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[824] | 295 | KruskalMapInput<GR,IN>(G,in), |
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[810] | 296 | out); |
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| 297 | } |
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| 298 | |
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| 299 | /// \brief Wrapper function to kruskal(). |
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| 300 | /// Input is from an edge map, output is an STL Sequence. |
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| 301 | /// |
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| 302 | /// Wrapper function to kruskal(). |
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| 303 | /// Input is from an edge map, output is an STL Sequence. |
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| 304 | /// |
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| 305 | ///\param G The type of the graph the algorithm runs on. |
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| 306 | ///\param in An edge map containing the cost of the edges. |
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| 307 | ///\par |
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| 308 | ///The cost type can be any type satisfying the |
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| 309 | ///STL 'LessThan Comparable' |
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| 310 | ///concept if it also has an operator+() implemented. (It is necessary for |
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| 311 | ///computing the total cost of the tree). |
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| 312 | /// |
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| 313 | /// \retval out This must be an iteraror of an STL Container with |
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[824] | 314 | /// <tt>GR::Edge</tt> as its <tt>value_type</tt>. |
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[810] | 315 | /// The algorithm copies the elements of the found tree into this sequence. |
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| 316 | /// For example, if we know that the spanning tree of the graph \c G has |
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| 317 | /// say 53 edges then |
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[824] | 318 | /// we can put its edges into a STL vector \c tree with a code like this. |
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[810] | 319 | /// \code |
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| 320 | /// std::vector<Edge> tree(53); |
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| 321 | /// kruskalEdgeMap_IteratorOut(G,cost,tree.begin()); |
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| 322 | /// \endcode |
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| 323 | /// Or if we don't know in advance the size of the tree, we can write this. |
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| 324 | /// \code |
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| 325 | /// std::vector<Edge> tree; |
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| 326 | /// kruskalEdgeMap_IteratorOut(G,cost,std::back_inserter(tree)); |
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| 327 | /// \endcode |
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| 328 | /// |
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| 329 | /// \return The cost of the found tree. |
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| 330 | /// |
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| 331 | /// \bug its name does not follow the coding style. |
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[885] | 332 | |
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[824] | 333 | template <class GR, class IN, class RET> |
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[810] | 334 | inline |
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[824] | 335 | typename IN::ValueType |
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| 336 | kruskalEdgeMap_IteratorOut(const GR& G, |
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| 337 | const IN& in, |
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| 338 | RET out) |
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[810] | 339 | { |
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[885] | 340 | KruskalSequenceOutput<RET> _out(out); |
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| 341 | return kruskal(G, KruskalMapInput<GR,IN>(G, in), _out); |
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[810] | 342 | } |
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| 343 | |
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| 344 | /// @} |
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| 345 | |
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[921] | 346 | } //namespace lemon |
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[810] | 347 | |
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[921] | 348 | #endif //LEMON_KRUSKAL_H |
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