COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/hypercube_graph.h @ 839:f3bc4e9b5f3a

Last change on this file since 839:f3bc4e9b5f3a was 788:c92296660262, checked in by Alpar Juttner <alpar@…>, 10 years ago

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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
31namespace 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    static int index(Node node) {
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  /// HypercubeGraph implements a special graph type. The nodes of the
286  /// graph are indexed with integers having 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  /// This class is completely static and it needs constant memory space.
290  /// Thus you can neither add nor delete nodes or edges, however,
291  /// the structure can be resized using resize().
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.
296  ///
297  /// This class provides constant time counting for nodes, edges and arcs.
298  ///
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 {
303    typedef ExtendedHypercubeGraphBase Parent;
304
305  public:
306
307    /// \brief Constructs a hypercube graph with \c dim dimensions.
308    ///
309    /// Constructs a hypercube graph with \c dim dimensions.
310    HypercubeGraph(int dim) { construct(dim); }
311
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
327    /// \brief The number of dimensions.
328    ///
329    /// Gives back the number of dimensions.
330    int dimension() const {
331      return Parent::dimension();
332    }
333
334    /// \brief Returns \c true if the n'th bit of the node is one.
335    ///
336    /// Returns \c true if the n'th bit of the node is one.
337    bool projection(Node node, int n) const {
338      return Parent::projection(node, n);
339    }
340
341    /// \brief The dimension id of an edge.
342    ///
343    /// Gives back the dimension id of the given edge.
344    /// It is in the range <tt>[0..dim-1]</tt>.
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.
352    /// It is in the range <tt>[0..dim-1]</tt>.
353    int dimension(Arc arc) const {
354      return Parent::dimension(arc);
355    }
356
357    /// \brief The index of a node.
358    ///
359    /// Gives back the index of the given node.
360    /// The lower bits of the integer describes the node.
361    static int index(Node node) {
362      return Parent::index(node);
363    }
364
365    /// \brief Gives back a node by its index.
366    ///
367    /// Gives back a node by its index.
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(); }
374    /// \brief Number of edges.
375    int edgeNum() const { return Parent::edgeNum(); }
376    /// \brief Number of arcs.
377    int arcNum() const { return Parent::arcNum(); }
378
379    /// \brief Linear combination map.
380    ///
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.
389    ///
390    ///\code
391    /// const int DIM = 3;
392    /// HypercubeGraph graph(DIM);
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    /// }
398    /// HypercubeGraph::HyperMap<dim2::Point<double> >
399    ///   pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));
400    ///\endcode
401    ///
402    /// \see HypercubeGraph
403    template <typename T, typename BF = std::plus<T> >
404    class HyperMap {
405    public:
406
407      /// \brief The key type of the map
408      typedef Node Key;
409      /// \brief The value type of the map
410      typedef T Value;
411
412      /// \brief Constructor for HyperMap.
413      ///
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.
418      ///
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.
422      template <typename It>
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)
426      {
427        LEMON_ASSERT(_values.size() == graph.dimension(),
428                     "Wrong size of range");
429      }
430
431      /// \brief The partial accumulated value.
432      ///
433      /// Gives back the partial accumulated value.
434      Value operator[](const Key& k) const {
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:
449      const Graph& _graph;
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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