[1699] | 1 | /* -*- C++ -*- |
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[1864] | 2 | * lemon/bellman_ford.h - Part of LEMON, a generic C++ optimization library |
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[1699] | 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_BELMANN_FORD_H |
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| 18 | #define LEMON_BELMANN_FORD_H |
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| 19 | |
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[1858] | 20 | /// \ingroup flowalgs |
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[1699] | 21 | /// \file |
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[1864] | 22 | /// \brief BellmanFord algorithm. |
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[1699] | 23 | /// |
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| 24 | |
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| 25 | #include <lemon/list_graph.h> |
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| 26 | #include <lemon/invalid.h> |
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| 27 | #include <lemon/error.h> |
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| 28 | #include <lemon/maps.h> |
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| 29 | |
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| 30 | #include <limits> |
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| 31 | |
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| 32 | namespace lemon { |
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| 33 | |
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[1864] | 34 | /// \brief Default OperationTraits for the BellmanFord algorithm class. |
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[1699] | 35 | /// |
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| 36 | /// It defines all computational operations and constants which are |
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[1864] | 37 | /// used in the bellman ford algorithm. The default implementation |
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[1699] | 38 | /// is based on the numeric_limits class. If the numeric type does not |
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| 39 | /// have infinity value then the maximum value is used as extremal |
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| 40 | /// infinity value. |
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| 41 | template < |
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| 42 | typename Value, |
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| 43 | bool has_infinity = std::numeric_limits<Value>::has_infinity> |
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[1864] | 44 | struct BellmanFordDefaultOperationTraits { |
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[1699] | 45 | /// \brief Gives back the zero value of the type. |
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| 46 | static Value zero() { |
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| 47 | return static_cast<Value>(0); |
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| 48 | } |
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| 49 | /// \brief Gives back the positive infinity value of the type. |
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| 50 | static Value infinity() { |
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| 51 | return std::numeric_limits<Value>::infinity(); |
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| 52 | } |
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| 53 | /// \brief Gives back the sum of the given two elements. |
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| 54 | static Value plus(const Value& left, const Value& right) { |
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| 55 | return left + right; |
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| 56 | } |
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| 57 | /// \brief Gives back true only if the first value less than the second. |
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| 58 | static bool less(const Value& left, const Value& right) { |
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| 59 | return left < right; |
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| 60 | } |
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| 61 | }; |
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| 62 | |
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| 63 | template <typename Value> |
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[1864] | 64 | struct BellmanFordDefaultOperationTraits<Value, false> { |
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[1699] | 65 | static Value zero() { |
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| 66 | return static_cast<Value>(0); |
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| 67 | } |
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| 68 | static Value infinity() { |
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| 69 | return std::numeric_limits<Value>::max(); |
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| 70 | } |
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| 71 | static Value plus(const Value& left, const Value& right) { |
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| 72 | if (left == infinity() || right == infinity()) return infinity(); |
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| 73 | return left + right; |
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| 74 | } |
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| 75 | static bool less(const Value& left, const Value& right) { |
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| 76 | return left < right; |
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| 77 | } |
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| 78 | }; |
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| 79 | |
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[1864] | 80 | /// \brief Default traits class of BellmanFord class. |
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[1699] | 81 | /// |
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[1864] | 82 | /// Default traits class of BellmanFord class. |
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[1699] | 83 | /// \param _Graph Graph type. |
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| 84 | /// \param _LegthMap Type of length map. |
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| 85 | template<class _Graph, class _LengthMap> |
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[1864] | 86 | struct BellmanFordDefaultTraits { |
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[1699] | 87 | /// The graph type the algorithm runs on. |
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| 88 | typedef _Graph Graph; |
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| 89 | |
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| 90 | /// \brief The type of the map that stores the edge lengths. |
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| 91 | /// |
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| 92 | /// The type of the map that stores the edge lengths. |
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| 93 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
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| 94 | typedef _LengthMap LengthMap; |
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| 95 | |
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| 96 | // The type of the length of the edges. |
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| 97 | typedef typename _LengthMap::Value Value; |
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| 98 | |
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[1864] | 99 | /// \brief Operation traits for bellman-ford algorithm. |
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[1699] | 100 | /// |
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| 101 | /// It defines the infinity type on the given Value type |
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| 102 | /// and the used operation. |
