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SearchTree.hh
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28 
29 
30 #ifndef __FASTJET_SEARCHTREE_HH__
31 #define __FASTJET_SEARCHTREE_HH__
32 
33 #include<vector>
34 #include<cassert>
35 #include<cstddef>
36 #include "fastjet/internal/base.hh"
37 
38 FASTJET_BEGIN_NAMESPACE // defined in fastjet/internal/base.hh
39 
40 
41 //======================================================================
42 /// \if internal_doc
43 /// @ingroup internal
44 /// \class SearchTree
45 /// Efficient class for a search tree
46 ///
47 /// This is the class for a search tree designed to be especially efficient
48 /// when looking for successors and predecessors (to be used in Chan's
49 /// CP algorithm). It has the requirement that the maximum size of the
50 /// search tree must be known in advance.
51 /// \endif
52 template<class T> class SearchTree {
53 public:
54 
55  class Node;
56  class circulator;
57  class const_circulator;
58 
59  /// constructor for a search tree from an ordered vector
60  SearchTree(const std::vector<T> & init);
61 
62  /// constructor for a search tree from an ordered vector allowing
63  /// for future growth beyond the current size, up to max_size
64  SearchTree(const std::vector<T> & init, unsigned int max_size);
65 
66  /// remove the node corresponding to node_index from the search tree
67  void remove(unsigned node_index);
68  void remove(typename SearchTree::Node * node);
69  void remove(typename SearchTree::circulator & circ);
70 
71  /// insert the supplied value into the tree and return a pointer to
72  /// the relevant SearchTreeNode.
73  //Node * insert(const T & value);
74  circulator insert(const T & value);
75 
76  const Node & operator[](int i) const {return _nodes[i];};
77 
78  /// return the number of elements currently in the search tree
79  unsigned int size() const {return _nodes.size() - _available_nodes.size();}
80 
81  /// check that the structure we've obtained makes sense...
82  void verify_structure();
83  void verify_structure_linear() const;
84  void verify_structure_recursive(const Node * , const Node * , const Node * ) const;
85 
86  /// print out all elements...
87  void print_elements();
88 
89  // tracking the depth may have some speed overhead -- so leave it
90  // out for the time being...
91 #ifdef TRACK_DEPTH
92  /// the max depth the tree has ever reached
93  inline unsigned int max_depth() const {return _max_depth;};
94 #else
95  inline unsigned int max_depth() const {return 0;};
96 #endif
97 
98  int loc(const Node * node) const ;
99 
100  /// return predecessor by walking through the tree
101  Node * _find_predecessor(const Node *);
102  /// return successor by walking through the tree
103  Node * _find_successor(const Node *);
104 
105  const Node & operator[](unsigned int i) const {return _nodes[i];};
106 
107  /// return a circulator to some place in the tree (with a circulator
108  /// you don't care where...)
109  const_circulator somewhere() const;
110  circulator somewhere();
111 
112 private:
113 
114  void _initialize(const std::vector<T> & init);
115 
116  std::vector<Node> _nodes;
117  std::vector<Node *> _available_nodes;
118  Node * _top_node;
119  unsigned int _n_removes;
120 
121 
122  /// recursive routine for doing the initial connections assuming things
123  /// are ordered. Assumes this_one's parent is labelled, and was
124  /// generated at a scale "scale" -- connections will be carried out
125  /// including left edge and excluding right edge
126  void _do_initial_connections(unsigned int this_one, unsigned int scale,
127  unsigned int left_edge, unsigned int right_edge,
128  unsigned int depth);
129 
130 
131 #ifdef TRACK_DEPTH
132  unsigned int _max_depth;
133 #endif
134 
135 };
136 
137 
138 //======================================================================
139 /// \if internal_doc
140 /// @ingroup internal
141 /// \class SearchTree::Node
142 /// A node in the search tree
143 /// \endif
144 template<class T> class SearchTree<T>::Node{
145 public:
146  Node() {}; /// default constructor
147 
148 
149  /// returns tree if all the tree-related links are set to null for this node
150  bool treelinks_null() const {
151  return ((parent==0) && (left==0) && (right==0));};
152 
153  /// set all the tree-related links are set to null for this node
154  inline void nullify_treelinks() {
155  parent = NULL;
156  left = NULL;
157  right = NULL;
158  };
159 
160  /// if my parent exists, determine whether I am it's left or right
161  /// node and set the relevant link equal to XX.
