[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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[1875] | 4 | * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1699] | 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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[1864] | 28 | #include <lemon/bellman_ford.h> |
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[1699] | 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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[1723] | 32 | #include <lemon/matrix_maps.h> |
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[1699] | 33 | |
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| 34 | #include <limits> |
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| 35 | |
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| 36 | namespace lemon { |
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| 37 | |
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| 38 | /// \brief Default OperationTraits for the Johnson algorithm class. |
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| 39 | /// |
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| 40 | /// It defines all computational operations and constants which are |
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| 41 | /// used in the Floyd-Warshall algorithm. The default implementation |
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| 42 | /// is based on the numeric_limits class. If the numeric type does not |
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| 43 | /// have infinity value then the maximum value is used as extremal |
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| 44 | /// infinity value. |
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| 45 | template < |
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| 46 | typename Value, |
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| 47 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
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| 48 | struct JohnsonDefaultOperationTraits { |
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| 49 | /// \brief Gives back the zero value of the type. |
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| 50 | static Value zero() { |
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| 51 | return static_cast<Value>(0); |
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| 52 | } |
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| 53 | /// \brief Gives back the positive infinity value of the type. |
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| 54 | static Value infinity() { |
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| 55 | return std::numeric_limits<Value>::infinity(); |
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| 56 | } |
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| 57 | /// \brief Gives back the sum of the given two elements. |
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| 58 | static Value plus(const Value& left, const Value& right) { |
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| 59 | return left + right; |
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| 60 | } |
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| 61 | /// \brief Gives back true only if the first value less than the second. |
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| 62 | static bool less(const Value& left, const Value& right) { |
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| 63 | return left < right; |
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| 64 | } |
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| 65 | }; |
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| 66 | |
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| 67 | template <typename Value> |
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| 68 | struct JohnsonDefaultOperationTraits<Value, false> { |
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| 69 | static Value zero() { |
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| 70 | return static_cast<Value>(0); |
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| 71 | } |
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| 72 | static Value infinity() { |
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| 73 | return std::numeric_limits<Value>::max(); |
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| 74 | } |
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| 75 | static Value plus(const Value& left, const Value& right) { |
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| 76 | if (left == infinity() || right == infinity()) return infinity(); |
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| 77 | return left + right; |
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| 78 | } |
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| 79 | static bool less(const Value& left, const Value& right) { |
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| 80 | return left < right; |
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| 81 | } |
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| 82 | }; |
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| 83 | |
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| 84 | /// \brief Default traits class of Johnson class. |
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| 85 | /// |
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| 86 | /// Default traits class of Johnson class. |
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| 87 | /// \param _Graph Graph type. |
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| 88 | /// \param _LegthMap Type of length map. |
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| 89 | template<class _Graph, class _LengthMap> |
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| 90 | struct JohnsonDefaultTraits { |
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| 91 | /// The graph type the algorithm runs on. |
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| 92 | typedef _Graph Graph; |
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| 93 | |
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| 94 | /// \brief The type of the map that stores the edge lengths. |
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| 95 | /// |
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| 96 | /// The type of the map that stores the edge lengths. |
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| 97 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
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| 98 | typedef _LengthMap LengthMap; |
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| 99 | |
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| 100 | // The type of the length of the edges. |
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| 101 | typedef typename _LengthMap::Value Value; |
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| 102 | |
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[1864] | 103 | /// \brief Operation traits for bellman-ford algorithm. |
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[1699] | 104 | /// |
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| 105 | /// It defines the infinity type on the given Value type |
