lemon/hypercube_graph.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 31 Aug 2009 07:22:26 +0200
changeset 692 33f417de9e70
parent 582 7a28e215f715
child 735 853fcddcf282
child 778 a143f19f465b
permissions -rw-r--r--
Merge
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     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  */
    18 
    19 #ifndef HYPERCUBE_GRAPH_H
    20 #define HYPERCUBE_GRAPH_H
    21 
    22 #include <vector>
    23 #include <lemon/core.h>
    24 #include <lemon/assert.h>
    25 #include <lemon/bits/graph_extender.h>
    26 
    27 ///\ingroup graphs
    28 ///\file
    29 ///\brief HypercubeGraph class.
    30 
    31 namespace lemon {
    32 
    33   class HypercubeGraphBase {
    34 
    35   public:
    36 
    37     typedef HypercubeGraphBase Graph;
    38 
    39     class Node;
    40     class Edge;
    41     class Arc;
    42 
    43   public:
    44 
    45     HypercubeGraphBase() {}
    46 
    47   protected:
    48 
    49     void construct(int dim) {
    50       LEMON_ASSERT(dim >= 1, "The number of dimensions must be at least 1.");
    51       _dim = dim;
    52       _node_num = 1 << dim;
    53       _edge_num = dim * (1 << (dim-1));
    54     }
    55 
    56   public:
    57 
    58     typedef True NodeNumTag;
    59     typedef True EdgeNumTag;
    60     typedef True ArcNumTag;
    61 
    62     int nodeNum() const { return _node_num; }
    63     int edgeNum() const { return _edge_num; }
    64     int arcNum() const { return 2 * _edge_num; }
    65 
    66     int maxNodeId() const { return _node_num - 1; }
    67     int maxEdgeId() const { return _edge_num - 1; }
    68     int maxArcId() const { return 2 * _edge_num - 1; }
    69 
    70     static Node nodeFromId(int id) { return Node(id); }
    71     static Edge edgeFromId(int id) { return Edge(id); }
    72     static Arc arcFromId(int id) { return Arc(id); }
    73 
    74     static int id(Node node) { return node._id; }
    75     static int id(Edge edge) { return edge._id; }
    76     static int id(Arc arc) { return arc._id; }
    77 
    78     Node u(Edge edge) const {
    79       int base = edge._id & ((1 << (_dim-1)) - 1);
    80       int k = edge._id >> (_dim-1);
    81       return ((base >> k) << (k+1)) | (base & ((1 << k) - 1));
    82     }
    83 
    84     Node v(Edge edge) const {
    85       int base = edge._id & ((1 << (_dim-1)) - 1);
    86       int k = edge._id >> (_dim-1);
    87       return ((base >> k) << (k+1)) | (base & ((1 << k) - 1)) | (1 << k);
    88     }
    89 
    90     Node source(Arc arc) const {
    91       return (arc._id & 1) == 1 ? u(arc) : v(arc);
    92     }
    93 
    94     Node target(Arc arc) const {
    95       return (arc._id & 1) == 1 ? v(arc) : u(arc);
    96     }
    97 
    98     typedef True FindEdgeTag;
    99     typedef True FindArcTag;
   100 
   101     Edge findEdge(Node u, Node v, Edge prev = INVALID) const {
   102       if (prev != INVALID) return INVALID;
   103       int d = u._id ^ v._id;
   104       int k = 0;
   105       if (d == 0) return INVALID;
   106       for ( ; (d & 1) == 0; d >>= 1) ++k;
   107       if (d >> 1 != 0) return INVALID;
   108       return (k << (_dim-1)) | ((u._id >> (k+1)) << k) |
   109         (u._id & ((1 << k) - 1));
   110     }
   111 
   112     Arc findArc(Node u, Node v, Arc prev = INVALID) const {
   113       Edge edge = findEdge(u, v, prev);
   114       if (edge == INVALID) return INVALID;
   115       int k = edge._id >> (_dim-1);
   116       return ((u._id >> k) & 1) == 1 ? edge._id << 1 : (edge._id << 1) | 1;
   117     }
   118 
   119     class Node {
   120       friend class HypercubeGraphBase;
   121 
   122     protected:
   123       int _id;
   124       Node(int id) : _id(id) {}
   125     public:
   126       Node() {}
   127       Node (Invalid) : _id(-1) {}
   128       bool operator==(const Node node) const {return _id == node._id;}
   129       bool operator!=(const Node node) const {return _id != node._id;}
   130       bool operator<(const Node node) const {return _id < node._id;}
   131     };
   132 
   133     class Edge {
   134       friend class HypercubeGraphBase;
   135       friend class Arc;
   136 
   137     protected:
   138       int _id;
   139 
   140       Edge(int id) : _id(id) {}
   141 
   142     public:
   143       Edge() {}
   144       Edge (Invalid) : _id(-1) {}
   145       bool operator==(const Edge edge) const {return _id == edge._id;}
   146       bool operator!=(const Edge edge) const {return _id != edge._id;}
   147       bool operator<(const Edge edge) const {return _id < edge._id;}
   148     };
   149 
