[520] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 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) 2003-2009 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 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_EULER_H |
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| 20 | #define LEMON_EULER_H |
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| 21 | |
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| 22 | #include<lemon/core.h> |
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| 23 | #include<lemon/adaptors.h> |
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| 24 | #include<lemon/connectivity.h> |
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| 25 | #include <list> |
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| 26 | |
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| 27 | /// \ingroup graph_prop |
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| 28 | /// \file |
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| 29 | /// \brief Euler tour |
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| 30 | /// |
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| 31 | ///This file provides an Euler tour iterator and ways to check |
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| 32 | ///if a digraph is euler. |
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| 33 | |
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| 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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| 37 | ///Euler iterator for digraphs. |
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| 38 | |
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| 39 | /// \ingroup graph_prop |
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| 40 | ///This iterator converts to the \c Arc type of the digraph and using |
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| 41 | ///operator ++, it provides an Euler tour of a \e directed |
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| 42 | ///graph (if there exists). |
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| 43 | /// |
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| 44 | ///For example |
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| 45 | ///if the given digraph is Euler (i.e it has only one nontrivial component |
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| 46 | ///and the in-degree is equal to the out-degree for all nodes), |
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| 47 | ///the following code will put the arcs of \c g |
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| 48 | ///to the vector \c et according to an |
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| 49 | ///Euler tour of \c g. |
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| 50 | ///\code |
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| 51 | /// std::vector<ListDigraph::Arc> et; |
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| 52 | /// for(DiEulerIt<ListDigraph> e(g),e!=INVALID;++e) |
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| 53 | /// et.push_back(e); |
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| 54 | ///\endcode |
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| 55 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
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| 56 | ///\sa EulerIt |
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[559] | 57 | template<typename GR> |
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[520] | 58 | class DiEulerIt |
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| 59 | { |
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[559] | 60 | typedef typename GR::Node Node; |
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| 61 | typedef typename GR::NodeIt NodeIt; |
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| 62 | typedef typename GR::Arc Arc; |
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| 63 | typedef typename GR::ArcIt ArcIt; |
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| 64 | typedef typename GR::OutArcIt OutArcIt; |
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| 65 | typedef typename GR::InArcIt InArcIt; |
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[520] | 66 | |
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[559] | 67 | const GR &g; |
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| 68 | typename GR::template NodeMap<OutArcIt> nedge; |
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[520] | 69 | std::list<Arc> euler; |
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| 70 | |
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| 71 | public: |
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| 72 | |
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| 73 | ///Constructor |
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| 74 | |
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[559] | 75 | ///\param gr A digraph. |
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[520] | 76 | ///\param start The starting point of the tour. If it is not given |
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| 77 | /// the tour will start from the first node. |
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[559] | 78 | DiEulerIt(const GR &gr, typename GR::Node start = INVALID) |
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| 79 | : g(gr), nedge(g) |
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[520] | 80 | { |
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| 81 | if(start==INVALID) start=NodeIt(g); |
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| 82 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n); |
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| 83 | while(nedge[start]!=INVALID) { |
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| 84 | euler.push_back(nedge[start]); |
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| 85 | Node next=g.target(nedge[start]); |
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| 86 | ++nedge[start]; |
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| 87 | start=next; |
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| 88 | } |
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| 89 | } |
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| 90 | |
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| 91 | ///Arc Conversion |
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| 92 | operator Arc() { return euler.empty()?INVALID:euler.front(); } |
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| 93 | bool operator==(Invalid) { return euler.empty(); } |
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| 94 | bool operator!=(Invalid) { return !euler.empty(); } |
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| 95 | |
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| 96 | ///Next arc of the tour |
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| 97 | DiEulerIt &operator++() { |
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| 98 | Node s=g.target(euler.front()); |
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| 99 | euler.pop_front(); |
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| 100 | //This produces a warning.Strange. |
