OpenTTD Source  20241108-master-g80f628063a
kdtree.hpp
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1 /*
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4  * OpenTTD is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
5  * See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with OpenTTD. If not, see <http://www.gnu.org/licenses/>.
6  */
7 
10 #ifndef KDTREE_HPP
11 #define KDTREE_HPP
12 
13 #include "../stdafx.h"
14 
34 template <typename T, typename TxyFunc, typename CoordT, typename DistT>
35 class Kdtree {
37  struct node {
38  T element;
39  size_t left;
40  size_t right;
41 
43  };
44 
45  static const size_t INVALID_NODE = SIZE_MAX;
46 
47  std::vector<node> nodes;
48  std::vector<size_t> free_list;
49  size_t root;
50  TxyFunc xyfunc;
51  size_t unbalanced;
52 
54  size_t AddNode(const T &element)
55  {
56  if (this->free_list.empty()) {
57  this->nodes.emplace_back(element);
58  return this->nodes.size() - 1;
59  } else {
60  size_t newidx = this->free_list.back();
61  this->free_list.pop_back();
62  this->nodes[newidx] = node{ element };
63  return newidx;
64  }
65  }
66 
68  template <typename It>
69  CoordT SelectSplitCoord(It begin, It end, int level)
70  {
71  It mid = begin + (end - begin) / 2;
72  std::nth_element(begin, mid, end, [&](T a, T b) { return this->xyfunc(a, level % 2) < this->xyfunc(b, level % 2); });
73  return this->xyfunc(*mid, level % 2);
74  }
75 
77  template <typename It>
78  size_t BuildSubtree(It begin, It end, int level)
79  {
80  ptrdiff_t count = end - begin;
81 
82  if (count == 0) {
83  return INVALID_NODE;
84  } else if (count == 1) {
85  return this->AddNode(*begin);
86  } else if (count > 1) {
87  CoordT split_coord = SelectSplitCoord(begin, end, level);
88  It split = std::partition(begin, end, [&](T v) { return this->xyfunc(v, level % 2) < split_coord; });
89  size_t newidx = this->AddNode(*split);
90  this->nodes[newidx].left = this->BuildSubtree(begin, split, level + 1);
91  this->nodes[newidx].right = this->BuildSubtree(split + 1, end, level + 1);
92  return newidx;
93  } else {
94  NOT_REACHED();
95  }
96  }
97 
99  bool Rebuild(const T *include_element, const T *exclude_element)
100  {
101  size_t initial_count = this->Count();
102  if (initial_count < 8) return false; // arbitrary value for "not worth rebalancing"
103 
104  T root_element = this->nodes[this->root].element;
105  std::vector<T> elements = this->FreeSubtree(this->root);
106  elements.push_back(root_element);
107 
108  if (include_element != nullptr) {
109  elements.push_back(*include_element);
110  initial_count++;
111  }
112  if (exclude_element != nullptr) {
113  typename std::vector<T>::iterator removed = std::remove(elements.begin(), elements.end(), *exclude_element);
114  elements.erase(removed, elements.end());
115  initial_count--;
116  }
117 
118  this->Build(elements.begin(), elements.end());
119  assert(initial_count == this->Count());
120  return true;
121  }
122 
124  void InsertRecursive(const T &element, size_t node_idx, int level)
125  {
126  /* Dimension index of current level */
127  int dim = level % 2;
128  /* Node reference */
129  node &n = this->nodes[node_idx];
130 
131  /* Coordinate of element splitting at this node */
132  CoordT nc = this->xyfunc(n.element, dim);
133  /* Coordinate of the new element */
134  CoordT ec = this->xyfunc(element, dim);
135  /* Which side to insert on */
136  size_t &next = (ec < nc) ? n.left : n.right;
137 
138  if (next == INVALID_NODE) {
