[1912] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[1956] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1912] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_PRIM_H |
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| 20 | #define LEMON_PRIM_H |
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| 21 | |
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| 22 | ///\ingroup spantree |
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| 23 | ///\file |
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| 24 | ///\brief Prim algorithm to compute minimum spanning tree. |
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| 25 | |
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| 26 | #include <lemon/list_graph.h> |
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| 27 | #include <lemon/bin_heap.h> |
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[1993] | 28 | #include <lemon/bits/invalid.h> |
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[1912] | 29 | #include <lemon/error.h> |
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| 30 | #include <lemon/maps.h> |
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[1993] | 31 | #include <lemon/bits/traits.h> |
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[1912] | 32 | |
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| 33 | #include <lemon/concept/ugraph.h> |
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| 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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| 37 | ///Default traits class of Prim class. |
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| 38 | |
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| 39 | ///Default traits class of Prim class. |
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| 40 | ///\param GR Graph type. |
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[2030] | 41 | ///\param CM Type of cost map. |
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| 42 | template<class GR, class CM> |
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[1912] | 43 | struct PrimDefaultTraits{ |
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| 44 | ///The graph type the algorithm runs on. |
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| 45 | typedef GR UGraph; |
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| 46 | ///The type of the map that stores the edge costs. |
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| 47 | |
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| 48 | ///The type of the map that stores the edge costs. |
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| 49 | ///It must meet the \ref concept::ReadMap "ReadMap" concept. |
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[2030] | 50 | typedef CM CostMap; |
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[1912] | 51 | //The type of the cost of the edges. |
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[2030] | 52 | typedef typename CM::Value Value; |
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[1912] | 53 | /// The cross reference type used by heap. |
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| 54 | |
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| 55 | /// The cross reference type used by heap. |
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| 56 | /// Usually it is \c UGraph::NodeMap<int>. |
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| 57 | typedef typename UGraph::template NodeMap<int> HeapCrossRef; |
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| 58 | ///Instantiates a HeapCrossRef. |
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| 59 | |
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| 60 | ///This function instantiates a \ref HeapCrossRef. |
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[1953] | 61 | /// \param _graph is the graph, to which we would like to define the |
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[1912] | 62 | /// HeapCrossRef. |
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| 63 | static HeapCrossRef *createHeapCrossRef(const GR &_graph){ |
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| 64 | return new HeapCrossRef(_graph); |
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| 65 | } |
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| 66 | |
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| 67 | ///The heap type used by Prim algorithm. |
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| 68 | |
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| 69 | ///The heap type used by Prim algorithm. |
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| 70 | /// |
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| 71 | ///\sa BinHeap |
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| 72 | ///\sa Prim |
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[2030] | 73 | typedef BinHeap<typename UGraph::Node, typename CM::Value, |
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[1912] | 74 | HeapCrossRef, std::less<Value> > Heap; |
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| 75 | |
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| 76 | static Heap *createHeap(HeapCrossRef& _ref){ |
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| 77 | return new Heap(_ref); |
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| 78 | } |
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| 79 | |
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| 80 | ///\brief The type of the map that stores the last |
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| 81 | ///edges of the minimum spanning tree. |
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| 82 | /// |
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| 83 | ///The type of the map that stores the last |
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| 84 | ///edges of the minimum spanning tree. |
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| 85 | ///It must meet the \ref concept::WriteMap "WriteMap" concept. |
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| 86 | /// |
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| 87 | typedef typename UGraph::template NodeMap<typename GR::UEdge> PredMap; |
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| 88 | ///Instantiates a PredMap. |
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| 89 | |
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| 90 | ///This function instantiates a \ref PredMap. |
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[1953] | 91 | ///\param _graph is the graph, to which we would like to define the PredMap. |
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[1912] | 92 | static PredMap *createPredMap(const GR &_graph){ |
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| 93 | return new PredMap(_graph); |
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| 94 | } |
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| 95 | |
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| 96 | ///The type of the map that stores whether an edge is in the |
