[1699] | 1 | /* -*- C++ -*- |
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| 2 | * lemon/floyd_warshall.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_FLOYD_WARSHALL_H |
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| 18 | #define LEMON_FLOYD_WARSHALL_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 FloydWarshall 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/invalid.h> |
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| 28 | #include <lemon/error.h> |
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[1723] | 29 | #include <lemon/matrix_maps.h> |
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[1699] | 30 | #include <lemon/maps.h> |
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| 31 | |
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| 32 | #include <limits> |
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| 33 | |
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| 34 | namespace lemon { |
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| 35 | |
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| 36 | /// \brief Default OperationTraits for the FloydWarshall algorithm class. |
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| 37 | /// |
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| 38 | /// It defines all computational operations and constants which are |
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| 39 | /// used in the Floyd-Warshall algorithm. The default implementation |
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| 40 | /// is based on the numeric_limits class. If the numeric type does not |
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| 41 | /// have infinity value then the maximum value is used as extremal |
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| 42 | /// infinity value. |
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| 43 | template < |
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| 44 | typename Value, |
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| 45 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
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| 46 | struct FloydWarshallDefaultOperationTraits { |
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| 47 | /// \brief Gives back the zero value of the type. |
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| 48 | static Value zero() { |
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| 49 | return static_cast<Value>(0); |
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| 50 | } |
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| 51 | /// \brief Gives back the positive infinity value of the type. |
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| 52 | static Value infinity() { |
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| 53 | return std::numeric_limits<Value>::infinity(); |
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| 54 | } |
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| 55 | /// \brief Gives back the sum of the given two elements. |
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| 56 | static Value plus(const Value& left, const Value& right) { |
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| 57 | return left + right; |
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| 58 | } |
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| 59 | /// \brief Gives back true only if the first value less than the second. |
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| 60 | static bool less(const Value& left, const Value& right) { |
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| 61 | return left < right; |
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| 62 | } |
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| 63 | }; |
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| 64 | |
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| 65 | template <typename Value> |
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| 66 | struct FloydWarshallDefaultOperationTraits<Value, false> { |
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| 67 | static Value zero() { |
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| 68 | return static_cast<Value>(0); |
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| 69 | } |
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| 70 | static Value infinity() { |
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| 71 | return std::numeric_limits<Value>::max(); |
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| 72 | } |
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| 73 | static Value plus(const Value& left, const Value& right) { |
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| 74 | if (left == infinity() || right == infinity()) return infinity(); |
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| 75 | return left + right; |
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| 76 | } |
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| 77 | static bool less(const Value& left, const Value& right) { |
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| 78 | return left < right; |
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| 79 | } |
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| 80 | }; |
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| 81 | |
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| 82 | /// \brief Default traits class of FloydWarshall class. |
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| 83 | /// |
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| 84 | /// Default traits class of FloydWarshall class. |
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| 85 | /// \param _Graph Graph type. |
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| 86 | /// \param _LegthMap Type of length map. |
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| 87 | template<class _Graph, class _LengthMap> |
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| 88 | struct FloydWarshallDefaultTraits { |
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| 89 | /// The graph type the algorithm runs on. |
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| 90 | typedef _Graph Graph; |
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| 91 | |
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| 92 | /// \brief The type of the map that stores the edge lengths. |
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| 93 | /// |
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| 94 | /// The type of the map that stores the edge lengths. |
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| 95 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
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| 96 | typedef _LengthMap LengthMap; |
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| 97 | |
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| 98 | // The type of the length of the edges. |
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| 99 | typedef typename _LengthMap::Value Value; |
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| 100 | |
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| 101 | /// \brief Operation traits for belmann-ford algorithm. |
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| 102 | /// |
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| 103 | /// It defines the infinity type on the given Value type |
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| 104 | /// and the used operation. |
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| 105 | /// \see FloydWarshallDefaultOperationTraits |
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| 106 | typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits; |
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| 107 | |
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[1723] | 108 | /// \brief The type of the matrix map that stores the last edges of the |
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[1699] | 109 | /// shortest paths. |
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| 110 | /// |
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[1723] | 111 | /// The type of the map that stores the last edges of the shortest paths. |
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[1699] | 112 | /// It must be a matrix map with \c Graph::Edge value type. |
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| 113 | /// |