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| 106 | /// and the used operation. |
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| 107 | /// \see JohnsonDefaultOperationTraits |
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| 108 | typedef JohnsonDefaultOperationTraits<Value> OperationTraits; |
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[1741] | 109 | |
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| 110 | /// The cross reference type used by heap. |
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| 111 | |
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| 112 | /// The cross reference type used by heap. |
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| 113 | /// Usually it is \c Graph::NodeMap<int>. |
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| 114 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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| 115 | |
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| 116 | ///Instantiates a HeapCrossRef. |
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| 117 | |
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| 118 | ///This function instantiates a \ref HeapCrossRef. |
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| 119 | /// \param graph is the graph, to which we would like to define the |
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| 120 | /// HeapCrossRef. |
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| 121 | static HeapCrossRef *createHeapCrossRef(const Graph& graph) { |
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| 122 | return new HeapCrossRef(graph); |
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| 123 | } |
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| 124 | |
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| 125 | ///The heap type used by Dijkstra algorithm. |
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| 126 | |
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| 127 | ///The heap type used by Dijkstra algorithm. |
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| 128 | /// |
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| 129 | ///\sa BinHeap |
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| 130 | ///\sa Dijkstra |
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| 131 | typedef BinHeap<typename Graph::Node, typename LengthMap::Value, |
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| 132 | HeapCrossRef, std::less<Value> > Heap; |
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| 133 | |
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| 134 | ///Instantiates a Heap. |
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| 135 | |
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| 136 | ///This function instantiates a \ref Heap. |
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| 137 | /// \param crossRef The cross reference for the heap. |
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| 138 | static Heap *createHeap(HeapCrossRef& crossRef) { |
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| 139 | return new Heap(crossRef); |
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| 140 | } |
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[1699] | 141 | |
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[1723] | 142 | /// \brief The type of the matrix map that stores the last edges of the |
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[1699] | 143 | /// shortest paths. |
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| 144 | /// |
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[1723] | 145 | /// The type of the map that stores the last edges of the shortest paths. |
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[1699] | 146 | /// It must be a matrix map with \c Graph::Edge value type. |
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| 147 | /// |
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[1723] | 148 | typedef DynamicMatrixMap<Graph, typename Graph::Node, |
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| 149 | typename Graph::Edge> PredMap; |
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[1699] | 150 | |
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| 151 | /// \brief Instantiates a PredMap. |
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| 152 | /// |
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| 153 | /// This function instantiates a \ref PredMap. |
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| 154 | /// \param G is the graph, to which we would like to define the PredMap. |
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| 155 | /// \todo The graph alone may be insufficient for the initialization |
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[1741] | 156 | static PredMap *createPredMap(const Graph& graph) { |
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[1699] | 157 | return new PredMap(graph); |
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| 158 | } |
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| 159 | |
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[1723] | 160 | /// \brief The type of the matrix map that stores the dists of the nodes. |
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[1699] | 161 | /// |
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[1723] | 162 | /// The type of the matrix map that stores the dists of the nodes. |
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| 163 | /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept. |
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[1699] | 164 | /// |
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[1723] | 165 | typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap; |
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| 166 | |
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[1699] | 167 | /// \brief Instantiates a DistMap. |
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| 168 | /// |
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| 169 | /// This function instantiates a \ref DistMap. |
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| 170 | /// \param G is the graph, to which we would like to define the |
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| 171 | /// \ref DistMap |
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| 172 | static DistMap *createDistMap(const _Graph& graph) { |
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| 173 | return new DistMap(graph); |
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| 174 | } |
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| 175 | |
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| 176 | }; |
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| 177 | |
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[1754] | 178 | /// \brief %Johnson algorithm class. |
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[1699] | 179 | /// |
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| 180 | /// \ingroup flowalgs |
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[1754] | 181 | /// This class provides an efficient implementation of \c %Johnson |
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[1699] | 182 | /// algorithm. The edge lengths are passed to the algorithm using a |
