[1699] | 1 | /* -*- C++ -*- |
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| 2 | * lemon/johnson.h - Part of LEMON, a generic C++ optimization library |
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| 3 | * |
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| 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 5 | * (Egervary Research Group on Combinatorial Optimization, 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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| 17 | #ifndef LEMON_JOHNSON_H |
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| 18 | #define LEMON_JOHNSON_H |
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| 19 | |
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| 20 | ///\ingroup flowalgs |
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| 21 | /// \file |
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| 22 | /// \brief Johnson algorithm. |
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| 23 | /// |
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| 24 | |
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| 25 | #include <lemon/list_graph.h> |
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| 26 | #include <lemon/graph_utils.h> |
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| 27 | #include <lemon/dijkstra.h> |
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| 28 | #include <lemon/belmann_ford.h> |
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| 29 | #include <lemon/invalid.h> |
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| 30 | #include <lemon/error.h> |
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| 31 | #include <lemon/maps.h> |
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| 32 | |
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| 33 | #include <limits> |
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| 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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| 37 | /// \brief Default OperationTraits for the Johnson algorithm class. |
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| 38 | /// |
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| 39 | /// It defines all computational operations and constants which are |
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| 40 | /// used in the Floyd-Warshall algorithm. The default implementation |
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| 41 | /// is based on the numeric_limits class. If the numeric type does not |
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| 42 | /// have infinity value then the maximum value is used as extremal |
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| 43 | /// infinity value. |
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| 44 | template < |
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| 45 | typename Value, |
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| 46 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
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| 47 | struct JohnsonDefaultOperationTraits { |
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| 48 | /// \brief Gives back the zero value of the type. |
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| 49 | static Value zero() { |
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| 50 | return static_cast<Value>(0); |
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| 51 | } |
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| 52 | /// \brief Gives back the positive infinity value of the type. |
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| 53 | static Value infinity() { |
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| 54 | return std::numeric_limits<Value>::infinity(); |
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| 55 | } |
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| 56 | /// \brief Gives back the sum of the given two elements. |
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| 57 | static Value plus(const Value& left, const Value& right) { |
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| 58 | return left + right; |
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| 59 | } |
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| 60 | /// \brief Gives back true only if the first value less than the second. |
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| 61 | static bool less(const Value& left, const Value& right) { |
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| 62 | return left < right; |
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| 63 | } |
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| 64 | }; |
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| 65 | |
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| 66 | template <typename Value> |
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| 67 | struct JohnsonDefaultOperationTraits<Value, false> { |
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| 68 | static Value zero() { |
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| 69 | return static_cast<Value>(0); |
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| 70 | } |
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| 71 | static Value infinity() { |
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| 72 | return std::numeric_limits<Value>::max(); |
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| 73 | } |
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| 74 | static Value plus(const Value& left, const Value& right) { |
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| 75 | if (left == infinity() || right == infinity()) return infinity(); |
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| 76 | return left + right; |
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| 77 | } |
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| 78 | static bool less(const Value& left, const Value& right) { |
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| 79 | return left < right; |
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| 80 | } |
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| 81 | }; |
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| 82 | |
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| 83 | /// \brief Default traits class of Johnson class. |
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| 84 | /// |
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| 85 | /// Default traits class of Johnson class. |
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| 86 | /// \param _Graph Graph type. |
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| 87 | /// \param _LegthMap Type of length map. |
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| 88 | template<class _Graph, class _LengthMap> |
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| 89 | struct JohnsonDefaultTraits { |
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| 90 | /// The graph type the algorithm runs on. |
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| 91 | typedef _Graph Graph; |
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| 92 | |
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| 93 | /// \brief The type of the map that stores the edge lengths. |
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| 94 | /// |
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| 95 | /// The type of the map that stores the edge lengths. |
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| 96 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
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| 97 | typedef _LengthMap LengthMap; |
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| 98 | |
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| 99 | // The type of the length of the edges. |
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| 100 | typedef typename _LengthMap::Value Value; |
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| 101 | |
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| 102 | /// \brief Operation traits for belmann-ford algorithm. |
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| 103 | /// |