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[1864] | 103 | /// \see BellmanFordDefaultOperationTraits |
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| 104 | typedef BellmanFordDefaultOperationTraits<Value> OperationTraits; |
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[1699] | 105 | |
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| 106 | /// \brief The type of the map that stores the last edges of the |
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| 107 | /// shortest paths. |
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| 108 | /// |
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| 109 | /// The type of the map that stores the last |
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| 110 | /// edges of the shortest paths. |
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| 111 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
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| 112 | /// |
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| 113 | typedef typename Graph::template NodeMap<typename _Graph::Edge> PredMap; |
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| 114 | |
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| 115 | /// \brief Instantiates a PredMap. |
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| 116 | /// |
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| 117 | /// This function instantiates a \ref PredMap. |
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[1858] | 118 | /// \param graph is the graph, to which we would like to define the PredMap. |
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[1699] | 119 | static PredMap *createPredMap(const _Graph& graph) { |
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| 120 | return new PredMap(graph); |
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| 121 | } |
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| 122 | |
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| 123 | /// \brief The type of the map that stores the dists of the nodes. |
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| 124 | /// |
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| 125 | /// The type of the map that stores the dists of the nodes. |
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| 126 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
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| 127 | /// |
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| 128 | typedef typename Graph::template NodeMap<typename _LengthMap::Value> |
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| 129 | DistMap; |
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| 130 | |
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| 131 | /// \brief Instantiates a DistMap. |
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| 132 | /// |
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| 133 | /// This function instantiates a \ref DistMap. |
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[1858] | 134 | /// \param graph is the graph, to which we would like to define the |
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[1699] | 135 | /// \ref DistMap |
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| 136 | static DistMap *createDistMap(const _Graph& graph) { |
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| 137 | return new DistMap(graph); |
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| 138 | } |
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| 139 | |
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| 140 | }; |
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| 141 | |
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[1864] | 142 | /// \brief %BellmanFord algorithm class. |
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[1699] | 143 | /// |
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| 144 | /// \ingroup flowalgs |
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[1864] | 145 | /// This class provides an efficient implementation of \c Bellman-Ford |
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[1699] | 146 | /// algorithm. The edge lengths are passed to the algorithm using a |
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| 147 | /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any |
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| 148 | /// kind of length. |
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| 149 | /// |
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[1864] | 150 | /// The Bellman-Ford algorithm solves the shortest path from one node |
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[1723] | 151 | /// problem when the edges can have negative length but the graph should |
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[1754] | 152 | /// not contain cycles with negative sum of length. If we can assume |
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[1723] | 153 | /// that all edge is non-negative in the graph then the dijkstra algorithm |
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| 154 | /// should be used rather. |
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| 155 | /// |
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| 156 | /// The complexity of the algorithm is O(n * e). |
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| 157 | /// |
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[1699] | 158 | /// The type of the length is determined by the |
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| 159 | /// \ref concept::ReadMap::Value "Value" of the length map. |
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| 160 | /// |
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| 161 | /// \param _Graph The graph type the algorithm runs on. The default value |
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| 162 | /// is \ref ListGraph. The value of _Graph is not used directly by |
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[1864] | 163 | /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits. |
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[1699] | 164 | /// \param _LengthMap This read-only EdgeMap determines the lengths of the |
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| 165 | /// edges. The default map type is \ref concept::StaticGraph::EdgeMap |
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| 166 | /// "Graph::EdgeMap<int>". The value of _LengthMap is not used directly |
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[1864] | 167 | /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits. |
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[1699] | 168 | /// \param _Traits Traits class to set various data types used by the |
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[1864] | 169 | /// algorithm. The default traits class is \ref BellmanFordDefaultTraits |
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| 170 | /// "BellmanFordDefaultTraits<_Graph,_LengthMap>". See \ref |
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| 171 | /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits |
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[1699] | 172 | /// class. |
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| 173 | /// |
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| 174 | /// \author Balazs Dezso |
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| 175 | |
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[1710] | 176 | #ifdef DOXYGEN |
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| 177 | template <typename _Graph, typename _LengthMap, typename _Traits> |
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| 178 | #else |
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[1699] | 179 | template <typename _Graph=ListGraph, |
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| 180 | typename _LengthMap=typename _Graph::template EdgeMap<int>, |
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[1864] | 181 | typename _Traits=BellmanFordDefaultTraits<_Graph,_LengthMap> > |
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[1710] | 182 | #endif |
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[1864] | 183 | class BellmanFord { |
