COIN-OR::LEMON - Graph Library

source: lemon/lemon/nagamochi_ibaraki.h @ 1017:5087694945e4

Last change on this file since 1017:5087694945e4 was 1017:5087694945e4, checked in by Balazs Dezso <deba@…>, 9 years ago

New implementation for Nagamochi-Ibaraki algorithm

File size: 21.5 KB
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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) 2003-2010
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 LEMON_NAGAMOCHI_IBARAKI_H
20#define LEMON_NAGAMOCHI_IBARAKI_H
21
22
23/// \ingroup min_cut
24/// \file
25/// \brief Implementation of the Nagamochi-Ibaraki algorithm.
26
27#include <lemon/core.h>
28#include <lemon/bin_heap.h>
29#include <lemon/bucket_heap.h>
30#include <lemon/maps.h>
31#include <lemon/radix_sort.h>
32#include <lemon/unionfind.h>
33
34#include <cassert>
35
36namespace lemon {
37
38  /// \brief Default traits class for NagamochiIbaraki class.
39  ///
40  /// Default traits class for NagamochiIbaraki class.
41  /// \param GR The undirected graph type.
42  /// \param CM Type of capacity map.
43  template <typename GR, typename CM>
44  struct NagamochiIbarakiDefaultTraits {
45    /// The type of the capacity map.
46    typedef typename CM::Value Value;
47
48    /// The undirected graph type the algorithm runs on.
49    typedef GR Graph;
50
51    /// \brief The type of the map that stores the edge capacities.
52    ///
53    /// The type of the map that stores the edge capacities.
54    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
55    typedef CM CapacityMap;
56
57    /// \brief Instantiates a CapacityMap.
58    ///
59    /// This function instantiates a \ref CapacityMap.
60#ifdef DOXYGEN
61    static CapacityMap *createCapacityMap(const Graph& graph)
62#else
63    static CapacityMap *createCapacityMap(const Graph&)
64#endif
65    {
66        LEMON_ASSERT(false, "CapacityMap is not initialized");
67        return 0; // ignore warnings
68    }
69
70    /// \brief The cross reference type used by heap.
71    ///
72    /// The cross reference type used by heap.
73    /// Usually \c Graph::NodeMap<int>.
74    typedef typename Graph::template NodeMap<int> HeapCrossRef;
75
76    /// \brief Instantiates a HeapCrossRef.
77    ///
78    /// This function instantiates a \ref HeapCrossRef.
79    /// \param g is the graph, to which we would like to define the
80    /// \ref HeapCrossRef.
81    static HeapCrossRef *createHeapCrossRef(const Graph& g) {
82      return new HeapCrossRef(g);
83    }
84
85    /// \brief The heap type used by NagamochiIbaraki algorithm.
86    ///
87    /// The heap type used by NagamochiIbaraki algorithm. It has to
88    /// maximize the priorities.
89    ///
90    /// \sa BinHeap
91    /// \sa NagamochiIbaraki
92    typedef BinHeap<Value, HeapCrossRef, std::greater<Value> > Heap;
93
94    /// \brief Instantiates a Heap.
95    ///
96    /// This function instantiates a \ref Heap.
97    /// \param r is the cross reference of the heap.
98    static Heap *createHeap(HeapCrossRef& r) {
99      return new Heap(r);
100    }
101  };
102
103  /// \ingroup min_cut
104  ///
105  /// \brief Calculates the minimum cut in an undirected graph.
106  ///
107  /// Calculates the minimum cut in an undirected graph with the
108  /// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's
109  /// nodes into two partitions with the minimum sum of edge capacities
110  /// between the two partitions. The algorithm can be used to test
111  /// the network reliability, especially to test how many links have
112  /// to be destroyed in the network to split it to at least two
113  /// distinict subnetworks.
114  ///
115  /// The complexity of the algorithm is \f$ O(nm\log(n)) \f$ but with
116  /// \ref FibHeap "Fibonacci heap" it can be decreased to
117  /// \f$ O(nm+n^2\log(n)) \f$.  When the edges have unit capacities,
118  /// \c BucketHeap can be used which yields \f$ O(nm) \f$ time
119  /// complexity.