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| 104 | /// It defines the infinity type on the given Value type |
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| 105 | /// and the used operation. |
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| 106 | /// \see JohnsonDefaultOperationTraits |
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| 107 | typedef JohnsonDefaultOperationTraits<Value> OperationTraits; |
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| 108 | |
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| 109 | /// \brief The type of the map that stores the last edges of the |
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| 110 | /// shortest paths. |
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| 111 | /// |
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| 112 | /// The type of the map that stores the last |
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| 113 | /// edges of the shortest paths. |
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| 114 | /// It must be a matrix map with \c Graph::Edge value type. |
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| 115 | /// |
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| 116 | typedef NodeMatrixMap<Graph, typename Graph::Edge> PredMap; |
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| 117 | |
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| 118 | /// \brief Instantiates a PredMap. |
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| 119 | /// |
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| 120 | /// This function instantiates a \ref PredMap. |
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| 121 | /// \param G is the graph, to which we would like to define the PredMap. |
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| 122 | /// \todo The graph alone may be insufficient for the initialization |
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| 123 | static PredMap *createPredMap(const _Graph& graph) { |
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| 124 | return new PredMap(graph); |
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| 125 | } |
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| 126 | |
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| 127 | /// \brief The type of the map that stores the dists of the nodes. |
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| 128 | /// |
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| 129 | /// The type of the map that stores the dists of the nodes. |
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| 130 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
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| 131 | /// |
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| 132 | typedef NodeMatrixMap<Graph, Value> DistMap; |
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| 133 | |
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| 134 | /// \brief Instantiates a DistMap. |
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| 135 | /// |
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| 136 | /// This function instantiates a \ref DistMap. |
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| 137 | /// \param G is the graph, to which we would like to define the |
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| 138 | /// \ref DistMap |
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| 139 | static DistMap *createDistMap(const _Graph& graph) { |
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| 140 | return new DistMap(graph); |
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| 141 | } |
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| 142 | |
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| 143 | }; |
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| 144 | |
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| 145 | /// \brief Johnson algorithm class. |
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| 146 | /// |
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| 147 | /// \ingroup flowalgs |
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| 148 | /// This class provides an efficient implementation of \c Johnson |
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| 149 | /// algorithm. The edge lengths are passed to the algorithm using a |
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| 150 | /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any |
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| 151 | /// kind of length. |
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| 152 | /// |
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| 153 | /// The type of the length is determined by the |
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| 154 | /// \ref concept::ReadMap::Value "Value" of the length map. |
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| 155 | /// |
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| 156 | /// \param _Graph The graph type the algorithm runs on. The default value |
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| 157 | /// is \ref ListGraph. The value of _Graph is not used directly by |
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| 158 | /// Johnson, it is only passed to \ref JohnsonDefaultTraits. |
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| 159 | /// \param _LengthMap This read-only EdgeMap determines the lengths of the |
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| 160 | /// edges. It is read once for each edge, so the map may involve in |
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| 161 | /// relatively time consuming process to compute the edge length if |
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| 162 | /// it is necessary. The default map type is \ref |
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| 163 | /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>". The value |
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| 164 | /// of _LengthMap is not used directly by Johnson, it is only passed |
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| 165 | /// to \ref JohnsonDefaultTraits. \param _Traits Traits class to set |
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| 166 | /// various data types used by the algorithm. The default traits |
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| 167 | /// class is \ref JohnsonDefaultTraits |
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| 168 | /// "JohnsonDefaultTraits<_Graph,_LengthMap>". See \ref |
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| 169 | /// JohnsonDefaultTraits for the documentation of a Johnson traits |
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| 170 | /// class. |
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| 171 | /// |
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| 172 | /// \author Balazs Dezso |
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| 173 | |
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[1710] | 174 | #ifdef DOXYGEN |
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| 175 | template <typename _Graph, typename _LengthMap, typename _Traits> |
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| 176 | #else |
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[1699] | 177 | template <typename _Graph=ListGraph, |
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| 178 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
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| 179 | typename _Traits=JohnsonDefaultTraits<_Graph,_LengthMap> > |
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[1710] | 180 | #endif |
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[1699] | 181 | class Johnson { |
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| 182 | public: |
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| 183 | |
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| 184 | /// \brief \ref Exception for uninitialized parameters. |
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| 185 | /// |