139  /* New leaf */
140  size_t newidx = this->AddNode(element);
141  /* Vector may have been reallocated at this point, n and next are invalid */
142  node &nn = this->nodes[node_idx];
143  if (ec < nc) nn.left = newidx; else nn.right = newidx;
144  } else {
145  this->InsertRecursive(element, next, level + 1);
146  }
147  }
148 
153  std::vector<T> FreeSubtree(size_t node_idx)
154  {
155  std::vector<T> subtree_elements;
156  node &n = this->nodes[node_idx];
157 
158  /* We'll be appending items to the free_list, get index of our first item */
159  size_t first_free = this->free_list.size();
160  /* Prepare the descent with our children */
161  if (n.left != INVALID_NODE) this->free_list.push_back(n.left);
162  if (n.right != INVALID_NODE) this->free_list.push_back(n.right);
163  n.left = n.right = INVALID_NODE;
164 
165  /* Recursively free the nodes being collected */
166  for (size_t i = first_free; i < this->free_list.size(); i++) {
167  node &fn = this->nodes[this->free_list[i]];
168  subtree_elements.push_back(fn.element);
169  if (fn.left != INVALID_NODE) this->free_list.push_back(fn.left);
170  if (fn.right != INVALID_NODE) this->free_list.push_back(fn.right);
171  fn.left = fn.right = INVALID_NODE;
172  }
173 
174  return subtree_elements;
175  }
176 
184  size_t RemoveRecursive(const T &element, size_t node_idx, int level)
185  {
186  /* Node reference */
187  node &n = this->nodes[node_idx];
188 
189  if (n.element == element) {
190  /* Remove this one */
191  this->free_list.push_back(node_idx);
192  if (n.left == INVALID_NODE && n.right == INVALID_NODE) {
193  /* Simple case, leaf, new child node for parent is "none" */
194  return INVALID_NODE;
195  } else {
196  /* Complex case, rebuild the sub-tree */
197  std::vector<T> subtree_elements = this->FreeSubtree(node_idx);
198  return this->BuildSubtree(subtree_elements.begin(), subtree_elements.end(), level);;
199  }
200  } else {
201  /* Search in a sub-tree */
202  /* Dimension index of current level */
203  int dim = level % 2;
204  /* Coordinate of element splitting at this node */
205  CoordT nc = this->xyfunc(n.element, dim);
206  /* Coordinate of the element being removed */
207  CoordT ec = this->xyfunc(element, dim);
208  /* Which side to remove from */
209  size_t next = (ec < nc) ? n.left : n.right;
210  assert(next != INVALID_NODE); // node must exist somewhere and must be found before a leaf is reached
211  /* Descend */
212  size_t new_branch = this->RemoveRecursive(element, next, level + 1);
213  if (new_branch != next) {
214  /* Vector may have been reallocated at this point, n and next are invalid */
215  node &nn = this->nodes[node_idx];
216  if (ec < nc) nn.left = new_branch; else nn.right = new_branch;
217  }
218  return node_idx;
219  }
220  }
221 
222 
223  DistT ManhattanDistance(const T &element, CoordT x, CoordT y) const
224  {
225  return abs((DistT)this->xyfunc(element, 0) - (DistT)x) + abs((DistT)this->xyfunc(element, 1) - (DistT)y);
226  }
227 
229  using node_distance = std::pair<T, DistT>;
232  {
233  if (a.second < b.second) return a;
234  if (b.second < a.second) return b;
235  if (a.first < b.first) return a;
236  if (b.first < a.first) return b;
237  NOT_REACHED(); // a.first == b.first: same element must not be inserted twice
238  }
240  node_distance FindNearestRecursive(CoordT xy[2], size_t node_idx, int level, DistT limit = std::numeric_limits<DistT>::max()) const
241  {
242  /* Dimension index of current level */
243  int dim = level % 2;
