[1077] | 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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[1359] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[1077] | 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_MAX_MATCHING_H |
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| 20 | #define LEMON_MAX_MATCHING_H |
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| 21 | |
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| 22 | #include <queue> |
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[1993] | 23 | #include <lemon/bits/invalid.h> |
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[1093] | 24 | #include <lemon/unionfind.h> |
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[1077] | 25 | #include <lemon/graph_utils.h> |
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| 26 | |
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[2042] | 27 | ///\ingroup matching |
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[1077] | 28 | ///\file |
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[2042] | 29 | ///\brief Maximum matching algorithm in undirected graph. |
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[1077] | 30 | |
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| 31 | namespace lemon { |
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| 32 | |
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[2042] | 33 | /// \ingroup matching |
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[1077] | 34 | |
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| 35 | ///Edmonds' alternating forest maximum matching algorithm. |
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| 36 | |
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| 37 | ///This class provides Edmonds' alternating forest matching |
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| 38 | ///algorithm. The starting matching (if any) can be passed to the |
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| 39 | ///algorithm using read-in functions \ref readNMapNode, \ref |
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| 40 | ///readNMapEdge or \ref readEMapBool depending on the container. The |
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| 41 | ///resulting maximum matching can be attained by write-out functions |
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| 42 | ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool |
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| 43 | ///depending on the preferred container. |
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| 44 | /// |
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| 45 | ///The dual side of a matching is a map of the nodes to |
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| 46 | ///MaxMatching::pos_enum, having values D, A and C showing the |
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| 47 | ///Gallai-Edmonds decomposition of the graph. The nodes in D induce |
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| 48 | ///a graph with factor-critical components, the nodes in A form the |
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| 49 | ///barrier, and the nodes in C induce a graph having a perfect |
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| 50 | ///matching. This decomposition can be attained by calling \ref |
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[1090] | 51 | ///writePos after running the algorithm. |
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[1077] | 52 | /// |
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| 53 | ///\param Graph The undirected graph type the algorithm runs on. |
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| 54 | /// |
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| 55 | ///\author Jacint Szabo |
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| 56 | template <typename Graph> |
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| 57 | class MaxMatching { |
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[1165] | 58 | |
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| 59 | protected: |
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| 60 | |
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[1077] | 61 | typedef typename Graph::Node Node; |
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| 62 | typedef typename Graph::Edge Edge; |
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[1909] | 63 | typedef typename Graph::UEdge UEdge; |
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| 64 | typedef typename Graph::UEdgeIt UEdgeIt; |
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[1077] | 65 | typedef typename Graph::NodeIt NodeIt; |
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| 66 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
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| 67 | |
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| 68 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
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| 69 | |
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| 70 | public: |
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| 71 | |
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| 72 | ///Indicates the Gallai-Edmonds decomposition of the graph. |
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| 73 | |
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| 74 | ///Indicates the Gallai-Edmonds decomposition of the graph, which |
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| 75 | ///shows an upper bound on the size of a maximum matching. The |
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| 76 | ///nodes with pos_enum \c D induce a graph with factor-critical |
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| 77 | ///components, the nodes in \c A form the canonical barrier, and the |
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| 78 | ///nodes in \c C induce a graph having a perfect matching. |
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| 79 | enum pos_enum { |
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| 80 | D=0, |
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| 81 | A=1, |
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| 82 | C=2 |
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| 83 | }; |
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| 84 | |
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[1165] | 85 | protected: |
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[1077] | 86 | |
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| 87 | static const int HEUR_density=2; |
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| 88 | const Graph& g; |
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[1093] | 89 | typename Graph::template NodeMap<Node> _mate; |
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[1077] | 90 | typename Graph::template NodeMap<pos_enum> position; |
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| 91 | |
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| 92 | public: |
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| 93 | |