120  ///
121  /// \warning The value type of the capacity map should be able to
122  /// hold any cut value of the graph, otherwise the result can
123  /// overflow.
124  /// \note This capacity is supposed to be integer type.
125#ifdef DOXYGEN
126  template <typename GR, typename CM, typename TR>
127#else
128  template <typename GR,
129            typename CM = typename GR::template EdgeMap<int>,
130            typename TR = NagamochiIbarakiDefaultTraits<GR, CM> >
131#endif
132  class NagamochiIbaraki {
133  public:
134
135    typedef TR Traits;
136    /// The type of the underlying graph.
137    typedef typename Traits::Graph Graph;
138
139    /// The type of the capacity map.
140    typedef typename Traits::CapacityMap CapacityMap;
141    /// The value type of the capacity map.
142    typedef typename Traits::CapacityMap::Value Value;
143
144    /// The heap type used by the algorithm.
145    typedef typename Traits::Heap Heap;
146    /// The cross reference type used for the heap.
147    typedef typename Traits::HeapCrossRef HeapCrossRef;
148
149    ///\name Named template parameters
150
151    ///@{
152
153    struct SetUnitCapacityTraits : public Traits {
154      typedef ConstMap<typename Graph::Edge, Const<int, 1> > CapacityMap;
155      static CapacityMap *createCapacityMap(const Graph&) {
156        return new CapacityMap();
157      }
158    };
159
160    /// \brief \ref named-templ-param "Named parameter" for setting
161    /// the capacity map to a constMap<Edge, int, 1>() instance
162    ///
163    /// \ref named-templ-param "Named parameter" for setting
164    /// the capacity map to a constMap<Edge, int, 1>() instance
165    struct SetUnitCapacity
166      : public NagamochiIbaraki<Graph, CapacityMap,
167                                SetUnitCapacityTraits> {
168      typedef NagamochiIbaraki<Graph, CapacityMap,
169                               SetUnitCapacityTraits> Create;
170    };
171
172
173    template <class H, class CR>
174    struct SetHeapTraits : public Traits {
175      typedef CR HeapCrossRef;
176      typedef H Heap;
177      static HeapCrossRef *createHeapCrossRef(int num) {
178        LEMON_ASSERT(false, "HeapCrossRef is not initialized");
179        return 0; // ignore warnings
180      }
181      static Heap *createHeap(HeapCrossRef &) {
182        LEMON_ASSERT(false, "Heap is not initialized");
183        return 0; // ignore warnings
184      }
185    };
186
187    /// \brief \ref named-templ-param "Named parameter" for setting
188    /// heap and cross reference type
189    ///
190    /// \ref named-templ-param "Named parameter" for setting heap and
191    /// cross reference type. The heap has to maximize the priorities.
192    template <class H, class CR = RangeMap<int> >
193    struct SetHeap
194      : public NagamochiIbaraki<Graph, CapacityMap, SetHeapTraits<H, CR> > {
195      typedef NagamochiIbaraki< Graph, CapacityMap, SetHeapTraits<H, CR> >
196      Create;
197    };
198
199    template <class H, class CR>
200    struct SetStandardHeapTraits : public Traits {
201      typedef CR HeapCrossRef;
202      typedef H Heap;
203      static HeapCrossRef *createHeapCrossRef(int size) {
204        return new HeapCrossRef(size);
205      }
206      static Heap *createHeap(HeapCrossRef &crossref) {
207        return new Heap(crossref);
208      }
209    };
210
211    /// \brief \ref named-templ-param "Named parameter" for setting
212    /// heap and cross reference type with automatic allocation
213    ///
214    /// \ref named-templ-param "Named parameter" for setting heap and
215    /// cross reference type with automatic allocation. They should
216    /// have standard constructor interfaces to be able to
217    /// automatically created by the algorithm (i.e. the graph should
218    /// be passed to the constructor of the cross reference and the
219    /// cross reference should be passed to the constructor of the
220    /// heap). However, external heap and cross reference objects
221    /// could also be passed to the algorithm using the \ref heap()
222    /// function before calling \ref run() or \ref init(). The heap
223    /// has to maximize the priorities.