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| 97 | ///spanning tree or not. |
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| 98 | |
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| 99 | ///The type of the map that stores whether an edge is in the |
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| 100 | ///spanning tree or not. |
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| 101 | ///By default it is a NullMap. |
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| 102 | typedef NullMap<typename UGraph::UEdge,bool> TreeMap; |
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| 103 | ///Instantiates a TreeMap. |
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| 104 | |
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| 105 | ///This function instantiates a \ref TreeMap. |
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[1953] | 106 | /// |
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| 107 | ///The first parameter is the graph, to which |
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[1912] | 108 | ///we would like to define the \ref TreeMap |
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| 109 | static TreeMap *createTreeMap(const GR &){ |
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| 110 | return new TreeMap(); |
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| 111 | } |
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| 112 | |
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| 113 | ///The type of the map that stores whether a nodes is processed. |
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| 114 | |
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| 115 | ///The type of the map that stores whether a nodes is processed. |
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| 116 | ///It must meet the \ref concept::WriteMap "WriteMap" concept. |
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| 117 | ///By default it is a NodeMap<bool>. |
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| 118 | typedef NullMap<typename UGraph::Node,bool> ProcessedMap; |
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| 119 | ///Instantiates a ProcessedMap. |
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| 120 | |
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| 121 | ///This function instantiates a \ref ProcessedMap. |
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[1953] | 122 | ///\param _graph is the graph, to which |
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[1912] | 123 | ///we would like to define the \ref ProcessedMap |
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| 124 | #ifdef DOXYGEN |
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| 125 | static ProcessedMap *createProcessedMap(const GR &_graph) |
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| 126 | #else |
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| 127 | static ProcessedMap *createProcessedMap(const GR &) |
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| 128 | #endif |
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| 129 | { |
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| 130 | return new ProcessedMap(); |
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| 131 | } |
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| 132 | }; |
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| 133 | |
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| 134 | ///%Prim algorithm class to find a minimum spanning tree. |
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| 135 | |
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| 136 | /// \ingroup spantree |
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| 137 | ///This class provides an efficient implementation of %Prim algorithm. |
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| 138 | /// |
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[2042] | 139 | ///The running time is \f$ O(e\log(n)) \f$ where e is the number of edges and |
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[1912] | 140 | ///n is the number of nodes in the graph. |
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| 141 | /// |
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| 142 | ///The edge costs are passed to the algorithm using a |
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| 143 | ///\ref concept::ReadMap "ReadMap", |
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| 144 | ///so it is easy to change it to any kind of cost. |
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| 145 | /// |
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| 146 | ///The type of the cost is determined by the |
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| 147 | ///\ref concept::ReadMap::Value "Value" of the cost map. |
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| 148 | /// |
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| 149 | ///It is also possible to change the underlying priority heap. |
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| 150 | /// |
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| 151 | ///\param GR The graph type the algorithm runs on. The default value |
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| 152 | ///is \ref ListUGraph. The value of GR is not used directly by |
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| 153 | ///Prim, it is only passed to \ref PrimDefaultTraits. |
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| 154 | /// |
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[2030] | 155 | ///\param CM This read-only UEdgeMap determines the costs of the |
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[1912] | 156 | ///edges. It is read once for each edge, so the map may involve in |
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| 157 | ///relatively time consuming process to compute the edge cost if |
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| 158 | ///it is necessary. The default map type is \ref |
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| 159 | ///concept::UGraph::UEdgeMap "UGraph::UEdgeMap<int>". The value |
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[2030] | 160 | ///of CM is not used directly by Prim, it is only passed to \ref |
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[1912] | 161 | ///PrimDefaultTraits. |
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| 162 | /// |
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| 163 | ///\param TR Traits class to set |
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| 164 | ///various data types used by the algorithm. The default traits |
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| 165 | ///class is \ref PrimDefaultTraits |
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[2030] | 166 | ///"PrimDefaultTraits<GR,CM>". See \ref |
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[1912] | 167 | ///PrimDefaultTraits for the documentation of a Prim traits |
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| 168 | ///class. |
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| 169 | /// |
