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