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[1723] | 114 | typedef DynamicMatrixMap<Graph, typename Graph::Node, |
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| 115 | typename Graph::Edge> PredMap; |
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[1699] | 116 | |
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| 117 | /// \brief Instantiates a PredMap. |
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| 118 | /// |
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| 119 | /// This function instantiates a \ref PredMap. |
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| 120 | /// \param G is the graph, to which we would like to define the PredMap. |
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| 121 | /// \todo The graph alone may be insufficient for the initialization |
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| 122 | static PredMap *createPredMap(const _Graph& graph) { |
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| 123 | return new PredMap(graph); |
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| 124 | } |
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| 125 | |
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| 126 | /// \brief The type of the map that stores the dists of the nodes. |
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| 127 | /// |
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| 128 | /// The type of the map that stores the dists of the nodes. |
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[1723] | 129 | /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept. |
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[1699] | 130 | /// |
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[1723] | 131 | typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap; |
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[1699] | 132 | |
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| 133 | /// \brief Instantiates a DistMap. |
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| 134 | /// |
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| 135 | /// This function instantiates a \ref DistMap. |
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| 136 | /// \param G is the graph, to which we would like to define the |
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| 137 | /// \ref DistMap |
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| 138 | static DistMap *createDistMap(const _Graph& graph) { |
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| 139 | return new DistMap(graph); |
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| 140 | } |
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| 141 | |
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| 142 | }; |
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| 143 | |
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[1754] | 144 | /// \brief %FloydWarshall algorithm class. |
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[1699] | 145 | /// |
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| 146 | /// \ingroup flowalgs |
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[1754] | 147 | /// This class provides an efficient implementation of \c Floyd-Warshall |
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[1699] | 148 | /// algorithm. The edge lengths are passed to the algorithm using a |
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| 149 | /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any |
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| 150 | /// kind of length. |
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| 151 | /// |
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[1757] | 152 | /// The algorithm solves the shortest path problem for each pair |
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[1723] | 153 | /// of node when the edges can have negative length but the graph should |
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[1754] | 154 | /// not contain cycles with negative sum of length. If we can assume |
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[1723] | 155 | /// that all edge is non-negative in the graph then the dijkstra algorithm |
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| 156 | /// should be used from each node rather and if the graph is sparse and |
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[1754] | 157 | /// there are negative circles then the johnson algorithm. |
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[1723] | 158 | /// |
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| 159 | /// The complexity of this algorithm is O(n^3 + e). |
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| 160 | /// |
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[1699] | 161 | /// The type of the length is determined by the |
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| 162 | /// \ref concept::ReadMap::Value "Value" of the length map. |
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| 163 | /// |
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| 164 | /// \param _Graph The graph type the algorithm runs on. The default value |
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| 165 | /// is \ref ListGraph. The value of _Graph is not used directly by |
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| 166 | /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits. |
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| 167 | /// \param _LengthMap This read-only EdgeMap determines the lengths of the |
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| 168 | /// edges. It is read once for each edge, so the map may involve in |
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| 169 | /// relatively time consuming process to compute the edge length if |
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| 170 | /// it is necessary. The default map type is \ref |
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| 171 | /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>". The value |
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| 172 | /// of _LengthMap is not used directly by FloydWarshall, it is only passed |
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| 173 | /// to \ref FloydWarshallDefaultTraits. \param _Traits Traits class to set |
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| 174 | /// various data types used by the algorithm. The default traits |
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| 175 | /// class is \ref FloydWarshallDefaultTraits |
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| 176 | /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>". See \ref |
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| 177 | /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall |
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| 178 | /// traits class. |
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| 179 | /// |
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| 180 | /// \author Balazs Dezso |
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| 181 | |
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[1710] | 182 | #ifdef DOXYGEN |
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| 183 | template <typename _Graph, typename _LengthMap typename _Traits > |
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| 184 | #else |
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[1699] | 185 | template <typename _Graph=ListGraph, |
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| 186 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
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| 187 | typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> > |
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[1710] | 188 | #endif |
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[1699] | 189 | class FloydWarshall { |
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| 190 | public: |
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| 191 | |
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| 192 | /// \brief \ref Exception for uninitialized parameters. |
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| 193 | /// |
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| 194 | /// This error represents problems in the initialization |
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| 195 | /// of the parameters of the algorithms. |