224    /// \sa SetHeap
225    template <class H, class CR = RangeMap<int> >
226    struct SetStandardHeap
227      : public NagamochiIbaraki<Graph, CapacityMap,
228                                SetStandardHeapTraits<H, CR> > {
229      typedef NagamochiIbaraki<Graph, CapacityMap,
230                               SetStandardHeapTraits<H, CR> > Create;
231    };
232
233    ///@}
234
235
236  private:
237
238    const Graph &_graph;
239    const CapacityMap *_capacity;
240    bool _local_capacity; // unit capacity
241
242    struct ArcData {
243      typename Graph::Node target;
244      int prev, next;
245    };
246    struct EdgeData {
247      Value capacity;
248      Value cut;
249    };
250
251    struct NodeData {
252      int first_arc;
253      typename Graph::Node prev, next;
254      int curr_arc;
255      typename Graph::Node last_rep;
256      Value sum;
257    };
258
259    typename Graph::template NodeMap<NodeData> *_nodes;
260    std::vector<ArcData> _arcs;
261    std::vector<EdgeData> _edges;
262
263    typename Graph::Node _first_node;
264    int _node_num;
265
266    Value _min_cut;
267
268    HeapCrossRef *_heap_cross_ref;
269    bool _local_heap_cross_ref;
270    Heap *_heap;
271    bool _local_heap;
272
273    typedef typename Graph::template NodeMap<typename Graph::Node> NodeList;
274    NodeList *_next_rep;
275
276    typedef typename Graph::template NodeMap<bool> MinCutMap;
277    MinCutMap *_cut_map;
278
279    void createStructures() {
280      if (!_nodes) {
281        _nodes = new (typename Graph::template NodeMap<NodeData>)(_graph);
282      }
283      if (!_capacity) {
284        _local_capacity = true;
285        _capacity = Traits::createCapacityMap(_graph);
286      }
287      if (!_heap_cross_ref) {
288        _local_heap_cross_ref = true;
289        _heap_cross_ref = Traits::createHeapCrossRef(_graph);
290      }
291      if (!_heap) {
292        _local_heap = true;
293        _heap = Traits::createHeap(*_heap_cross_ref);
294      }
295      if (!_next_rep) {
296        _next_rep = new NodeList(_graph);
297      }
298      if (!_cut_map) {
299        _cut_map = new MinCutMap(_graph);
300      }
301    }
302
303  public :
304
305    typedef NagamochiIbaraki Create;
306
307
308    /// \brief Constructor.
309    ///
310    /// \param graph The graph the algorithm runs on.
311    /// \param capacity The capacity map used by the algorithm.
312    NagamochiIbaraki(const Graph& graph, const CapacityMap& capacity)
313      : _graph(graph), _capacity(&capacity), _local_capacity(false),
314        _nodes(0), _arcs(), _edges(), _min_cut(),
315        _heap_cross_ref(0), _local_heap_cross_ref(false),
316        _heap(0), _local_heap(false),
317        _next_rep(0), _cut_map(0) {}
318
319    /// \brief Constructor.
320    ///
321    /// This constructor can be used only when the Traits class
322    /// defines how can the local capacity map be instantiated.
323    /// If the SetUnitCapacity used the algorithm automatically
324    /// constructs the capacity map.
325    ///
326    ///\param graph The graph the algorithm runs on.
327    NagamochiIbaraki(const Graph& graph)
328      : _graph(graph), _capacity(0), _local_capacity(false),
329        _nodes(0), _arcs(), _edges(), _min_cut(),
330        _heap_cross_ref(0), _local_heap_cross_ref(false),
331        _heap(0), _local_heap(false),
332        _next_rep(0), _cut_map(0) {}
333
334    /// \brief Destructor.
335    ///
336    /// Destructor.