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| 170 | ///\author Balazs Attila Mihaly |
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| 171 | |
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| 172 | #ifdef DOXYGEN |
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| 173 | template <typename GR, |
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[2030] | 174 | typename CM, |
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[1912] | 175 | typename TR> |
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| 176 | #else |
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| 177 | template <typename GR=ListUGraph, |
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[2030] | 178 | typename CM=typename GR::template UEdgeMap<int>, |
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| 179 | typename TR=PrimDefaultTraits<GR,CM> > |
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[1912] | 180 | #endif |
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| 181 | class Prim { |
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| 182 | public: |
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[2030] | 183 | |
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| 184 | /// \brief \ref Exception for uninitialized parameters. |
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| 185 | /// |
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| 186 | /// This error represents problems in the initialization |
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| 187 | /// of the parameters of the algorithms. |
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[1912] | 188 | class UninitializedParameter : public lemon::UninitializedParameter { |
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| 189 | public: |
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[2151] | 190 | virtual const char* what() const throw() { |
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[1912] | 191 | return "lemon::Prim::UninitializedParameter"; |
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| 192 | } |
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| 193 | }; |
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| 194 | |
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| 195 | typedef TR Traits; |
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| 196 | ///The type of the underlying graph. |
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| 197 | typedef typename TR::UGraph UGraph; |
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| 198 | ///\e |
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| 199 | typedef typename UGraph::Node Node; |
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| 200 | ///\e |
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| 201 | typedef typename UGraph::NodeIt NodeIt; |
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| 202 | ///\e |
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| 203 | typedef typename UGraph::UEdge UEdge; |
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| 204 | ///\e |
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| 205 | typedef typename UGraph::IncEdgeIt IncEdgeIt; |
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| 206 | |
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| 207 | ///The type of the cost of the edges. |
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| 208 | typedef typename TR::CostMap::Value Value; |
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| 209 | ///The type of the map that stores the edge costs. |
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| 210 | typedef typename TR::CostMap CostMap; |
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| 211 | ///\brief The type of the map that stores the last |
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| 212 | ///predecessor edges of the spanning tree. |
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| 213 | typedef typename TR::PredMap PredMap; |
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| 214 | ///Edges of the spanning tree. |
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| 215 | typedef typename TR::TreeMap TreeMap; |
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| 216 | ///The type of the map indicating if a node is processed. |
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| 217 | typedef typename TR::ProcessedMap ProcessedMap; |
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| 218 | ///The cross reference type used for the current heap. |
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| 219 | typedef typename TR::HeapCrossRef HeapCrossRef; |
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| 220 | ///The heap type used by the prim algorithm. |
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| 221 | typedef typename TR::Heap Heap; |
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| 222 | private: |
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| 223 | /// Pointer to the underlying graph. |
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| 224 | const UGraph *graph; |
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| 225 | /// Pointer to the cost map |
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| 226 | const CostMap *cost; |
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| 227 | ///Pointer to the map of predecessors edges. |
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| 228 | PredMap *_pred; |
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| 229 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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| 230 | bool local_pred; |
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| 231 | ///Pointer to the map of tree edges. |
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| 232 | TreeMap *_tree; |
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| 233 | ///Indicates if \ref _tree is locally allocated (\c true) or not. |
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| 234 | bool local_tree; |
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| 235 | ///Pointer to the map of processed status of the nodes. |
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| 236 | ProcessedMap *_processed; |
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| 237 | ///Indicates if \ref _processed is locally allocated (\c true) or not. |
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| 238 | bool local_processed; |
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| 239 | ///Pointer to the heap cross references. |
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| 240 | HeapCrossRef *_heap_cross_ref; |
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| 241 | ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not. |
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| 242 | bool local_heap_cross_ref; |
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| 243 | ///Pointer to the heap. |
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| 244 | Heap *_heap; |
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| 245 | ///Indicates if \ref _heap is locally allocated (\c true) or not. |
