COIN-OR::LEMON - Graph Library

source: lemon/lemon/hypercube_graph.h

Last change on this file was 835:c92296660262, checked in by Alpar Juttner <alpar@…>, 10 years ago

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[376]1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
[463]5 * Copyright (C) 2003-2009
[376]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>
[377]24#include <lemon/assert.h>
[376]25#include <lemon/bits/graph_extender.h>
26
27///\ingroup graphs
28///\file
[377]29///\brief HypercubeGraph class.
[376]30
31namespace lemon {
32
[377]33  class HypercubeGraphBase {
[376]34
35  public:
36
[377]37    typedef HypercubeGraphBase Graph;
[376]38
39    class Node;
[377]40    class Edge;
[376]41    class Arc;
42
43  public:
44
[377]45    HypercubeGraphBase() {}
[376]46
47  protected:
48
49    void construct(int dim) {
[377]50      LEMON_ASSERT(dim >= 1, "The number of dimensions must be at least 1.");
[376]51      _dim = dim;
[377]52      _node_num = 1 << dim;
[385]53      _edge_num = dim * (1 << (dim-1));
[376]54    }
55
56  public:
57
58    typedef True NodeNumTag;
[377]59    typedef True EdgeNumTag;
[376]60    typedef True ArcNumTag;
61
[377]62    int nodeNum() const { return _node_num; }
63    int edgeNum() const { return _edge_num; }
64    int arcNum() const { return 2 * _edge_num; }
[376]65
[377]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; }
[376]69
[377]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 {
[385]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));
[376]82    }
83
[377]84    Node v(Edge edge) const {
[385]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);
[376]88    }
89
[377]90    Node source(Arc arc) const {
91      return (arc._id & 1) == 1 ? u(arc) : v(arc);
92    }
[376]93
[377]94    Node target(Arc arc) const {
95      return (arc._id & 1) == 1 ? v(arc) : u(arc);
96    }
[376]97
[377]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;
[385]108      return (k << (_dim-1)) | ((u._id >> (k+1)) << k) |
109        (u._id & ((1 << k) - 1));
[377]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;
[385]115      int k = edge._id >> (_dim-1);
[377]116      return ((u._id >> k) & 1) == 1 ? edge._id << 1 : (edge._id << 1) | 1;
117    }
[376]118
119    class Node {
[377]120      friend class HypercubeGraphBase;
121
[376]122    protected:
[377]123      int _id;
124      Node(int id) : _id(id) {}
[376]125    public:
126      Node() {}
[377]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;}
[376]148    };
149
150    class Arc {
[377]151      friend class HypercubeGraphBase;
152
[376]153    protected:
[377]154      int _id;
155
156      Arc(int id) : _id(id) {}
157
[376]158    public:
[377]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;}
[376]165    };
166
167    void first(Node& node) const {
[377]168      node._id = _node_num - 1;
[376]169    }
170
171    static void next(Node& node) {
[377]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;
[376]181    }
182
183    void first(Arc& arc) const {
[377]184      arc._id = 2 * _edge_num - 1;
[376]185    }
186
187    static void next(Arc& arc) {
[377]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);
[385]198      int k = (edge._id >> (_dim-1)) + 1;
[377]199      if (k < _dim) {
[385]200        edge._id = (k << (_dim-1)) |
201          ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
[377]202        dir = ((n._id >> k) & 1) == 0;
203      } else {
204        edge._id = -1;
205        dir = true;
206      }
[376]207    }
208
209    void firstOut(Arc& arc, const Node& node) const {
[377]210      arc._id = ((node._id >> 1) << 1) | (~node._id & 1);
[376]211    }
212
213    void nextOut(Arc& arc) const {
[377]214      Node n = (arc._id & 1) == 1 ? u(arc) : v(arc);
215      int k = (arc._id >> _dim) + 1;
216      if (k < _dim) {
[385]217        arc._id = (k << (_dim-1)) |
218          ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
[377]219        arc._id = (arc._id << 1) | (~(n._id >> k) & 1);
220      } else {
