COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/grid_graph.h @ 909:f112c18bc304

Last change on this file since 909:f112c18bc304 was 787:c2230649a493, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Various doc improvements (#331)

  • Add notes to the graph classes about the time of item counting.
  • Clarify the doc for run() in BFS and DFS.
  • Other improvements.
File size: 18.5 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) 2003-2009
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 GRID_GRAPH_H
20#define GRID_GRAPH_H
21
22#include <lemon/core.h>
23#include <lemon/bits/graph_extender.h>
24#include <lemon/dim2.h>
25#include <lemon/assert.h>
26
27///\ingroup graphs
28///\file
29///\brief GridGraph class.
30
31namespace lemon {
32
33  class GridGraphBase {
34
35  public:
36
37    typedef GridGraphBase Graph;
38
39    class Node;
40    class Edge;
41    class Arc;
42
43  public:
44
45    GridGraphBase() {}
46
47  protected:
48
49    void construct(int width, int height) {
50       _width = width; _height = height;
51      _node_num = width * height;
52      _edge_num = 2 * _node_num - width - height;
53      _edge_limit = _node_num - _width;
54    }
55
56  public:
57
58    Node operator()(int i, int j) const {
59      LEMON_DEBUG(0 <= i && i < _width &&
60                  0 <= j  && j < _height, "Index out of range");
61      return Node(i + j * _width);
62    }
63
64    int col(Node n) const {
65      return n._id % _width;
66    }
67
68    int row(Node n) const {
69      return n._id / _width;
70    }
71
72    dim2::Point<int> pos(Node n) const {
73      return dim2::Point<int>(col(n), row(n));
74    }
75
76    int width() const {
77      return _width;
78    }
79
80    int height() const {
81      return _height;
82    }
83
84    typedef True NodeNumTag;
85    typedef True EdgeNumTag;
86    typedef True ArcNumTag;
87
88    int nodeNum() const { return _node_num; }
89    int edgeNum() const { return _edge_num; }
90    int arcNum() const { return 2 * _edge_num; }
91
92    Node u(Edge edge) const {
93      if (edge._id < _edge_limit) {
94        return edge._id;
95      } else {
96        return (edge._id - _edge_limit) % (_width - 1) +
97          (edge._id - _edge_limit) / (_width - 1) * _width;
98      }
99    }
100
101    Node v(Edge edge) const {
102      if (edge._id < _edge_limit) {
103        return edge._id + _width;
104      } else {
105        return (edge._id - _edge_limit) % (_width - 1) +
106          (edge._id - _edge_limit) / (_width - 1) * _width + 1;
107      }
108    }
109
110    Node source(Arc arc) const {
111      return (arc._id & 1) == 1 ? u(arc) : v(arc);
112    }
113
114    Node target(Arc arc) const {
115      return (arc._id & 1) == 1 ? v(arc) : u(arc);
116    }
117
118    static int id(Node node) { return node._id; }
119    static int id(Edge edge) { return edge._id; }
120    static int id(Arc arc) { return arc._id; }
121
122    int maxNodeId() const { return _node_num - 1; }
123    int maxEdgeId() const { return _edge_num - 1; }
124    int maxArcId() const { return 2 * _edge_num - 1; }
125
126    static Node nodeFromId(int id) { return Node(id);}
127    static Edge edgeFromId(int id) { return Edge(id);}
128    static Arc arcFromId(int id) { return Arc(id);}
129
130    typedef True FindEdgeTag;
131    typedef True FindArcTag;
132
133    Edge findEdge(Node u, Node v, Edge prev = INVALID) const {
134      if (prev != INVALID) return INVALID;
135      if (v._id > u._id) {
136        if (v._id - u._id == _width)
137          return Edge(u._id);
138        if (v._id - u._id == 1 && u._id % _width < _width - 1) {
139          return Edge(u._id / _width * (_width - 1) +
140                      u._id % _width + _edge_limit);
141        }
142      } else {
143        if (u._id - v._id == _width)
144          return Edge(v._id);
145        if (u._id - v._id == 1 && v._id % _width < _width - 1) {
146          return Edge(v._id / _width * (_width - 1) +
147                      v._id % _width + _edge_limit);
148        }