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[1699] | 184 | public: |
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| 185 | |
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| 186 | /// \brief \ref Exception for uninitialized parameters. |
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| 187 | /// |
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| 188 | /// This error represents problems in the initialization |
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| 189 | /// of the parameters of the algorithms. |
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| 190 | |
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| 191 | class UninitializedParameter : public lemon::UninitializedParameter { |
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| 192 | public: |
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| 193 | virtual const char* exceptionName() const { |
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[1864] | 194 | return "lemon::BellmanFord::UninitializedParameter"; |
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[1699] | 195 | } |
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| 196 | }; |
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| 197 | |
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| 198 | typedef _Traits Traits; |
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| 199 | ///The type of the underlying graph. |
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| 200 | typedef typename _Traits::Graph Graph; |
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| 201 | |
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| 202 | typedef typename Graph::Node Node; |
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| 203 | typedef typename Graph::NodeIt NodeIt; |
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| 204 | typedef typename Graph::Edge Edge; |
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[1781] | 205 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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[1699] | 206 | |
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| 207 | /// \brief The type of the length of the edges. |
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| 208 | typedef typename _Traits::LengthMap::Value Value; |
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| 209 | /// \brief The type of the map that stores the edge lengths. |
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| 210 | typedef typename _Traits::LengthMap LengthMap; |
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| 211 | /// \brief The type of the map that stores the last |
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| 212 | /// edges of the shortest paths. |
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| 213 | typedef typename _Traits::PredMap PredMap; |
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| 214 | /// \brief The type of the map that stores the dists of the nodes. |
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| 215 | typedef typename _Traits::DistMap DistMap; |
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| 216 | /// \brief The operation traits. |
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| 217 | typedef typename _Traits::OperationTraits OperationTraits; |
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| 218 | private: |
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| 219 | /// Pointer to the underlying graph. |
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| 220 | const Graph *graph; |
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| 221 | /// Pointer to the length map |
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| 222 | const LengthMap *length; |
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| 223 | ///Pointer to the map of predecessors edges. |
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| 224 | PredMap *_pred; |
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| 225 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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| 226 | bool local_pred; |
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| 227 | ///Pointer to the map of distances. |
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| 228 | DistMap *_dist; |
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| 229 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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| 230 | bool local_dist; |
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| 231 | |
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[1781] | 232 | typedef typename Graph::template NodeMap<bool> MaskMap; |
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| 233 | MaskMap *_mask; |
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| 234 | |
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| 235 | std::vector<Node> _process; |
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| 236 | |
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[1699] | 237 | /// Creates the maps if necessary. |
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| 238 | void create_maps() { |
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| 239 | if(!_pred) { |
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| 240 | local_pred = true; |
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| 241 | _pred = Traits::createPredMap(*graph); |
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| 242 | } |
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| 243 | if(!_dist) { |
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| 244 | local_dist = true; |
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| 245 | _dist = Traits::createDistMap(*graph); |
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| 246 | } |
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[1781] | 247 | _mask = new MaskMap(*graph, false); |
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[1699] | 248 | } |
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| 249 | |
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| 250 | public : |
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| 251 | |
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[1864] | 252 | typedef BellmanFord Create; |
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[1710] | 253 | |
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[1699] | 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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[1710] | 261 | static PredMap *createPredMap(const Graph&) { |
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[1699] | 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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[1858] | 271 | struct DefPredMap |
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[1864] | 272 | : public BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > { |
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| 273 | typedef BellmanFord< Graph, LengthMap, DefPredMapTraits<T> > Create; |
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[1710] | 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 | |
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| 284 | /// \brief \ref named-templ-param "Named parameter" for setting DistMap |
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| 285 | /// type |
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| 286 | /// |
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| 287 | /// \ref named-templ-param "Named parameter" for setting DistMap type |
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| 288 | /// |
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| 289 | template <class T> |
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[1710] | 290 | struct DefDistMap |
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[1864] | 291 | : public BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > { |
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| 292 | typedef BellmanFord< Graph, LengthMap, DefDistMapTraits<T> > Create; |
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[1710] | 293 | }; |