337    ~NagamochiIbaraki() {
338      if (_local_capacity) delete _capacity;
339      if (_nodes) delete _nodes;
340      if (_local_heap) delete _heap;
341      if (_local_heap_cross_ref) delete _heap_cross_ref;
342      if (_next_rep) delete _next_rep;
343      if (_cut_map) delete _cut_map;
344    }
345
346    /// \brief Sets the heap and the cross reference used by algorithm.
347    ///
348    /// Sets the heap and the cross reference used by algorithm.
349    /// If you don't use this function before calling \ref run(),
350    /// it will allocate one. The destuctor deallocates this
351    /// automatically allocated heap and cross reference, of course.
352    /// \return <tt> (*this) </tt>
353    NagamochiIbaraki &heap(Heap& hp, HeapCrossRef &cr)
354    {
355      if (_local_heap_cross_ref) {
356        delete _heap_cross_ref;
357        _local_heap_cross_ref = false;
358      }
359      _heap_cross_ref = &cr;
360      if (_local_heap) {
361        delete _heap;
362        _local_heap = false;
363      }
364      _heap = &hp;
365      return *this;
366    }
367
368    /// \name Execution control
369    /// The simplest way to execute the algorithm is to use
370    /// one of the member functions called \c run().
371    /// \n
372    /// If you need more control on the execution,
373    /// first you must call \ref init() and then call the start()
374    /// or proper times the processNextPhase() member functions.
375
376    ///@{
377
378    /// \brief Initializes the internal data structures.
379    ///
380    /// Initializes the internal data structures.
381    void init() {
382      createStructures();
383
384      int edge_num = countEdges(_graph);
385      _edges.resize(edge_num);
386      _arcs.resize(2 * edge_num);
387
388      typename Graph::Node prev = INVALID;
389      _node_num = 0;
390      for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
391        (*_cut_map)[n] = false;
392        (*_next_rep)[n] = INVALID;
393        (*_nodes)[n].last_rep = n;
394        (*_nodes)[n].first_arc = -1;
395        (*_nodes)[n].curr_arc = -1;
396        (*_nodes)[n].prev = prev;
397        if (prev != INVALID) {
398          (*_nodes)[prev].next = n;
399        }
400        (*_nodes)[n].next = INVALID;
401        (*_nodes)[n].sum = 0;
402        prev = n;
403        ++_node_num;
404      }
405
406      _first_node = typename Graph::NodeIt(_graph);
407
408      int index = 0;
409      for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
410        for (typename Graph::OutArcIt a(_graph, n); a != INVALID; ++a) {
411          typename Graph::Node m = _graph.target(a);
412         
413          if (!(n < m)) continue;
414
415          (*_nodes)[n].sum += (*_capacity)[a];
416          (*_nodes)[m].sum += (*_capacity)[a];
417         
418          int c = (*_nodes)[m].curr_arc;
419          if (c != -1 && _arcs[c ^ 1].target == n) {
420            _edges[c >> 1].capacity += (*_capacity)[a];
421          } else {
422            _edges[index].capacity = (*_capacity)[a];
423           
424            _arcs[index << 1].prev = -1;
425            if ((*_nodes)[n].first_arc != -1) {
426              _arcs[(*_nodes)[n].first_arc].prev = (index << 1);
427            }
428            _arcs[index << 1].next = (*_nodes)[n].first_arc;
429            (*_nodes)[n].first_arc = (index << 1);
430            _arcs[index << 1].target = m;
431
432            (*_nodes)[m].curr_arc = (index << 1);
433           
434            _arcs[(index << 1) | 1].prev = -1;
435            if ((*_nodes)[m].first_arc != -1) {
436              _arcs[(*_nodes)[m].first_arc].prev = ((index << 1) | 1);
437            }
438            _arcs[(index << 1) | 1].next = (*_nodes)[m].first_arc;
439            (*_nodes)[m].first_arc = ((index << 1) | 1);
440            _arcs[(index << 1) | 1].target = n;
441           
442            ++index;
443          }
444        }
445      }
446
447      typename Graph::Node cut_node = INVALID;
448      _min_cut = std::numeric_limits<Value>::max();
449
450      for (typename Graph::Node n = _first_node;
451           n != INVALID; n = (*_nodes)[n].next) {
452        if ((*_nodes)[n].sum < _min_cut) {
453          cut_node = n;
454          _min_cut = (*_nodes)[n].sum;
455        }
456      }
457      (*_cut_map)[cut_node] = true;
458      if (_min_cut == 0) {
459        _first_node = INVALID;
460      }
461    }
462
463  public:
464
465    /// \brief Processes the next phase
466    ///
467    /// Processes the next phase in the algorithm. It must be called
468    /// at most one less the number of the nodes in the graph.