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[1093] | 94 | MaxMatching(const Graph& _g) : g(_g), _mate(_g,INVALID), position(_g) {} |
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[1077] | 95 | |
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| 96 | ///Runs Edmonds' algorithm. |
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| 97 | |
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| 98 | ///Runs Edmonds' algorithm for sparse graphs (number of edges < |
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| 99 | ///2*number of nodes), and a heuristical Edmonds' algorithm with a |
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[1090] | 100 | ///heuristic of postponing shrinks for dense graphs. |
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[1587] | 101 | void run() { |
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[1909] | 102 | if ( countUEdges(g) < HEUR_density*countNodes(g) ) { |
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[1587] | 103 | greedyMatching(); |
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| 104 | runEdmonds(0); |
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| 105 | } else runEdmonds(1); |
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| 106 | } |
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| 107 | |
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[1077] | 108 | |
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| 109 | ///Runs Edmonds' algorithm. |
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| 110 | |
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| 111 | ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs |
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| 112 | ///Edmonds' algorithm with a heuristic of postponing shrinks, |
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[1090] | 113 | ///giving a faster algorithm for dense graphs. |
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[1587] | 114 | void runEdmonds( int heur = 1 ) { |
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| 115 | |
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[2023] | 116 | //each vertex is put to C |
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[1587] | 117 | for(NodeIt v(g); v!=INVALID; ++v) |
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| 118 | position.set(v,C); |
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| 119 | |
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| 120 | typename Graph::template NodeMap<Node> ear(g,INVALID); |
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| 121 | //undefined for the base nodes of the blossoms (i.e. for the |
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| 122 | //representative elements of UFE blossom) and for the nodes in C |
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| 123 | |
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| 124 | typename UFE::MapType blossom_base(g); |
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| 125 | UFE blossom(blossom_base); |
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| 126 | typename UFE::MapType tree_base(g); |
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| 127 | UFE tree(tree_base); |
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| 128 | //If these UFE's would be members of the class then also |
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| 129 | //blossom_base and tree_base should be a member. |
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| 130 | |
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[2023] | 131 | //We build only one tree and the other vertices uncovered by the |
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| 132 | //matching belong to C. (They can be considered as singleton |
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| 133 | //trees.) If this tree can be augmented or no more |
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| 134 | //grow/augmentation/shrink is possible then we return to this |
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| 135 | //"for" cycle. |
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[1587] | 136 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 137 | if ( position[v]==C && _mate[v]==INVALID ) { |
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| 138 | blossom.insert(v); |
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| 139 | tree.insert(v); |
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| 140 | position.set(v,D); |
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| 141 | if ( heur == 1 ) lateShrink( v, ear, blossom, tree ); |
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| 142 | else normShrink( v, ear, blossom, tree ); |
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| 143 | } |
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| 144 | } |
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| 145 | } |
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| 146 | |
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[1077] | 147 | |
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| 148 | ///Finds a greedy matching starting from the actual matching. |
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| 149 | |
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| 150 | ///Starting form the actual matching stored, it finds a maximal |
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| 151 | ///greedy matching. |
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[1587] | 152 | void greedyMatching() { |
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| 153 | for(NodeIt v(g); v!=INVALID; ++v) |
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| 154 | if ( _mate[v]==INVALID ) { |
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| 155 | for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) { |
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| 156 | Node y=g.runningNode(e); |
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| 157 | if ( _mate[y]==INVALID && y!=v ) { |
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| 158 | _mate.set(v,y); |
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| 159 | _mate.set(y,v); |
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| 160 | break; |
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| 161 | } |
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| 162 | } |
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| 163 | } |
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| 164 | } |
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[1077] | 165 | |
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| 166 | ///Returns the size of the actual matching stored. |
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| 167 | |
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| 168 | ///Returns the size of the actual matching stored. After \ref |
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| 169 | ///run() it returns the size of a maximum matching in the graph. |
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[1587] | 170 | int size() const { |
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| 171 | int s=0; |