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| 183 | /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any |
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| 184 | /// kind of length. |
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| 185 | /// |
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[1757] | 186 | /// The algorithm solves the shortest path problem for each pair |
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[1723] | 187 | /// of node when the edges can have negative length but the graph should |
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[1754] | 188 | /// not contain cycles with negative sum of length. If we can assume |
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[1723] | 189 | /// that all edge is non-negative in the graph then the dijkstra algorithm |
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| 190 | /// should be used from each node. |
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| 191 | /// |
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| 192 | /// The complexity of this algorithm is $O(n^2 * log(n) + n * log(n) * e)$ or |
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[1741] | 193 | /// with fibonacci heap O(n^2 * log(n) + n * e). Usually the fibonacci heap |
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| 194 | /// implementation is slower than either binary heap implementation or the |
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| 195 | /// Floyd-Warshall algorithm. |
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[1723] | 196 | /// |
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[1699] | 197 | /// The type of the length is determined by the |
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| 198 | /// \ref concept::ReadMap::Value "Value" of the length map. |
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| 199 | /// |
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| 200 | /// \param _Graph The graph type the algorithm runs on. The default value |
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| 201 | /// is \ref ListGraph. The value of _Graph is not used directly by |
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| 202 | /// Johnson, it is only passed to \ref JohnsonDefaultTraits. |
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| 203 | /// \param _LengthMap This read-only EdgeMap determines the lengths of the |
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| 204 | /// edges. It is read once for each edge, so the map may involve in |
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| 205 | /// relatively time consuming process to compute the edge length if |
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| 206 | /// it is necessary. The default map type is \ref |
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| 207 | /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>". The value |
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| 208 | /// of _LengthMap is not used directly by Johnson, it is only passed |
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| 209 | /// to \ref JohnsonDefaultTraits. \param _Traits Traits class to set |
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| 210 | /// various data types used by the algorithm. The default traits |
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| 211 | /// class is \ref JohnsonDefaultTraits |
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| 212 | /// "JohnsonDefaultTraits<_Graph,_LengthMap>". See \ref |
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| 213 | /// JohnsonDefaultTraits for the documentation of a Johnson traits |
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| 214 | /// class. |
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| 215 | /// |
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| 216 | /// \author Balazs Dezso |
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| 217 | |
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[1710] | 218 | #ifdef DOXYGEN |
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| 219 | template <typename _Graph, typename _LengthMap, typename _Traits> |
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| 220 | #else |
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[1699] | 221 | template <typename _Graph=ListGraph, |
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| 222 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
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| 223 | typename _Traits=JohnsonDefaultTraits<_Graph,_LengthMap> > |
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[1710] | 224 | #endif |
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[1699] | 225 | class Johnson { |
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| 226 | public: |
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| 227 | |
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| 228 | /// \brief \ref Exception for uninitialized parameters. |
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| 229 | /// |
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| 230 | /// This error represents problems in the initialization |
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| 231 | /// of the parameters of the algorithms. |
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| 232 | |
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| 233 | class UninitializedParameter : public lemon::UninitializedParameter { |
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| 234 | public: |
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| 235 | virtual const char* exceptionName() const { |
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| 236 | return "lemon::Johnson::UninitializedParameter"; |
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| 237 | } |
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| 238 | }; |
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| 239 | |
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| 240 | typedef _Traits Traits; |
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| 241 | ///The type of the underlying graph. |
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| 242 | typedef typename _Traits::Graph Graph; |
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| 243 | |
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| 244 | typedef typename Graph::Node Node; |
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| 245 | typedef typename Graph::NodeIt NodeIt; |
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| 246 | typedef typename Graph::Edge Edge; |
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| 247 | typedef typename Graph::EdgeIt EdgeIt; |
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| 248 | |
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| 249 | /// \brief The type of the length of the edges. |
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| 250 | typedef typename _Traits::LengthMap::Value Value; |
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| 251 | /// \brief The type of the map that stores the edge lengths. |
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| 252 | typedef typename _Traits::LengthMap LengthMap; |