149      }
150      return INVALID;
151    }
152
153    Arc findArc(Node u, Node v, Arc prev = INVALID) const {
154      if (prev != INVALID) return INVALID;
155      if (v._id > u._id) {
156        if (v._id - u._id == _width)
157          return Arc((u._id << 1) | 1);
158        if (v._id - u._id == 1 && u._id % _width < _width - 1) {
159          return Arc(((u._id / _width * (_width - 1) +
160                       u._id % _width + _edge_limit) << 1) | 1);
161        }
162      } else {
163        if (u._id - v._id == _width)
164          return Arc(v._id << 1);
165        if (u._id - v._id == 1 && v._id % _width < _width - 1) {
166          return Arc((v._id / _width * (_width - 1) +
167                       v._id % _width + _edge_limit) << 1);
168        }
169      }
170      return INVALID;
171    }
172
173    class Node {
174      friend class GridGraphBase;
175
176    protected:
177      int _id;
178      Node(int id) : _id(id) {}
179    public:
180      Node() {}
181      Node (Invalid) : _id(-1) {}
182      bool operator==(const Node node) const {return _id == node._id;}
183      bool operator!=(const Node node) const {return _id != node._id;}
184      bool operator<(const Node node) const {return _id < node._id;}
185    };
186
187    class Edge {
188      friend class GridGraphBase;
189      friend class Arc;
190
191    protected:
192      int _id;
193
194      Edge(int id) : _id(id) {}
195
196    public:
197      Edge() {}
198      Edge (Invalid) : _id(-1) {}
199      bool operator==(const Edge edge) const {return _id == edge._id;}
200      bool operator!=(const Edge edge) const {return _id != edge._id;}
201      bool operator<(const Edge edge) const {return _id < edge._id;}
202    };
203
204    class Arc {
205      friend class GridGraphBase;
206
207    protected:
208      int _id;
209
210      Arc(int id) : _id(id) {}
211
212    public:
213      Arc() {}
214      Arc (Invalid) : _id(-1) {}
215      operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }
216      bool operator==(const Arc arc) const {return _id == arc._id;}
217      bool operator!=(const Arc arc) const {return _id != arc._id;}
218      bool operator<(const Arc arc) const {return _id < arc._id;}
219    };
220
221    static bool direction(Arc arc) {
222      return (arc._id & 1) == 1;
223    }
224
225    static Arc direct(Edge edge, bool dir) {
226      return Arc((edge._id << 1) | (dir ? 1 : 0));
227    }
228
229    void first(Node& node) const {
230      node._id = _node_num - 1;
231    }
232
233    static void next(Node& node) {
234      --node._id;
235    }
236
237    void first(Edge& edge) const {
238      edge._id = _edge_num - 1;
239    }
240
241    static void next(Edge& edge) {
242      --edge._id;
243    }
244
245    void first(Arc& arc) const {
246      arc._id = 2 * _edge_num - 1;
247    }
248
249    static void next(Arc& arc) {
250      --arc._id;
251    }
252
253    void firstOut(Arc& arc, const Node& node) const {
254      if (node._id % _width < _width - 1) {
255        arc._id = (_edge_limit + node._id % _width +
256                   (node._id / _width) * (_width - 1)) << 1 | 1;
257        return;
258      }
259      if (node._id < _node_num - _width) {
260        arc._id = node._id << 1 | 1;
261        return;
262      }
263      if (node._id % _width > 0) {
264        arc._id = (_edge_limit + node._id % _width +
265                   (node._id / _width) * (_width - 1) - 1) << 1;
266        return;
267      }
268      if (node._id >= _width) {
269        arc._id = (node._id - _width) << 1;
270        return;
271      }
272      arc._id = -1;
273    }
274
275    void nextOut(Arc& arc) const {
276      int nid = arc._id >> 1;
277      if ((arc._id & 1) == 1) {
278        if (nid >= _edge_limit) {
279          nid = (nid - _edge_limit) % (_width - 1) +
280            (nid - _edge_limit) / (_width - 1) * _width;
281          if (nid < _node_num - _width) {
282            arc._id = nid << 1 | 1;
283            return;
284          }
285        }