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| 172 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 173 | if ( _mate[v]!=INVALID ) { |
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| 174 | ++s; |
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| 175 | } |
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| 176 | } |
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| 177 | return s/2; |
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| 178 | } |
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| 179 | |
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[1077] | 180 | |
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| 181 | ///Resets the actual matching to the empty matching. |
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| 182 | |
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| 183 | ///Resets the actual matching to the empty matching. |
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| 184 | /// |
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[1587] | 185 | void resetMatching() { |
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| 186 | for(NodeIt v(g); v!=INVALID; ++v) |
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| 187 | _mate.set(v,INVALID); |
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| 188 | } |
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[1077] | 189 | |
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[1093] | 190 | ///Returns the mate of a node in the actual matching. |
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| 191 | |
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| 192 | ///Returns the mate of a \c node in the actual matching. |
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| 193 | ///Returns INVALID if the \c node is not covered by the actual matching. |
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| 194 | Node mate(Node& node) const { |
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| 195 | return _mate[node]; |
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| 196 | } |
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| 197 | |
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[1165] | 198 | ///Reads a matching from a \c Node valued \c Node map. |
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[1077] | 199 | |
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[1165] | 200 | ///Reads a matching from a \c Node valued \c Node map. This map |
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| 201 | ///must be \e symmetric, i.e. if \c map[u]==v then \c map[v]==u |
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| 202 | ///must hold, and \c uv will be an edge of the matching. |
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[1077] | 203 | template<typename NMapN> |
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| 204 | void readNMapNode(NMapN& map) { |
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| 205 | for(NodeIt v(g); v!=INVALID; ++v) { |
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[1093] | 206 | _mate.set(v,map[v]); |
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[1077] | 207 | } |
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| 208 | } |
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| 209 | |
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[1165] | 210 | ///Writes the stored matching to a \c Node valued \c Node map. |
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[1077] | 211 | |
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[1165] | 212 | ///Writes the stored matching to a \c Node valued \c Node map. The |
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[1077] | 213 | ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c |
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| 214 | ///map[v]==u will hold, and now \c uv is an edge of the matching. |
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| 215 | template<typename NMapN> |
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| 216 | void writeNMapNode (NMapN& map) const { |
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| 217 | for(NodeIt v(g); v!=INVALID; ++v) { |
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[1093] | 218 | map.set(v,_mate[v]); |
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[1077] | 219 | } |
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| 220 | } |
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| 221 | |
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[1909] | 222 | ///Reads a matching from an \c UEdge valued \c Node map. |
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[1077] | 223 | |
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[1909] | 224 | ///Reads a matching from an \c UEdge valued \c Node map. \c |
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| 225 | ///map[v] must be an \c UEdge incident to \c v. This map must |
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[1165] | 226 | ///have the property that if \c g.oppositeNode(u,map[u])==v then |
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| 227 | ///\c \c g.oppositeNode(v,map[v])==u holds, and now some edge |
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[1172] | 228 | ///joining \c u to \c v will be an edge of the matching. |
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[1077] | 229 | template<typename NMapE> |
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| 230 | void readNMapEdge(NMapE& map) { |
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[2023] | 231 | for(NodeIt v(g); v!=INVALID; ++v) { |
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| 232 | UEdge e=map[v]; |
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[1165] | 233 | if ( e!=INVALID ) |
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[1166] | 234 | _mate.set(v,g.oppositeNode(v,e)); |
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[1077] | 235 | } |
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| 236 | } |
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| 237 | |
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[1909] | 238 | ///Writes the matching stored to an \c UEdge valued \c Node map. |
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[1077] | 239 | |
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[1909] | 240 | ///Writes the stored matching to an \c UEdge valued \c Node |
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| 241 | ///map. \c map[v] will be an \c UEdge incident to \c v. This |
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[1165] | 242 | ///map will have the property that if \c g.oppositeNode(u,map[u]) |
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| 243 | ///== v then \c map[u]==map[v] holds, and now this edge is an edge |
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| 244 | ///of the matching. |
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[1077] | 245 | template<typename NMapE> |
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| 246 | void writeNMapEdge (NMapE& map) const { |
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| 247 | typename Graph::template NodeMap<bool> todo(g,true); |