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| 253 | /// \brief The type of the map that stores the last |
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| 254 | /// edges of the shortest paths. The type of the PredMap |
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| 255 | /// is a matrix map for Edges |
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| 256 | typedef typename _Traits::PredMap PredMap; |
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| 257 | /// \brief The type of the map that stores the dists of the nodes. |
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| 258 | /// The type of the DistMap is a matrix map for Values |
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| 259 | typedef typename _Traits::DistMap DistMap; |
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| 260 | /// \brief The operation traits. |
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| 261 | typedef typename _Traits::OperationTraits OperationTraits; |
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[1741] | 262 | ///The cross reference type used for the current heap. |
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| 263 | typedef typename _Traits::HeapCrossRef HeapCrossRef; |
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| 264 | ///The heap type used by the dijkstra algorithm. |
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| 265 | typedef typename _Traits::Heap Heap; |
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[1699] | 266 | private: |
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| 267 | /// Pointer to the underlying graph. |
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| 268 | const Graph *graph; |
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| 269 | /// Pointer to the length map |
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| 270 | const LengthMap *length; |
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| 271 | ///Pointer to the map of predecessors edges. |
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| 272 | PredMap *_pred; |
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| 273 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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| 274 | bool local_pred; |
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| 275 | ///Pointer to the map of distances. |
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| 276 | DistMap *_dist; |
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| 277 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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| 278 | bool local_dist; |
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[1741] | 279 | ///Pointer to the heap cross references. |
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| 280 | HeapCrossRef *_heap_cross_ref; |
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| 281 | ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not. |
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| 282 | bool local_heap_cross_ref; |
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| 283 | ///Pointer to the heap. |
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| 284 | Heap *_heap; |
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| 285 | ///Indicates if \ref _heap is locally allocated (\c true) or not. |
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| 286 | bool local_heap; |
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[1699] | 287 | |
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| 288 | /// Creates the maps if necessary. |
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| 289 | void create_maps() { |
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| 290 | if(!_pred) { |
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| 291 | local_pred = true; |
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| 292 | _pred = Traits::createPredMap(*graph); |
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| 293 | } |
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| 294 | if(!_dist) { |
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| 295 | local_dist = true; |
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| 296 | _dist = Traits::createDistMap(*graph); |
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| 297 | } |
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[1741] | 298 | if (!_heap_cross_ref) { |
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| 299 | local_heap_cross_ref = true; |
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| 300 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
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| 301 | } |
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| 302 | if (!_heap) { |
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| 303 | local_heap = true; |
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| 304 | _heap = Traits::createHeap(*_heap_cross_ref); |
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| 305 | } |
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[1699] | 306 | } |
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[1741] | 307 | |
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[1699] | 308 | public : |
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[1741] | 309 | |
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[1699] | 310 | /// \name Named template parameters |
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| 311 | |
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| 312 | ///@{ |
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| 313 | |
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| 314 | template <class T> |
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| 315 | struct DefPredMapTraits : public Traits { |
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| 316 | typedef T PredMap; |
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| 317 | static PredMap *createPredMap(const Graph& graph) { |
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| 318 | throw UninitializedParameter(); |
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| 319 | } |
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| 320 | }; |
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| 321 | |
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| 322 | /// \brief \ref named-templ-param "Named parameter" for setting PredMap |
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| 323 | /// type |
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| 324 | /// \ref named-templ-param "Named parameter" for setting PredMap type |
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| 325 | /// |
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| 326 | template <class T> |
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[1710] | 327 | struct DefPredMap |
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| 328 | : public Johnson< Graph, LengthMap, DefPredMapTraits<T> > { |
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| 329 | typedef Johnson< Graph, LengthMap, DefPredMapTraits<T> > Create; |
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| 330 | }; |
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[1699] | 331 | |
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| 332 | template <class T> |