286        if (nid % _width > 0) {
287          arc._id = (_edge_limit + nid % _width +
288                     (nid / _width) * (_width - 1) - 1) << 1;
289          return;
290        }
291        if (nid >= _width) {
292          arc._id = (nid - _width) << 1;
293          return;
294        }
295      } else {
296        if (nid >= _edge_limit) {
297          nid = (nid - _edge_limit) % (_width - 1) +
298            (nid - _edge_limit) / (_width - 1) * _width + 1;
299          if (nid >= _width) {
300            arc._id = (nid - _width) << 1;
301            return;
302          }
303        }
304      }
305      arc._id = -1;
306    }
307
308    void firstIn(Arc& arc, const Node& node) const {
309      if (node._id % _width < _width - 1) {
310        arc._id = (_edge_limit + node._id % _width +
311                   (node._id / _width) * (_width - 1)) << 1;
312        return;
313      }
314      if (node._id < _node_num - _width) {
315        arc._id = node._id << 1;
316        return;
317      }
318      if (node._id % _width > 0) {
319        arc._id = (_edge_limit + node._id % _width +
320                   (node._id / _width) * (_width - 1) - 1) << 1 | 1;
321        return;
322      }
323      if (node._id >= _width) {
324        arc._id = (node._id - _width) << 1 | 1;
325        return;
326      }
327      arc._id = -1;
328    }
329
330    void nextIn(Arc& arc) const {
331      int nid = arc._id >> 1;
332      if ((arc._id & 1) == 0) {
333        if (nid >= _edge_limit) {
334          nid = (nid - _edge_limit) % (_width - 1) +
335            (nid - _edge_limit) / (_width - 1) * _width;
336          if (nid < _node_num - _width) {
337            arc._id = nid << 1;
338            return;
339          }
340        }
341        if (nid % _width > 0) {
342          arc._id = (_edge_limit + nid % _width +
343                     (nid / _width) * (_width - 1) - 1) << 1 | 1;
344          return;
345        }
346        if (nid >= _width) {
347          arc._id = (nid - _width) << 1 | 1;
348          return;
349        }
350      } else {
351        if (nid >= _edge_limit) {
352          nid = (nid - _edge_limit) % (_width - 1) +
353            (nid - _edge_limit) / (_width - 1) * _width + 1;
354          if (nid >= _width) {
355            arc._id = (nid - _width) << 1 | 1;
356            return;
357          }
358        }
359      }
360      arc._id = -1;
361    }
362
363    void firstInc(Edge& edge, bool& dir, const Node& node) const {
364      if (node._id % _width < _width - 1) {
365        edge._id = _edge_limit + node._id % _width +
366          (node._id / _width) * (_width - 1);
367        dir = true;
368        return;
369      }
370      if (node._id < _node_num - _width) {
371        edge._id = node._id;
372        dir = true;
373        return;
374      }
375      if (node._id % _width > 0) {
376        edge._id = _edge_limit + node._id % _width +
377          (node._id / _width) * (_width - 1) - 1;
378        dir = false;
379        return;
380      }
381      if (node._id >= _width) {
382        edge._id = node._id - _width;
383        dir = false;
384        return;
385      }
386      edge._id = -1;
387      dir = true;
388    }
389
390    void nextInc(Edge& edge, bool& dir) const {
391      int nid = edge._id;
392      if (dir) {
393        if (nid >= _edge_limit) {
394          nid = (nid - _edge_limit) % (_width - 1) +
395            (nid - _edge_limit) / (_width - 1) * _width;
396          if (nid < _node_num - _width) {
397            edge._id = nid;
398            return;
399          }
400        }
401        if (nid % _width > 0) {
402          edge._id = _edge_limit + nid % _width +
403            (nid / _width) * (_width - 1) - 1;
404          dir = false;
405          return;
406        }
407        if (nid >= _width) {
408          edge._id = nid - _width;
409          dir = false;
410          return;
411        }
412      } else {
413        if (nid >= _edge_limit) {
414          nid = (nid - _edge_limit) % (_width - 1) +