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[1699] | 294 | |
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| 295 | template <class T> |
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| 296 | struct DefOperationTraitsTraits : public Traits { |
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| 297 | typedef T OperationTraits; |
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| 298 | }; |
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| 299 | |
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| 300 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 301 | /// OperationTraits type |
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| 302 | /// |
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[1710] | 303 | /// \ref named-templ-param "Named parameter" for setting OperationTraits |
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| 304 | /// type |
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[1699] | 305 | template <class T> |
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[1710] | 306 | struct DefOperationTraits |
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[1864] | 307 | : public BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> > { |
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| 308 | typedef BellmanFord< Graph, LengthMap, DefOperationTraitsTraits<T> > |
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[1710] | 309 | Create; |
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[1699] | 310 | }; |
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| 311 | |
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| 312 | ///@} |
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| 313 | |
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[1710] | 314 | protected: |
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| 315 | |
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[1864] | 316 | BellmanFord() {} |
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[1710] | 317 | |
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[1699] | 318 | public: |
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| 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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[1864] | 324 | BellmanFord(const Graph& _graph, const LengthMap& _length) : |
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[1699] | 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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[1864] | 330 | ~BellmanFord() { |
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[1699] | 331 | if(local_pred) delete _pred; |
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| 332 | if(local_dist) delete _dist; |
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[1781] | 333 | delete _mask; |
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[1699] | 334 | } |
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| 335 | |
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| 336 | /// \brief Sets the length map. |
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| 337 | /// |
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| 338 | /// Sets the length map. |
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| 339 | /// \return \c (*this) |
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[1864] | 340 | BellmanFord &lengthMap(const LengthMap &m) { |
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[1699] | 341 | length = &m; |
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| 342 | return *this; |
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| 343 | } |
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| 344 | |
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| 345 | /// \brief Sets the map storing the predecessor edges. |
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| 346 | /// |
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| 347 | /// Sets the map storing the predecessor edges. |
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| 348 | /// If you don't use this function before calling \ref run(), |
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| 349 | /// it will allocate one. The destuctor deallocates this |
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| 350 | /// automatically allocated map, of course. |
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| 351 | /// \return \c (*this) |
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[1864] | 352 | BellmanFord &predMap(PredMap &m) { |
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[1699] | 353 | if(local_pred) { |
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| 354 | delete _pred; |
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| 355 | local_pred=false; |
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| 356 | } |
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| 357 | _pred = &m; |
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| 358 | return *this; |
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| 359 | } |
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| 360 | |
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| 361 | /// \brief Sets the map storing the distances calculated by the algorithm. |
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| 362 | /// |
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| 363 | /// Sets the map storing the distances calculated by the algorithm. |
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| 364 | /// If you don't use this function before calling \ref run(), |
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| 365 | /// it will allocate one. The destuctor deallocates this |
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| 366 | /// automatically allocated map, of course. |
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| 367 | /// \return \c (*this) |
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[1864] | 368 | BellmanFord &distMap(DistMap &m) { |
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[1699] | 369 | if(local_dist) { |
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| 370 | delete _dist; |
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| 371 | local_dist=false; |
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| 372 | } |
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| 373 | _dist = &m; |
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| 374 | return *this; |
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| 375 | } |
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| 376 | |
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| 377 | /// \name Execution control |
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| 378 | /// The simplest way to execute the algorithm is to use |
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| 379 | /// one of the member functions called \c run(...). |
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| 380 | /// \n |
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| 381 | /// If you need more control on the execution, |
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| 382 | /// first you must call \ref init(), then you can add several source nodes |
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| 383 | /// with \ref addSource(). |
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| 384 | /// Finally \ref start() will perform the actual path |
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| 385 | /// computation. |
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| 386 | |
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| 387 | ///@{ |
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| 388 | |
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| 389 | /// \brief Initializes the internal data structures. |
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| 390 | /// |
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| 391 | /// Initializes the internal data structures. |
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[1710] | 392 | void init(const Value value = OperationTraits::infinity()) { |
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[1699] | 393 | create_maps(); |