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| 101 | //std::list<Arc>::iterator next=euler.begin(); |
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| 102 | typename std::list<Arc>::iterator next=euler.begin(); |
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| 103 | while(nedge[s]!=INVALID) { |
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| 104 | euler.insert(next,nedge[s]); |
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| 105 | Node n=g.target(nedge[s]); |
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| 106 | ++nedge[s]; |
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| 107 | s=n; |
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| 108 | } |
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| 109 | return *this; |
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| 110 | } |
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| 111 | ///Postfix incrementation |
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| 112 | |
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| 113 | ///\warning This incrementation |
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| 114 | ///returns an \c Arc, not an \ref DiEulerIt, as one may |
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| 115 | ///expect. |
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| 116 | Arc operator++(int) |
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| 117 | { |
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| 118 | Arc e=*this; |
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| 119 | ++(*this); |
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| 120 | return e; |
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| 121 | } |
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| 122 | }; |
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| 123 | |
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| 124 | ///Euler iterator for graphs. |
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| 125 | |
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| 126 | /// \ingroup graph_prop |
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| 127 | ///This iterator converts to the \c Arc (or \c Edge) |
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| 128 | ///type of the digraph and using |
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| 129 | ///operator ++, it provides an Euler tour of an undirected |
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| 130 | ///digraph (if there exists). |
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| 131 | /// |
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| 132 | ///For example |
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| 133 | ///if the given digraph if Euler (i.e it has only one nontrivial component |
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| 134 | ///and the degree of each node is even), |
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| 135 | ///the following code will print the arc IDs according to an |
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| 136 | ///Euler tour of \c g. |
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| 137 | ///\code |
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| 138 | /// for(EulerIt<ListGraph> e(g),e!=INVALID;++e) { |
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| 139 | /// std::cout << g.id(Edge(e)) << std::eol; |
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| 140 | /// } |
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| 141 | ///\endcode |
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| 142 | ///Although the iterator provides an Euler tour of an graph, |
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| 143 | ///it still returns Arcs in order to indicate the direction of the tour. |
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| 144 | ///(But Arc will convert to Edges, of course). |
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| 145 | /// |
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| 146 | ///If \c g is not Euler then the resulted tour will not be full or closed. |
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| 147 | ///\sa EulerIt |
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[559] | 148 | template<typename GR> |
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[520] | 149 | class EulerIt |
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| 150 | { |
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[559] | 151 | typedef typename GR::Node Node; |
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| 152 | typedef typename GR::NodeIt NodeIt; |
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| 153 | typedef typename GR::Arc Arc; |
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| 154 | typedef typename GR::Edge Edge; |
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| 155 | typedef typename GR::ArcIt ArcIt; |
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| 156 | typedef typename GR::OutArcIt OutArcIt; |
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| 157 | typedef typename GR::InArcIt InArcIt; |
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[520] | 158 | |
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[559] | 159 | const GR &g; |
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| 160 | typename GR::template NodeMap<OutArcIt> nedge; |
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| 161 | typename GR::template EdgeMap<bool> visited; |
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[520] | 162 | std::list<Arc> euler; |
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| 163 | |
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| 164 | public: |
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| 165 | |
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| 166 | ///Constructor |
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| 167 | |
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[559] | 168 | ///\param gr An graph. |
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[520] | 169 | ///\param start The starting point of the tour. If it is not given |
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| 170 | /// the tour will start from the first node. |
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[559] | 171 | EulerIt(const GR &gr, typename GR::Node start = INVALID) |
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| 172 | : g(gr), nedge(g), visited(g, false) |
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[520] | 173 | { |
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| 174 | if(start==INVALID) start=NodeIt(g); |
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| 175 | for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n); |
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| 176 | while(nedge[start]!=INVALID) { |
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| 177 | euler.push_back(nedge[start]); |
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| 178 | visited[nedge[start]]=true; |
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| 179 | Node next=g.target(nedge[start]); |
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| 180 | ++nedge[start]; |
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| 181 | start=next; |
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| 182 | while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start]; |