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| 246 | bool local_heap; |
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| 247 | |
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| 248 | ///Creates the maps if necessary. |
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| 249 | void create_maps(){ |
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| 250 | if(!_pred) { |
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| 251 | local_pred = true; |
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| 252 | _pred = Traits::createPredMap(*graph); |
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| 253 | } |
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| 254 | if(!_tree) { |
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| 255 | local_tree = true; |
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| 256 | _tree = Traits::createTreeMap(*graph); |
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| 257 | } |
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| 258 | if(!_processed) { |
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| 259 | local_processed = true; |
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| 260 | _processed = Traits::createProcessedMap(*graph); |
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| 261 | } |
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| 262 | if (!_heap_cross_ref) { |
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| 263 | local_heap_cross_ref = true; |
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| 264 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
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| 265 | } |
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| 266 | if (!_heap) { |
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| 267 | local_heap = true; |
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| 268 | _heap = Traits::createHeap(*_heap_cross_ref); |
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| 269 | } |
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| 270 | } |
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| 271 | |
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| 272 | public : |
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| 273 | |
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| 274 | typedef Prim Create; |
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| 275 | |
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| 276 | ///\name Named template parameters |
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| 277 | |
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| 278 | ///@{ |
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| 279 | |
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| 280 | template <class T> |
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| 281 | struct DefPredMapTraits : public Traits { |
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| 282 | typedef T PredMap; |
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| 283 | static PredMap *createPredMap(const UGraph &_graph){ |
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| 284 | throw UninitializedParameter(); |
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| 285 | } |
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| 286 | }; |
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| 287 | ///\ref named-templ-param "Named parameter" for setting PredMap type |
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| 288 | |
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| 289 | ///\ref named-templ-param "Named parameter" for setting PredMap type |
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| 290 | /// |
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| 291 | template <class T> |
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| 292 | struct DefPredMap |
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| 293 | : public Prim< UGraph, CostMap, DefPredMapTraits<T> > { |
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| 294 | typedef Prim< UGraph, CostMap, DefPredMapTraits<T> > Create; |
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| 295 | }; |
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| 296 | |
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| 297 | template <class T> |
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| 298 | struct DefProcessedMapTraits : public Traits { |
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| 299 | typedef T ProcessedMap; |
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| 300 | static ProcessedMap *createProcessedMap(const UGraph &_graph){ |
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| 301 | throw UninitializedParameter(); |
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| 302 | } |
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| 303 | }; |
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| 304 | ///\ref named-templ-param "Named parameter" for setting ProcessedMap type |
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| 305 | |
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| 306 | ///\ref named-templ-param "Named parameter" for setting ProcessedMap type |
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| 307 | /// |
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| 308 | template <class T> |
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| 309 | struct DefProcessedMap |
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| 310 | : public Prim< UGraph, CostMap, DefProcessedMapTraits<T> > { |
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| 311 | typedef Prim< UGraph, CostMap, DefProcessedMapTraits<T> > Create; |
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| 312 | }; |
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| 313 | |
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| 314 | struct DefGraphProcessedMapTraits : public Traits { |
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| 315 | typedef typename UGraph::template NodeMap<bool> ProcessedMap; |
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| 316 | static ProcessedMap *createProcessedMap(const UGraph &_graph){ |
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| 317 | return new ProcessedMap(_graph); |
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| 318 | } |
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| 319 | }; |
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| 320 | |
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| 321 | |
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| 322 | template <class H, class CR> |
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| 323 | struct DefHeapTraits : public Traits { |
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| 324 | typedef CR HeapCrossRef; |
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| 325 | typedef H Heap; |
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| 326 | static HeapCrossRef *createHeapCrossRef(const UGraph &) { |
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| 327 | throw UninitializedParameter(); |
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| 328 | } |