221        arc._id = -1;
222      }
[376]223    }
224
225    void firstIn(Arc& arc, const Node& node) const {
[377]226      arc._id = ((node._id >> 1) << 1) | (node._id & 1);
[376]227    }
228
229    void nextIn(Arc& arc) const {
[377]230      Node n = (arc._id & 1) == 1 ? v(arc) : u(arc);
231      int k = (arc._id >> _dim) + 1;
232      if (k < _dim) {
[385]233        arc._id = (k << (_dim-1)) |
234          ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
[377]235        arc._id = (arc._id << 1) | ((n._id >> k) & 1);
[376]236      } else {
[377]237        arc._id = -1;
[376]238      }
239    }
240
[377]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
[376]249    int dimension() const {
250      return _dim;
251    }
252
253    bool projection(Node node, int n) const {
[377]254      return static_cast<bool>(node._id & (1 << n));
255    }
256
257    int dimension(Edge edge) const {
[385]258      return edge._id >> (_dim-1);
[376]259    }
260
261    int dimension(Arc arc) const {
[377]262      return arc._id >> _dim;
[376]263    }
264
[825]265    static int index(Node node) {
[377]266      return node._id;
[376]267    }
268
269    Node operator()(int ix) const {
270      return Node(ix);
271    }
272
273  private:
[377]274    int _dim;
275    int _node_num, _edge_num;
[376]276  };
277
278
[377]279  typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase;
[376]280
[377]281  /// \ingroup graphs
[376]282  ///
[377]283  /// \brief Hypercube graph class
[376]284  ///
[782]285  /// HypercubeGraph implements a special graph type. The nodes of the
286  /// graph are indexed with integers having at most \c dim binary digits.
[377]287  /// Two nodes are connected in the graph if and only if their indices
288  /// differ only on one position in the binary form.
[782]289  /// This class is completely static and it needs constant memory space.
[833]290  /// Thus you can neither add nor delete nodes or edges, however,
[784]291  /// the structure can be resized using resize().
[782]292  ///
293  /// This type fully conforms to the \ref concepts::Graph "Graph concept".
294  /// Most of its member functions and nested classes are documented
295  /// only in the concept class.
[376]296  ///
[834]297  /// This class provides constant time counting for nodes, edges and arcs.
298  ///
[377]299  /// \note The type of the indices is chosen to \c int for efficiency
300  /// reasons. Thus the maximum dimension of this implementation is 26
301  /// (assuming that the size of \c int is 32 bit).
302  class HypercubeGraph : public ExtendedHypercubeGraphBase {
[664]303    typedef ExtendedHypercubeGraphBase Parent;
304
[376]305  public:
306
[377]307    /// \brief Constructs a hypercube graph with \c dim dimensions.
[376]308    ///
[377]309    /// Constructs a hypercube graph with \c dim dimensions.
310    HypercubeGraph(int dim) { construct(dim); }
[376]311
[784]312    /// \brief Resizes the graph
313    ///
314    /// This function resizes the graph. It fully destroys and
315    /// rebuilds the structure, therefore the maps of the graph will be
316    /// reallocated automatically and the previous values will be lost.
317    void resize(int dim) {
318      Parent::notifier(Arc()).clear();
319      Parent::notifier(Edge()).clear();
320      Parent::notifier(Node()).clear();
321      construct(dim);
322      Parent::notifier(Node()).build();
323      Parent::notifier(Edge()).build();
324      Parent::notifier(Arc()).build();
325    }
326
[377]327    /// \brief The number of dimensions.
[376]328    ///
[377]329    /// Gives back the number of dimensions.
[376]330    int dimension() const {
331      return Parent::dimension();
332    }
333
[377]334    /// \brief Returns \c true if the n'th bit of the node is one.
[376]335    ///
[377]336    /// Returns \c true if the n'th bit of the node is one.
[376]337    bool projection(Node node, int n) const {
338      return Parent::projection(node, n);
339    }
340
[377]341    /// \brief The dimension id of an edge.