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| 248 | for(NodeIt v(g); v!=INVALID; ++v) { |
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[1093] | 249 | if ( todo[v] && _mate[v]!=INVALID ) { |
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| 250 | Node u=_mate[v]; |
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[1077] | 251 | for(IncEdgeIt e(g,v); e!=INVALID; ++e) { |
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[1158] | 252 | if ( g.runningNode(e) == u ) { |
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[1077] | 253 | map.set(u,e); |
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| 254 | map.set(v,e); |
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| 255 | todo.set(u,false); |
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| 256 | todo.set(v,false); |
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| 257 | break; |
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| 258 | } |
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| 259 | } |
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| 260 | } |
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| 261 | } |
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| 262 | } |
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| 263 | |
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| 264 | |
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[1165] | 265 | ///Reads a matching from a \c bool valued \c Edge map. |
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[1077] | 266 | |
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[1165] | 267 | ///Reads a matching from a \c bool valued \c Edge map. This map |
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| 268 | ///must have the property that there are no two incident edges \c |
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| 269 | ///e, \c f with \c map[e]==map[f]==true. The edges \c e with \c |
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[1077] | 270 | ///map[e]==true form the matching. |
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| 271 | template<typename EMapB> |
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| 272 | void readEMapBool(EMapB& map) { |
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[1909] | 273 | for(UEdgeIt e(g); e!=INVALID; ++e) { |
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[1077] | 274 | if ( map[e] ) { |
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| 275 | Node u=g.source(e); |
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| 276 | Node v=g.target(e); |
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[1093] | 277 | _mate.set(u,v); |
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| 278 | _mate.set(v,u); |
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[1077] | 279 | } |
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| 280 | } |
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| 281 | } |
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| 282 | |
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| 283 | |
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[1165] | 284 | ///Writes the matching stored to a \c bool valued \c Edge map. |
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[1077] | 285 | |
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[1165] | 286 | ///Writes the matching stored to a \c bool valued \c Edge |
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| 287 | ///map. This map will have the property that there are no two |
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| 288 | ///incident edges \c e, \c f with \c map[e]==map[f]==true. The |
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| 289 | ///edges \c e with \c map[e]==true form the matching. |
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[1077] | 290 | template<typename EMapB> |
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| 291 | void writeEMapBool (EMapB& map) const { |
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[1909] | 292 | for(UEdgeIt e(g); e!=INVALID; ++e) map.set(e,false); |
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[1077] | 293 | |
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| 294 | typename Graph::template NodeMap<bool> todo(g,true); |
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| 295 | for(NodeIt v(g); v!=INVALID; ++v) { |
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[1093] | 296 | if ( todo[v] && _mate[v]!=INVALID ) { |
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| 297 | Node u=_mate[v]; |
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[1077] | 298 | for(IncEdgeIt e(g,v); e!=INVALID; ++e) { |
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[1158] | 299 | if ( g.runningNode(e) == u ) { |
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[1077] | 300 | map.set(e,true); |
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| 301 | todo.set(u,false); |
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| 302 | todo.set(v,false); |
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| 303 | break; |
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| 304 | } |
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| 305 | } |
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| 306 | } |
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| 307 | } |
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| 308 | } |
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| 309 | |
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| 310 | |
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| 311 | ///Writes the canonical decomposition of the graph after running |
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| 312 | ///the algorithm. |
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| 313 | |
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[1090] | 314 | ///After calling any run methods of the class, it writes the |
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| 315 | ///Gallai-Edmonds canonical decomposition of the graph. \c map |
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| 316 | ///must be a node map of \ref pos_enum 's. |
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[1077] | 317 | template<typename NMapEnum> |
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| 318 | void writePos (NMapEnum& map) const { |
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| 319 | for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]); |
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| 320 | } |
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| 321 | |
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| 322 | private: |
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| 323 | |
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[1165] | 324 | |
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[1077] | 325 | void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
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| 326 | UFE& blossom, UFE& tree); |
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| 327 | |