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| 329 | static Heap *createHeap(HeapCrossRef &){ |
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| 330 | return UninitializedParameter(); |
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| 331 | } |
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| 332 | }; |
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| 333 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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| 334 | ///reference type |
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| 335 | |
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| 336 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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| 337 | ///reference type |
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| 338 | /// |
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| 339 | template <class H, class CR = typename UGraph::template NodeMap<int> > |
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| 340 | struct DefHeap |
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| 341 | : public Prim< UGraph, CostMap, DefHeapTraits<H, CR> > { |
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| 342 | typedef Prim< UGraph, CostMap, DefHeapTraits<H, CR> > Create; |
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| 343 | }; |
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| 344 | |
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| 345 | template <class H, class CR> |
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| 346 | struct DefStandardHeapTraits : public Traits { |
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| 347 | typedef CR HeapCrossRef; |
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| 348 | typedef H Heap; |
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| 349 | static HeapCrossRef *createHeapCrossRef(const UGraph &_graph) { |
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| 350 | return new HeapCrossRef(_graph); |
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| 351 | } |
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| 352 | static Heap *createHeap(HeapCrossRef &ref){ |
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| 353 | return new Heap(ref); |
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| 354 | } |
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| 355 | }; |
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| 356 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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| 357 | ///reference type with automatic allocation |
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| 358 | |
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| 359 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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| 360 | ///reference type. It can allocate the heap and the cross reference |
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| 361 | ///object if the cross reference's constructor waits for the graph as |
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| 362 | ///parameter and the heap's constructor waits for the cross reference. |
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| 363 | template <class H, class CR = typename UGraph::template NodeMap<int> > |
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| 364 | struct DefStandardHeap |
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| 365 | : public Prim< UGraph, CostMap, DefStandardHeapTraits<H, CR> > { |
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| 366 | typedef Prim< UGraph, CostMap, DefStandardHeapTraits<H, CR> > |
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| 367 | Create; |
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| 368 | }; |
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| 369 | |
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| 370 | template <class TM> |
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| 371 | struct DefTreeMapTraits : public Traits { |
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| 372 | typedef TM TreeMap; |
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| 373 | static TreeMap *createTreeMap(const UGraph &) { |
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| 374 | throw UninitializedParameter(); |
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| 375 | } |
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| 376 | }; |
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| 377 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
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| 378 | |
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| 379 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
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| 380 | /// |
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| 381 | template <class TM> |
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| 382 | struct DefTreeMap |
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| 383 | : public Prim< UGraph, CostMap, DefTreeMapTraits<TM> > { |
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| 384 | typedef Prim< UGraph, CostMap, DefTreeMapTraits<TM> > Create; |
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| 385 | }; |
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| 386 | |
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| 387 | struct DefGraphTreeMapTraits : public Traits { |
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| 388 | typedef typename UGraph::template NodeMap<bool> TreeMap; |
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| 389 | static TreeMap *createTreeMap(const UGraph &_graph){ |
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| 390 | return new TreeMap(_graph); |
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| 391 | } |
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| 392 | }; |
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| 393 | |
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| 394 | ///@} |
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| 395 | |
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| 396 | |
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| 397 | protected: |
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| 398 | |
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| 399 | Prim() {} |
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| 400 | |
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| 401 | public: |
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| 402 | |
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| 403 | ///Constructor. |
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| 404 | |
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| 405 | ///\param _graph the graph the algorithm will run on. |
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| 406 | ///\param _cost the cost map used by the algorithm. |
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| 407 | Prim(const UGraph& _graph, const CostMap& _cost) : |
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| 408 | graph(&_graph), cost(&_cost), |
