[1738] | 1 | /* -*- C++ -*- |
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[1818] | 2 | * lemon/euler.h - Part of LEMON, a generic C++ optimization library |
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[1738] | 3 | * |
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[1875] | 4 | * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1738] | 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | #include<lemon/invalid.h> |
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[1818] | 17 | #include<lemon/topology.h> |
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[1738] | 18 | #include <list> |
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| 19 | |
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[1769] | 20 | /// \ingroup topology |
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[1738] | 21 | /// \file |
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| 22 | /// \brief Euler tour |
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| 23 | /// |
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| 24 | ///This file provides an Euler tour iterator and ways to check |
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| 25 | ///if a graph is euler. |
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| 26 | |
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| 27 | |
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| 28 | namespace lemon { |
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| 29 | |
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[1818] | 30 | ///Euler iterator for directed graphs. |
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[1738] | 31 | |
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[1769] | 32 | /// \ingroup topology |
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[1738] | 33 | ///This iterator converts to the \c Edge type of the graph and using |
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[1803] | 34 | ///operator ++ it provides an Euler tour of the graph (if there exists). |
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[1738] | 35 | /// |
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| 36 | ///For example |
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| 37 | ///if the given graph if Euler (i.e it has only one nontrivial component |
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| 38 | ///and the in-degree is equal to the out-degree for all nodes), |
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[1803] | 39 | ///the following code will print the edge IDs according to an |
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[1738] | 40 | ///Euler tour of \c g. |
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| 41 | ///\code |
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| 42 | /// for(EulerIt<ListGraph> e(g),e!=INVALID;++e) { |
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| 43 | /// std::cout << g.id(e) << std::eol; |
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| 44 | /// } |
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| 45 | ///\endcode |
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| 46 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
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| 47 | ///\todo Test required |
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| 48 | template<class Graph> |
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| 49 | class EulerIt |
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| 50 | { |
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| 51 | typedef typename Graph::Node Node; |
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| 52 | typedef typename Graph::NodeIt NodeIt; |
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| 53 | typedef typename Graph::Edge Edge; |
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| 54 | typedef typename Graph::EdgeIt EdgeIt; |
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| 55 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 56 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 57 | |
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| 58 | const Graph &g; |
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| 59 | typename Graph::NodeMap<OutEdgeIt> nedge; |
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| 60 | std::list<Edge> euler; |
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| 61 | |
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| 62 | public: |
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| 63 | |
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| 64 | ///Constructor |
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| 65 | |
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| 66 | ///\param _g A directed graph. |
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| 67 | ///\param start The starting point of the tour. If it is not given |
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[1803] | 68 | /// the tour will start from the first node. |
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[1738] | 69 | EulerIt(const Graph &_g,typename Graph::Node start=INVALID) |
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| 70 | : g(_g), nedge(g) |
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| 71 | { |
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| 72 | if(start==INVALID) start=NodeIt(g); |
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| 73 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutEdgeIt(g,n); |
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| 74 | while(nedge[start]!=INVALID) { |
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| 75 | euler.push_back(nedge[start]); |
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| 76 | Node next=g.target(nedge[start]); |
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| 77 | ++nedge[start]; |
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| 78 | start=next; |
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| 79 | } |
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| 80 | } |
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| 81 | |
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| 82 | ///Edge Conversion |
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| 83 | operator Edge() { return euler.empty()?INVALID:euler.front(); } |
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| 84 | bool operator==(Invalid) { return euler.empty(); } |
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| 85 | bool operator!=(Invalid) { return !euler.empty(); } |
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| 86 | |
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| 87 | ///Next edge of the tour |
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| 88 | EulerIt &operator++() { |
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| 89 | Node s=g.target(euler.front()); |
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| 90 | euler.pop_front(); |
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| 91 | //This produces a warning.Strange. |
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| 92 | //std::list<Edge>::iterator next=euler.begin(); |
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| 93 | typename std::list<Edge>::iterator next=euler.begin(); |
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| 94 | while(nedge[s]!=INVALID) { |
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| 95 | euler.insert(next,nedge[s]); |
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| 96 | Node n=g.target(nedge[s]); |
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| 97 | ++nedge[s]; |
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| 98 | s=n; |
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| 99 | } |
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| 100 | return *this; |
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| 101 | } |
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| 102 | ///Postfix incrementation |
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| 103 | |
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[1803] | 104 | ///\warning This incrementation |
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| 105 | ///returns an \c Edge, not an \ref EulerIt, as one may |
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| 106 | ///expect. |
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[1738] | 107 | Edge operator++(int) |
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| 108 | { |
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| 109 | Edge e=*this; |
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| 110 | ++(*this); |
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| 111 | return e; |
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| 112 | } |
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| 113 | }; |
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| 114 | |
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[1818] | 115 | ///Euler iterator for undirected graphs. |
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| 116 | |
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| 117 | /// \ingroup topology |
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| 118 | ///This iterator converts to the \c Edge type of the graph and using |
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| 119 | ///operator ++ it provides an Euler tour of the graph (if there exists). |
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| 120 | /// |
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| 121 | ///For example |
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| 122 | ///if the given graph if Euler (i.e it has only one nontrivial component |
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| 123 | ///and the degree of each node is even), |
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| 124 | ///the following code will print the edge IDs according to an |
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| 125 | ///Euler tour of \c g. |
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| 126 | ///\code |
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[1909] | 127 | /// for(UEulerIt<ListUGraph> e(g),e!=INVALID;++e) { |
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| 128 | /// std::cout << g.id(UEdge(e)) << std::eol; |
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[1818] | 129 | /// } |