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[1234] | 328 | void normShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
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[1077] | 329 | UFE& blossom, UFE& tree); |
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| 330 | |
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[2023] | 331 | void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear, |
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| 332 | UFE& blossom, UFE& tree,std::queue<Node>& Q); |
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[1077] | 333 | |
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[1234] | 334 | void shrinkStep(Node& top, Node& middle, Node& bottom, |
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| 335 | typename Graph::template NodeMap<Node>& ear, |
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[1077] | 336 | UFE& blossom, UFE& tree, std::queue<Node>& Q); |
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| 337 | |
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[2023] | 338 | bool growOrAugment(Node& y, Node& x, typename Graph::template |
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| 339 | NodeMap<Node>& ear, UFE& blossom, UFE& tree, |
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| 340 | std::queue<Node>& Q); |
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| 341 | |
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[1234] | 342 | void augment(Node x, typename Graph::template NodeMap<Node>& ear, |
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[1077] | 343 | UFE& blossom, UFE& tree); |
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| 344 | |
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| 345 | }; |
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| 346 | |
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| 347 | |
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| 348 | // ********************************************************************** |
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| 349 | // IMPLEMENTATIONS |
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| 350 | // ********************************************************************** |
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| 351 | |
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| 352 | |
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| 353 | template <typename Graph> |
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[2023] | 354 | void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template |
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| 355 | NodeMap<Node>& ear, UFE& blossom, UFE& tree) { |
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| 356 | //We have one tree which we grow, and also shrink but only if it cannot be |
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| 357 | //postponed. If we augment then we return to the "for" cycle of |
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| 358 | //runEdmonds(). |
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[1077] | 359 | |
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| 360 | std::queue<Node> Q; //queue of the totally unscanned nodes |
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| 361 | Q.push(v); |
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| 362 | std::queue<Node> R; |
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| 363 | //queue of the nodes which must be scanned for a possible shrink |
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| 364 | |
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| 365 | while ( !Q.empty() ) { |
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| 366 | Node x=Q.front(); |
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| 367 | Q.pop(); |
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[2023] | 368 | for( IncEdgeIt e(g,x); e!= INVALID; ++e ) { |
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| 369 | Node y=g.runningNode(e); |
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| 370 | //growOrAugment grows if y is covered by the matching and |
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| 371 | //augments if not. In this latter case it returns 1. |
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| 372 | if ( position[y]==C && growOrAugment(y, x, ear, blossom, tree, Q) ) return; |
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| 373 | } |
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| 374 | R.push(x); |
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[1077] | 375 | } |
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| 376 | |
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| 377 | while ( !R.empty() ) { |
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| 378 | Node x=R.front(); |
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| 379 | R.pop(); |
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| 380 | |
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| 381 | for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) { |
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[1158] | 382 | Node y=g.runningNode(e); |
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[1077] | 383 | |
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[2023] | 384 | if ( position[y] == D && blossom.find(x) != blossom.find(y) ) |
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| 385 | //Recall that we have only one tree. |
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| 386 | shrink( x, y, ear, blossom, tree, Q); |
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[1077] | 387 | |
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| 388 | while ( !Q.empty() ) { |
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| 389 | Node x=Q.front(); |
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| 390 | Q.pop(); |
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[2023] | 391 | for( IncEdgeIt e(g,x); e!= INVALID; ++e ) { |
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| 392 | Node y=g.runningNode(e); |
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| 393 | //growOrAugment grows if y is covered by the matching and |
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| 394 | //augments if not. In this latter case it returns 1. |
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| 395 | if ( position[y]==C && growOrAugment(y, x, ear, blossom, tree, Q) ) return; |
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| 396 | } |
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| 397 | R.push(x); |
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[1077] | 398 | } |
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| 399 | } //for e |
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| 400 | } // while ( !R.empty() ) |
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| 401 | } |
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| 402 | |
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| 403 | |
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| 404 | template <typename Graph> |