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| 394 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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| 395 | _pred->set(it, INVALID); |
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[1710] | 396 | _dist->set(it, value); |
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[1699] | 397 | } |
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[1781] | 398 | _process.clear(); |
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| 399 | if (OperationTraits::less(value, OperationTraits::infinity())) { |
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| 400 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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| 401 | _process.push_back(it); |
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[1783] | 402 | _mask->set(it, true); |
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[1781] | 403 | } |
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| 404 | } |
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[1699] | 405 | } |
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| 406 | |
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| 407 | /// \brief Adds a new source node. |
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| 408 | /// |
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| 409 | /// The optional second parameter is the initial distance of the node. |
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| 410 | /// It just sets the distance of the node to the given value. |
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| 411 | void addSource(Node source, Value dst = OperationTraits::zero()) { |
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| 412 | _dist->set(source, dst); |
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[1781] | 413 | if (!(*_mask)[source]) { |
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| 414 | _process.push_back(source); |
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| 415 | _mask->set(source, true); |
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| 416 | } |
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| 417 | } |
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| 418 | |
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[1864] | 419 | /// \brief Executes one round from the bellman ford algorithm. |
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[1781] | 420 | /// |
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| 421 | /// If the algoritm calculated the distances in the previous round |
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[1816] | 422 | /// strictly for all at most k length paths then it will calculate the |
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| 423 | /// distances strictly for all at most k + 1 length paths. With k |
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| 424 | /// iteration this function calculates the at most k length paths. |
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[1858] | 425 | /// \return %True when the algorithm have not found more shorter paths. |
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[1781] | 426 | bool processNextRound() { |
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| 427 | for (int i = 0; i < (int)_process.size(); ++i) { |
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| 428 | _mask->set(_process[i], false); |
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| 429 | } |
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| 430 | std::vector<Node> nextProcess; |
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| 431 | std::vector<Value> values(_process.size()); |
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| 432 | for (int i = 0; i < (int)_process.size(); ++i) { |
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[1857] | 433 | values[i] = (*_dist)[_process[i]]; |
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[1781] | 434 | } |
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| 435 | for (int i = 0; i < (int)_process.size(); ++i) { |
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| 436 | for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) { |
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| 437 | Node target = graph->target(it); |
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| 438 | Value relaxed = OperationTraits::plus(values[i], (*length)[it]); |
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| 439 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
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| 440 | _pred->set(target, it); |
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| 441 | _dist->set(target, relaxed); |
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| 442 | if (!(*_mask)[target]) { |
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| 443 | _mask->set(target, true); |
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| 444 | nextProcess.push_back(target); |
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| 445 | } |
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| 446 | } |
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| 447 | } |
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| 448 | } |
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| 449 | _process.swap(nextProcess); |
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| 450 | return _process.empty(); |
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| 451 | } |
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| 452 | |
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[1864] | 453 | /// \brief Executes one weak round from the bellman ford algorithm. |
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[1781] | 454 | /// |
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| 455 | /// If the algorithm calculated the distances in the |
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[1816] | 456 | /// previous round at least for all at most k length paths then it will |
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| 457 | /// calculate the distances at least for all at most k + 1 length paths. |
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| 458 | /// This function does not make it possible to calculate strictly the |
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| 459 | /// at most k length minimal paths, this is why it is |
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| 460 | /// called just weak round. |
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[1858] | 461 | /// \return %True when the algorithm have not found more shorter paths. |
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[1781] | 462 | bool processNextWeakRound() { |
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| 463 | for (int i = 0; i < (int)_process.size(); ++i) { |
---|
| 464 | _mask->set(_process[i], false); |
---|
| 465 | } |
---|
| 466 | std::vector<Node> nextProcess; |
---|
| 467 | for (int i = 0; i < (int)_process.size(); ++i) { |
---|
| 468 | for (OutEdgeIt it(*graph, _process[i]); it != INVALID; ++it) { |
---|
| 469 | Node target = graph->target(it); |
---|
| 470 | Value relaxed = |
---|
| 471 | OperationTraits::plus((*_dist)[_process[i]], (*length)[it]); |
---|
| 472 | if (OperationTraits::less(relaxed, (*_dist)[target])) { |
---|
| 473 | _pred->set(target, it); |
---|
| 474 | _dist->set(target, relaxed); |
---|
| 475 | if (!(*_mask)[target]) { |
---|
| 476 | _mask->set(target, true); |
---|
| 477 | nextProcess.push_back(target); |
---|
| 478 | } |
---|
| 479 | } |
---|
| 480 | } |
---|
| 481 | } |
---|
| 482 | _process.swap(nextProcess); |
---|
| 483 | return _process.empty(); |
---|
[1699] | 484 | } |
---|
| 485 | |
---|
| 486 | /// \brief Executes the algorithm. |
---|
| 487 | /// |
---|
| 488 | /// \pre init() must be called and at least one node should be added |
---|
| 489 | /// with addSource() before using this function. |
---|
| 490 | /// |
---|
[1864] | 491 | /// This method runs the %BellmanFord algorithm from the root node(s) |
---|
[1699] | 492 | /// in order to compute the shortest path to each node. The algorithm |
---|
| 493 | /// computes |
---|
| 494 | /// - The shortest path tree. |