469    ///
470    ///\return %True when the algorithm finished.
471    bool processNextPhase() {
472      if (_first_node == INVALID) return true;
473
474      _heap->clear();
475      for (typename Graph::Node n = _first_node;
476           n != INVALID; n = (*_nodes)[n].next) {
477        (*_heap_cross_ref)[n] = Heap::PRE_HEAP;
478      }
479
480      std::vector<typename Graph::Node> order;
481      order.reserve(_node_num);
482      int sep = 0;
483
484      Value alpha = 0;
485      Value pmc = std::numeric_limits<Value>::max();
486
487      _heap->push(_first_node, static_cast<Value>(0));
488      while (!_heap->empty()) {
489        typename Graph::Node n = _heap->top();
490        Value v = _heap->prio();
491
492        _heap->pop();
493        for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) {
494          switch (_heap->state(_arcs[a].target)) {
495          case Heap::PRE_HEAP:
496            {
497              Value nv = _edges[a >> 1].capacity;
498              _heap->push(_arcs[a].target, nv);
499              _edges[a >> 1].cut = nv;
500            } break;
501          case Heap::IN_HEAP:
502            {
503              Value nv = _edges[a >> 1].capacity + (*_heap)[_arcs[a].target];
504              _heap->decrease(_arcs[a].target, nv);
505              _edges[a >> 1].cut = nv;
506            } break;
507          case Heap::POST_HEAP:
508            break;
509          }
510        }
511
512        alpha += (*_nodes)[n].sum;
513        alpha -= 2 * v;
514
515        order.push_back(n);
516        if (!_heap->empty()) {
517          if (alpha < pmc) {
518            pmc = alpha;
519            sep = order.size();
520          }
521        }
522      }
523
524      if (static_cast<int>(order.size()) < _node_num) {
525        _first_node = INVALID;
526        for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
527          (*_cut_map)[n] = false;
528        }
529        for (int i = 0; i < static_cast<int>(order.size()); ++i) {
530          typename Graph::Node n = order[i];
531          while (n != INVALID) {
532            (*_cut_map)[n] = true;
533            n = (*_next_rep)[n];
534          }
535        }
536        _min_cut = 0;
537        return true;
538      }
539
540      if (pmc < _min_cut) {
541        for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
542          (*_cut_map)[n] = false;
543        }
544        for (int i = 0; i < sep; ++i) {
545          typename Graph::Node n = order[i];
546          while (n != INVALID) {
547            (*_cut_map)[n] = true;
548            n = (*_next_rep)[n];
549          }
550        }
551        _min_cut = pmc;
552      }
553
554      for (typename Graph::Node n = _first_node;
555           n != INVALID; n = (*_nodes)[n].next) {
556        bool merged = false;
557        for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) {
558          if (!(_edges[a >> 1].cut < pmc)) {
559            if (!merged) {
560              for (int b = (*_nodes)[n].first_arc; b != -1; b = _arcs[b].next) {
561                (*_nodes)[_arcs[b].target].curr_arc = b;         
562              }
563              merged = true;
564            }
565            typename Graph::Node m = _arcs[a].target;
566            int nb = 0;
567            for (int b = (*_nodes)[m].first_arc; b != -1; b = nb) {
568              nb = _arcs[b].next;
569              if ((b ^ a) == 1) continue;
570              typename Graph::Node o = _arcs[b].target;
571              int c = (*_nodes)[o].curr_arc;
572              if (c != -1 && _arcs[c ^ 1].target == n) {
573                _edges[c >> 1].capacity += _edges[b >> 1].capacity;
574                (*_nodes)[n].sum += _edges[b >> 1].capacity;
575                if (_edges[b >> 1].cut < _edges[c >> 1].cut) {
