[1738] | 1 | /* -*- C++ -*- |
---|
| 2 | * |
---|
[1956] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
| 4 | * |
---|
| 5 | * Copyright (C) 2003-2006 |
---|
| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
[1738] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
| 8 | * |
---|
| 9 | * Permission to use, modify and distribute this software is granted |
---|
| 10 | * provided that this copyright notice appears in all copies. For |
---|
| 11 | * precise terms see the accompanying LICENSE file. |
---|
| 12 | * |
---|
| 13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
| 14 | * express or implied, and with no claim as to its suitability for any |
---|
| 15 | * purpose. |
---|
| 16 | * |
---|
| 17 | */ |
---|
[1956] | 18 | |
---|
[1993] | 19 | #include<lemon/bits/invalid.h> |
---|
[1818] | 20 | #include<lemon/topology.h> |
---|
[1738] | 21 | #include <list> |
---|
| 22 | |
---|
[1769] | 23 | /// \ingroup topology |
---|
[1738] | 24 | /// \file |
---|
| 25 | /// \brief Euler tour |
---|
| 26 | /// |
---|
| 27 | ///This file provides an Euler tour iterator and ways to check |
---|
| 28 | ///if a graph is euler. |
---|
| 29 | |
---|
| 30 | |
---|
| 31 | namespace lemon { |
---|
| 32 | |
---|
[1818] | 33 | ///Euler iterator for directed graphs. |
---|
[1738] | 34 | |
---|
[1769] | 35 | /// \ingroup topology |
---|
[1738] | 36 | ///This iterator converts to the \c Edge type of the graph and using |
---|
[1970] | 37 | ///operator ++ it provides an Euler tour of a \e directed |
---|
| 38 | ///graph (if there exists). |
---|
[1738] | 39 | /// |
---|
| 40 | ///For example |
---|
| 41 | ///if the given graph if Euler (i.e it has only one nontrivial component |
---|
| 42 | ///and the in-degree is equal to the out-degree for all nodes), |
---|
[1970] | 43 | ///the following code will put the edges of \c g |
---|
| 44 | ///to the vector \c et according to an |
---|
[1738] | 45 | ///Euler tour of \c g. |
---|
| 46 | ///\code |
---|
[1970] | 47 | /// std::vector<ListGraph::Edge> et; |
---|
| 48 | /// for(EulerIt<ListGraph> e(g),e!=INVALID;++e) |
---|
| 49 | /// et.push_back(e); |
---|
[1738] | 50 | ///\endcode |
---|
| 51 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
---|
[1970] | 52 | ///\sa UEulerIt |
---|
[1738] | 53 | ///\todo Test required |
---|
| 54 | template<class Graph> |
---|
| 55 | class EulerIt |
---|
| 56 | { |
---|
| 57 | typedef typename Graph::Node Node; |
---|
| 58 | typedef typename Graph::NodeIt NodeIt; |
---|
| 59 | typedef typename Graph::Edge Edge; |
---|
| 60 | typedef typename Graph::EdgeIt EdgeIt; |
---|
| 61 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
| 62 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
| 63 | |
---|
| 64 | const Graph &g; |
---|
| 65 | typename Graph::NodeMap<OutEdgeIt> nedge; |
---|
| 66 | std::list<Edge> euler; |
---|
| 67 | |
---|
| 68 | public: |
---|
| 69 | |
---|
| 70 | ///Constructor |
---|
| 71 | |
---|
| 72 | ///\param _g A directed graph. |
---|
| 73 | ///\param start The starting point of the tour. If it is not given |
---|
[1803] | 74 | /// the tour will start from the first node. |
---|
[1738] | 75 | EulerIt(const Graph &_g,typename Graph::Node start=INVALID) |
---|
| 76 | : g(_g), nedge(g) |
---|
| 77 | { |
---|
| 78 | if(start==INVALID) start=NodeIt(g); |
---|
| 79 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutEdgeIt(g,n); |
---|
| 80 | while(nedge[start]!=INVALID) { |
---|
| 81 | euler.push_back(nedge[start]); |
---|
| 82 | Node next=g.target(nedge[start]); |
---|
| 83 | ++nedge[start]; |
---|
| 84 | start=next; |