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| 130 | ///\endcode |
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| 131 | ///Although the iterator provides an Euler tour of an undirected graph, |
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[1909] | 132 | ///in order to indicate the direction of the tour, UEulerIt |
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[1818] | 133 | ///returns directed edges (that convert to the undirected ones, of course). |
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| 134 | /// |
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| 135 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
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| 136 | ///\todo Test required |
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| 137 | template<class Graph> |
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[1909] | 138 | class UEulerIt |
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[1818] | 139 | { |
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| 140 | typedef typename Graph::Node Node; |
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| 141 | typedef typename Graph::NodeIt NodeIt; |
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| 142 | typedef typename Graph::Edge Edge; |
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| 143 | typedef typename Graph::EdgeIt EdgeIt; |
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| 144 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 145 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 146 | |
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| 147 | const Graph &g; |
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| 148 | typename Graph::NodeMap<OutEdgeIt> nedge; |
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[1909] | 149 | typename Graph::UEdgeMap<bool> visited; |
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[1818] | 150 | std::list<Edge> euler; |
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| 151 | |
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| 152 | public: |
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| 153 | |
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| 154 | ///Constructor |
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| 155 | |
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| 156 | ///\param _g An undirected graph. |
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| 157 | ///\param start The starting point of the tour. If it is not given |
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| 158 | /// the tour will start from the first node. |
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[1909] | 159 | UEulerIt(const Graph &_g,typename Graph::Node start=INVALID) |
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[1818] | 160 | : g(_g), nedge(g), visited(g,false) |
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| 161 | { |
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| 162 | if(start==INVALID) start=NodeIt(g); |
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| 163 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutEdgeIt(g,n); |
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| 164 | while(nedge[start]!=INVALID) { |
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| 165 | euler.push_back(nedge[start]); |
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| 166 | Node next=g.target(nedge[start]); |
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| 167 | ++nedge[start]; |
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| 168 | start=next; while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start]; |
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| 169 | } |
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| 170 | } |
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| 171 | |
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| 172 | ///Edge Conversion |
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| 173 | operator Edge() { return euler.empty()?INVALID:euler.front(); } |
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| 174 | bool operator==(Invalid) { return euler.empty(); } |
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| 175 | bool operator!=(Invalid) { return !euler.empty(); } |
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| 176 | |
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| 177 | ///Next edge of the tour |
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[1909] | 178 | UEulerIt &operator++() { |
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[1818] | 179 | Node s=g.target(euler.front()); |
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| 180 | euler.pop_front(); |
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| 181 | typename std::list<Edge>::iterator next=euler.begin(); |
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| 182 | |
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| 183 | while(nedge[s]!=INVALID) { |
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| 184 | while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s]; |
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| 185 | if(nedge[s]==INVALID) break; |
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| 186 | else { |
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| 187 | euler.insert(next,nedge[s]); |
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| 188 | Node n=g.target(nedge[s]); |
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| 189 | ++nedge[s]; |
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| 190 | s=n; |
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| 191 | } |
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| 192 | } |
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| 193 | return *this; |
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| 194 | } |
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| 195 | |
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| 196 | ///Postfix incrementation |
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| 197 | |
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| 198 | ///\warning This incrementation |
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[1909] | 199 | ///returns an \c Edge, not an \ref UEulerIt, as one may |
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[1818] | 200 | ///expect. |
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| 201 | Edge operator++(int) |
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| 202 | { |
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| 203 | Edge e=*this; |
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| 204 | ++(*this); |
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| 205 | return e; |
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| 206 | } |
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| 207 | }; |
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| 208 | |
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| 209 | |
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[1738] | 210 | ///Checks if the graph is Euler |
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| 211 | |
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[1818] | 212 | /// \ingroup topology |
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[1738] | 213 | ///Checks if the graph is Euler. It works for both directed and |
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| 214 | ///undirected graphs. |
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[1818] | 215 | ///\note By definition, a directed graph is called \e Euler if |
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| 216 | ///and only if connected and the number of it is incoming and outgoing edges |
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| 217 | ///are the same for each node. |
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| 218 | ///Similarly, an undirected graph is called \e Euler if |
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| 219 | ///and only if it is connected and the number of incident edges is even |
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| 220 | ///for each node. <em>Therefore, there are graphs which are not Euler, but |
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| 221 | ///still have an Euler tour</em>. |
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[1738] | 222 | ///\todo Test required |
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| 223 | template<class Graph> |
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| 224 | #ifdef DOXYGEN |
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| 225 | bool |
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| 226 | #else |
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[1909] | 227 | typename enable_if<typename Graph::UTag,bool>::type |
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[1818] | 228 | euler(const Graph &g) |
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| 229 | { |
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| 230 | for(typename Graph::NodeIt n(g);n!=INVALID;++n) |
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| 231 | if(countIncEdges(g,n)%2) return false; |
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| 232 | return connected(g); |
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| 233 | } |
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| 234 | template<class Graph> |
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[1909] | 235 | typename disable_if<typename Graph::UTag,bool>::type |
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[1738] | 236 | #endif |
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| 237 | euler(const Graph &g) |
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| 238 | { |
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| 239 | for(typename Graph::NodeIt n(g);n!=INVALID;++n) |
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| 240 | if(countInEdges(g,n)!=countOutEdges(g,n)) return false; |
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[1818] | 241 | return connected(g); |
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[1738] | 242 | } |
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| 243 | |
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| 244 | } |
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