576                  _edges[b >> 1].cut = _edges[c >> 1].cut;
577                }
578                if (_arcs[b ^ 1].prev != -1) {
579                  _arcs[_arcs[b ^ 1].prev].next = _arcs[b ^ 1].next;
580                } else {
581                  (*_nodes)[o].first_arc = _arcs[b ^ 1].next;
582                }
583                if (_arcs[b ^ 1].next != -1) {
584                  _arcs[_arcs[b ^ 1].next].prev = _arcs[b ^ 1].prev;
585                }
586              } else {
587                if (_arcs[a].next != -1) {
588                  _arcs[_arcs[a].next].prev = b;
589                }
590                _arcs[b].next = _arcs[a].next;
591                _arcs[b].prev = a;
592                _arcs[a].next = b;
593                _arcs[b ^ 1].target = n;
594
595                (*_nodes)[n].sum += _edges[b >> 1].capacity;
596                (*_nodes)[o].curr_arc = b;
597              }
598            }
599
600            if (_arcs[a].prev != -1) {
601              _arcs[_arcs[a].prev].next = _arcs[a].next;
602            } else {
603              (*_nodes)[n].first_arc = _arcs[a].next;
604            }           
605            if (_arcs[a].next != -1) {
606              _arcs[_arcs[a].next].prev = _arcs[a].prev;
607            }
608
609            (*_nodes)[n].sum -= _edges[a >> 1].capacity;
610            (*_next_rep)[(*_nodes)[n].last_rep] = m;
611            (*_nodes)[n].last_rep = (*_nodes)[m].last_rep;
612           
613            if ((*_nodes)[m].prev != INVALID) {
614              (*_nodes)[(*_nodes)[m].prev].next = (*_nodes)[m].next;
615            } else{
616              _first_node = (*_nodes)[m].next;
617            }
618            if ((*_nodes)[m].next != INVALID) {
619              (*_nodes)[(*_nodes)[m].next].prev = (*_nodes)[m].prev;
620            }
621            --_node_num;
622          }
623        }
624      }
625
626      if (_node_num == 1) {
627        _first_node = INVALID;
628        return true;
629      }
630
631      return false;
632    }
633
634    /// \brief Executes the algorithm.
635    ///
636    /// Executes the algorithm.
637    ///
638    /// \pre init() must be called
639    void start() {
640      while (!processNextPhase()) {}
641    }
642
643
644    /// \brief Runs %NagamochiIbaraki algorithm.
645    ///
646    /// This method runs the %Min cut algorithm
647    ///
648    /// \note mc.run(s) is just a shortcut of the following code.
649    ///\code
650    ///  mc.init();
651    ///  mc.start();
652    ///\endcode
653    void run() {
654      init();
655      start();
656    }
657
658    ///@}
659
660    /// \name Query Functions
661    ///
662    /// The result of the %NagamochiIbaraki
663    /// algorithm can be obtained using these functions.\n
664    /// Before the use of these functions, either run() or start()
665    /// must be called.
666
667    ///@{
668
669    /// \brief Returns the min cut value.
670    ///
671    /// Returns the min cut value if the algorithm finished.
672    /// After the first processNextPhase() it is a value of a
673    /// valid cut in the graph.
674    Value minCutValue() const {
675      return _min_cut;
676    }
677
678    /// \brief Returns a min cut in a NodeMap.
679    ///
680    /// It sets the nodes of one of the two partitions to true and
681    /// the other partition to false.
682    /// \param cutMap A \ref concepts::WriteMap "writable" node map with
683    /// \c bool (or convertible) value type.
684    template <typename CutMap>
685    Value minCutMap(CutMap& cutMap) const {
686      for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
687        cutMap.set(n, (*_cut_map)[n]);
688      }
689      return minCutValue();
690    }
691
692    ///@}
693
694  };
695}
696
697#endif
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