COIN-OR::LEMON - Graph Library

source: lemon/lemon/hypercube_graph.h @ 377:a12eef1f82b2

Last change on this file since 377:a12eef1f82b2 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
RevLine 
[376]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>
[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;
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 {
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 {
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;
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    }
[376]117
118    class Node {
[377]119      friend class HypercubeGraphBase;
120
[376]121    protected:
[377]122      int _id;
123      Node(int id) : _id(id) {}
[376]124    public:
125      Node() {}
[377]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;}
[376]147    };
148
149    class Arc {
[377]150      friend class HypercubeGraphBase;
151
[376]152    protected:
[377]153      int _id;
154
155      Arc(int id) : _id(id) {}
156
[376]157    public:
[377]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;}
[376]164    };
165
166    void first(Node& node) const {
[377]167      node._id = _node_num - 1;
[376]168    }
169
170    static void next(Node& node) {
[377]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;
[376]180    }
181
182    void first(Arc& arc) const {
[377]183      arc._id = 2 * _edge_num - 1;
[376]184    }
185
186    static void next(Arc& arc) {
[377]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      }
[376]206    }
207
208    void firstOut(Arc& arc, const Node& node) const {
[377]209      arc._id = ((node._id >> 1) << 1) | (~node._id & 1);
[376]210    }
211
212    void nextOut(Arc& arc) const {
[377]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      }
[376]222    }
223
224    void firstIn(Arc& arc, const Node& node) const {
[377]225      arc._id = ((node._id >> 1) << 1) | (node._id & 1);
[376]226    }
227
228    void nextIn(Arc& arc) const {
[377]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);
[376]235      } else {
[377]236        arc._id = -1;
[376]237      }
238    }
239
[377]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
[376]248    int dimension() const {
249      return _dim;
250    }
251
252    bool projection(Node node, int n) const {
[377]253      return static_cast<bool>(node._id & (1 << n));
254    }
255
256    int dimension(Edge edge) const {
257      return edge._id >> _dim-1;
[376]258    }
259
260    int dimension(Arc arc) const {
[377]261      return arc._id >> _dim;
[376]262    }
263
264    int index(Node node) const {
[377]265      return node._id;
[376]266    }
267
268    Node operator()(int ix) const {
269      return Node(ix);
270    }
271
272  private:
[377]273    int _dim;
274    int _node_num, _edge_num;
[376]275  };
276
277
[377]278  typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase;
[376]279
[377]280  /// \ingroup graphs
[376]281  ///
[377]282  /// \brief Hypercube graph class
[376]283  ///
[377]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.
[376]288  ///
[377]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).
[376]292  ///
[377]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 {
[376]298  public:
299
[377]300    typedef ExtendedHypercubeGraphBase Parent;
[376]301
[377]302    /// \brief Constructs a hypercube graph with \c dim dimensions.
[376]303    ///
[377]304    /// Constructs a hypercube graph with \c dim dimensions.
305    HypercubeGraph(int dim) { construct(dim); }
[376]306
[377]307    /// \brief The number of dimensions.
[376]308    ///
[377]309    /// Gives back the number of dimensions.
[376]310    int dimension() const {
311      return Parent::dimension();
312    }
313
[377]314    /// \brief Returns \c true if the n'th bit of the node is one.
[376]315    ///
[377]316    /// Returns \c true if the n'th bit of the node is one.
[376]317    bool projection(Node node, int n) const {
318      return Parent::projection(node, n);
319    }
320
[377]321    /// \brief The dimension id of an edge.
[376]322    ///
[377]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.
[376]333    int dimension(Arc arc) const {
334      return Parent::dimension(arc);
335    }
336
[377]337    /// \brief The index of a node.
[376]338    ///
[377]339    /// Gives back the index of the given node.
340    /// The lower bits of the integer describes the node.
[376]341    int index(Node node) const {
342      return Parent::index(node);
343    }
344
[377]345    /// \brief Gives back a node by its index.
[376]346    ///
[377]347    /// Gives back a node by its index.
[376]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(); }
[377]354    /// \brief Number of edges.
355    int edgeNum() const { return Parent::edgeNum(); }
[376]356    /// \brief Number of arcs.
357    int arcNum() const { return Parent::arcNum(); }
358
359    /// \brief Linear combination map.
360    ///
[377]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.
[376]369    ///
370    ///\code
371    /// const int DIM = 3;
[377]372    /// HypercubeGraph graph(DIM);
[376]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    /// }
[377]378    /// HypercubeGraph::HyperMap<dim2::Point<double> >
379    ///   pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));
[376]380    ///\endcode
381    ///
[377]382    /// \see HypercubeGraph
[376]383    template <typename T, typename BF = std::plus<T> >
384    class HyperMap {
385    public:
386
[377]387      /// \brief The key type of the map
[376]388      typedef Node Key;
[377]389      /// \brief The value type of the map
[376]390      typedef T Value;
391
392      /// \brief Constructor for HyperMap.
393      ///
[377]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.
[376]398      ///
[377]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.
[376]402      template <typename It>
[377]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)
[376]406      {
[377]407        LEMON_ASSERT(_values.size() == graph.dimension(),
408                     "Wrong size of range");
[376]409      }
410
[377]411      /// \brief The partial accumulated value.
[376]412      ///
413      /// Gives back the partial accumulated value.
[377]414      Value operator[](const Key& k) const {
[376]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:
[377]429      const Graph& _graph;
[376]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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