[376]342    ///
[377]343    /// Gives back the dimension id of the given edge.
[782]344    /// It is in the range <tt>[0..dim-1]</tt>.
[377]345    int dimension(Edge edge) const {
346      return Parent::dimension(edge);
347    }
348
349    /// \brief The dimension id of an arc.
350    ///
351    /// Gives back the dimension id of the given arc.
[782]352    /// It is in the range <tt>[0..dim-1]</tt>.
[376]353    int dimension(Arc arc) const {
354      return Parent::dimension(arc);
355    }
356
[377]357    /// \brief The index of a node.
[376]358    ///
[377]359    /// Gives back the index of the given node.
360    /// The lower bits of the integer describes the node.
[825]361    static int index(Node node) {
[376]362      return Parent::index(node);
363    }
364
[377]365    /// \brief Gives back a node by its index.
[376]366    ///
[377]367    /// Gives back a node by its index.
[376]368    Node operator()(int ix) const {
369      return Parent::operator()(ix);
370    }
371
372    /// \brief Number of nodes.
373    int nodeNum() const { return Parent::nodeNum(); }
[377]374    /// \brief Number of edges.
375    int edgeNum() const { return Parent::edgeNum(); }
[376]376    /// \brief Number of arcs.
377    int arcNum() const { return Parent::arcNum(); }
378
379    /// \brief Linear combination map.
380    ///
[377]381    /// This map makes possible to give back a linear combination
382    /// for each node. It works like the \c std::accumulate function,
383    /// so it accumulates the \c bf binary function with the \c fv first
384    /// value. The map accumulates only on that positions (dimensions)
385    /// where the index of the node is one. The values that have to be
386    /// accumulated should be given by the \c begin and \c end iterators
387    /// and the length of this range should be equal to the dimension
388    /// number of the graph.
[376]389    ///
390    ///\code
391    /// const int DIM = 3;
[377]392    /// HypercubeGraph graph(DIM);
[376]393    /// dim2::Point<double> base[DIM];
394    /// for (int k = 0; k < DIM; ++k) {
395    ///   base[k].x = rnd();
396    ///   base[k].y = rnd();
397    /// }
[377]398    /// HypercubeGraph::HyperMap<dim2::Point<double> >
399    ///   pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));
[376]400    ///\endcode
401    ///
[377]402    /// \see HypercubeGraph
[376]403    template <typename T, typename BF = std::plus<T> >
404    class HyperMap {
405    public:
406
[377]407      /// \brief The key type of the map
[376]408      typedef Node Key;
[377]409      /// \brief The value type of the map
[376]410      typedef T Value;
411
412      /// \brief Constructor for HyperMap.
413      ///
[377]414      /// Construct a HyperMap for the given graph. The values that have
415      /// to be accumulated should be given by the \c begin and \c end
416      /// iterators and the length of this range should be equal to the
417      /// dimension number of the graph.
[376]418      ///
[377]419      /// This map accumulates the \c bf binary function with the \c fv
420      /// first value on that positions (dimensions) where the index of
421      /// the node is one.
[376]422      template <typename It>
[377]423      HyperMap(const Graph& graph, It begin, It end,
424               T fv = 0, const BF& bf = BF())
425        : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf)
[376]426      {
[377]427        LEMON_ASSERT(_values.size() == graph.dimension(),
428                     "Wrong size of range");
[376]429      }
430
[377]431      /// \brief The partial accumulated value.
[376]432      ///
433      /// Gives back the partial accumulated value.
[377]434      Value operator[](const Key& k) const {
[376]435        Value val = _first_value;
436        int id = _graph.index(k);
437        int n = 0;
438        while (id != 0) {
439          if (id & 1) {
440            val = _bin_func(val, _values[n]);
441          }
442          id >>= 1;
443          ++n;
444        }
445        return val;
446      }
447
448    private:
[377]449      const Graph& _graph;
[376]450      std::vector<T> _values;
451      T _first_value;
452      BF _bin_func;
453    };
454
455  };
456
457}
458
459#endif
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