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[1234] | 405 | void MaxMatching<Graph>::normShrink(Node v, |
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| 406 | typename Graph::template |
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| 407 | NodeMap<Node>& ear, |
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[1077] | 408 | UFE& blossom, UFE& tree) { |
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[2023] | 409 | //We have one tree, which we grow and shrink. If we augment then we |
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| 410 | //return to the "for" cycle of runEdmonds(). |
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| 411 | |
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[1077] | 412 | std::queue<Node> Q; //queue of the unscanned nodes |
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| 413 | Q.push(v); |
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| 414 | while ( !Q.empty() ) { |
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| 415 | |
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| 416 | Node x=Q.front(); |
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| 417 | Q.pop(); |
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| 418 | |
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| 419 | for( IncEdgeIt e(g,x); e!=INVALID; ++e ) { |
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[1158] | 420 | Node y=g.runningNode(e); |
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[1077] | 421 | |
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| 422 | switch ( position[y] ) { |
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| 423 | case D: //x and y must be in the same tree |
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[2023] | 424 | if ( blossom.find(x) != blossom.find(y) ) |
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| 425 | //x and y are in the same tree |
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| 426 | shrink( x, y, ear, blossom, tree, Q); |
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[1077] | 427 | break; |
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| 428 | case C: |
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[2023] | 429 | //growOrAugment grows if y is covered by the matching and |
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| 430 | //augments if not. In this latter case it returns 1. |
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| 431 | if ( growOrAugment(y, x, ear, blossom, tree, Q) ) return; |
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[1077] | 432 | break; |
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| 433 | default: break; |
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[2023] | 434 | } |
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[1077] | 435 | } |
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| 436 | } |
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| 437 | } |
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[2023] | 438 | |
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[1077] | 439 | |
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| 440 | template <typename Graph> |
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[2023] | 441 | void MaxMatching<Graph>::shrink(Node x,Node y, typename |
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| 442 | Graph::template NodeMap<Node>& ear, |
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| 443 | UFE& blossom, UFE& tree, std::queue<Node>& Q) { |
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| 444 | //x and y are the two adjacent vertices in two blossoms. |
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| 445 | |
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| 446 | typename Graph::template NodeMap<bool> path(g,false); |
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| 447 | |
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| 448 | Node b=blossom.find(x); |
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| 449 | path.set(b,true); |
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| 450 | b=_mate[b]; |
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| 451 | while ( b!=INVALID ) { |
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| 452 | b=blossom.find(ear[b]); |
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| 453 | path.set(b,true); |
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| 454 | b=_mate[b]; |
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| 455 | } //we go until the root through bases of blossoms and odd vertices |
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| 456 | |
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| 457 | Node top=y; |
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| 458 | Node middle=blossom.find(top); |
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| 459 | Node bottom=x; |
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| 460 | while ( !path[middle] ) |
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| 461 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
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| 462 | //Until we arrive to a node on the path, we update blossom, tree |
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| 463 | //and the positions of the odd nodes. |
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| 464 | |
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| 465 | Node base=middle; |
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| 466 | top=x; |
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| 467 | middle=blossom.find(top); |
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| 468 | bottom=y; |
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| 469 | Node blossom_base=blossom.find(base); |
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| 470 | while ( middle!=blossom_base ) |
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| 471 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
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| 472 | //Until we arrive to a node on the path, we update blossom, tree |
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| 473 | //and the positions of the odd nodes. |
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| 474 | |
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| 475 | blossom.makeRep(base); |
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[1077] | 476 | } |
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| 477 | |
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[2023] | 478 | |
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| 479 | |
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[1077] | 480 | template <typename Graph> |
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[1234] | 481 | void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom, |
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| 482 | typename Graph::template |
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| 483 | NodeMap<Node>& ear, |
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| 484 | UFE& blossom, UFE& tree, |
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| 485 | std::queue<Node>& Q) { |