244  /* Node reference */
245  const node &n = this->nodes[node_idx];
246 
247  /* Coordinate of element splitting at this node */
248  CoordT c = this->xyfunc(n.element, dim);
249  /* This node's distance to target */
250  DistT thisdist = ManhattanDistance(n.element, xy[0], xy[1]);
251  /* Assume this node is the best choice for now */
252  node_distance best = std::make_pair(n.element, thisdist);
253 
254  /* Next node to visit */
255  size_t next = (xy[dim] < c) ? n.left : n.right;
256  if (next != INVALID_NODE) {
257  /* Check if there is a better node down the tree */
258  best = SelectNearestNodeDistance(best, this->FindNearestRecursive(xy, next, level + 1));
259  }
260 
261  limit = std::min(best.second, limit);
262 
263  /* Check if the distance from current best is worse than distance from target to splitting line,
264  * if it is we also need to check the other side of the split. */
265  size_t opposite = (xy[dim] >= c) ? n.left : n.right; // reverse of above
266  if (opposite != INVALID_NODE && limit >= abs((int)xy[dim] - (int)c)) {
267  node_distance other_candidate = this->FindNearestRecursive(xy, opposite, level + 1, limit);
268  best = SelectNearestNodeDistance(best, other_candidate);
269  }
270 
271  return best;
272  }
273 
274  template <typename Outputter>
275  void FindContainedRecursive(CoordT p1[2], CoordT p2[2], size_t node_idx, int level, const Outputter &outputter) const
276  {
277  /* Dimension index of current level */
278  int dim = level % 2;
279  /* Node reference */
280  const node &n = this->nodes[node_idx];
281 
282  /* Coordinate of element splitting at this node */
283  CoordT ec = this->xyfunc(n.element, dim);
284  /* Opposite coordinate of element */
285  CoordT oc = this->xyfunc(n.element, 1 - dim);
286 
287  /* Test if this element is within rectangle */
288  if (ec >= p1[dim] && ec < p2[dim] && oc >= p1[1 - dim] && oc < p2[1 - dim]) outputter(n.element);
289 
290  /* Recurse left if part of rectangle is left of split */
291  if (p1[dim] < ec && n.left != INVALID_NODE) this->FindContainedRecursive(p1, p2, n.left, level + 1, outputter);
292 
293  /* Recurse right if part of rectangle is right of split */
294  if (p2[dim] > ec && n.right != INVALID_NODE) this->FindContainedRecursive(p1, p2, n.right, level + 1, outputter);
295  }
296 
298  size_t CountValue(const T &element, size_t node_idx) const
299  {
300  if (node_idx == INVALID_NODE) return 0;
301  const node &n = this->nodes[node_idx];
302  return CountValue(element, n.left) + CountValue(element, n.right) + ((n.element == element) ? 1 : 0);
303  }
304 
305  void IncrementUnbalanced(size_t amount = 1)
306  {
307  this->unbalanced += amount;
308  }
309 
312  {
313  size_t count = this->Count();
314  if (count < 8) return false;
315  return this->unbalanced > this->Count() / 4;
316  }
317 
319  void CheckInvariant(size_t node_idx, int level, CoordT min_x, CoordT max_x, CoordT min_y, CoordT max_y)
320  {
321  if (node_idx == INVALID_NODE) return;
322 
323  const node &n = this->nodes[node_idx];
324  CoordT cx = this->xyfunc(n.element, 0);
325  CoordT cy = this->xyfunc(n.element, 1);
326 
327  assert(cx >= min_x);
328  assert(cx < max_x);
329  assert(cy >= min_y);
330  assert(cy < max_y);
331 
332  if (level % 2 == 0) {
333  // split in dimension 0 = x
334  CheckInvariant(n.left, level + 1, min_x, cx, min_y, max_y);
335  CheckInvariant(n.right, level + 1, cx, max_x, min_y, max_y);
336  } else {
337  // split in dimension 1 = y