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| 186 | /// This error represents problems in the initialization |
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| 187 | /// of the parameters of the algorithms. |
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| 188 | |
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| 189 | class UninitializedParameter : public lemon::UninitializedParameter { |
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| 190 | public: |
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| 191 | virtual const char* exceptionName() const { |
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| 192 | return "lemon::Johnson::UninitializedParameter"; |
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| 193 | } |
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| 194 | }; |
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| 195 | |
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| 196 | typedef _Traits Traits; |
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| 197 | ///The type of the underlying graph. |
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| 198 | typedef typename _Traits::Graph Graph; |
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| 199 | |
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| 200 | typedef typename Graph::Node Node; |
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| 201 | typedef typename Graph::NodeIt NodeIt; |
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| 202 | typedef typename Graph::Edge Edge; |
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| 203 | typedef typename Graph::EdgeIt EdgeIt; |
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| 204 | |
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| 205 | /// \brief The type of the length of the edges. |
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| 206 | typedef typename _Traits::LengthMap::Value Value; |
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| 207 | /// \brief The type of the map that stores the edge lengths. |
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| 208 | typedef typename _Traits::LengthMap LengthMap; |
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| 209 | /// \brief The type of the map that stores the last |
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| 210 | /// edges of the shortest paths. The type of the PredMap |
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| 211 | /// is a matrix map for Edges |
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| 212 | typedef typename _Traits::PredMap PredMap; |
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| 213 | /// \brief The type of the map that stores the dists of the nodes. |
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| 214 | /// The type of the DistMap is a matrix map for Values |
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| 215 | typedef typename _Traits::DistMap DistMap; |
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| 216 | /// \brief The operation traits. |
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| 217 | typedef typename _Traits::OperationTraits OperationTraits; |
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| 218 | private: |
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| 219 | /// Pointer to the underlying graph. |
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| 220 | const Graph *graph; |
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| 221 | /// Pointer to the length map |
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| 222 | const LengthMap *length; |
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| 223 | ///Pointer to the map of predecessors edges. |
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| 224 | PredMap *_pred; |
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| 225 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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| 226 | bool local_pred; |
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| 227 | ///Pointer to the map of distances. |
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| 228 | DistMap *_dist; |
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| 229 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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| 230 | bool local_dist; |
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| 231 | |
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| 232 | /// Creates the maps if necessary. |
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| 233 | void create_maps() { |
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| 234 | if(!_pred) { |
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| 235 | local_pred = true; |
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| 236 | _pred = Traits::createPredMap(*graph); |
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| 237 | } |
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| 238 | if(!_dist) { |
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| 239 | local_dist = true; |
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| 240 | _dist = Traits::createDistMap(*graph); |
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| 241 | } |
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| 242 | } |
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| 243 | |
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| 244 | public : |
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| 245 | |
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| 246 | /// \name Named template parameters |
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| 247 | |
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| 248 | ///@{ |
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| 249 | |
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| 250 | template <class T> |
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| 251 | struct DefPredMapTraits : public Traits { |
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| 252 | typedef T PredMap; |
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| 253 | static PredMap *createPredMap(const Graph& graph) { |
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| 254 | throw UninitializedParameter(); |
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| 255 | } |
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| 256 | }; |
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| 257 | |
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| 258 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
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| 259 | /// type |
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| 260 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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| 261 | /// |
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| 262 | template <class T> |
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[1710] | 263 | struct DefPredMap |
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| 264 | : public Johnson< Graph, LengthMap, DefPredMapTraits<T> > { |
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| 265 | typedef Johnson< Graph, LengthMap, DefPredMapTraits<T> > Create; |
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| 266 | }; |
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[1699] | 267 | |
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| 268 | template <class T> |
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| 269 | struct DefDistMapTraits : public Traits { |
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| 270 | typedef T DistMap; |
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| 271 | static DistMap *createDistMap(const Graph& graph) { |
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| 272 | throw UninitializedParameter(); |
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| 273 | } |
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| 274 | }; |
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| 275 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
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| 276 | /// type |