---|
| 495 | /// - The distance of each node from the root(s). |
---|
| 496 | void start() { |
---|
[1723] | 497 | int num = countNodes(*graph) - 1; |
---|
| 498 | for (int i = 0; i < num; ++i) { |
---|
[1781] | 499 | if (processNextWeakRound()) break; |
---|
[1699] | 500 | } |
---|
| 501 | } |
---|
[1723] | 502 | |
---|
[1754] | 503 | /// \brief Executes the algorithm and checks the negative cycles. |
---|
[1723] | 504 | /// |
---|
| 505 | /// \pre init() must be called and at least one node should be added |
---|
| 506 | /// with addSource() before using this function. If there is |
---|
[1754] | 507 | /// a negative cycles in the graph it gives back false. |
---|
[1723] | 508 | /// |
---|
[1864] | 509 | /// This method runs the %BellmanFord algorithm from the root node(s) |
---|
[1723] | 510 | /// in order to compute the shortest path to each node. The algorithm |
---|
| 511 | /// computes |
---|
| 512 | /// - The shortest path tree. |
---|
| 513 | /// - The distance of each node from the root(s). |
---|
| 514 | bool checkedStart() { |
---|
| 515 | int num = countNodes(*graph); |
---|
| 516 | for (int i = 0; i < num; ++i) { |
---|
[1781] | 517 | if (processNextWeakRound()) return true; |
---|
[1723] | 518 | } |
---|
| 519 | return false; |
---|
| 520 | } |
---|
[1781] | 521 | |
---|
| 522 | /// \brief Executes the algorithm with path length limit. |
---|
| 523 | /// |
---|
| 524 | /// \pre init() must be called and at least one node should be added |
---|
| 525 | /// with addSource() before using this function. |
---|
| 526 | /// |
---|
[1864] | 527 | /// This method runs the %BellmanFord algorithm from the root node(s) |
---|
[1781] | 528 | /// in order to compute the shortest path with at most \c length edge |
---|
[1816] | 529 | /// long paths to each node. The algorithm computes |
---|
[1781] | 530 | /// - The shortest path tree. |
---|
| 531 | /// - The limited distance of each node from the root(s). |
---|
| 532 | void limitedStart(int length) { |
---|
| 533 | for (int i = 0; i < length; ++i) { |
---|
| 534 | if (processNextRound()) break; |
---|
| 535 | } |
---|
| 536 | } |
---|
[1699] | 537 | |
---|
[1864] | 538 | /// \brief Runs %BellmanFord algorithm from node \c s. |
---|
[1699] | 539 | /// |
---|
[1864] | 540 | /// This method runs the %BellmanFord algorithm from a root node \c s |
---|
[1699] | 541 | /// in order to compute the shortest path to each node. The algorithm |
---|
| 542 | /// computes |
---|
| 543 | /// - The shortest path tree. |
---|
| 544 | /// - The distance of each node from the root. |
---|
| 545 | /// |
---|
| 546 | /// \note d.run(s) is just a shortcut of the following code. |
---|
| 547 | /// \code |
---|
| 548 | /// d.init(); |
---|
| 549 | /// d.addSource(s); |
---|
| 550 | /// d.start(); |
---|
| 551 | /// \endcode |
---|
| 552 | void run(Node s) { |
---|
| 553 | init(); |
---|
| 554 | addSource(s); |
---|
| 555 | start(); |
---|
| 556 | } |
---|
| 557 | |
---|
[1864] | 558 | /// \brief Runs %BellmanFord algorithm with limited path length |
---|
[1857] | 559 | /// from node \c s. |
---|
| 560 | /// |
---|
[1864] | 561 | /// This method runs the %BellmanFord algorithm from a root node \c s |
---|
[1857] | 562 | /// in order to compute the shortest path with at most \c len edges |
---|
| 563 | /// to each node. The algorithm computes |
---|
| 564 | /// - The shortest path tree. |
---|
| 565 | /// - The distance of each node from the root. |
---|
| 566 | /// |
---|
| 567 | /// \note d.run(s, len) is just a shortcut of the following code. |
---|
| 568 | /// \code |
---|
| 569 | /// d.init(); |
---|
| 570 | /// d.addSource(s); |
---|
| 571 | /// d.limitedStart(len); |
---|
| 572 | /// \endcode |
---|
| 573 | void run(Node s, int len) { |
---|
| 574 | init(); |
---|
| 575 | addSource(s); |
---|
| 576 | limitedStart(len); |
---|
| 577 | } |
---|
| 578 | |
---|
[1699] | 579 | ///@} |
---|
| 580 | |
---|
| 581 | /// \name Query Functions |
---|
[1864] | 582 | /// The result of the %BellmanFord algorithm can be obtained using these |
---|
[1699] | 583 | /// functions.\n |
---|
| 584 | /// Before the use of these functions, |
---|
| 585 | /// either run() or start() must be called. |
---|
| 586 | |
---|
| 587 | ///@{ |
---|
| 588 | |
---|
| 589 | /// \brief Copies the shortest path to \c t into \c p |
---|
| 590 | /// |
---|
| 591 | /// This function copies the shortest path to \c t into \c p. |
---|
| 592 | /// If it \c t is a source itself or unreachable, then it does not |
---|
| 593 | /// alter \c p. |
---|
[1765] | 594 | /// |
---|
[1699] | 595 | /// \return Returns \c true if a path to \c t was actually copied to \c p, |
---|
| 596 | /// \c false otherwise. |
---|
| 597 | /// \sa DirPath |
---|
| 598 | template <typename Path> |
---|
| 599 | bool getPath(Path &p, Node t) { |
---|
| 600 | if(reached(t)) { |
---|
| 601 | p.clear(); |
---|
| 602 | typename Path::Builder b(p); |
---|
[1763] | 603 | for(b.setStartNode(t);predEdge(t)!=INVALID;t=predNode(t)) |
---|
| 604 | b.pushFront(predEdge(t)); |
---|
[1699] | 605 | b.commit(); |
---|
| 606 | return true; |
---|
| 607 | } |
---|
| 608 | return false; |
---|
| 609 | } |
---|
| 610 | |
---|
| 611 | /// \brief The distance of a node from the root. |
---|
| 612 | /// |
---|
| 613 | /// Returns the distance of a node from the root. |
---|
| 614 | /// \pre \ref run() must be called before using this function. |
---|
| 615 | /// \warning If node \c v in unreachable from the root the return value |
---|
| 616 | /// of this funcion is undefined. |
---|
| 617 | Value dist(Node v) const { return (*_dist)[v]; } |
---|
| 618 | |
---|
| 619 | /// \brief Returns the 'previous edge' of the shortest path tree. |
---|
| 620 | /// |
---|
| 621 | /// For a node \c v it returns the 'previous edge' of the shortest path |
---|
| 622 | /// tree, i.e. it returns the last edge of a shortest path from the root |
---|
| 623 | /// to \c v. It is \ref INVALID if \c v is unreachable from the root or |
---|
| 624 | /// if \c v=s. The shortest path tree used here is equal to the shortest |
---|
| 625 | /// path tree used in \ref predNode(). |
---|
| 626 | /// \pre \ref run() must be called before using |
---|
| 627 | /// this function. |
---|
[1763] | 628 | Edge predEdge(Node v) const { return (*_pred)[v]; } |
---|
[1699] | 629 | |
---|
| 630 | /// \brief Returns the 'previous node' of the shortest path tree. |
---|
| 631 | /// |
---|
| 632 | /// For a node \c v it returns the 'previous node' of the shortest path |
---|
| 633 | /// tree, i.e. it returns the last but one node from a shortest path from |
---|
| 634 | /// the root to \c /v. It is INVALID if \c v is unreachable from the root |
---|
| 635 | /// or if \c v=s. The shortest path tree used here is equal to the |
---|
[1763] | 636 | /// shortest path tree used in \ref predEdge(). \pre \ref run() must be |
---|
[1699] | 637 | /// called before using this function. |
---|
| 638 | Node predNode(Node v) const { |
---|
| 639 | return (*_pred)[v] == INVALID ? INVALID : graph->source((*_pred)[v]); |
---|
| 640 | } |
---|
| 641 | |
---|
| 642 | /// \brief Returns a reference to the NodeMap of distances. |
---|
| 643 | /// |
---|
| 644 | /// Returns a reference to the NodeMap of distances. \pre \ref run() must |
---|
| 645 | /// be called before using this function. |
---|
| 646 | const DistMap &distMap() const { return *_dist;} |
---|
| 647 | |
---|
| 648 | /// \brief Returns a reference to the shortest path tree map. |
---|
| 649 | /// |
---|
| 650 | /// Returns a reference to the NodeMap of the edges of the |
---|
| 651 | /// shortest path tree. |
---|
| 652 | /// \pre \ref run() must be called before using this function. |
---|
| 653 | const PredMap &predMap() const { return *_pred; } |
---|
| 654 | |
---|
| 655 | /// \brief Checks if a node is reachable from the root. |
---|
| 656 | /// |
---|
| 657 | /// Returns \c true if \c v is reachable from the root. |
---|
| 658 | /// \pre \ref run() must be called before using this function. |
---|
| 659 | /// |
---|
| 660 | bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); } |
---|
| 661 | |
---|
| 662 | ///@} |
---|
| 663 | }; |
---|
| 664 | |
---|
[1864] | 665 | /// \brief Default traits class of BellmanFord function. |