---|
| 85 | } |
---|
| 86 | } |
---|
| 87 | |
---|
| 88 | ///Edge Conversion |
---|
| 89 | operator Edge() { return euler.empty()?INVALID:euler.front(); } |
---|
| 90 | bool operator==(Invalid) { return euler.empty(); } |
---|
| 91 | bool operator!=(Invalid) { return !euler.empty(); } |
---|
| 92 | |
---|
| 93 | ///Next edge of the tour |
---|
| 94 | EulerIt &operator++() { |
---|
| 95 | Node s=g.target(euler.front()); |
---|
| 96 | euler.pop_front(); |
---|
| 97 | //This produces a warning.Strange. |
---|
| 98 | //std::list<Edge>::iterator next=euler.begin(); |
---|
| 99 | typename std::list<Edge>::iterator next=euler.begin(); |
---|
| 100 | while(nedge[s]!=INVALID) { |
---|
| 101 | euler.insert(next,nedge[s]); |
---|
| 102 | Node n=g.target(nedge[s]); |
---|
| 103 | ++nedge[s]; |
---|
| 104 | s=n; |
---|
| 105 | } |
---|
| 106 | return *this; |
---|
| 107 | } |
---|
| 108 | ///Postfix incrementation |
---|
| 109 | |
---|
[1803] | 110 | ///\warning This incrementation |
---|
| 111 | ///returns an \c Edge, not an \ref EulerIt, as one may |
---|
| 112 | ///expect. |
---|
[1738] | 113 | Edge operator++(int) |
---|
| 114 | { |
---|
| 115 | Edge e=*this; |
---|
| 116 | ++(*this); |
---|
| 117 | return e; |
---|
| 118 | } |
---|
| 119 | }; |
---|
| 120 | |
---|
[1818] | 121 | ///Euler iterator for undirected graphs. |
---|
| 122 | |
---|
| 123 | /// \ingroup topology |
---|
[2350] | 124 | ///This iterator converts to the \c Edge (or \c UEdge) |
---|
[1970] | 125 | ///type of the graph and using |
---|
[2350] | 126 | ///operator ++ it provides an Euler tour of an undirected |
---|
[1970] | 127 | ///graph (if there exists). |
---|
[1818] | 128 | /// |
---|
| 129 | ///For example |
---|
| 130 | ///if the given graph if Euler (i.e it has only one nontrivial component |
---|
| 131 | ///and the degree of each node is even), |
---|
| 132 | ///the following code will print the edge IDs according to an |
---|
| 133 | ///Euler tour of \c g. |
---|
| 134 | ///\code |
---|
[1909] | 135 | /// for(UEulerIt<ListUGraph> e(g),e!=INVALID;++e) { |
---|
| 136 | /// std::cout << g.id(UEdge(e)) << std::eol; |
---|
[1818] | 137 | /// } |
---|
| 138 | ///\endcode |
---|
| 139 | ///Although the iterator provides an Euler tour of an undirected graph, |
---|
[1909] | 140 | ///in order to indicate the direction of the tour, UEulerIt |
---|
[1818] | 141 | ///returns directed edges (that convert to the undirected ones, of course). |
---|
| 142 | /// |
---|
| 143 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
---|
[1970] | 144 | ///\sa EulerIt |
---|
[1818] | 145 | ///\todo Test required |
---|
| 146 | template<class Graph> |
---|
[1909] | 147 | class UEulerIt |
---|
[1818] | 148 | { |
---|
| 149 | typedef typename Graph::Node Node; |
---|
| 150 | typedef typename Graph::NodeIt NodeIt; |
---|
| 151 | typedef typename Graph::Edge Edge; |
---|
| 152 | typedef typename Graph::EdgeIt EdgeIt; |
---|
| 153 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
| 154 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
| 155 | |
---|
| 156 | const Graph &g; |
---|
| 157 | typename Graph::NodeMap<OutEdgeIt> nedge; |
---|
[1909] | 158 | typename Graph::UEdgeMap<bool> visited; |
---|
[1818] | 159 | std::list<Edge> euler; |
---|
| 160 | |
---|
| 161 | public: |
---|
| 162 | |
---|
| 163 | ///Constructor |
---|
| 164 | |
---|
| 165 | ///\param _g An undirected graph. |
---|
| 166 | ///\param start The starting point of the tour. If it is not given |
---|
| 167 | /// the tour will start from the first node. |
---|