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| 409 | _pred(NULL), local_pred(false), |
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| 410 | _tree(NULL), local_tree(false), |
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| 411 | _processed(NULL), local_processed(false), |
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| 412 | _heap_cross_ref(NULL), local_heap_cross_ref(false), |
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| 413 | _heap(NULL), local_heap(false) |
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| 414 | { |
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| 415 | checkConcept<concept::UGraph, UGraph>(); |
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| 416 | } |
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| 417 | |
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| 418 | ///Destructor. |
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| 419 | ~Prim(){ |
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| 420 | if(local_pred) delete _pred; |
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| 421 | if(local_tree) delete _tree; |
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| 422 | if(local_processed) delete _processed; |
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| 423 | if(local_heap_cross_ref) delete _heap_cross_ref; |
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| 424 | if(local_heap) delete _heap; |
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| 425 | } |
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| 426 | |
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| 427 | ///\brief Sets the cost map. |
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| 428 | |
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| 429 | ///Sets the cost map. |
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| 430 | ///\return <tt> (*this) </tt> |
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| 431 | Prim &costMap(const CostMap &m){ |
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| 432 | cost = &m; |
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| 433 | return *this; |
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| 434 | } |
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| 435 | |
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| 436 | ///\brief Sets the map storing the predecessor edges. |
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| 437 | |
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| 438 | ///Sets the map storing the predecessor edges. |
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| 439 | ///If you don't use this function before calling \ref run(), |
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| 440 | ///it will allocate one. The destuctor deallocates this |
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| 441 | ///automatically allocated map, of course. |
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| 442 | ///\return <tt> (*this) </tt> |
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| 443 | Prim &predMap(PredMap &m){ |
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| 444 | if(local_pred) { |
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| 445 | delete _pred; |
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| 446 | local_pred=false; |
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| 447 | } |
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| 448 | _pred = &m; |
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| 449 | return *this; |
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| 450 | } |
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| 451 | |
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| 452 | ///\brief Sets the map storing the tree edges. |
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| 453 | |
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| 454 | ///Sets the map storing the tree edges. |
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| 455 | ///If you don't use this function before calling \ref run(), |
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| 456 | ///it will allocate one. The destuctor deallocates this |
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| 457 | ///automatically allocated map, of course. |
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| 458 | ///By default this is a NullMap. |
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| 459 | ///\return <tt> (*this) </tt> |
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| 460 | Prim &treeMap(TreeMap &m){ |
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| 461 | if(local_tree) { |
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| 462 | delete _tree; |
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| 463 | local_tree=false; |
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| 464 | } |
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| 465 | _tree = &m; |
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| 466 | return *this; |
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| 467 | } |
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| 468 | |
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| 469 | ///\brief Sets the heap and the cross reference used by algorithm. |
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| 470 | |
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| 471 | ///Sets the heap and the cross reference used by algorithm. |
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| 472 | ///If you don't use this function before calling \ref run(), |
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| 473 | ///it will allocate one. The destuctor deallocates this |
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| 474 | ///automatically allocated map, of course. |
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| 475 | ///\return <tt> (*this) </tt> |
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| 476 | Prim &heap(Heap& heap, HeapCrossRef &crossRef){ |
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| 477 | if(local_heap_cross_ref) { |
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| 478 | delete _heap_cross_ref; |
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| 479 | local_heap_cross_ref=false; |
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| 480 | } |
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| 481 | _heap_cross_ref = &crossRef; |
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| 482 | if(local_heap) { |
---|
| 483 | delete _heap; |
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| 484 | local_heap=false; |
---|
| 485 | } |
---|
| 486 | _heap = &heap; |
---|
| 487 | return *this; |
---|
| 488 | } |
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| 489 | |
---|
| 490 | public: |
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| 491 | ///\name Execution control |
---|
| 492 | ///The simplest way to execute the algorithm is to use |
---|
| 493 | ///one of the member functions called \c run(...). |
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| 494 | ///\n |