---|
[1699] | 666 | /// |
---|
[1864] | 667 | /// Default traits class of BellmanFord function. |
---|
[1699] | 668 | /// \param _Graph Graph type. |
---|
| 669 | /// \param _LengthMap Type of length map. |
---|
| 670 | template <typename _Graph, typename _LengthMap> |
---|
[1864] | 671 | struct BellmanFordWizardDefaultTraits { |
---|
[1699] | 672 | /// \brief The graph type the algorithm runs on. |
---|
| 673 | typedef _Graph Graph; |
---|
| 674 | |
---|
| 675 | /// \brief The type of the map that stores the edge lengths. |
---|
| 676 | /// |
---|
| 677 | /// The type of the map that stores the edge lengths. |
---|
| 678 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
---|
| 679 | typedef _LengthMap LengthMap; |
---|
| 680 | |
---|
| 681 | /// \brief The value type of the length map. |
---|
| 682 | typedef typename _LengthMap::Value Value; |
---|
| 683 | |
---|
[1864] | 684 | /// \brief Operation traits for bellman-ford algorithm. |
---|
[1699] | 685 | /// |
---|
| 686 | /// It defines the infinity type on the given Value type |
---|
| 687 | /// and the used operation. |
---|
[1864] | 688 | /// \see BellmanFordDefaultOperationTraits |
---|
| 689 | typedef BellmanFordDefaultOperationTraits<Value> OperationTraits; |
---|
[1699] | 690 | |
---|
| 691 | /// \brief The type of the map that stores the last |
---|
| 692 | /// edges of the shortest paths. |
---|
| 693 | /// |
---|
| 694 | /// The type of the map that stores the last |
---|
| 695 | /// edges of the shortest paths. |
---|
| 696 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
| 697 | typedef NullMap <typename _Graph::Node,typename _Graph::Edge> PredMap; |
---|
| 698 | |
---|
| 699 | /// \brief Instantiates a PredMap. |
---|
| 700 | /// |
---|
| 701 | /// This function instantiates a \ref PredMap. |
---|
| 702 | static PredMap *createPredMap(const _Graph &) { |
---|
| 703 | return new PredMap(); |
---|
| 704 | } |
---|
| 705 | /// \brief The type of the map that stores the dists of the nodes. |
---|
| 706 | /// |
---|
| 707 | /// The type of the map that stores the dists of the nodes. |
---|
| 708 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
---|
| 709 | typedef NullMap<typename Graph::Node, Value> DistMap; |
---|
| 710 | /// \brief Instantiates a DistMap. |
---|
| 711 | /// |
---|
| 712 | /// This function instantiates a \ref DistMap. |
---|
| 713 | static DistMap *createDistMap(const _Graph &) { |
---|
| 714 | return new DistMap(); |
---|
| 715 | } |
---|
| 716 | }; |
---|
| 717 | |
---|
[1864] | 718 | /// \brief Default traits used by \ref BellmanFordWizard |
---|
[1699] | 719 | /// |
---|
[1864] | 720 | /// To make it easier to use BellmanFord algorithm |
---|
[1699] | 721 | /// we have created a wizard class. |
---|
[1864] | 722 | /// This \ref BellmanFordWizard class needs default traits, |
---|
| 723 | /// as well as the \ref BellmanFord class. |
---|
| 724 | /// The \ref BellmanFordWizardBase is a class to be the default traits of the |
---|
| 725 | /// \ref BellmanFordWizard class. |
---|
[1699] | 726 | /// \todo More named parameters are required... |
---|
| 727 | template<class _Graph,class _LengthMap> |
---|
[1864] | 728 | class BellmanFordWizardBase |
---|
| 729 | : public BellmanFordWizardDefaultTraits<_Graph,_LengthMap> { |
---|
[1699] | 730 | |
---|
[1864] | 731 | typedef BellmanFordWizardDefaultTraits<_Graph,_LengthMap> Base; |
---|
[1699] | 732 | protected: |
---|
| 733 | /// Type of the nodes in the graph. |
---|
| 734 | typedef typename Base::Graph::Node Node; |
---|
| 735 | |
---|
| 736 | /// Pointer to the underlying graph. |
---|
| 737 | void *_graph; |
---|
| 738 | /// Pointer to the length map |
---|
| 739 | void *_length; |
---|
| 740 | ///Pointer to the map of predecessors edges. |
---|
| 741 | void *_pred; |
---|
| 742 | ///Pointer to the map of distances. |
---|
| 743 | void *_dist; |
---|
| 744 | ///Pointer to the source node. |
---|
| 745 | Node _source; |
---|
| 746 | |
---|
| 747 | public: |
---|
| 748 | /// Constructor. |
---|
| 749 | |
---|
| 750 | /// This constructor does not require parameters, therefore it initiates |
---|
| 751 | /// all of the attributes to default values (0, INVALID). |
---|
[1864] | 752 | BellmanFordWizardBase() : _graph(0), _length(0), _pred(0), |
---|
[1699] | 753 | _dist(0), _source(INVALID) {} |
---|
| 754 | |
---|
| 755 | /// Constructor. |
---|
| 756 | |
---|
| 757 | /// This constructor requires some parameters, |
---|
| 758 | /// listed in the parameters list. |
---|
| 759 | /// Others are initiated to 0. |
---|
| 760 | /// \param graph is the initial value of \ref _graph |
---|
| 761 | /// \param length is the initial value of \ref _length |
---|
| 762 | /// \param source is the initial value of \ref _source |
---|
[1864] | 763 | BellmanFordWizardBase(const _Graph& graph, |
---|
[1699] | 764 | const _LengthMap& length, |
---|
| 765 | Node source = INVALID) : |
---|
| 766 | _graph((void *)&graph), _length((void *)&length), _pred(0), |
---|
| 767 | _dist(0), _source(source) {} |
---|
| 768 | |
---|
| 769 | }; |
---|
| 770 | |
---|
[1864] | 771 | /// A class to make the usage of BellmanFord algorithm easier |
---|
[1699] | 772 | |
---|
[1864] | 773 | /// This class is created to make it easier to use BellmanFord algorithm. |
---|
| 774 | /// It uses the functions and features of the plain \ref BellmanFord, |
---|
[1699] | 775 | /// but it is much simpler to use it. |
---|
| 776 | /// |
---|
| 777 | /// Simplicity means that the way to change the types defined |
---|
| 778 | /// in the traits class is based on functions that returns the new class |
---|
| 779 | /// and not on templatable built-in classes. |
---|
[1864] | 780 | /// When using the plain \ref BellmanFord |
---|
[1699] | 781 | /// the new class with the modified type comes from |
---|
| 782 | /// the original class by using the :: |
---|
[1864] | 783 | /// operator. In the case of \ref BellmanFordWizard only |
---|
[1699] | 784 | /// a function have to be called and it will |
---|
| 785 | /// return the needed class. |
---|
| 786 | /// |
---|
| 787 | /// It does not have own \ref run method. When its \ref run method is called |
---|
[1864] | 788 | /// it initiates a plain \ref BellmanFord class, and calls the \ref |
---|
| 789 | /// BellmanFord::run method of it. |
---|
[1699] | 790 | template<class _Traits> |
---|
[1864] | 791 | class BellmanFordWizard : public _Traits { |
---|
[1699] | 792 | typedef _Traits Base; |
---|
| 793 | |
---|
| 794 | ///The type of the underlying graph. |
---|
| 795 | typedef typename _Traits::Graph Graph; |
---|
| 796 | |
---|
| 797 | typedef typename Graph::Node Node; |
---|
| 798 | typedef typename Graph::NodeIt NodeIt; |
---|
| 799 | typedef typename Graph::Edge Edge; |
---|
| 800 | typedef typename Graph::OutEdgeIt EdgeIt; |
---|
| 801 | |
---|
| 802 | ///The type of the map that stores the edge lengths. |
---|
| 803 | typedef typename _Traits::LengthMap LengthMap; |
---|
| 804 | |
---|
| 805 | ///The type of the length of the edges. |
---|
| 806 | typedef typename LengthMap::Value Value; |
---|
| 807 | |
---|
| 808 | ///\brief The type of the map that stores the last |
---|
| 809 | ///edges of the shortest paths. |
---|
| 810 | typedef typename _Traits::PredMap PredMap; |
---|
| 811 | |
---|
| 812 | ///The type of the map that stores the dists of the nodes. |
---|
| 813 | typedef typename _Traits::DistMap DistMap; |
---|
| 814 | |
---|
| 815 | public: |
---|
| 816 | /// Constructor. |
---|
[1864] | 817 | BellmanFordWizard() : _Traits() {} |
---|
[1699] | 818 | |
---|
| 819 | /// \brief Constructor that requires parameters. |
---|
| 820 | /// |
---|
| 821 | /// Constructor that requires parameters. |
---|
| 822 | /// These parameters will be the default values for the traits class. |
---|
[1864] | 823 | BellmanFordWizard(const Graph& graph, const LengthMap& length, |
---|
[1699] | 824 | Node source = INVALID) |
---|
| 825 | : _Traits(graph, length, source) {} |
---|
| 826 | |
---|
| 827 | /// \brief Copy constructor |
---|
[1864] | 828 | BellmanFordWizard(const _Traits &b) : _Traits(b) {} |
---|
[1699] | 829 | |
---|
[1864] | 830 | ~BellmanFordWizard() {} |
---|
[1699] | 831 | |
---|