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| 277 | /// |
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| 278 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
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| 279 | /// |
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| 280 | template <class T> |
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[1710] | 281 | struct DefDistMap |
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| 282 | : public Johnson< Graph, LengthMap, DefDistMapTraits<T> > { |
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| 283 | typedef Johnson< Graph, LengthMap, DefDistMapTraits<T> > Create; |
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| 284 | }; |
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[1699] | 285 | |
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| 286 | template <class T> |
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| 287 | struct DefOperationTraitsTraits : public Traits { |
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| 288 | typedef T OperationTraits; |
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| 289 | }; |
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| 290 | |
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| 291 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 292 | /// OperationTraits type |
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| 293 | /// |
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[1710] | 294 | /// \ref named-templ-param "Named parameter" for setting |
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| 295 | /// OperationTraits type |
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[1699] | 296 | template <class T> |
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[1710] | 297 | struct DefOperationTraits |
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| 298 | : public Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
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| 299 | typedef Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > Create; |
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| 300 | }; |
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[1699] | 301 | |
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| 302 | ///@} |
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| 303 | |
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[1710] | 304 | protected: |
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| 305 | |
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| 306 | Johnson() {} |
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| 307 | |
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[1699] | 308 | public: |
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| 309 | |
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| 310 | /// \brief Constructor. |
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| 311 | /// |
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| 312 | /// \param _graph the graph the algorithm will run on. |
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| 313 | /// \param _length the length map used by the algorithm. |
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| 314 | Johnson(const Graph& _graph, const LengthMap& _length) : |
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| 315 | graph(&_graph), length(&_length), |
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| 316 | _pred(0), local_pred(false), |
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| 317 | _dist(0), local_dist(false) {} |
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| 318 | |
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| 319 | ///Destructor. |
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| 320 | ~Johnson() { |
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| 321 | if(local_pred) delete _pred; |
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| 322 | if(local_dist) delete _dist; |
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| 323 | } |
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| 324 | |
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| 325 | /// \brief Sets the length map. |
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| 326 | /// |
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| 327 | /// Sets the length map. |
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| 328 | /// \return \c (*this) |
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| 329 | Johnson &lengthMap(const LengthMap &m) { |
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| 330 | length = &m; |
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| 331 | return *this; |
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| 332 | } |
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| 333 | |
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| 334 | /// \brief Sets the map storing the predecessor edges. |
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| 335 | /// |
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| 336 | /// Sets the map storing the predecessor edges. |
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| 337 | /// If you don't use this function before calling \ref run(), |
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| 338 | /// it will allocate one. The destuctor deallocates this |
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| 339 | /// automatically allocated map, of course. |
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| 340 | /// \return \c (*this) |
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| 341 | Johnson &predMap(PredMap &m) { |
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| 342 | if(local_pred) { |
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| 343 | delete _pred; |
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| 344 | local_pred=false; |
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| 345 | } |
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| 346 | _pred = &m; |
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| 347 | return *this; |
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| 348 | } |
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| 349 | |
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| 350 | /// \brief Sets the map storing the distances calculated by the algorithm. |
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| 351 | /// |
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| 352 | /// Sets the map storing the distances calculated by the algorithm. |
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| 353 | /// If you don't use this function before calling \ref run(), |
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| 354 | /// it will allocate one. The destuctor deallocates this |
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| 355 | /// automatically allocated map, of course. |
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| 356 | /// \return \c (*this) |
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| 357 | Johnson &distMap(DistMap &m) { |
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| 358 | if(local_dist) { |
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| 359 | delete _dist; |
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| 360 | local_dist=false; |
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| 361 | } |
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| 362 | _dist = &m; |
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| 363 | return *this; |
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| 364 | } |
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| 365 | |
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| 366 | ///\name Execution control |
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| 367 | /// The simplest way to execute the algorithm is to use |
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| 368 | /// one of the member functions called \c run(...). |
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| 369 | /// \n |
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| 370 | /// If you need more control on the execution, |