162  void reset_parents_link_to_me(Node * XX);
163 
164  T value;
165  Node * left;
166  Node * right;
167  Node * parent;
168  Node * successor;
169  Node * predecessor;
170 };
171 
172 //----------------------------------------------------------------------
173 template<class T> void SearchTree<T>::Node::reset_parents_link_to_me(typename SearchTree<T>::Node * XX) {
174  if (parent == NULL) {return;}
175  if (parent->right == this) {parent->right = XX;}
176  else {parent->left = XX;}
177 }
178 
179 
180 
181 //======================================================================
182 /// \if internal_doc
183 /// @ingroup internal
184 /// \class SearchTree::circulator
185 /// circulator for the search tree
186 /// \endif
187 template<class T> class SearchTree<T>::circulator{
188 public:
189 
190  // so that it can access out _node object;
191  friend class SearchTree<T>::const_circulator;
192  friend class SearchTree<T>;
193 
194  circulator() : _node(NULL) {}
195 
196  circulator(Node * node) : _node(node) {}
197 
198  const T * operator->() const {return &(_node->value);}
199  T * operator->() {return &(_node->value);}
200  const T & operator*() const {return _node->value;}
201  T & operator*() {return _node->value;}
202 
203  /// prefix increment (structure copied from stl_bvector.h)
204  circulator & operator++() {
205  _node = _node->successor;
206  return *this;}
207 
208  /// postfix increment ["int" argument tells compiler it's postfix]
209  /// (structure copied from stl_bvector.h)
210  circulator operator++(int) {
211  circulator tmp = *this;
212  _node = _node->successor;
213  return tmp;}
214 
215  /// prefix decrement (structure copied from stl_bvector.h)
216  circulator & operator--() {
217  _node = _node->predecessor;
218  return *this;}
219 
220  /// postfix decrement ["int" argument tells compiler it's postfix]
221  /// (structure copied from stl_bvector.h)
222  circulator operator--(int) {
223  circulator tmp = *this;
224  _node = _node->predecessor;
225  return tmp;}
226 
227  /// return a circulator referring to the next node
228  circulator next() const {
229  return circulator(_node->successor);}
230 
231  /// return a circulator referring to the previous node
232  circulator previous() const {
233  return circulator(_node->predecessor);}
234 
235  bool operator!=(const circulator & other) const {return other._node != _node;}
236  bool operator==(const circulator & other) const {return other._node == _node;}
237 
238 private:
239  Node * _node;
240 };
241 
242 
243 //======================================================================
244 /// \if internal_doc
245 /// @ingroup internal
246 /// \class SearchTree::const_circulator
247 /// A const_circulator for the search tree
248 /// \endif
249 template<class T> class SearchTree<T>::const_circulator{
250 public:
251 
252  const_circulator() : _node(NULL) {}
253 
254  const_circulator(const Node * node) : _node(node) {}
255  const_circulator(const circulator & circ) :_node(circ._node) {}
256 
257  const T * operator->() {return &(_node->value);}
258  const T & operator*() const {return _node->value;}
259 
260  /// prefix increment (structure copied from stl_bvector.h)
261  const_circulator & operator++() {
262  _node = _node->successor;
263  return *this;}
264 
265  /// postfix increment ["int" argument tells compiler it's postfix]
266  /// (structure copied from stl_bvector.h)
267  const_circulator operator++(int) {
268  const_circulator tmp = *this;
269  _node = _node->successor;
270  return tmp;}
271 
272 
273  /// prefix decrement (structure copied from stl_bvector.h)
274  const_circulator & operator--() {
275  _node = _node->predecessor;
276  return *this;}
277 
278  /// postfix decrement ["int" argument tells compiler it's postfix]
279  /// (structure copied from stl_bvector.h)
280  const_circulator operator--(int) {
281  const_circulator tmp = *this;
282  _node = _node->predecessor;
283  return tmp;}
284 
285  /// return a circulator referring to the next node
286  const_circulator next() const {
287  return const_circulator(_node->successor);}
288 
289  /// return a circulator referring to the previous node
290  const_circulator previous() const {
291  return const_circulator(_node->predecessor);}
292 
293 
294 
295  bool operator!=(const const_circulator & other) const {return other._node != _node;}
296  bool operator==(const const_circulator & other) const {return other._node == _node;}
297 
298 private:
299  const Node * _node;
300 };
301 
302 
303 
304 
305 //----------------------------------------------------------------------
306 /// initialise from a sorted initial array allowing for a larger
307 /// maximum size of the array...