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| 196 | |
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| 197 | class UninitializedParameter : public lemon::UninitializedParameter { |
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| 198 | public: |
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| 199 | virtual const char* exceptionName() const { |
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| 200 | return "lemon::FloydWarshall::UninitializedParameter"; |
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| 201 | } |
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| 202 | }; |
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| 203 | |
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| 204 | typedef _Traits Traits; |
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| 205 | ///The type of the underlying graph. |
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| 206 | typedef typename _Traits::Graph Graph; |
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| 207 | |
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| 208 | typedef typename Graph::Node Node; |
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| 209 | typedef typename Graph::NodeIt NodeIt; |
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| 210 | typedef typename Graph::Edge Edge; |
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| 211 | typedef typename Graph::EdgeIt EdgeIt; |
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| 212 | |
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| 213 | /// \brief The type of the length of the edges. |
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| 214 | typedef typename _Traits::LengthMap::Value Value; |
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| 215 | /// \brief The type of the map that stores the edge lengths. |
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| 216 | typedef typename _Traits::LengthMap LengthMap; |
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| 217 | /// \brief The type of the map that stores the last |
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| 218 | /// edges of the shortest paths. The type of the PredMap |
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| 219 | /// is a matrix map for Edges |
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| 220 | typedef typename _Traits::PredMap PredMap; |
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| 221 | /// \brief The type of the map that stores the dists of the nodes. |
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| 222 | /// The type of the DistMap is a matrix map for Values |
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| 223 | typedef typename _Traits::DistMap DistMap; |
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| 224 | /// \brief The operation traits. |
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| 225 | typedef typename _Traits::OperationTraits OperationTraits; |
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| 226 | private: |
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| 227 | /// Pointer to the underlying graph. |
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| 228 | const Graph *graph; |
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| 229 | /// Pointer to the length map |
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| 230 | const LengthMap *length; |
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| 231 | ///Pointer to the map of predecessors edges. |
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| 232 | PredMap *_pred; |
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| 233 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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| 234 | bool local_pred; |
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| 235 | ///Pointer to the map of distances. |
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| 236 | DistMap *_dist; |
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| 237 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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| 238 | bool local_dist; |
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| 239 | |
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| 240 | /// Creates the maps if necessary. |
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| 241 | void create_maps() { |
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| 242 | if(!_pred) { |
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| 243 | local_pred = true; |
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| 244 | _pred = Traits::createPredMap(*graph); |
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| 245 | } |
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| 246 | if(!_dist) { |
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| 247 | local_dist = true; |
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| 248 | _dist = Traits::createDistMap(*graph); |
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| 249 | } |
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| 250 | } |
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| 251 | |
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| 252 | public : |
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| 253 | |
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| 254 | /// \name Named template parameters |
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| 255 | |
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| 256 | ///@{ |
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| 257 | |
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| 258 | template <class T> |
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| 259 | struct DefPredMapTraits : public Traits { |
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| 260 | typedef T PredMap; |
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| 261 | static PredMap *createPredMap(const Graph& graph) { |
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| 262 | throw UninitializedParameter(); |
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| 263 | } |
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| 264 | }; |
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| 265 | |
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| 266 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
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| 267 | /// type |
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| 268 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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| 269 | /// |
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| 270 | template <class T> |
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[1710] | 271 | struct DefPredMap |
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| 272 | : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > { |
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| 273 | typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create; |
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| 274 | }; |
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[1699] | 275 | |
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| 276 | template <class T> |
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| 277 | struct DefDistMapTraits : public Traits { |
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| 278 | typedef T DistMap; |
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| 279 | static DistMap *createDistMap(const Graph& graph) { |
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| 280 | throw UninitializedParameter(); |
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| 281 | } |
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| 282 | }; |
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| 283 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
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| 284 | /// type |
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| 285 | /// |
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| 286 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
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| 287 | /// |
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| 288 | template <class T> |
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[1710] | 289 | struct DefDistMap |