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| 371 | /// Finally \ref start() will perform the actual path |
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| 372 | /// computation. |
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| 373 | |
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| 374 | ///@{ |
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| 375 | |
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| 376 | /// \brief Initializes the internal data structures. |
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| 377 | /// |
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| 378 | /// Initializes the internal data structures. |
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| 379 | void init() { |
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| 380 | create_maps(); |
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| 381 | } |
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| 382 | |
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| 383 | /// \brief Executes the algorithm. |
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| 384 | /// |
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| 385 | /// This method runs the %Johnson algorithm in order to compute |
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| 386 | /// the shortest path to each node pairs. The algorithm |
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| 387 | /// computes |
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| 388 | /// - The shortest path tree for each node. |
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| 389 | /// - The distance between each node pairs. |
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| 390 | void start() { |
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[1710] | 391 | typedef typename BelmannFord<Graph, LengthMap>:: |
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[1699] | 392 | template DefOperationTraits<OperationTraits>:: |
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[1710] | 393 | template DefPredMap<NullMap<Node, Edge> >:: |
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| 394 | Create BelmannFordType; |
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| 395 | |
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| 396 | BelmannFordType belmannford(*graph, *length); |
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| 397 | |
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| 398 | NullMap<Node, Edge> predMap; |
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| 399 | |
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| 400 | belmannford.predMap(predMap); |
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[1699] | 401 | |
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[1710] | 402 | belmannford.init(OperationTraits::zero()); |
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[1699] | 403 | belmannford.start(); |
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| 404 | |
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| 405 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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| 406 | typedef PotentialDifferenceMap<Graph, |
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[1710] | 407 | typename BelmannFordType::DistMap> PotDiffMap; |
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[1699] | 408 | PotDiffMap potdiff(*graph, belmannford.distMap()); |
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| 409 | typedef SubMap<LengthMap, PotDiffMap> ShiftLengthMap; |
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| 410 | ShiftLengthMap shiftlen(*length, potdiff); |
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| 411 | Dijkstra<Graph, ShiftLengthMap> dijkstra(*graph, shiftlen); |
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| 412 | dijkstra.run(it); |
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| 413 | for (NodeIt jt(*graph); jt != INVALID; ++jt) { |
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| 414 | if (dijkstra.reached(jt)) { |
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| 415 | _dist->set(it, jt, dijkstra.dist(jt) + |
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| 416 | belmannford.dist(jt) - belmannford.dist(it)); |
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| 417 | _pred->set(it, jt, dijkstra.pred(jt)); |
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| 418 | } else { |
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| 419 | _dist->set(it, jt, OperationTraits::infinity()); |
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| 420 | _pred->set(it, jt, INVALID); |
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| 421 | } |
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| 422 | } |
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| 423 | } |
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| 424 | } |
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| 425 | |
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| 426 | /// \brief Runs %Johnson algorithm. |
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| 427 | /// |
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| 428 | /// This method runs the %Johnson algorithm from a each node |
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| 429 | /// in order to compute the shortest path to each node pairs. |
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| 430 | /// The algorithm computes |
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| 431 | /// - The shortest path tree for each node. |
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| 432 | /// - The distance between each node pairs. |
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| 433 | /// |
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| 434 | /// \note d.run(s) is just a shortcut of the following code. |
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| 435 | /// \code |
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| 436 | /// d.init(); |
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| 437 | /// d.start(); |
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| 438 | /// \endcode |
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| 439 | void run() { |
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| 440 | init(); |
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| 441 | start(); |
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| 442 | } |
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| 443 | |
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| 444 | ///@} |
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| 445 | |
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| 446 | /// \name Query Functions |
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| 447 | /// The result of the %Johnson algorithm can be obtained using these |
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| 448 | /// functions.\n |
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| 449 | /// Before the use of these functions, |
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| 450 | /// either run() or start() must be called. |
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| 451 | |
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| 452 | ///@{ |
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| 453 | |
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| 454 | /// \brief Copies the shortest path to \c t into \c p |
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| 455 | /// |
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| 456 | /// This function copies the shortest path to \c t into \c p. |
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| 457 | /// If it \c t is a source itself or unreachable, then it does not |
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| 458 | /// alter \c p. |
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| 459 | /// \todo Is it the right way to handle unreachable nodes? |
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| 460 | /// \return Returns \c true if a path to \c t was actually copied to \c p, |