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| 333 | struct DefDistMapTraits : public Traits { |
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| 334 | typedef T DistMap; |
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| 335 | static DistMap *createDistMap(const Graph& graph) { |
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| 336 | throw UninitializedParameter(); |
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| 337 | } |
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| 338 | }; |
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| 339 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
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| 340 | /// type |
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| 341 | /// |
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| 342 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
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| 343 | /// |
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| 344 | template <class T> |
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[1710] | 345 | struct DefDistMap |
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| 346 | : public Johnson< Graph, LengthMap, DefDistMapTraits<T> > { |
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| 347 | typedef Johnson< Graph, LengthMap, DefDistMapTraits<T> > Create; |
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| 348 | }; |
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[1699] | 349 | |
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| 350 | template <class T> |
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| 351 | struct DefOperationTraitsTraits : public Traits { |
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| 352 | typedef T OperationTraits; |
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| 353 | }; |
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| 354 | |
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| 355 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 356 | /// OperationTraits type |
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| 357 | /// |
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[1710] | 358 | /// \ref named-templ-param "Named parameter" for setting |
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| 359 | /// OperationTraits type |
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[1699] | 360 | template <class T> |
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[1710] | 361 | struct DefOperationTraits |
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| 362 | : public Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
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| 363 | typedef Johnson< Graph, LengthMap, DefOperationTraitsTraits<T> > Create; |
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| 364 | }; |
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[1741] | 365 | |
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| 366 | template <class H, class CR> |
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| 367 | struct DefHeapTraits : public Traits { |
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| 368 | typedef CR HeapCrossRef; |
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| 369 | typedef H Heap; |
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| 370 | static HeapCrossRef *createHeapCrossRef(const Graph &) { |
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| 371 | throw UninitializedParameter(); |
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| 372 | } |
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| 373 | static Heap *createHeap(HeapCrossRef &) |
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| 374 | { |
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| 375 | throw UninitializedParameter(); |
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| 376 | } |
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| 377 | }; |
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[1754] | 378 | ///\brief \ref named-templ-param "Named parameter" for setting heap and |
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| 379 | ///cross reference type |
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[1741] | 380 | |
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| 381 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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| 382 | ///reference type |
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| 383 | /// |
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| 384 | template <class H, class CR = typename Graph::template NodeMap<int> > |
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| 385 | struct DefHeap |
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| 386 | : public Johnson< Graph, LengthMap, DefHeapTraits<H, CR> > { |
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| 387 | typedef Johnson< Graph, LengthMap, DefHeapTraits<H, CR> > Create; |
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| 388 | }; |
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| 389 | |
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| 390 | template <class H, class CR> |
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| 391 | struct DefStandardHeapTraits : public Traits { |
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| 392 | typedef CR HeapCrossRef; |
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| 393 | typedef H Heap; |
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| 394 | static HeapCrossRef *createHeapCrossRef(const Graph &G) { |
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| 395 | return new HeapCrossRef(G); |
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| 396 | } |
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| 397 | static Heap *createHeap(HeapCrossRef &R) |
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| 398 | { |
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| 399 | return new Heap(R); |
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| 400 | } |
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| 401 | }; |
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| 402 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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| 403 | ///reference type with automatic allocation |
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| 404 | |
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| 405 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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| 406 | ///reference type. It can allocate the heap and the cross reference |
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| 407 | ///object if the cross reference's constructor waits for the graph as |
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| 408 | ///parameter and the heap's constructor waits for the cross reference. |
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| 409 | template <class H, class CR = typename Graph::template NodeMap<int> > |
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| 410 | struct DefStandardHeap |
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| 411 | : public Johnson< Graph, LengthMap, DefStandardHeapTraits<H, CR> > { |