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[2023] | 486 | //We traverse a blossom and update everything. |
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| 487 | |
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[1077] | 488 | ear.set(top,bottom); |
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| 489 | Node t=top; |
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| 490 | while ( t!=middle ) { |
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[1093] | 491 | Node u=_mate[t]; |
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[1077] | 492 | t=ear[u]; |
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| 493 | ear.set(t,u); |
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| 494 | } |
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[1093] | 495 | bottom=_mate[middle]; |
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[1077] | 496 | position.set(bottom,D); |
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| 497 | Q.push(bottom); |
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| 498 | top=ear[bottom]; |
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| 499 | Node oldmiddle=middle; |
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| 500 | middle=blossom.find(top); |
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| 501 | tree.erase(bottom); |
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| 502 | tree.erase(oldmiddle); |
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| 503 | blossom.insert(bottom); |
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| 504 | blossom.join(bottom, oldmiddle); |
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| 505 | blossom.join(top, oldmiddle); |
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| 506 | } |
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| 507 | |
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[2023] | 508 | |
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| 509 | template <typename Graph> |
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| 510 | bool MaxMatching<Graph>::growOrAugment(Node& y, Node& x, typename Graph::template |
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| 511 | NodeMap<Node>& ear, UFE& blossom, UFE& tree, |
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| 512 | std::queue<Node>& Q) { |
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| 513 | //x is in a blossom in the tree, y is outside. If y is covered by |
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| 514 | //the matching we grow, otherwise we augment. In this case we |
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| 515 | //return 1. |
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| 516 | |
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| 517 | if ( _mate[y]!=INVALID ) { //grow |
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| 518 | ear.set(y,x); |
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| 519 | Node w=_mate[y]; |
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| 520 | blossom.insert(w); |
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| 521 | position.set(y,A); |
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| 522 | position.set(w,D); |
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| 523 | tree.insert(y); |
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| 524 | tree.insert(w); |
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| 525 | tree.join(y,blossom.find(x)); |
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| 526 | tree.join(w,y); |
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| 527 | Q.push(w); |
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| 528 | } else { //augment |
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| 529 | augment(x, ear, blossom, tree); |
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| 530 | _mate.set(x,y); |
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| 531 | _mate.set(y,x); |
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| 532 | return true; |
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| 533 | } |
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| 534 | return false; |
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| 535 | } |
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| 536 | |
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| 537 | |
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[1077] | 538 | template <typename Graph> |
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[1234] | 539 | void MaxMatching<Graph>::augment(Node x, |
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| 540 | typename Graph::template NodeMap<Node>& ear, |
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[1077] | 541 | UFE& blossom, UFE& tree) { |
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[1093] | 542 | Node v=_mate[x]; |
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[1077] | 543 | while ( v!=INVALID ) { |
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| 544 | |
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| 545 | Node u=ear[v]; |
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[1093] | 546 | _mate.set(v,u); |
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[1077] | 547 | Node tmp=v; |
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[1093] | 548 | v=_mate[u]; |
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| 549 | _mate.set(u,tmp); |
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[1077] | 550 | } |
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[2023] | 551 | Node y=blossom.find(x); |
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[1077] | 552 | typename UFE::ItemIt it; |
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| 553 | for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) { |
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| 554 | if ( position[it] == D ) { |
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| 555 | typename UFE::ItemIt b_it; |
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| 556 | for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) { |
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| 557 | position.set( b_it ,C); |
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| 558 | } |
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| 559 | blossom.eraseClass(it); |
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| 560 | } else position.set( it ,C); |
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| 561 | } |
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[2023] | 562 | tree.eraseClass(y); |
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[1077] | 563 | |
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| 564 | } |
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| 565 | |
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| 566 | |
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| 567 | } //END OF NAMESPACE LEMON |
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| 568 | |
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[1165] | 569 | #endif //LEMON_MAX_MATCHING_H |
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