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| 290 | : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > { |
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| 291 | typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create; |
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| 292 | }; |
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[1699] | 293 | |
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| 294 | template <class T> |
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| 295 | struct DefOperationTraitsTraits : public Traits { |
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| 296 | typedef T OperationTraits; |
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| 297 | }; |
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| 298 | |
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| 299 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 300 | /// OperationTraits type |
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| 301 | /// |
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| 302 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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| 303 | template <class T> |
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[1710] | 304 | struct DefOperationTraits |
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[1699] | 305 | : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
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[1710] | 306 | typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > |
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| 307 | Create; |
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[1699] | 308 | }; |
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| 309 | |
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| 310 | ///@} |
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| 311 | |
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[1710] | 312 | protected: |
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| 313 | |
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| 314 | FloydWarshall() {} |
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| 315 | |
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[1699] | 316 | public: |
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[1710] | 317 | |
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| 318 | typedef FloydWarshall Create; |
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[1699] | 319 | |
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| 320 | /// \brief Constructor. |
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| 321 | /// |
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| 322 | /// \param _graph the graph the algorithm will run on. |
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| 323 | /// \param _length the length map used by the algorithm. |
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| 324 | FloydWarshall(const Graph& _graph, const LengthMap& _length) : |
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| 325 | graph(&_graph), length(&_length), |
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| 326 | _pred(0), local_pred(false), |
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| 327 | _dist(0), local_dist(false) {} |
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| 328 | |
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| 329 | ///Destructor. |
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| 330 | ~FloydWarshall() { |
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| 331 | if(local_pred) delete _pred; |
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| 332 | if(local_dist) delete _dist; |
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| 333 | } |
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| 334 | |
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| 335 | /// \brief Sets the length map. |
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| 336 | /// |
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| 337 | /// Sets the length map. |
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| 338 | /// \return \c (*this) |
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| 339 | FloydWarshall &lengthMap(const LengthMap &m) { |
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| 340 | length = &m; |
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| 341 | return *this; |
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| 342 | } |
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| 343 | |
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| 344 | /// \brief Sets the map storing the predecessor edges. |
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| 345 | /// |
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| 346 | /// Sets the map storing the predecessor edges. |
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| 347 | /// If you don't use this function before calling \ref run(), |
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| 348 | /// it will allocate one. The destuctor deallocates this |
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| 349 | /// automatically allocated map, of course. |
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| 350 | /// \return \c (*this) |
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| 351 | FloydWarshall &predMap(PredMap &m) { |
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| 352 | if(local_pred) { |
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| 353 | delete _pred; |
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| 354 | local_pred=false; |
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| 355 | } |
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| 356 | _pred = &m; |
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| 357 | return *this; |
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| 358 | } |
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| 359 | |
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| 360 | /// \brief Sets the map storing the distances calculated by the algorithm. |
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| 361 | /// |
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| 362 | /// Sets the map storing the distances calculated by the algorithm. |
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| 363 | /// If you don't use this function before calling \ref run(), |
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| 364 | /// it will allocate one. The destuctor deallocates this |
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| 365 | /// automatically allocated map, of course. |
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| 366 | /// \return \c (*this) |
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| 367 | FloydWarshall &distMap(DistMap &m) { |
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| 368 | if(local_dist) { |
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| 369 | delete _dist; |
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| 370 | local_dist=false; |
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| 371 | } |
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| 372 | _dist = &m; |
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| 373 | return *this; |
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| 374 | } |
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| 375 | |
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| 376 | ///\name Execution control |
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| 377 | /// The simplest way to execute the algorithm is to use |
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| 378 | /// one of the member functions called \c run(...). |
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| 379 | /// \n |
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| 380 | /// If you need more control on the execution, |
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| 381 | /// Finally \ref start() will perform the actual path |
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| 382 | /// computation. |
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| 383 | |
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| 384 | ///@{ |
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| 385 | |
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| 386 | /// \brief Initializes the internal data structures. |