308 template<class T> SearchTree<T>::SearchTree(const std::vector<T> & init,
309  unsigned int max_size) :
310  _nodes(max_size) {
311 
312  _available_nodes.reserve(max_size);
313  _available_nodes.resize(max_size - init.size());
314  for (unsigned int i = init.size(); i < max_size; i++) {
315  _available_nodes[i-init.size()] = &(_nodes[i]);
316  }
317 
318  _initialize(init);
319 }
320 
321 //----------------------------------------------------------------------
322 /// initialise from a sorted initial array
323 template<class T> SearchTree<T>::SearchTree(const std::vector<T> & init) :
324  _nodes(init.size()), _available_nodes(0) {
325 
326  // reserve space for the list of available nodes
327  _available_nodes.reserve(init.size());
328  _initialize(init);
329 }
330 
331 //----------------------------------------------------------------------
332 /// do the actual hard work of initialization
333 template<class T> void SearchTree<T>::_initialize(const std::vector<T> & init) {
334 
335  _n_removes = 0;
336  unsigned n = init.size();
337  assert(n>=1);
338 
339  // reserve space for the list of available nodes
340  //_available_nodes.reserve();
341 
342 #ifdef TRACK_DEPTH
343  _max_depth = 0;
344 #endif
345 
346 
347  // validate the input
348  for (unsigned int i = 1; i<n; i++) {
349  assert(!(init[i] < init[i-1]));
350  }
351 
352  // now initialise the vector; link neighbours in the sequence
353  for(unsigned int i = 0; i < n; i++) {
354  _nodes[i].value = init[i];
355  _nodes[i].predecessor = (& (_nodes[i])) - 1;
356  _nodes[i].successor = (& (_nodes[i])) + 1;
357  _nodes[i].nullify_treelinks();
358  }
359  // make a loop structure so that we can circulate...
360  _nodes[0].predecessor = (& (_nodes[n-1]));
361  _nodes[n-1].successor = (& (_nodes[0]));
362 
363  // now label the rest of the nodes
364  unsigned int scale = (n+1)/2;
365  unsigned int top = std::min(n-1,scale);
366  _nodes[top].parent = NULL;
367  _top_node = &(_nodes[top]);
368  _do_initial_connections(top, scale, 0, n, 0);
369 
370  // make sure things are sensible...
371  //verify_structure();
372 }
373 
374 
375 
376 //----------------------------------------------------------------------
377 template<class T> inline int SearchTree<T>::loc(const Node * node) const {return node == NULL?
378  -999 : node - &(_nodes[0]);}
379 
380 
381 //----------------------------------------------------------------------
382 /// Recursive creation of connections, assuming the _nodes vector is
383 /// completely filled and ordered
384 template<class T> void SearchTree<T>::_do_initial_connections(
385  unsigned int this_one,
386  unsigned int scale,
387  unsigned int left_edge,
388  unsigned int right_edge,
389  unsigned int depth
390  ) {
391 
392 #ifdef TRACK_DEPTH
393  // keep track of tree depth for checking things stay reasonable...
394  _max_depth = max(depth, _max_depth);
395 #endif
396 
397  //std::cout << this_one << " "<< scale<< std::endl;
398  unsigned int ref_new_scale = (scale+1)/2;
399 
400  // work through children to our left
401  unsigned new_scale = ref_new_scale;
402  bool did_child = false;
403  while(true) {
404  int left = this_one - new_scale; // be careful here to use signed int...