[1909] | 168 | UEulerIt(const Graph &_g,typename Graph::Node start=INVALID) |
---|
[1818] | 169 | : g(_g), nedge(g), visited(g,false) |
---|
| 170 | { |
---|
| 171 | if(start==INVALID) start=NodeIt(g); |
---|
| 172 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutEdgeIt(g,n); |
---|
| 173 | while(nedge[start]!=INVALID) { |
---|
| 174 | euler.push_back(nedge[start]); |
---|
| 175 | Node next=g.target(nedge[start]); |
---|
| 176 | ++nedge[start]; |
---|
| 177 | start=next; while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start]; |
---|
| 178 | } |
---|
| 179 | } |
---|
| 180 | |
---|
| 181 | ///Edge Conversion |
---|
| 182 | operator Edge() { return euler.empty()?INVALID:euler.front(); } |
---|
| 183 | bool operator==(Invalid) { return euler.empty(); } |
---|
| 184 | bool operator!=(Invalid) { return !euler.empty(); } |
---|
| 185 | |
---|
| 186 | ///Next edge of the tour |
---|
[1909] | 187 | UEulerIt &operator++() { |
---|
[1818] | 188 | Node s=g.target(euler.front()); |
---|
| 189 | euler.pop_front(); |
---|
| 190 | typename std::list<Edge>::iterator next=euler.begin(); |
---|
| 191 | |
---|
| 192 | while(nedge[s]!=INVALID) { |
---|
| 193 | while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s]; |
---|
| 194 | if(nedge[s]==INVALID) break; |
---|
| 195 | else { |
---|
| 196 | euler.insert(next,nedge[s]); |
---|
| 197 | Node n=g.target(nedge[s]); |
---|
| 198 | ++nedge[s]; |
---|
| 199 | s=n; |
---|
| 200 | } |
---|
| 201 | } |
---|
| 202 | return *this; |
---|
| 203 | } |
---|
| 204 | |
---|
| 205 | ///Postfix incrementation |
---|
| 206 | |
---|
| 207 | ///\warning This incrementation |
---|
[1909] | 208 | ///returns an \c Edge, not an \ref UEulerIt, as one may |
---|
[1818] | 209 | ///expect. |
---|
| 210 | Edge operator++(int) |
---|
| 211 | { |
---|
| 212 | Edge e=*this; |
---|
| 213 | ++(*this); |
---|
| 214 | return e; |
---|
| 215 | } |
---|
| 216 | }; |
---|
| 217 | |
---|
| 218 | |
---|
[1738] | 219 | ///Checks if the graph is Euler |
---|
| 220 | |
---|
[1818] | 221 | /// \ingroup topology |
---|
[1738] | 222 | ///Checks if the graph is Euler. It works for both directed and |
---|
| 223 | ///undirected graphs. |
---|
[1818] | 224 | ///\note By definition, a directed graph is called \e Euler if |
---|
| 225 | ///and only if connected and the number of it is incoming and outgoing edges |
---|
| 226 | ///are the same for each node. |
---|
| 227 | ///Similarly, an undirected graph is called \e Euler if |
---|
| 228 | ///and only if it is connected and the number of incident edges is even |
---|
| 229 | ///for each node. <em>Therefore, there are graphs which are not Euler, but |
---|
| 230 | ///still have an Euler tour</em>. |
---|
[1738] | 231 | ///\todo Test required |
---|
| 232 | template<class Graph> |
---|
| 233 | #ifdef DOXYGEN |
---|
| 234 | bool |
---|
| 235 | #else |
---|
[1979] | 236 | typename enable_if<UndirectedTagIndicator<Graph>,bool>::type |
---|
[1818] | 237 | euler(const Graph &g) |
---|
| 238 | { |
---|
| 239 | for(typename Graph::NodeIt n(g);n!=INVALID;++n) |
---|
| 240 | if(countIncEdges(g,n)%2) return false; |
---|
| 241 | return connected(g); |
---|
| 242 | } |
---|
| 243 | template<class Graph> |
---|
[1979] | 244 | typename disable_if<UndirectedTagIndicator<Graph>,bool>::type |
---|
[1738] | 245 | #endif |
---|
| 246 | euler(const Graph &g) |
---|
| 247 | { |
---|
| 248 | for(typename Graph::NodeIt n(g);n!=INVALID;++n) |
---|
| 249 | if(countInEdges(g,n)!=countOutEdges(g,n)) return false; |
---|
[1818] | 250 | return connected(g); |
---|
[1738] | 251 | } |
---|
| 252 | |
---|
| 253 | } |
---|