415            (nid - _edge_limit) / (_width - 1) * _width + 1;
416          if (nid >= _width) {
417            edge._id = nid - _width;
418            return;
419          }
420        }
421      }
422      edge._id = -1;
423      dir = true;
424    }
425
426    Arc right(Node n) const {
427      if (n._id % _width < _width - 1) {
428        return Arc(((_edge_limit + n._id % _width +
429                    (n._id / _width) * (_width - 1)) << 1) | 1);
430      } else {
431        return INVALID;
432      }
433    }
434
435    Arc left(Node n) const {
436      if (n._id % _width > 0) {
437        return Arc((_edge_limit + n._id % _width +
438                     (n._id / _width) * (_width - 1) - 1) << 1);
439      } else {
440        return INVALID;
441      }
442    }
443
444    Arc up(Node n) const {
445      if (n._id < _edge_limit) {
446        return Arc((n._id << 1) | 1);
447      } else {
448        return INVALID;
449      }
450    }
451
452    Arc down(Node n) const {
453      if (n._id >= _width) {
454        return Arc((n._id - _width) << 1);
455      } else {
456        return INVALID;
457      }
458    }
459
460  private:
461    int _width, _height;
462    int _node_num, _edge_num;
463    int _edge_limit;
464  };
465
466
467  typedef GraphExtender<GridGraphBase> ExtendedGridGraphBase;
468
469  /// \ingroup graphs
470  ///
471  /// \brief Grid graph class
472  ///
473  /// GridGraph implements a special graph type. The nodes of the
474  /// graph can be indexed by two integer values \c (i,j) where \c i is
475  /// in the range <tt>[0..width()-1]</tt> and j is in the range
476  /// <tt>[0..height()-1]</tt>. Two nodes are connected in the graph if
477  /// the indices differ exactly on one position and the difference is
478  /// also exactly one. The nodes of the graph can be obtained by position
479  /// using the \c operator()() function and the indices of the nodes can
480  /// be obtained using \c pos(), \c col() and \c row() members. The outgoing
481  /// arcs can be retrieved with the \c right(), \c up(), \c left()
482  /// and \c down() functions, where the bottom-left corner is the
483  /// origin.
484  ///
485  /// This class is completely static and it needs constant memory space.
486  /// Thus you can neither add nor delete nodes or edges, however
487  /// the structure can be resized using resize().
488  ///
489  /// \image html grid_graph.png
490  /// \image latex grid_graph.eps "Grid graph" width=\textwidth
491  ///
492  /// A short example about the basic usage:
493  ///\code
494  /// GridGraph graph(rows, cols);
495  /// GridGraph::NodeMap<int> val(graph);
496  /// for (int i = 0; i < graph.width(); ++i) {
497  ///   for (int j = 0; j < graph.height(); ++j) {
498  ///     val[graph(i, j)] = i + j;
499  ///   }
500  /// }
501  ///\endcode
502  ///
503  /// This type fully conforms to the \ref concepts::Graph "Graph concept".
504  /// Most of its member functions and nested classes are documented
505  /// only in the concept class.
506  ///
507  /// This class provides constant time counting for nodes, edges and arcs.
508  class GridGraph : public ExtendedGridGraphBase {
509    typedef ExtendedGridGraphBase Parent;
510
511  public:
512
513    /// \brief Map to get the indices of the nodes as \ref dim2::Point
514    /// "dim2::Point<int>".
515    ///
516    /// Map to get the indices of the nodes as \ref dim2::Point
517    /// "dim2::Point<int>".
518    class IndexMap {
519    public:
520      /// \brief The key type of the map
521      typedef GridGraph::Node Key;
522      /// \brief The value type of the map
523      typedef dim2::Point<int> Value;
524
525      /// \brief Constructor
526      IndexMap(const GridGraph& graph) : _graph(graph) {}
527
528      /// \brief The subscript operator
529      Value operator[](Key key) const {
530        return _graph.pos(key);
531      }
532
533    private:
534      const GridGraph& _graph;
535    };
536
537    /// \brief Map to get the column of the nodes.
538    ///
539    /// Map to get the column of the nodes.