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| 183 | } |
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| 184 | } |
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| 185 | |
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| 186 | ///Arc Conversion |
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| 187 | operator Arc() const { return euler.empty()?INVALID:euler.front(); } |
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| 188 | ///Arc Conversion |
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| 189 | operator Edge() const { return euler.empty()?INVALID:euler.front(); } |
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| 190 | ///\e |
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| 191 | bool operator==(Invalid) const { return euler.empty(); } |
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| 192 | ///\e |
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| 193 | bool operator!=(Invalid) const { return !euler.empty(); } |
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| 194 | |
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| 195 | ///Next arc of the tour |
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| 196 | EulerIt &operator++() { |
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| 197 | Node s=g.target(euler.front()); |
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| 198 | euler.pop_front(); |
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| 199 | typename std::list<Arc>::iterator next=euler.begin(); |
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| 200 | |
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| 201 | while(nedge[s]!=INVALID) { |
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| 202 | while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s]; |
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| 203 | if(nedge[s]==INVALID) break; |
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| 204 | else { |
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| 205 | euler.insert(next,nedge[s]); |
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| 206 | visited[nedge[s]]=true; |
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| 207 | Node n=g.target(nedge[s]); |
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| 208 | ++nedge[s]; |
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| 209 | s=n; |
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| 210 | } |
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| 211 | } |
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| 212 | return *this; |
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| 213 | } |
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| 214 | |
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| 215 | ///Postfix incrementation |
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| 216 | |
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| 217 | ///\warning This incrementation |
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| 218 | ///returns an \c Arc, not an \ref EulerIt, as one may |
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| 219 | ///expect. |
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| 220 | Arc operator++(int) |
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| 221 | { |
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| 222 | Arc e=*this; |
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| 223 | ++(*this); |
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| 224 | return e; |
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| 225 | } |
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| 226 | }; |
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| 227 | |
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| 228 | |
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[521] | 229 | ///Checks if the graph is Eulerian |
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[520] | 230 | |
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| 231 | /// \ingroup graph_prop |
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[521] | 232 | ///Checks if the graph is Eulerian. It works for both directed and undirected |
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[520] | 233 | ///graphs. |
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[521] | 234 | ///\note By definition, a digraph is called \e Eulerian if |
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[520] | 235 | ///and only if it is connected and the number of its incoming and outgoing |
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| 236 | ///arcs are the same for each node. |
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[521] | 237 | ///Similarly, an undirected graph is called \e Eulerian if |
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[520] | 238 | ///and only if it is connected and the number of incident arcs is even |
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[521] | 239 | ///for each node. <em>Therefore, there are digraphs which are not Eulerian, |
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| 240 | ///but still have an Euler tour</em>. |
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[559] | 241 | template<typename GR> |
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[520] | 242 | #ifdef DOXYGEN |
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| 243 | bool |
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| 244 | #else |
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[559] | 245 | typename enable_if<UndirectedTagIndicator<GR>,bool>::type |
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| 246 | eulerian(const GR &g) |
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[520] | 247 | { |
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[559] | 248 | for(typename GR::NodeIt n(g);n!=INVALID;++n) |
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[520] | 249 | if(countIncEdges(g,n)%2) return false; |
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| 250 | return connected(g); |
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| 251 | } |
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[559] | 252 | template<class GR> |
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| 253 | typename disable_if<UndirectedTagIndicator<GR>,bool>::type |
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[520] | 254 | #endif |
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[559] | 255 | eulerian(const GR &g) |
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[520] | 256 | { |
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[559] | 257 | for(typename GR::NodeIt n(g);n!=INVALID;++n) |
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[520] | 258 | if(countInArcs(g,n)!=countOutArcs(g,n)) return false; |
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[559] | 259 | return connected(Undirector<const GR>(g)); |
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[520] | 260 | } |
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| 261 | |
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| 262 | } |
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| 263 | |
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| 264 | #endif |
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