405  // if there is something unitialised to our left, link to it
406  if (left >= static_cast<int>(left_edge)
407  && _nodes[left].treelinks_null() ) {
408  _nodes[left].parent = &(_nodes[this_one]);
409  _nodes[this_one].left = &(_nodes[left]);
410  // create connections between left_edge and this_one
411  _do_initial_connections(left, new_scale, left_edge, this_one, depth+1);
412  did_child = true;
413  break;
414  }
415  // reduce the scale so as to try again
416  unsigned int old_new_scale = new_scale;
417  new_scale = (old_new_scale + 1)/2;
418  // unless we've reached end of tree
419  if (new_scale == old_new_scale) break;
420  }
421  if (!did_child) {_nodes[this_one].left = NULL;}
422 
423 
424  // work through children to our right
425  new_scale = ref_new_scale;
426  did_child = false;
427  while(true) {
428  unsigned int right = this_one + new_scale;
429  if (right < right_edge && _nodes[right].treelinks_null()) {
430  _nodes[right].parent = &(_nodes[this_one]);
431  _nodes[this_one].right = &(_nodes[right]);
432  // create connections between this_one+1 and right_edge
433  _do_initial_connections(right, new_scale, this_one+1,right_edge,depth+1);
434  did_child = true;
435  break;
436  }
437  // reduce the scale so as to try again
438  unsigned int old_new_scale = new_scale;
439  new_scale = (old_new_scale + 1)/2;
440  // unless we've reached end of tree
441  if (new_scale == old_new_scale) break;
442  }
443  if (!did_child) {_nodes[this_one].right = NULL;}
444 
445 }
446 
447 
448 
449 //----------------------------------------------------------------------
450 template<class T> void SearchTree<T>::remove(unsigned int node_index) {
451  remove(&(_nodes[node_index]));
452 }
453 
454 //----------------------------------------------------------------------
455 template<class T> void SearchTree<T>::remove(circulator & circ) {
456  remove(circ._node);
457 }
458 
459 //----------------------------------------------------------------------
460 // Useful reference for this:
461 // http://en.wikipedia.org/wiki/Binary_search_tree#Deletion
462 template<class T> void SearchTree<T>::remove(typename SearchTree<T>::Node * node) {
463 
464  // we don't remove things from the tree if we've reached the last
465  // elements... (is this wise?)
466  assert(size() > 1); // switch this to throw...?
467  assert(!node->treelinks_null());
468 
469  // deal with relinking predecessor and successor
470  node->predecessor->successor = node->successor;
471  node->successor->predecessor = node->predecessor;
472 
473  if (node->left == NULL && node->right == NULL) {
474  // node has no children, so remove it by nullifying the pointer
475  // from the parent
476  node->reset_parents_link_to_me(NULL);
477 
478  } else if (node->left != NULL && node->right == NULL){
479  // make parent point to my child
480  node->reset_parents_link_to_me(node->left);
481  // and child to parent
482  node->left->parent = node->parent;
483  // sort out the top node...
484  if (_top_node == node) {_top_node = node->left;}
485 
486  } else if (node->left == NULL && node->right != NULL){
487  // make parent point to my child
488  node->reset_parents_link_to_me(node->right);
489  // and child to parent
490  node->right->parent = node->parent;
491  // sort out the top node...
492  if (_top_node == node) {_top_node = node->right;}
493 
494  } else {
495  // we have two children; we will put a replacement in our place
496  Node * replacement;
497  //SearchTree<T>::Node * replacements_child;
498  // chose predecessor or successor (one, then other, then first, etc...)
499  bool use_predecessor = (_n_removes % 2 == 1);
500  if (use_predecessor) {
501  // Option 1: put predecessor in our place, and have its parent
502  // point to its left child (as a predecessor it has no right child)
503  replacement = node->predecessor;
504  assert(replacement->right == NULL); // guaranteed if it's our predecessor
505  // we have to be careful of replacing certain links when the
506  // replacement is this node's child
507  if (replacement != node->left) {
508  if (replacement->left != NULL) {
509  replacement->left->parent = replacement->parent;}
510  replacement->reset_parents_link_to_me(replacement->left);
511  replacement->left = node->left;
512  }
513  replacement->parent = node->parent;
514  replacement->right = node->right;
515  } else {
516  // Option 2: put successor in our place, and have its parent
517  // point to its right child (as a successor it has no left child)
518  replacement = node->successor;
519  assert(replacement->left == NULL); // guaranteed if it's our successor
520  if (replacement != node->right) {
521  if (replacement->right != NULL) {
522  replacement->right->parent = replacement->parent;}
523  replacement->reset_parents_link_to_me(replacement->right);
524  replacement->right = node->right;
525  }
526  replacement->parent = node->parent;
527  replacement->left = node->left;
528  }
529  node->reset_parents_link_to_me(replacement);
530 
531  // make sure node's original children now point to the replacement
532  if (node->left != replacement) {node->left->parent = replacement;}
533  if (node->right != replacement) {node->right->parent = replacement;}
534 
535  // sort out the top node...