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| 495 | ///If you need more control on the execution, |
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| 496 | ///first you must call \ref init(), then you can add several source nodes |
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| 497 | ///with \ref addSource(). |
---|
| 498 | ///Finally \ref start() will perform the actual path |
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| 499 | ///computation. |
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| 500 | |
---|
| 501 | ///@{ |
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| 502 | |
---|
| 503 | ///\brief Initializes the internal data structures. |
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| 504 | |
---|
| 505 | ///Initializes the internal data structures. |
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| 506 | /// |
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| 507 | void init(){ |
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| 508 | create_maps(); |
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| 509 | _heap->clear(); |
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| 510 | for ( NodeIt u(*graph) ; u!=INVALID ; ++u ) { |
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| 511 | _pred->set(u,INVALID); |
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| 512 | _processed->set(u,false); |
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| 513 | _heap_cross_ref->set(u,Heap::PRE_HEAP); |
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| 514 | } |
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| 515 | } |
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| 516 | |
---|
| 517 | ///\brief Adds a new source node. |
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| 518 | |
---|
| 519 | ///Adds a new source node to the priority heap. |
---|
| 520 | /// |
---|
| 521 | ///It checks if the node has already been added to the heap and |
---|
| 522 | ///it is pushed to the heap only if it was not in the heap. |
---|
| 523 | void addSource(Node s){ |
---|
| 524 | if(_heap->state(s) != Heap::IN_HEAP) { |
---|
| 525 | _heap->push(s,Value()); |
---|
| 526 | } |
---|
| 527 | } |
---|
| 528 | ///\brief Processes the next node in the priority heap |
---|
| 529 | |
---|
| 530 | ///Processes the next node in the priority heap. |
---|
| 531 | /// |
---|
| 532 | ///\return The processed node. |
---|
| 533 | /// |
---|
| 534 | ///\warning The priority heap must not be empty! |
---|
| 535 | Node processNextNode(){ |
---|
| 536 | Node v=_heap->top(); |
---|
| 537 | _heap->pop(); |
---|
| 538 | _processed->set(v,true); |
---|
| 539 | |
---|
| 540 | for(IncEdgeIt e(*graph,v); e!=INVALID; ++e) { |
---|
| 541 | Node w=graph->oppositeNode(v,e); |
---|
| 542 | switch(_heap->state(w)) { |
---|
| 543 | case Heap::PRE_HEAP: |
---|
| 544 | _heap->push(w,(*cost)[e]); |
---|
| 545 | _pred->set(w,e); |
---|
| 546 | break; |
---|
| 547 | case Heap::IN_HEAP: |
---|
| 548 | if ( (*cost)[e] < (*_heap)[w] ) { |
---|
| 549 | _heap->decrease(w,(*cost)[e]); |
---|
| 550 | _pred->set(w,e); |
---|
| 551 | } |
---|
| 552 | break; |
---|
| 553 | case Heap::POST_HEAP: |
---|
| 554 | break; |
---|
| 555 | } |
---|
| 556 | } |
---|
| 557 | if ((*_pred)[v]!=INVALID)_tree->set((*_pred)[v],true); |
---|
| 558 | return v; |
---|
| 559 | } |
---|
| 560 | |
---|
| 561 | ///\brief Next node to be processed. |
---|
| 562 | |
---|
| 563 | ///Next node to be processed. |
---|
| 564 | /// |
---|
| 565 | ///\return The next node to be processed or INVALID if the priority heap |
---|
| 566 | /// is empty. |
---|
| 567 | Node nextNode(){ |
---|
| 568 | return _heap->empty()?_heap->top():INVALID; |
---|
| 569 | } |
---|
| 570 | |
---|
| 571 | ///\brief Returns \c false if there are nodes to be processed in the priority heap |
---|
| 572 | /// |
---|
| 573 | ///Returns \c false if there are nodes |
---|
| 574 | ///to be processed in the priority heap |
---|
| 575 | bool emptyQueue() { return _heap->empty(); } |
---|
| 576 | ///\brief Returns the number of the nodes to be processed in the priority heap |
---|
| 577 | |
---|
| 578 | ///Returns the number of the nodes to be processed in the priority heap |
---|
| 579 | /// |
---|
| 580 | int queueSize() { return _heap->size(); } |
---|
| 581 | |
---|
| 582 | ///\brief Executes the algorithm. |
---|
| 583 | |
---|
| 584 | ///Executes the algorithm. |
---|
| 585 | /// |
---|
| 586 | ///\pre init() must be called and at least one node should be added |
---|
| 587 | ///with addSource() before using this function. |
---|
| 588 | /// |
---|
| 589 | ///This method runs the %Prim algorithm from the node(s) |
---|
| 590 | ///in order to compute the |
---|
| 591 | ///minimum spanning tree. |
---|
| 592 | /// |
---|
| 593 | void start(){ |
---|
| 594 | while ( !_heap->empty() ) processNextNode(); |
---|
| 595 | } |
---|
| 596 | |
---|
| 597 | ///\brief Executes the algorithm until a condition is met. |
---|
| 598 | |
---|
| 599 | ///Executes the algorithm until a condition is met. |
---|
| 600 | /// |
---|
| 601 | ///\pre init() must be called and at least one node should be added |
---|
| 602 | ///with addSource() before using this function. |
---|
| 603 | /// |
---|
| 604 | ///\param nm must be a bool (or convertible) node map. The algorithm |
---|
| 605 | ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>. |
---|
| 606 | template<class NodeBoolMap> |
---|
| 607 | void start(const NodeBoolMap &nm){ |
---|
| 608 | while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode(); |
---|
| 609 | if ( !_heap->empty() ) _processed->set(_heap->top(),true); |
---|
| 610 | } |
---|
| 611 | |
---|
| 612 | ///\brief Runs %Prim algorithm. |
---|
| 613 | |
---|
| 614 | ///This method runs the %Prim algorithm |
---|
| 615 | ///in order to compute the |
---|
| 616 | ///minimum spanning tree (or minimum spanning forest). |
---|
| 617 | ///The method also works on graphs that has more than one components. |
---|
| 618 | ///In this case it computes the minimum spanning forest. |
---|
| 619 | void run() { |
---|
| 620 | init(); |
---|
| 621 | for(NodeIt it(*graph);it!=INVALID;++it){ |
---|
| 622 | if(!processed(it)){ |
---|
| 623 | addSource(it); |
---|
| 624 | start(); |
---|
| 625 | } |
---|
| 626 | } |
---|
| 627 | } |
---|
| 628 | |
---|
| 629 | ///\brief Runs %Prim algorithm from node \c s. |
---|
| 630 | |
---|
| 631 | ///This method runs the %Prim algorithm from node \c s |
---|
| 632 | ///in order to |
---|
| 633 | ///compute the |
---|
| 634 | ///minimun spanning tree |
---|
| 635 | /// |
---|
| 636 | ///\note d.run(s) is just a shortcut of the following code. |
---|
| 637 | ///\code |
---|
| 638 | /// d.init(); |
---|
| 639 | /// d.addSource(s); |
---|
| 640 | /// d.start(); |
---|
| 641 | ///\endcode |
---|
| 642 | ///\note If the graph has more than one components, the method |
---|
| 643 | ///will compute the minimun spanning tree for only one component. |
---|
| 644 | /// |
---|
| 645 | ///See \ref run() if you want to compute the minimal spanning forest. |
---|
| 646 | void run(Node s){ |
---|
| 647 | init(); |
---|
| 648 | addSource(s); |
---|
| 649 | start(); |
---|
| 650 | } |