[1864] | 832 | /// \brief Runs BellmanFord algorithm from a given node. |
---|
[1699] | 833 | /// |
---|
[1864] | 834 | /// Runs BellmanFord algorithm from a given node. |
---|
[1699] | 835 | /// The node can be given by the \ref source function. |
---|
| 836 | void run() { |
---|
| 837 | if(Base::_source == INVALID) throw UninitializedParameter(); |
---|
[1864] | 838 | BellmanFord<Graph,LengthMap,_Traits> |
---|
[1699] | 839 | bf(*(Graph*)Base::_graph, *(LengthMap*)Base::_length); |
---|
| 840 | if (Base::_pred) bf.predMap(*(PredMap*)Base::_pred); |
---|
| 841 | if (Base::_dist) bf.distMap(*(DistMap*)Base::_dist); |
---|
| 842 | bf.run(Base::_source); |
---|
| 843 | } |
---|
| 844 | |
---|
[1864] | 845 | /// \brief Runs BellmanFord algorithm from the given node. |
---|
[1699] | 846 | /// |
---|
[1864] | 847 | /// Runs BellmanFord algorithm from the given node. |
---|
[1858] | 848 | /// \param source is the given source. |
---|
[1699] | 849 | void run(Node source) { |
---|
| 850 | Base::_source = source; |
---|
| 851 | run(); |
---|
| 852 | } |
---|
| 853 | |
---|
| 854 | template<class T> |
---|
| 855 | struct DefPredMapBase : public Base { |
---|
| 856 | typedef T PredMap; |
---|
| 857 | static PredMap *createPredMap(const Graph &) { return 0; }; |
---|
| 858 | DefPredMapBase(const _Traits &b) : _Traits(b) {} |
---|
| 859 | }; |
---|
| 860 | |
---|
| 861 | ///\brief \ref named-templ-param "Named parameter" |
---|
| 862 | ///function for setting PredMap type |
---|
| 863 | /// |
---|
| 864 | /// \ref named-templ-param "Named parameter" |
---|
| 865 | ///function for setting PredMap type |
---|
| 866 | /// |
---|
| 867 | template<class T> |
---|
[1864] | 868 | BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t) |
---|
[1699] | 869 | { |
---|
| 870 | Base::_pred=(void *)&t; |
---|
[1864] | 871 | return BellmanFordWizard<DefPredMapBase<T> >(*this); |
---|
[1699] | 872 | } |
---|
| 873 | |
---|
| 874 | template<class T> |
---|
| 875 | struct DefDistMapBase : public Base { |
---|
| 876 | typedef T DistMap; |
---|
| 877 | static DistMap *createDistMap(const Graph &) { return 0; }; |
---|
| 878 | DefDistMapBase(const _Traits &b) : _Traits(b) {} |
---|
| 879 | }; |
---|
| 880 | |
---|
| 881 | ///\brief \ref named-templ-param "Named parameter" |
---|
| 882 | ///function for setting DistMap type |
---|
| 883 | /// |
---|
| 884 | /// \ref named-templ-param "Named parameter" |
---|
| 885 | ///function for setting DistMap type |
---|
| 886 | /// |
---|
| 887 | template<class T> |
---|
[1864] | 888 | BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) { |
---|
[1699] | 889 | Base::_dist=(void *)&t; |
---|
[1864] | 890 | return BellmanFordWizard<DefDistMapBase<T> >(*this); |
---|
[1699] | 891 | } |
---|
[1710] | 892 | |
---|
| 893 | template<class T> |
---|
| 894 | struct DefOperationTraitsBase : public Base { |
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| 895 | typedef T OperationTraits; |
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| 896 | DefOperationTraitsBase(const _Traits &b) : _Traits(b) {} |
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| 897 | }; |
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| 898 | |
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| 899 | ///\brief \ref named-templ-param "Named parameter" |
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| 900 | ///function for setting OperationTraits type |
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| 901 | /// |
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| 902 | /// \ref named-templ-param "Named parameter" |
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| 903 | ///function for setting OperationTraits type |
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| 904 | /// |
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| 905 | template<class T> |
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[1864] | 906 | BellmanFordWizard<DefOperationTraitsBase<T> > distMap() { |
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| 907 | return BellmanFordWizard<DefDistMapBase<T> >(*this); |
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[1710] | 908 | } |
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[1699] | 909 | |
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[1864] | 910 | /// \brief Sets the source node, from which the BellmanFord algorithm runs. |
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[1699] | 911 | /// |
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[1864] | 912 | /// Sets the source node, from which the BellmanFord algorithm runs. |
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[1858] | 913 | /// \param source is the source node. |
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[1864] | 914 | BellmanFordWizard<_Traits>& source(Node source) { |
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[1699] | 915 | Base::_source = source; |
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| 916 | return *this; |
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| 917 | } |
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| 918 | |
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| 919 | }; |
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| 920 | |
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[1864] | 921 | /// \brief Function type interface for BellmanFord algorithm. |
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[1699] | 922 | /// |
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| 923 | /// \ingroup flowalgs |
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[1864] | 924 | /// Function type interface for BellmanFord algorithm. |
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[1699] | 925 | /// |
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| 926 | /// This function also has several \ref named-templ-func-param |
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| 927 | /// "named parameters", they are declared as the members of class |
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[1864] | 928 | /// \ref BellmanFordWizard. |
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[1699] | 929 | /// The following |
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| 930 | /// example shows how to use these parameters. |
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| 931 | /// \code |
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[1864] | 932 | /// bellmanford(g,length,source).predMap(preds).run(); |
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[1699] | 933 | /// \endcode |
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[1864] | 934 | /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()" |
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[1699] | 935 | /// to the end of the parameter list. |
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[1864] | 936 | /// \sa BellmanFordWizard |
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| 937 | /// \sa BellmanFord |
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[1699] | 938 | template<class _Graph, class _LengthMap> |
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[1864] | 939 | BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> > |
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| 940 | bellmanFord(const _Graph& graph, |
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[1699] | 941 | const _LengthMap& length, |
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| 942 | typename _Graph::Node source = INVALID) { |
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[1864] | 943 | return BellmanFordWizard<BellmanFordWizardBase<_Graph,_LengthMap> > |
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[1699] | 944 | (graph, length, source); |
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| 945 | } |
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| 946 | |
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| 947 | } //END OF NAMESPACE LEMON |
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| 948 | |
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| 949 | #endif |
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| 950 | |
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