536  if (_top_node == node) {_top_node = replacement;}
537  }
538 
539  // make sure we leave something nice and clean...
540  node->nullify_treelinks();
541  node->predecessor = NULL;
542  node->successor = NULL;
543 
544  // for bookkeeping (and choosing whether to use pred. or succ.)
545  _n_removes++;
546  // for when we next need access to a free node...
547  _available_nodes.push_back(node);
548 }
549 
550 
551 //----------------------------------------------------------------------
552 //template<class T> typename SearchTree<T>::Node * SearchTree<T>::insert(const T & value) {
553 
554 //----------------------------------------------------------------------
555 template<class T> typename SearchTree<T>::circulator SearchTree<T>::insert(const T & value) {
556  // make sure we don't exceed allowed number of nodes...
557  assert(_available_nodes.size() > 0);
558 
559  Node * node = _available_nodes.back();
560  _available_nodes.pop_back();
561  node->value = value;
562 
563  Node * location = _top_node;
564  Node * old_location = NULL;
565  bool on_left = true; // (init not needed -- but soothes g++4)
566  // work through tree until we reach its end
567 #ifdef TRACK_DEPTH
568  unsigned int depth = 0;
569 #endif
570  while(location != NULL) {
571 #ifdef TRACK_DEPTH
572  depth++;
573 #endif
574  old_location = location;
575  on_left = value < location->value;
576  if (on_left) {location = location->left;}
577  else {location = location->right;}
578  }
579 #ifdef TRACK_DEPTH
580  _max_depth = max(depth, _max_depth);
581 #endif
582  // now create tree links
583  node->parent = old_location;
584  if (on_left) {node->parent->left = node;}
585  else {node->parent->right = node;}
586  node->left = NULL;
587  node->right = NULL;
588  // and create predecessor / successor links
589  node->predecessor = _find_predecessor(node);
590  if (node->predecessor != NULL) {
591  // it exists, so make use of its info (will include a cyclic case,
592  // when successor is round the bend)
593  node->successor = node->predecessor->successor;
594  node->predecessor->successor = node;
595  node->successor->predecessor = node;
596  } else {
597  // deal with case when we are left-most edge of tree (then successor
598  // will exist...)
599  node->successor = _find_successor(node);
600  assert(node->successor != NULL); // can only happen if we're sole element
601  // (but not allowed, since tree size>=1)
602  node->predecessor = node->successor->predecessor;
603  node->successor->predecessor = node;
604  node->predecessor->successor = node;
605  }
606 
607  return circulator(node);
608 }
609 
610 
611 //----------------------------------------------------------------------
612 template<class T> void SearchTree<T>::verify_structure() {
613 
614  // do a check running through all elements
615  verify_structure_linear();
616 
617  // do a recursive check down tree from top
618 
619  // first establish the extremities
620  const Node * left_limit = _top_node;
621  while (left_limit->left != NULL) {left_limit = left_limit->left;}
622  const Node * right_limit = _top_node;
623  while (right_limit->right != NULL) {right_limit = right_limit->right;}
624 
625  // then actually do recursion
626  verify_structure_recursive(_top_node, left_limit, right_limit);
627 }
628 
629 
630 //----------------------------------------------------------------------
631 template<class T> void SearchTree<T>::verify_structure_recursive(
632  const typename SearchTree<T>::Node * element,
633  const typename SearchTree<T>::Node * left_limit,
634  const typename SearchTree<T>::Node * right_limit) const {
635 
636  assert(!(element->value < left_limit->value));
637  assert(!(right_limit->value < element->value));
638 
639  const Node * left = element->left;
640  if (left != NULL) {
641  assert(!(element->value < left->value));
642  if (left != left_limit) {
643  // recurse down the tree with this element as the right-hand limit
644  verify_structure_recursive(left, left_limit, element);}
645  }
646 
647  const Node * right = element->right;
648  if (right != NULL) {
649  assert(!(right->value < element->value));
650  if (right != right_limit) {
651  // recurse down the tree with this element as the left-hand limit
652  verify_structure_recursive(right, element, right_limit);}
653  }
654 }
655 
656 //----------------------------------------------------------------------
657 template<class T> void SearchTree<T>::verify_structure_linear() const {
658 
659  //print_elements();
660 
661  unsigned n_top = 0;
662  unsigned n_null = 0;
663  for(unsigned i = 0; i < _nodes.size(); i++) {
664  const typename SearchTree<T>::Node * node = &(_nodes[i]);
665  // make sure node is defined
666  if (node->treelinks_null()) {n_null++; continue;}
667 
668  // make sure of the number of "top" nodes
669  if (node->parent == NULL) {
670  n_top++;
671  //assert(node->left != NULL);
672  //assert(node->right != NULL);
673  } else {
674  // make sure that I am a child of my parent...