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| 461 | /// \c false otherwise. |
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| 462 | /// \sa DirPath |
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| 463 | template <typename Path> |
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| 464 | bool getPath(Path &p, Node source, Node target) { |
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| 465 | if (connected(source, target)) { |
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| 466 | p.clear(); |
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| 467 | typename Path::Builder b(target); |
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| 468 | for(b.setStartNode(target); pred(source, target) != INVALID; |
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| 469 | target = predNode(target)) { |
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| 470 | b.pushFront(pred(source, target)); |
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| 471 | } |
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| 472 | b.commit(); |
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| 473 | return true; |
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| 474 | } |
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| 475 | return false; |
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| 476 | } |
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| 477 | |
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| 478 | /// \brief The distance between two nodes. |
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| 479 | /// |
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| 480 | /// Returns the distance between two nodes. |
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| 481 | /// \pre \ref run() must be called before using this function. |
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| 482 | /// \warning If node \c v in unreachable from the root the return value |
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| 483 | /// of this funcion is undefined. |
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| 484 | Value dist(Node source, Node target) const { |
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| 485 | return (*_dist)(source, target); |
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| 486 | } |
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| 487 | |
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| 488 | /// \brief Returns the 'previous edge' of the shortest path tree. |
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| 489 | /// |
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| 490 | /// For the node \c node it returns the 'previous edge' of the shortest |
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| 491 | /// path tree to direction of the node \c root |
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| 492 | /// i.e. it returns the last edge of a shortest path from the node \c root |
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| 493 | /// to \c node. It is \ref INVALID if \c node is unreachable from the root |
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| 494 | /// or if \c node=root. The shortest path tree used here is equal to the |
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| 495 | /// shortest path tree used in \ref predNode(). |
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| 496 | /// \pre \ref run() must be called before using this function. |
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| 497 | /// \todo predEdge could be a better name. |
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| 498 | Edge pred(Node root, Node node) const { |
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| 499 | return (*_pred)(root, node); |
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| 500 | } |
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| 501 | |
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| 502 | /// \brief Returns the 'previous node' of the shortest path tree. |
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| 503 | /// |
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| 504 | /// For a node \c node it returns the 'previous node' of the shortest path |
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| 505 | /// tree to direction of the node \c root, i.e. it returns the last but |
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| 506 | /// one node from a shortest path from the \c root to \c node. It is |
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| 507 | /// INVALID if \c node is unreachable from the root or if \c node=root. |
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| 508 | /// The shortest path tree used here is equal to the |
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| 509 | /// shortest path tree used in \ref pred(). |
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| 510 | /// \pre \ref run() must be called before using this function. |
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| 511 | Node predNode(Node root, Node node) const { |
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| 512 | return (*_pred)(root, node) == INVALID ? |
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| 513 | INVALID : graph->source((*_pred)(root, node)); |
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| 514 | } |
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| 515 | |
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| 516 | /// \brief Returns a reference to the matrix node map of distances. |
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| 517 | /// |
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| 518 | /// Returns a reference to the matrix node map of distances. |
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| 519 | /// |
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| 520 | /// \pre \ref run() must be called before using this function. |
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| 521 | const DistMap &distMap() const { return *_dist;} |
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| 522 | |
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| 523 | /// \brief Returns a reference to the shortest path tree map. |
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| 524 | /// |
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| 525 | /// Returns a reference to the matrix node map of the edges of the |
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| 526 | /// shortest path tree. |
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| 527 | /// \pre \ref run() must be called before using this function. |
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| 528 | const PredMap &predMap() const { return *_pred;} |
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| 529 | |
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| 530 | /// \brief Checks if a node is reachable from the root. |
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| 531 | /// |
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| 532 | /// Returns \c true if \c v is reachable from the root. |
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| 533 | /// \pre \ref run() must be called before using this function. |
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| 534 | /// |
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| 535 | bool connected(Node source, Node target) { |
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| 536 | return (*_dist)(source, target) != OperationTraits::infinity(); |
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| 537 | } |
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| 538 | |
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| 539 | ///@} |
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| 540 | }; |
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| 541 | |
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| 542 | } //END OF NAMESPACE LEMON |
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| 543 | |
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| 544 | #endif |
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