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| 412 | typedef Johnson< Graph, LengthMap, DefStandardHeapTraits<H, CR> > |
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| 413 | Create; |
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| 414 | }; |
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[1699] | 415 | |
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| 416 | ///@} |
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| 417 | |
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[1710] | 418 | protected: |
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| 419 | |
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| 420 | Johnson() {} |
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| 421 | |
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[1699] | 422 | public: |
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[1741] | 423 | |
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| 424 | typedef Johnson Create; |
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[1699] | 425 | |
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| 426 | /// \brief Constructor. |
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| 427 | /// |
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| 428 | /// \param _graph the graph the algorithm will run on. |
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| 429 | /// \param _length the length map used by the algorithm. |
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| 430 | Johnson(const Graph& _graph, const LengthMap& _length) : |
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| 431 | graph(&_graph), length(&_length), |
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| 432 | _pred(0), local_pred(false), |
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[1741] | 433 | _dist(0), local_dist(false), |
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| 434 | _heap_cross_ref(0), local_heap_cross_ref(false), |
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| 435 | _heap(0), local_heap(false) {} |
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[1699] | 436 | |
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| 437 | ///Destructor. |
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| 438 | ~Johnson() { |
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[1741] | 439 | if (local_pred) delete _pred; |
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| 440 | if (local_dist) delete _dist; |
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| 441 | if (local_heap_cross_ref) delete _heap_cross_ref; |
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| 442 | if (local_heap) delete _heap; |
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[1699] | 443 | } |
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| 444 | |
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| 445 | /// \brief Sets the length map. |
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| 446 | /// |
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| 447 | /// Sets the length map. |
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| 448 | /// \return \c (*this) |
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| 449 | Johnson &lengthMap(const LengthMap &m) { |
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| 450 | length = &m; |
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| 451 | return *this; |
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| 452 | } |
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| 453 | |
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| 454 | /// \brief Sets the map storing the predecessor edges. |
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| 455 | /// |
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| 456 | /// Sets the map storing the predecessor edges. |
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| 457 | /// If you don't use this function before calling \ref run(), |
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| 458 | /// it will allocate one. The destuctor deallocates this |
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| 459 | /// automatically allocated map, of course. |
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| 460 | /// \return \c (*this) |
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| 461 | Johnson &predMap(PredMap &m) { |
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| 462 | if(local_pred) { |
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| 463 | delete _pred; |
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| 464 | local_pred=false; |
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| 465 | } |
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| 466 | _pred = &m; |
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| 467 | return *this; |
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| 468 | } |
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| 469 | |
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| 470 | /// \brief Sets the map storing the distances calculated by the algorithm. |
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| 471 | /// |
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| 472 | /// Sets the map storing the distances calculated by the algorithm. |
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| 473 | /// If you don't use this function before calling \ref run(), |
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| 474 | /// it will allocate one. The destuctor deallocates this |
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| 475 | /// automatically allocated map, of course. |
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| 476 | /// \return \c (*this) |
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| 477 | Johnson &distMap(DistMap &m) { |
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| 478 | if(local_dist) { |
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| 479 | delete _dist; |
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| 480 | local_dist=false; |
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| 481 | } |
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| 482 | _dist = &m; |
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| 483 | return *this; |
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| 484 | } |
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| 485 | |
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[1916] | 486 | public: |
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| 487 | |
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| 488 | ///\name Execution control |
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| 489 | /// The simplest way to execute the algorithm is to use |
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| 490 | /// one of the member functions called \c run(...). |
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| 491 | /// \n |
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| 492 | /// If you need more control on the execution, |
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| 493 | /// Finally \ref start() will perform the actual path |
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| 494 | /// computation. |
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| 495 | |