---|
| 651 | |
---|
| 652 | ///@} |
---|
| 653 | |
---|
| 654 | ///\name Query Functions |
---|
| 655 | ///The result of the %Prim algorithm can be obtained using these |
---|
| 656 | ///functions.\n |
---|
| 657 | ///Before the use of these functions, |
---|
| 658 | ///either run() or start() must be called. |
---|
| 659 | |
---|
| 660 | ///@{ |
---|
| 661 | |
---|
| 662 | ///\brief Returns the 'previous edge' of the minimum spanning tree. |
---|
| 663 | |
---|
| 664 | ///For a node \c v it returns the 'previous edge' of the minimum spanning tree, |
---|
| 665 | ///i.e. it returns the edge from where \c v was reached. For a source node |
---|
| 666 | ///or an unreachable node it is \ref INVALID. |
---|
| 667 | ///The minimum spanning tree used here is equal to the minimum spanning tree used |
---|
| 668 | ///in \ref predNode(). \pre \ref run() or \ref start() must be called before |
---|
| 669 | ///using this function. |
---|
| 670 | UEdge predEdge(Node v) const { return (*_pred)[v]; } |
---|
| 671 | |
---|
| 672 | ///\brief Returns the 'previous node' of the minimum spanning tree. |
---|
| 673 | |
---|
| 674 | ///For a node \c v it returns the 'previous node' of the minimum spanning tree, |
---|
| 675 | ///i.e. it returns the node from where \c v was reached. For a source node |
---|
| 676 | ///or an unreachable node it is \ref INVALID. |
---|
| 677 | //The minimum spanning tree used here is equal to the minimum spanning |
---|
| 678 | ///tree used in \ref predEdge(). \pre \ref run() or \ref start() must be called |
---|
| 679 | ///before using this function. |
---|
| 680 | Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID: |
---|
| 681 | graph->source((*_pred)[v]); } |
---|
| 682 | |
---|
| 683 | ///\brief Returns a reference to the NodeMap of the edges of the minimum spanning tree. |
---|
| 684 | |
---|
| 685 | ///Returns a reference to the NodeMap of the edges of the |
---|
| 686 | ///minimum spanning tree. |
---|
| 687 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
| 688 | const PredMap &predMap() const { return *_pred;} |
---|
| 689 | |
---|
| 690 | ///\brief Returns a reference to the tree edges map. |
---|
| 691 | |
---|
| 692 | ///Returns a reference to the TreeEdgeMap of the edges of the |
---|
| 693 | ///minimum spanning tree. The value of the map is \c true only if the edge is in |
---|
| 694 | ///the minimum spanning tree. |
---|
| 695 | ///\warning By default, the TreeEdgeMap is a NullMap. |
---|
| 696 | /// |
---|
| 697 | ///If it is not set before the execution of the algorithm, use the \ref |
---|
| 698 | ///treeMap(TreeMap&) function (after the execution) to set an UEdgeMap with the |
---|
| 699 | ///edges of the minimum spanning tree in O(n) time where n is the number of |
---|
| 700 | ///nodes in the graph. |
---|
| 701 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
| 702 | const TreeMap &treeMap() const { return *_tree;} |
---|
| 703 | |
---|
| 704 | ///\brief Sets the tree edges map. |
---|
| 705 | |
---|
| 706 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
---|
| 707 | ///The map values belonging to the edges of the minimum |
---|
[1953] | 708 | ///spanning tree are set to \c tree_edge_value or \c true by default, |
---|
[1912] | 709 | ///the other map values remain untouched. |
---|
| 710 | /// |
---|
| 711 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
| 712 | |
---|
| 713 | template<class TreeMap> |
---|
| 714 | void quickTreeEdges( |
---|
| 715 | TreeMap& tree, |
---|
| 716 | const typename TreeMap::Value& tree_edge_value=true) const { |
---|
| 717 | for(NodeIt i(*graph);i!=INVALID;++i){ |
---|
| 718 | if((*_pred)[i]!=INVALID) tree.set((*_pred)[i],tree_edge_value); |
---|
| 719 | } |
---|
| 720 | } |
---|
| 721 | |
---|
| 722 | ///\brief Sets the tree edges map. |
---|
| 723 | |
---|
| 724 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
---|
| 725 | ///The map values belonging to the edges of the minimum |
---|
[1953] | 726 | ///spanning tree are set to \c tree_edge_value or \c true by default while |
---|
[1912] | 727 | ///the edge values not belonging to the minimum spanning tree are set to |
---|
[1953] | 728 | ///\c tree_default_value or \c false by default. |
---|
[1912] | 729 | /// |
---|
| 730 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
| 731 | |
---|
| 732 | template<class TreeMap> |
---|
| 733 | void treeEdges( |
---|
| 734 | TreeMap& tree, |
---|
| 735 | const typename TreeMap::Value& tree_edge_value=true, |
---|
| 736 | const typename TreeMap::Value& tree_default_value=false) const { |
---|
| 737 | for(typename ItemSetTraits<UGraph,UEdge>::ItemIt i(*graph);i!=INVALID;++i) |
---|
| 738 | tree.set(i,tree_default_value); |
---|
| 739 | for(NodeIt i(*graph);i!=INVALID;++i){ |
---|
| 740 | if((*_pred)[i]!=INVALID) tree.set((*_pred)[i],tree_edge_value); |
---|
| 741 | } |
---|
| 742 | } |
---|
| 743 | |
---|
| 744 | ///\brief Checks if a node is reachable from the starting node. |
---|
| 745 | |
---|
| 746 | ///Returns \c true if \c v is reachable from the starting node. |
---|
| 747 | ///\warning The source nodes are inditated as unreached. |
---|
| 748 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
| 749 | /// |
---|
| 750 | bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; } |
---|
| 751 | |
---|
| 752 | ///\brief Checks if a node is processed. |
---|
| 753 | |
---|
| 754 | ///Returns \c true if \c v is processed, i.e. \c v is already connencted to the |
---|
| 755 | ///minimum spanning tree. |
---|
| 756 | ///\pre \ref run() or \ref start() must be called before using this function. |
---|
| 757 | /// |
---|
| 758 | bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; } |
---|
| 759 | |
---|
| 760 | |
---|
| 761 | ///\brief Checks if an edge is in the spanning tree or not. |
---|
| 762 | |
---|
| 763 | ///Checks if an edge is in the spanning tree or not. |
---|
| 764 | ///\param e is the edge that will be checked |
---|
| 765 | ///\return \c true if e is in the spanning tree, \c false otherwise |
---|
| 766 | bool tree(UEdge e){ |
---|
| 767 | return (*_pred)[*graph.source(e)]==e || (*_pred)[*graph.target(e)]==e; |
---|
| 768 | } |
---|
| 769 | ///@} |
---|
| 770 | }; |
---|
| 771 | |
---|
| 772 | |
---|
| 773 | /// \ingroup spantree |
---|
| 774 | /// |
---|
| 775 | /// \brief Function type interface for Prim algorithm. |
---|
| 776 | /// |
---|
| 777 | /// Function type interface for Prim algorithm. |
---|
| 778 | /// \param graph the UGraph that the algorithm runs on |
---|
| 779 | /// \param cost the CostMap of the edges |
---|
| 780 | /// \retval tree the EdgeMap that contains whether an edge is in |
---|
| 781 | /// the spanning tree or not |
---|
| 782 | /// |
---|
| 783 | ///\sa Prim |
---|
| 784 | template<class Graph,class CostMap,class TreeMap> |
---|
| 785 | void prim(const Graph& graph, const CostMap& cost,TreeMap& tree){ |
---|
| 786 | typename Prim<Graph,CostMap>::template DefTreeMap<TreeMap>:: |
---|
| 787 | Create prm(graph,cost); |
---|
| 788 | prm.treeMap(tree); |
---|
| 789 | prm.run(); |
---|
[1979] | 790 | } |
---|
[1912] | 791 | |
---|
| 792 | } //END OF NAMESPACE LEMON |
---|
| 793 | |
---|
| 794 | #endif |
---|