   150     class Arc {
   151       friend class HypercubeGraphBase;
   152 
   153     protected:
   154       int _id;
   155 
   156       Arc(int id) : _id(id) {}
   157 
   158     public:
   159       Arc() {}
   160       Arc (Invalid) : _id(-1) {}
   161       operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }
   162       bool operator==(const Arc arc) const {return _id == arc._id;}
   163       bool operator!=(const Arc arc) const {return _id != arc._id;}
   164       bool operator<(const Arc arc) const {return _id < arc._id;}
   165     };
   166 
   167     void first(Node& node) const {
   168       node._id = _node_num - 1;
   169     }
   170 
   171     static void next(Node& node) {
   172       --node._id;
   173     }
   174 
   175     void first(Edge& edge) const {
   176       edge._id = _edge_num - 1;
   177     }
   178 
   179     static void next(Edge& edge) {
   180       --edge._id;
   181     }
   182 
   183     void first(Arc& arc) const {
   184       arc._id = 2 * _edge_num - 1;
   185     }
   186 
   187     static void next(Arc& arc) {
   188       --arc._id;
   189     }
   190 
   191     void firstInc(Edge& edge, bool& dir, const Node& node) const {
   192       edge._id = node._id >> 1;
   193       dir = (node._id & 1) == 0;
   194     }
   195 
   196     void nextInc(Edge& edge, bool& dir) const {
   197       Node n = dir ? u(edge) : v(edge);
   198       int k = (edge._id >> (_dim-1)) + 1;
   199       if (k < _dim) {
   200         edge._id = (k << (_dim-1)) |
   201           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
   202         dir = ((n._id >> k) & 1) == 0;
   203       } else {
   204         edge._id = -1;
   205         dir = true;
   206       }
   207     }
   208 
   209     void firstOut(Arc& arc, const Node& node) const {
   210       arc._id = ((node._id >> 1) << 1) | (~node._id & 1);
   211     }
   212 
   213     void nextOut(Arc& arc) const {
   214       Node n = (arc._id & 1) == 1 ? u(arc) : v(arc);
   215       int k = (arc._id >> _dim) + 1;
   216       if (k < _dim) {
   217         arc._id = (k << (_dim-1)) |
   218           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
   219         arc._id = (arc._id << 1) | (~(n._id >> k) & 1);
   220       } else {
   221         arc._id = -1;
   222       }
   223     }
   224 
   225     void firstIn(Arc& arc, const Node& node) const {
   226       arc._id = ((node._id >> 1) << 1) | (node._id & 1);
   227     }
   228 
   229     void nextIn(Arc& arc) const {
   230       Node n = (arc._id & 1) == 1 ? v(arc) : u(arc);
   231       int k = (arc._id >> _dim) + 1;
   232       if (k < _dim) {
   233         arc._id = (k << (_dim-1)) |
   234           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
   235         arc._id = (arc._id << 1) | ((n._id >> k) & 1);
   236       } else {
   237         arc._id = -1;
   238       }
   239     }
   240 
   241     static bool direction(Arc arc) {
   242       return (arc._id & 1) == 1;
   243     }
   244 
   245     static Arc direct(Edge edge, bool dir) {
   246       return Arc((edge._id << 1) | (dir ? 1 : 0));
   247     }
   248 
   249     int dimension() const {
   250       return _dim;
   251     }
   252 
   253     bool projection(Node node, int n) const {
   254       return static_cast<bool>(node._id & (1 << n));
   255     }
   256 
   257     int dimension(Edge edge) const {
   258       return edge._id >> (_dim-1);
   259     }
   260 
   261     int dimension(Arc arc) const {
   262       return arc._id >> _dim;
   263     }
   264 
   265     int index(Node node) const {
   266       return node._id;
   267     }
   268 
   269     Node operator()(int ix) const {
   270       return Node(ix);
   271     }
   272 
   273   private:
   274     int _dim;
   275     int _node_num, _edge_num;
   276   };
   277 
   278 
   279   typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase;
   280 
   281   /// \ingroup graphs
   282   ///
   283   /// \brief Hypercube graph class
   284   ///
   285   /// This class implements a special graph type. The nodes of the graph
   286   /// are indiced with integers with at most \c dim binary digits.
   287   /// Two nodes are connected in the graph if and only if their indices
   288   /// differ only on one position in the binary form.
   289   ///
   290   /// \note The type of the indices is chosen to \c int for efficiency
   291   /// reasons. Thus the maximum dimension of this implementation is 26
   292   /// (assuming that the size of \c int is 32 bit).
   293   ///
   294   /// This graph type fully conforms to the \ref concepts::Graph
   295   /// "Graph concept".