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| 496 | ///@{ |
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| 497 | |
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| 498 | /// \brief Initializes the internal data structures. |
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| 499 | /// |
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| 500 | /// Initializes the internal data structures. |
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| 501 | void init() { |
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| 502 | create_maps(); |
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| 503 | } |
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| 504 | |
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| 505 | /// \brief Executes the algorithm with own potential map. |
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| 506 | /// |
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| 507 | /// This method runs the %Johnson algorithm in order to compute |
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| 508 | /// the shortest path to each node pairs. The potential map |
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| 509 | /// can be given for this algorithm which usually calculated |
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| 510 | /// by the Bellman-Ford algorithm. If the graph does not have |
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| 511 | /// negative length edge then this start function can be used |
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| 512 | /// with constMap<Node, int>(0) parameter to omit the running time of |
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| 513 | /// the Bellman-Ford. |
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| 514 | /// The algorithm computes |
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| 515 | /// - The shortest path tree for each node. |
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| 516 | /// - The distance between each node pairs. |
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[1754] | 517 | template <typename PotentialMap> |
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[1916] | 518 | void shiftedStart(const PotentialMap& potential) { |
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[1747] | 519 | typename Graph::template EdgeMap<Value> shiftlen(*graph); |
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| 520 | for (EdgeIt it(*graph); it != INVALID; ++it) { |
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| 521 | shiftlen[it] = (*length)[it] |
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[1754] | 522 | + potential[graph->source(it)] |
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| 523 | - potential[graph->target(it)]; |
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[1747] | 524 | } |
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| 525 | |
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| 526 | typename Dijkstra<Graph, typename Graph::template EdgeMap<Value> >:: |
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| 527 | template DefHeap<Heap, HeapCrossRef>:: |
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| 528 | Create dijkstra(*graph, shiftlen); |
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[1741] | 529 | |
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| 530 | dijkstra.heap(*_heap, *_heap_cross_ref); |
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| 531 | |
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| 532 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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| 533 | dijkstra.run(it); |
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| 534 | for (NodeIt jt(*graph); jt != INVALID; ++jt) { |
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| 535 | if (dijkstra.reached(jt)) { |
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| 536 | _dist->set(it, jt, dijkstra.dist(jt) + |
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[1754] | 537 | potential[jt] - potential[it]); |
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[1763] | 538 | _pred->set(it, jt, dijkstra.predEdge(jt)); |
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[1741] | 539 | } else { |
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| 540 | _dist->set(it, jt, OperationTraits::infinity()); |
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| 541 | _pred->set(it, jt, INVALID); |
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| 542 | } |
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| 543 | } |
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| 544 | } |
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| 545 | } |
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| 546 | |
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[1699] | 547 | /// \brief Executes the algorithm. |
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| 548 | /// |
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| 549 | /// This method runs the %Johnson algorithm in order to compute |
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| 550 | /// the shortest path to each node pairs. The algorithm |
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| 551 | /// computes |
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| 552 | /// - The shortest path tree for each node. |
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| 553 | /// - The distance between each node pairs. |
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| 554 | void start() { |
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[1710] | 555 | |
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[1864] | 556 | typedef typename BellmanFord<Graph, LengthMap>:: |
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[1754] | 557 | template DefOperationTraits<OperationTraits>:: |
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| 558 | template DefPredMap<NullMap<Node, Edge> >:: |
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[1864] | 559 | Create BellmanFordType; |
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[1754] | 560 | |
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[1864] | 561 | BellmanFordType bellmanford(*graph, *length); |
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[1710] | 562 | |
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| 563 | NullMap<Node, Edge> predMap; |
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| 564 | |
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[1864] | 565 | bellmanford.predMap(predMap); |
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[1699] | 566 | |
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[1864] | 567 | bellmanford.init(OperationTraits::zero()); |
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| 568 | bellmanford.start(); |
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[1699] | 569 | |
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[1916] | 570 | shiftedStart(bellmanford.distMap()); |
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[1699] | 571 | } |
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[1741] | 572 | |
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[1754] | 573 | /// \brief Executes the algorithm and checks the negatvie cycles. |