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| 387 | /// |
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| 388 | /// Initializes the internal data structures. |
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| 389 | void init() { |
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| 390 | create_maps(); |
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| 391 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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| 392 | for (NodeIt jt(*graph); jt != INVALID; ++jt) { |
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| 393 | _pred->set(it, jt, INVALID); |
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[1741] | 394 | _dist->set(it, jt, OperationTraits::infinity()); |
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[1699] | 395 | } |
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[1741] | 396 | _dist->set(it, it, OperationTraits::zero()); |
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[1699] | 397 | } |
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| 398 | for (EdgeIt it(*graph); it != INVALID; ++it) { |
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| 399 | Node source = graph->source(it); |
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| 400 | Node target = graph->target(it); |
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| 401 | if (OperationTraits::less((*length)[it], (*_dist)(source, target))) { |
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| 402 | _dist->set(source, target, (*length)[it]); |
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| 403 | _pred->set(source, target, it); |
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| 404 | } |
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| 405 | } |
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| 406 | } |
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| 407 | |
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| 408 | /// \brief Executes the algorithm. |
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| 409 | /// |
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| 410 | /// This method runs the %FloydWarshall algorithm in order to compute |
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| 411 | /// the shortest path to each node pairs. The algorithm |
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| 412 | /// computes |
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| 413 | /// - The shortest path tree for each node. |
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| 414 | /// - The distance between each node pairs. |
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| 415 | void start() { |
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| 416 | for (NodeIt kt(*graph); kt != INVALID; ++kt) { |
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| 417 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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| 418 | for (NodeIt jt(*graph); jt != INVALID; ++jt) { |
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| 419 | Value relaxed = OperationTraits::plus((*_dist)(it, kt), |
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| 420 | (*_dist)(kt, jt)); |
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| 421 | if (OperationTraits::less(relaxed, (*_dist)(it, jt))) { |
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| 422 | _dist->set(it, jt, relaxed); |
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| 423 | _pred->set(it, jt, (*_pred)(kt, jt)); |
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| 424 | } |
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| 425 | } |
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| 426 | } |
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| 427 | } |
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| 428 | } |
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[1741] | 429 | |
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[1754] | 430 | /// \brief Executes the algorithm and checks the negative cycles. |
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[1741] | 431 | /// |
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| 432 | /// This method runs the %FloydWarshall algorithm in order to compute |
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[1754] | 433 | /// the shortest path to each node pairs. If there is a negative cycle |
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[1741] | 434 | /// in the graph it gives back false. |
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| 435 | /// The algorithm computes |
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| 436 | /// - The shortest path tree for each node. |
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| 437 | /// - The distance between each node pairs. |
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| 438 | bool checkedStart() { |
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| 439 | start(); |
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| 440 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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| 441 | if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) { |
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| 442 | return false; |
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| 443 | } |
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| 444 | } |
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| 445 | return true; |
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| 446 | } |
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[1699] | 447 | |
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| 448 | /// \brief Runs %FloydWarshall algorithm. |
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| 449 | /// |
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| 450 | /// This method runs the %FloydWarshall algorithm from a each node |
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| 451 | /// in order to compute the shortest path to each node pairs. |
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| 452 | /// The algorithm computes |
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| 453 | /// - The shortest path tree for each node. |
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| 454 | /// - The distance between each node pairs. |
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| 455 | /// |
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| 456 | /// \note d.run(s) is just a shortcut of the following code. |
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| 457 | /// \code |
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| 458 | /// d.init(); |
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| 459 | /// d.start(); |
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| 460 | /// \endcode |
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| 461 | void run() { |
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| 462 | init(); |
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| 463 | start(); |
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| 464 | } |
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| 465 | |
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| 466 | ///@} |
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| 467 | |
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| 468 | /// \name Query Functions |
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| 469 | /// The result of the %FloydWarshall algorithm can be obtained using these |
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| 470 | /// functions.\n |
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| 471 | /// Before the use of these functions, |
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| 472 | /// either run() or start() must be called. |
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| 473 | |
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| 474 | ///@{ |
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| 475 | |
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| 476 | /// \brief Copies the shortest path to \c t into \c p |
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| 477 | /// |
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| 478 | /// This function copies the shortest path to \c t into \c p. |
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| 479 | /// If it \c t is a source itself or unreachable, then it does not |
