COIN-OR::LEMON - Graph Library

source: lemon/lemon/hypercube_graph.h @ 384:164fe3abc024

Last change on this file since 384:164fe3abc024 was 377:a12eef1f82b2, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Rework hypercube graph implementation to be undirected (#57)

File size: 11.9 KB
Line 
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) 2003-2008
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) | (u._id & ((1 << k) - 1));
109    }
110
111    Arc findArc(Node u, Node v, Arc prev = INVALID) const {
112      Edge edge = findEdge(u, v, prev);
113      if (edge == INVALID) return INVALID;
114      int k = edge._id >> _dim-1;
115      return ((u._id >> k) & 1) == 1 ? edge._id << 1 : (edge._id << 1) | 1;
116    }
117
118    class Node {
119      friend class HypercubeGraphBase;
120
121    protected:
122      int _id;
123      Node(int id) : _id(id) {}
124    public:
125      Node() {}
126      Node (Invalid) : _id(-1) {}
127      bool operator==(const Node node) const {return _id == node._id;}
128      bool operator!=(const Node node) const {return _id != node._id;}
129      bool operator<(const Node node) const {return _id < node._id;}
130    };
131
132    class Edge {
133      friend class HypercubeGraphBase;
134      friend class Arc;
135
136    protected:
137      int _id;
138
139      Edge(int id) : _id(id) {}
140
141    public:
142      Edge() {}
143      Edge (Invalid) : _id(-1) {}
144      bool operator==(const Edge edge) const {return _id == edge._id;}
145      bool operator!=(const Edge edge) const {return _id != edge._id;}
146      bool operator<(const Edge edge) const {return _id < edge._id;}
147    };
148
149    class Arc {
150      friend class HypercubeGraphBase;
151
152    protected:
153      int _id;
154
155      Arc(int id) : _id(id) {}
156
157    public:
158      Arc() {}
159      Arc (Invalid) : _id(-1) {}
160      operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }
161      bool operator==(const Arc arc) const {return _id == arc._id;}
162      bool operator!=(const Arc arc) const {return _id != arc._id;}
163      bool operator<(const Arc arc) const {return _id < arc._id;}
164    };
165
166    void first(Node& node) const {
167      node._id = _node_num - 1;
168    }
169
170    static void next(Node& node) {
171      --node._id;
172    }
173
174    void first(Edge& edge) const {
175      edge._id = _edge_num - 1;
176    }
177
178    static void next(Edge& edge) {
179      --edge._id;
180    }
181
182    void first(Arc& arc) const {
183      arc._id = 2 * _edge_num - 1;
184    }
185
186    static void next(Arc& arc) {
187      --arc._id;
188    }
189
190    void firstInc(Edge& edge, bool& dir, const Node& node) const {
191      edge._id = node._id >> 1;
192      dir = (node._id & 1) == 0;
193    }
194
195    void nextInc(Edge& edge, bool& dir) const {
196      Node n = dir ? u(edge) : v(edge);
197      int k = (edge._id >> _dim-1) + 1;
198      if (k < _dim) {
199        edge._id = (k << _dim-1) |
200                   ((n._id >> k+1) << k) | (n._id & ((1 << k) - 1));
201        dir = ((n._id >> k) & 1) == 0;
202      } else {
203        edge._id = -1;
204        dir = true;
205      }
206    }
207
208    void firstOut(Arc& arc, const Node& node) const {
209      arc._id = ((node._id >> 1) << 1) | (~node._id & 1);
210    }
211
212    void nextOut(Arc& arc) const {
213      Node n = (arc._id & 1) == 1 ? u(arc) : v(arc);
214      int k = (arc._id >> _dim) + 1;
215      if (k < _dim) {
216        arc._id = (k << _dim-1) |
217                  ((n._id >> k+1) << k) | (n._id & ((1 << k) - 1));
218        arc._id = (arc._id << 1) | (~(n._id >> k) & 1);
219      } else {
220        arc._id = -1;
221      }
222    }
223
224    void firstIn(Arc& arc, const Node& node) const {
225      arc._id = ((node._id >> 1) << 1) | (node._id & 1);
226    }
227
228    void nextIn(Arc& arc) const {
229      Node n = (arc._id & 1) == 1 ? v(arc) : u(arc);
230      int k = (arc._id >> _dim) + 1;
231      if (k < _dim) {
232        arc._id = (k << _dim-1) |
233                  ((n._id >> k+1) << k) | (n._id & ((1 << k) - 1));
234        arc._id = (arc._id << 1) | ((n._id >> k) & 1);
235      } else {
236        arc._id = -1;
237      }
238    }
239
240    static bool direction(Arc arc) {
241      return (arc._id & 1) == 1;
242    }
243
244    static Arc direct(Edge edge, bool dir) {
245      return Arc((edge._id << 1) | (dir ? 1 : 0));
246    }
247
248    int dimension() const {
249      return _dim;
250    }
251
252    bool projection(Node node, int n) const {
253      return static_cast<bool>(node._id & (1 << n));
254    }
255
256    int dimension(Edge edge) const {
257      return edge._id >> _dim-1;
258    }
259
260    int dimension(Arc arc) const {
261      return arc._id >> _dim;
262    }
263
264    int index(Node node) const {
265      return node._id;
266    }
267
268    Node operator()(int ix) const {
269      return Node(ix);
270    }
271
272  private:
273    int _dim;
274    int _node_num, _edge_num;
275  };
276
277
278  typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase;
279
280  /// \ingroup graphs
281  ///
282  /// \brief Hypercube graph class
283  ///
284  /// This class implements a special graph type. The nodes of the graph
285  /// are indiced with integers with at most \c dim binary digits.
286  /// Two nodes are connected in the graph if and only if their indices