540    class ColMap {
541    public:
542      /// \brief The key type of the map
543      typedef GridGraph::Node Key;
544      /// \brief The value type of the map
545      typedef int Value;
546
547      /// \brief Constructor
548      ColMap(const GridGraph& graph) : _graph(graph) {}
549
550      /// \brief The subscript operator
551      Value operator[](Key key) const {
552        return _graph.col(key);
553      }
554
555    private:
556      const GridGraph& _graph;
557    };
558
559    /// \brief Map to get the row of the nodes.
560    ///
561    /// Map to get the row of the nodes.
562    class RowMap {
563    public:
564      /// \brief The key type of the map
565      typedef GridGraph::Node Key;
566      /// \brief The value type of the map
567      typedef int Value;
568
569      /// \brief Constructor
570      RowMap(const GridGraph& graph) : _graph(graph) {}
571
572      /// \brief The subscript operator
573      Value operator[](Key key) const {
574        return _graph.row(key);
575      }
576
577    private:
578      const GridGraph& _graph;
579    };
580
581    /// \brief Constructor
582    ///
583    /// Construct a grid graph with the given size.
584    GridGraph(int width, int height) { construct(width, height); }
585
586    /// \brief Resizes the graph
587    ///
588    /// This function resizes the graph. It fully destroys and
589    /// rebuilds the structure, therefore the maps of the graph will be
590    /// reallocated automatically and the previous values will be lost.
591    void resize(int width, int height) {
592      Parent::notifier(Arc()).clear();
593      Parent::notifier(Edge()).clear();
594      Parent::notifier(Node()).clear();
595      construct(width, height);
596      Parent::notifier(Node()).build();
597      Parent::notifier(Edge()).build();
598      Parent::notifier(Arc()).build();
599    }
600
601    /// \brief The node on the given position.
602    ///
603    /// Gives back the node on the given position.
604    Node operator()(int i, int j) const {
605      return Parent::operator()(i, j);
606    }
607
608    /// \brief The column index of the node.
609    ///
610    /// Gives back the column index of the node.
611    int col(Node n) const {
612      return Parent::col(n);
613    }
614
615    /// \brief The row index of the node.
616    ///
617    /// Gives back the row index of the node.
618    int row(Node n) const {
619      return Parent::row(n);
620    }
621
622    /// \brief The position of the node.
623    ///
624    /// Gives back the position of the node, ie. the <tt>(col,row)</tt> pair.
625    dim2::Point<int> pos(Node n) const {
626      return Parent::pos(n);
627    }
628
629    /// \brief The number of the columns.
630    ///
631    /// Gives back the number of the columns.
632    int width() const {
633      return Parent::width();
634    }
635
636    /// \brief The number of the rows.
637    ///
638    /// Gives back the number of the rows.
639    int height() const {
640      return Parent::height();
641    }
642
643    /// \brief The arc goes right from the node.
644    ///
645    /// Gives back the arc goes right from the node. If there is not
646    /// outgoing arc then it gives back INVALID.
647    Arc right(Node n) const {
648      return Parent::right(n);
649    }
650
651    /// \brief The arc goes left from the node.
652    ///
653    /// Gives back the arc goes left from the node. If there is not
654    /// outgoing arc then it gives back INVALID.
655    Arc left(Node n) const {
656      return Parent::left(n);
657    }
658
659    /// \brief The arc goes up from the node.
660    ///
661    /// Gives back the arc goes up from the node. If there is not
662    /// outgoing arc then it gives back INVALID.
663    Arc up(Node n) const {
664      return Parent::up(n);
665    }
666
667    /// \brief The arc goes down from the node.
668    ///
669    /// Gives back the arc goes down from the node. If there is not
670    /// outgoing arc then it gives back INVALID.
671    Arc down(Node n) const {
672      return Parent::down(n);
673    }
674
675    /// \brief Index map of the grid graph
676    ///
677    /// Just returns an IndexMap for the grid graph.
678    IndexMap indexMap() const {
679      return IndexMap(*this);
680    }
681
682    /// \brief Row map of the grid graph
683    ///
684    /// Just returns a RowMap for the grid graph.
685    RowMap rowMap() const {
686      return RowMap(*this);
687    }
688
689    /// \brief Column map of the grid graph
690    ///
691    /// Just returns a ColMap for the grid graph.
692    ColMap colMap() const {
693      return ColMap(*this);
694    }
695
696  };
697
698}
699#endif
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