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| 480 | /// alter \c p. |
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| 481 | /// \return Returns \c true if a path to \c t was actually copied to \c p, |
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| 482 | /// \c false otherwise. |
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| 483 | /// \sa DirPath |
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| 484 | template <typename Path> |
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| 485 | bool getPath(Path &p, Node source, Node target) { |
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| 486 | if (connected(source, target)) { |
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| 487 | p.clear(); |
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| 488 | typename Path::Builder b(target); |
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[1763] | 489 | for(b.setStartNode(target); predEdge(source, target) != INVALID; |
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[1699] | 490 | target = predNode(target)) { |
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[1763] | 491 | b.pushFront(predEdge(source, target)); |
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[1699] | 492 | } |
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| 493 | b.commit(); |
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| 494 | return true; |
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| 495 | } |
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| 496 | return false; |
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| 497 | } |
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| 498 | |
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| 499 | /// \brief The distance between two nodes. |
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| 500 | /// |
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| 501 | /// Returns the distance between two nodes. |
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| 502 | /// \pre \ref run() must be called before using this function. |
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| 503 | /// \warning If node \c v in unreachable from the root the return value |
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| 504 | /// of this funcion is undefined. |
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| 505 | Value dist(Node source, Node target) const { |
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| 506 | return (*_dist)(source, target); |
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| 507 | } |
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| 508 | |
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| 509 | /// \brief Returns the 'previous edge' of the shortest path tree. |
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| 510 | /// |
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| 511 | /// For the node \c node it returns the 'previous edge' of the shortest |
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| 512 | /// path tree to direction of the node \c root |
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| 513 | /// i.e. it returns the last edge of a shortest path from the node \c root |
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| 514 | /// to \c node. It is \ref INVALID if \c node is unreachable from the root |
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| 515 | /// or if \c node=root. The shortest path tree used here is equal to the |
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| 516 | /// shortest path tree used in \ref predNode(). |
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| 517 | /// \pre \ref run() must be called before using this function. |
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[1763] | 518 | Edge predEdge(Node root, Node node) const { |
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[1699] | 519 | return (*_pred)(root, node); |
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| 520 | } |
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| 521 | |
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| 522 | /// \brief Returns the 'previous node' of the shortest path tree. |
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| 523 | /// |
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| 524 | /// For a node \c node it returns the 'previous node' of the shortest path |
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| 525 | /// tree to direction of the node \c root, i.e. it returns the last but |
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| 526 | /// one node from a shortest path from the \c root to \c node. It is |
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| 527 | /// INVALID if \c node is unreachable from the root or if \c node=root. |
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| 528 | /// The shortest path tree used here is equal to the |
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[1763] | 529 | /// shortest path tree used in \ref predEdge(). |
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[1699] | 530 | /// \pre \ref run() must be called before using this function. |
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| 531 | Node predNode(Node root, Node node) const { |
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| 532 | return (*_pred)(root, node) == INVALID ? |
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| 533 | INVALID : graph->source((*_pred)(root, node)); |
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| 534 | } |
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| 535 | |
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| 536 | /// \brief Returns a reference to the matrix node map of distances. |
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| 537 | /// |
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| 538 | /// Returns a reference to the matrix node map of distances. |
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| 539 | /// |
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| 540 | /// \pre \ref run() must be called before using this function. |
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| 541 | const DistMap &distMap() const { return *_dist;} |
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| 542 | |
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| 543 | /// \brief Returns a reference to the shortest path tree map. |
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| 544 | /// |
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| 545 | /// Returns a reference to the matrix node map of the edges of the |
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| 546 | /// shortest path tree. |
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| 547 | /// \pre \ref run() must be called before using this function. |
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| 548 | const PredMap &predMap() const { return *_pred;} |
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| 549 | |
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| 550 | /// \brief Checks if a node is reachable from the root. |
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| 551 | /// |
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| 552 | /// Returns \c true if \c v is reachable from the root. |
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| 553 | /// \pre \ref run() must be called before using this function. |
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| 554 | /// |
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| 555 | bool connected(Node source, Node target) { |
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| 556 | return (*_dist)(source, target) != OperationTraits::infinity(); |
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| 557 | } |
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| 558 | |
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| 559 | ///@} |
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| 560 | }; |
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| 561 | |
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| 562 | } //END OF NAMESPACE LEMON |
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| 563 | |
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| 564 | #endif |
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| 565 | |
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