675  //assert((node->parent->left == node) || (node->parent->right == node));
676  assert((node->parent->left == node) ^ (node->parent->right == node));
677  }
678 
679  // when there is a left child make sure it's value is ordered
680  // (note use of !(b<a), to allow for a<=b while using just the <
681  // operator)
682  if (node->left != NULL) {
683  assert(!(node->value < node->left->value ));}
684 
685  // when there is a right child make sure it's value is ordered
686  if (node->right != NULL) {
687  assert(!(node->right->value < node->value ));}
688 
689  }
690  assert(n_top == 1 || (n_top == 0 && size() <= 1) );
691  assert(n_null == _available_nodes.size() ||
692  (n_null == _available_nodes.size() + 1 && size() == 1));
693 }
694 
695 
696 //----------------------------------------------------------------------
697 template<class T> typename SearchTree<T>::Node * SearchTree<T>::_find_predecessor(const typename SearchTree<T>::Node * node) {
698 
699  typename SearchTree<T>::Node * newnode;
700  if (node->left != NULL) {
701  // go down left, and then down right as far as possible.
702  newnode = node->left;
703  while(newnode->right != NULL) {newnode = newnode->right;}
704  return newnode;
705  } else {
706  const typename SearchTree<T>::Node * lastnode = node;
707  newnode = node->parent;
708  // go up the tree as long as we're going right (when we go left then
709  // we've found something smaller, so stop)
710  while(newnode != NULL) {
711  if (newnode->right == lastnode) {return newnode;}
712  lastnode = newnode;
713  newnode = newnode->parent;
714  }
715  return newnode;
716  }
717 }
718 
719 
720 //----------------------------------------------------------------------
721 template<class T> typename SearchTree<T>::Node * SearchTree<T>::_find_successor(const typename SearchTree<T>::Node * node) {
722 
723  typename SearchTree<T>::Node * newnode;
724  if (node->right != NULL) {
725  // go down right, and then down left as far as possible.
726  newnode = node->right;
727  while(newnode->left != NULL) {newnode = newnode->left;}
728  return newnode;
729  } else {
730  const typename SearchTree<T>::Node * lastnode = node;
731  newnode = node->parent;
732  // go up the tree as long as we're going left (when we go right then
733  // we've found something larger, so stop)
734  while(newnode != NULL) {
735  if (newnode->left == lastnode) {return newnode;}
736  lastnode = newnode;
737  newnode = newnode->parent;
738  }
739  return newnode;
740  }
741 }
742 
743 
744 //----------------------------------------------------------------------
745 // print out all the elements for visual checking...
746 template<class T> void SearchTree<T>::print_elements() {
747  typename SearchTree<T>::Node * base_node = &(_nodes[0]);
748  typename SearchTree<T>::Node * node = base_node;
749 
750  int n = _nodes.size();
751  for(; node - base_node < n ; node++) {
752  printf("%4d parent:%4d left:%4d right:%4d pred:%4d succ:%4d value:%10.6f\n",loc(node), loc(node->parent), loc(node->left), loc(node->right), loc(node->predecessor),loc(node->successor),node->value);
753  }
754 }
755 
756 //----------------------------------------------------------------------
757 template<class T> typename SearchTree<T>::circulator SearchTree<T>::somewhere() {
758  return circulator(_top_node);
759 }
760 
761 
762 //----------------------------------------------------------------------
763 template<class T> typename SearchTree<T>::const_circulator SearchTree<T>::somewhere() const {
764  return const_circulator(_top_node);
765 }
766 
767 
768 FASTJET_END_NAMESPACE
769 
770 #endif // __FASTJET_SEARCHTREE_HH__