   296   class HypercubeGraph : public ExtendedHypercubeGraphBase {
   297     typedef ExtendedHypercubeGraphBase Parent;
   298 
   299   public:
   300 
   301     /// \brief Constructs a hypercube graph with \c dim dimensions.
   302     ///
   303     /// Constructs a hypercube graph with \c dim dimensions.
   304     HypercubeGraph(int dim) { construct(dim); }
   305 
   306     /// \brief The number of dimensions.
   307     ///
   308     /// Gives back the number of dimensions.
   309     int dimension() const {
   310       return Parent::dimension();
   311     }
   312 
   313     /// \brief Returns \c true if the n'th bit of the node is one.
   314     ///
   315     /// Returns \c true if the n'th bit of the node is one.
   316     bool projection(Node node, int n) const {
   317       return Parent::projection(node, n);
   318     }
   319 
   320     /// \brief The dimension id of an edge.
   321     ///
   322     /// Gives back the dimension id of the given edge.
   323     /// It is in the [0..dim-1] range.
   324     int dimension(Edge edge) const {
   325       return Parent::dimension(edge);
   326     }
   327 
   328     /// \brief The dimension id of an arc.
   329     ///
   330     /// Gives back the dimension id of the given arc.
   331     /// It is in the [0..dim-1] range.
   332     int dimension(Arc arc) const {
   333       return Parent::dimension(arc);
   334     }
   335 
   336     /// \brief The index of a node.
   337     ///
   338     /// Gives back the index of the given node.
   339     /// The lower bits of the integer describes the node.
   340     int index(Node node) const {
   341       return Parent::index(node);
   342     }
   343 
   344     /// \brief Gives back a node by its index.
   345     ///
   346     /// Gives back a node by its index.
   347     Node operator()(int ix) const {
   348       return Parent::operator()(ix);
   349     }
   350 
   351     /// \brief Number of nodes.
   352     int nodeNum() const { return Parent::nodeNum(); }
   353     /// \brief Number of edges.
   354     int edgeNum() const { return Parent::edgeNum(); }
   355     /// \brief Number of arcs.
   356     int arcNum() const { return Parent::arcNum(); }
   357 
   358     /// \brief Linear combination map.
   359     ///
   360     /// This map makes possible to give back a linear combination
   361     /// for each node. It works like the \c std::accumulate function,
   362     /// so it accumulates the \c bf binary function with the \c fv first
   363     /// value. The map accumulates only on that positions (dimensions)
   364     /// where the index of the node is one. The values that have to be
   365     /// accumulated should be given by the \c begin and \c end iterators
   366     /// and the length of this range should be equal to the dimension
   367     /// number of the graph.
   368     ///
   369     ///\code
   370     /// const int DIM = 3;
   371     /// HypercubeGraph graph(DIM);
   372     /// dim2::Point<double> base[DIM];
   373     /// for (int k = 0; k < DIM; ++k) {
   374     ///   base[k].x = rnd();
   375     ///   base[k].y = rnd();
   376     /// }
   377     /// HypercubeGraph::HyperMap<dim2::Point<double> >
   378     ///   pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));
   379     ///\endcode
   380     ///
   381     /// \see HypercubeGraph
   382     template <typename T, typename BF = std::plus<T> >
   383     class HyperMap {
   384     public:
   385 
   386       /// \brief The key type of the map
   387       typedef Node Key;
   388       /// \brief The value type of the map
   389       typedef T Value;
   390 
   391       /// \brief Constructor for HyperMap.
   392       ///
   393       /// Construct a HyperMap for the given graph. The values that have
   394       /// to be accumulated should be given by the \c begin and \c end
   395       /// iterators and the length of this range should be equal to the
   396       /// dimension number of the graph.
   397       ///
   398       /// This map accumulates the \c bf binary function with the \c fv
   399       /// first value on that positions (dimensions) where the index of
   400       /// the node is one.
   401       template <typename It>
   402       HyperMap(const Graph& graph, It begin, It end,
   403                T fv = 0, const BF& bf = BF())
   404         : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf)
   405       {
   406         LEMON_ASSERT(_values.size() == graph.dimension(),
   407                      "Wrong size of range");
   408       }
   409 
   410       /// \brief The partial accumulated value.
   411       ///
   412       /// Gives back the partial accumulated value.
   413       Value operator[](const Key& k) const {
   414         Value val = _first_value;
   415         int id = _graph.index(k);
   416         int n = 0;
   417         while (id != 0) {
   418           if (id & 1) {
   419             val = _bin_func(val, _values[n]);
   420           }
   421           id >>= 1;
   422           ++n;
   423         }
   424         return val;
   425       }
   426 
   427     private:
   428       const Graph& _graph;
   429       std::vector<T> _values;
   430       T _first_value;
   431       BF _bin_func;
   432     };
   433 
   434   };
   435 
   436 }
   437 
   438 #endif