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[1741] | 574 | /// |
---|
| 575 | /// This method runs the %Johnson algorithm in order to compute |
---|
| 576 | /// the shortest path to each node pairs. If the graph contains |
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[1754] | 577 | /// negative cycle it gives back false. The algorithm |
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[1741] | 578 | /// computes |
---|
| 579 | /// - The shortest path tree for each node. |
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| 580 | /// - The distance between each node pairs. |
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| 581 | bool checkedStart() { |
---|
[1754] | 582 | |
---|
[1864] | 583 | typedef typename BellmanFord<Graph, LengthMap>:: |
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[1754] | 584 | template DefOperationTraits<OperationTraits>:: |
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| 585 | template DefPredMap<NullMap<Node, Edge> >:: |
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[1864] | 586 | Create BellmanFordType; |
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[1741] | 587 | |
---|
[1864] | 588 | BellmanFordType bellmanford(*graph, *length); |
---|
[1741] | 589 | |
---|
| 590 | NullMap<Node, Edge> predMap; |
---|
| 591 | |
---|
[1864] | 592 | bellmanford.predMap(predMap); |
---|
[1741] | 593 | |
---|
[1864] | 594 | bellmanford.init(OperationTraits::zero()); |
---|
| 595 | if (!bellmanford.checkedStart()) return false; |
---|
[1741] | 596 | |
---|
[1916] | 597 | shiftedStart(bellmanford.distMap()); |
---|
[1741] | 598 | return true; |
---|
| 599 | } |
---|
| 600 | |
---|
[1699] | 601 | |
---|
| 602 | /// \brief Runs %Johnson algorithm. |
---|
| 603 | /// |
---|
| 604 | /// This method runs the %Johnson algorithm from a each node |
---|
| 605 | /// in order to compute the shortest path to each node pairs. |
---|
| 606 | /// The algorithm computes |
---|
| 607 | /// - The shortest path tree for each node. |
---|
| 608 | /// - The distance between each node pairs. |
---|
| 609 | /// |
---|
| 610 | /// \note d.run(s) is just a shortcut of the following code. |
---|
[1946] | 611 | ///\code |
---|
[1699] | 612 | /// d.init(); |
---|
| 613 | /// d.start(); |
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[1946] | 614 | ///\endcode |
---|
[1699] | 615 | void run() { |
---|
| 616 | init(); |
---|
| 617 | start(); |
---|
| 618 | } |
---|
| 619 | |
---|
| 620 | ///@} |
---|
| 621 | |
---|
| 622 | /// \name Query Functions |
---|
| 623 | /// The result of the %Johnson algorithm can be obtained using these |
---|
| 624 | /// functions.\n |
---|
| 625 | /// Before the use of these functions, |
---|
| 626 | /// either run() or start() must be called. |
---|
| 627 | |
---|
| 628 | ///@{ |
---|
| 629 | |
---|
| 630 | /// \brief Copies the shortest path to \c t into \c p |
---|
| 631 | /// |
---|
| 632 | /// This function copies the shortest path to \c t into \c p. |
---|
| 633 | /// If it \c t is a source itself or unreachable, then it does not |
---|
| 634 | /// alter \c p. |
---|
| 635 | /// \return Returns \c true if a path to \c t was actually copied to \c p, |
---|
| 636 | /// \c false otherwise. |
---|
| 637 | /// \sa DirPath |
---|
| 638 | template <typename Path> |
---|
| 639 | bool getPath(Path &p, Node source, Node target) { |
---|
| 640 | if (connected(source, target)) { |
---|
| 641 | p.clear(); |
---|
| 642 | typename Path::Builder b(target); |
---|
[1763] | 643 | for(b.setStartNode(target); predEdge(source, target) != INVALID; |
---|
[1699] | 644 | target = predNode(target)) { |
---|
[1763] | 645 | b.pushFront(predEdge(source, target)); |
---|
[1699] | 646 | } |
---|
| 647 | b.commit(); |
---|
| 648 | return true; |
---|
| 649 | } |
---|
| 650 | return false; |
---|
| 651 | } |
---|
| 652 | |
---|
| 653 | /// \brief The distance between two nodes. |
---|
| 654 | /// |
---|
| 655 | /// Returns the distance between two nodes. |
---|
| 656 | /// \pre \ref run() must be called before using this function. |
---|
| 657 | /// \warning If node \c v in unreachable from the root the return value |
---|
| 658 | /// of this funcion is undefined. |
---|
| 659 | Value dist(Node source, Node target) const { |
---|
| 660 | return (*_dist)(source, target); |
---|
| 661 | } |
---|
| 662 | |
---|
| 663 | /// \brief Returns the 'previous edge' of the shortest path tree. |
---|
| 664 | /// |
---|
| 665 | /// For the node \c node it returns the 'previous edge' of the shortest |
---|
| 666 | /// path tree to direction of the node \c root |
---|
| 667 | /// i.e. it returns the last edge of a shortest path from the node \c root |
---|
| 668 | /// to \c node. It is \ref INVALID if \c node is unreachable from the root |
---|
| 669 | /// or if \c node=root. The shortest path tree used here is equal to the |
---|
| 670 | /// shortest path tree used in \ref predNode(). |
---|
| 671 | /// \pre \ref run() must be called before using this function. |
---|
[1763] | 672 | Edge predEdge(Node root, Node node) const { |
---|
[1699] | 673 | return (*_pred)(root, node); |
---|
| 674 | } |
---|
| 675 | |
---|
| 676 | /// \brief Returns the 'previous node' of the shortest path tree. |
---|
| 677 | /// |
---|
| 678 | /// For a node \c node it returns the 'previous node' of the shortest path |
---|
| 679 | /// tree to direction of the node \c root, i.e. it returns the last but |
---|
| 680 | /// one node from a shortest path from the \c root to \c node. It is |
---|
| 681 | /// INVALID if \c node is unreachable from the root or if \c node=root. |
---|
| 682 | /// The shortest path tree used here is equal to the |
---|
[1763] | 683 | /// shortest path tree used in \ref predEdge(). |
---|
[1699] | 684 | /// \pre \ref run() must be called before using this function. |
---|
| 685 | Node predNode(Node root, Node node) const { |
---|
| 686 | return (*_pred)(root, node) == INVALID ? |
---|
| 687 | INVALID : graph->source((*_pred)(root, node)); |
---|
| 688 | } |
---|
| 689 | |
---|
| 690 | /// \brief Returns a reference to the matrix node map of distances. |
---|
| 691 | /// |
---|
| 692 | /// Returns a reference to the matrix node map of distances. |
---|
| 693 | /// |
---|
| 694 | /// \pre \ref run() must be called before using this function. |
---|
| 695 | const DistMap &distMap() const { return *_dist;} |
---|
| 696 | |
---|
| 697 | /// \brief Returns a reference to the shortest path tree map. |
---|
| 698 | /// |
---|
| 699 | /// Returns a reference to the matrix node map of the edges of the |
---|
| 700 | /// shortest path tree. |
---|
| 701 | /// \pre \ref run() must be called before using this function. |
---|
| 702 | const PredMap &predMap() const { return *_pred;} |
---|
| 703 | |
---|
| 704 | /// \brief Checks if a node is reachable from the root. |
---|
| 705 | /// |
---|
| 706 | /// Returns \c true if \c v is reachable from the root. |
---|
| 707 | /// \pre \ref run() must be called before using this function. |
---|
| 708 | /// |
---|
| 709 | bool connected(Node source, Node target) { |
---|
| 710 | return (*_dist)(source, target) != OperationTraits::infinity(); |
---|
| 711 | } |
---|
| 712 | |
---|
| 713 | ///@} |
---|
| 714 | }; |
---|
| 715 | |
---|
| 716 | } //END OF NAMESPACE LEMON |
---|
| 717 | |
---|
| 718 | #endif |
---|