287  /// differ only on one position in the binary form.
288  ///
289  /// \note The type of the indices is chosen to \c int for efficiency
290  /// reasons. Thus the maximum dimension of this implementation is 26
291  /// (assuming that the size of \c int is 32 bit).
292  ///
293  /// This graph type is fully conform to the \ref concepts::Graph
294  /// "Graph" concept, and it also has an important extra feature
295  /// that its maps are real \ref concepts::ReferenceMap
296  /// "reference map"s.
297  class HypercubeGraph : public ExtendedHypercubeGraphBase {
298  public:
299
300    typedef ExtendedHypercubeGraphBase Parent;
301
302    /// \brief Constructs a hypercube graph with \c dim dimensions.
303    ///
304    /// Constructs a hypercube graph with \c dim dimensions.
305    HypercubeGraph(int dim) { construct(dim); }
306
307    /// \brief The number of dimensions.
308    ///
309    /// Gives back the number of dimensions.
310    int dimension() const {
311      return Parent::dimension();
312    }
313
314    /// \brief Returns \c true if the n'th bit of the node is one.
315    ///
316    /// Returns \c true if the n'th bit of the node is one.
317    bool projection(Node node, int n) const {
318      return Parent::projection(node, n);
319    }
320
321    /// \brief The dimension id of an edge.
322    ///
323    /// Gives back the dimension id of the given edge.
324    /// It is in the [0..dim-1] range.
325    int dimension(Edge edge) const {
326      return Parent::dimension(edge);
327    }
328
329    /// \brief The dimension id of an arc.
330    ///
331    /// Gives back the dimension id of the given arc.
332    /// It is in the [0..dim-1] range.
333    int dimension(Arc arc) const {
334      return Parent::dimension(arc);
335    }
336
337    /// \brief The index of a node.
338    ///
339    /// Gives back the index of the given node.
340    /// The lower bits of the integer describes the node.
341    int index(Node node) const {
342      return Parent::index(node);
343    }
344
345    /// \brief Gives back a node by its index.
346    ///
347    /// Gives back a node by its index.
348    Node operator()(int ix) const {
349      return Parent::operator()(ix);
350    }
351
352    /// \brief Number of nodes.
353    int nodeNum() const { return Parent::nodeNum(); }
354    /// \brief Number of edges.
355    int edgeNum() const { return Parent::edgeNum(); }
356    /// \brief Number of arcs.
357    int arcNum() const { return Parent::arcNum(); }
358
359    /// \brief Linear combination map.
360    ///
361    /// This map makes possible to give back a linear combination
362    /// for each node. It works like the \c std::accumulate function,
363    /// so it accumulates the \c bf binary function with the \c fv first
364    /// value. The map accumulates only on that positions (dimensions)
365    /// where the index of the node is one. The values that have to be
366    /// accumulated should be given by the \c begin and \c end iterators
367    /// and the length of this range should be equal to the dimension
368    /// number of the graph.
369    ///
370    ///\code
371    /// const int DIM = 3;
372    /// HypercubeGraph graph(DIM);
373    /// dim2::Point<double> base[DIM];
374    /// for (int k = 0; k < DIM; ++k) {
375    ///   base[k].x = rnd();
376    ///   base[k].y = rnd();
377    /// }
378    /// HypercubeGraph::HyperMap<dim2::Point<double> >
379    ///   pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));
380    ///\endcode
381    ///
382    /// \see HypercubeGraph
383    template <typename T, typename BF = std::plus<T> >
384    class HyperMap {
385    public:
386
387      /// \brief The key type of the map
388      typedef Node Key;
389      /// \brief The value type of the map
390      typedef T Value;
391
392      /// \brief Constructor for HyperMap.
393      ///
394      /// Construct a HyperMap for the given graph. The values that have
395      /// to be accumulated should be given by the \c begin and \c end
396      /// iterators and the length of this range should be equal to the
397      /// dimension number of the graph.
398      ///
399      /// This map accumulates the \c bf binary function with the \c fv
400      /// first value on that positions (dimensions) where the index of
401      /// the node is one.
402      template <typename It>
403      HyperMap(const Graph& graph, It begin, It end,
404               T fv = 0, const BF& bf = BF())
405        : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf)
406      {
407        LEMON_ASSERT(_values.size() == graph.dimension(),
408                     "Wrong size of range");
409      }
410
411      /// \brief The partial accumulated value.
412      ///
413      /// Gives back the partial accumulated value.
414      Value operator[](const Key& k) const {
415        Value val = _first_value;
416        int id = _graph.index(k);
417        int n = 0;
418        while (id != 0) {
419          if (id & 1) {
420            val = _bin_func(val, _values[n]);
421          }
422          id >>= 1;
423          ++n;
424        }
425        return val;
426      }
427
428    private:
429      const Graph& _graph;
430      std::vector<T> _values;
431      T _first_value;
432      BF _bin_func;
433    };
434
435  };
436
437}
438
439#endif
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