338  CheckInvariant(n.left, level + 1, min_x, max_x, min_y, cy);
339  CheckInvariant(n.right, level + 1, min_x, max_x, cy, max_y);
340  }
341  }
342 
345  {
346 #ifdef KDTREE_DEBUG
347  CheckInvariant(this->root, 0, std::numeric_limits<CoordT>::min(), std::numeric_limits<CoordT>::max(), std::numeric_limits<CoordT>::min(), std::numeric_limits<CoordT>::max());
348 #endif
349  }
350 
351 public:
354 
361  template <typename It>
362  void Build(It begin, It end)
363  {
364  this->nodes.clear();
365  this->free_list.clear();
366  this->unbalanced = 0;
367  if (begin == end) return;
368  this->nodes.reserve(end - begin);
369 
370  this->root = this->BuildSubtree(begin, end, 0);
371  CheckInvariant();
372  }
373 
377  void Clear()
378  {
379  this->nodes.clear();
380  this->free_list.clear();
381  this->unbalanced = 0;
382  return;
383  }
384 
388  void Rebuild()
389  {
390  this->Rebuild(nullptr, nullptr);
391  }
392 
398  void Insert(const T &element)
399  {
400  if (this->Count() == 0) {
401  this->root = this->AddNode(element);
402  } else {
403  if (!this->IsUnbalanced() || !this->Rebuild(&element, nullptr)) {
404  this->InsertRecursive(element, this->root, 0);
405  this->IncrementUnbalanced();
406  }
407  CheckInvariant();
408  }
409  }
410 
417  void Remove(const T &element)
418  {
419  size_t count = this->Count();
420  if (count == 0) return;
421  if (!this->IsUnbalanced() || !this->Rebuild(nullptr, &element)) {
422  /* If the removed element is the root node, this modifies this->root */
423  this->root = this->RemoveRecursive(element, this->root, 0);
424  this->IncrementUnbalanced();
425  }
426  CheckInvariant();
427  }
428 
430  size_t Count() const
431  {
432  assert(this->free_list.size() <= this->nodes.size());
433  return this->nodes.size() - this->free_list.size();
434  }
435 
441  T FindNearest(CoordT x, CoordT y) const
442  {
443  assert(this->Count() > 0);
444 
445  CoordT xy[2] = { x, y };
446  return this->FindNearestRecursive(xy, this->root, 0).first;
447  }
448 
458  template <typename Outputter>
459  void FindContained(CoordT x1, CoordT y1, CoordT x2, CoordT y2, const Outputter &outputter) const
460  {
461  assert(x1 < x2);
462  assert(y1 < y2);
463 
464  if (this->Count() == 0) return;
465 
466  CoordT p1[2] = { x1, y1 };
467  CoordT p2[2] = { x2, y2 };
468  this->FindContainedRecursive(p1, p2, this->root, 0, outputter);
469  }
470 
475  std::vector<T> FindContained(CoordT x1, CoordT y1, CoordT x2, CoordT y2) const
476  {
477  std::vector<T> result;
478  this->FindContained(x1, y1, x2, y2, [&result](T e) {result.push_back(e); });
479  return result;
480  }
481 };
482 
483 #endif
K-dimensional tree, specialised for 2-dimensional space.
Definition: kdtree.hpp:35
void Build(It begin, It end)
Clear and rebuild the tree from a new sequence of elements,.
Definition: kdtree.hpp:362
size_t Count() const
Get number of elements stored in tree.
Definition: kdtree.hpp:430
void FindContained(CoordT x1, CoordT y1, CoordT x2, CoordT y2, const Outputter &outputter) const
Find all items contained within the given rectangle.
Definition: kdtree.hpp:459
bool Rebuild(const T *include_element, const T *exclude_element)
Rebuild the tree with all existing elements, optionally adding or removing one more.
Definition: kdtree.hpp:99
std::vector< size_t > free_list
List of dead indices in the nodes vector.
Definition: kdtree.hpp:48
node_distance FindNearestRecursive(CoordT xy[2], size_t node_idx, int level, DistT limit=std::numeric_limits< DistT >::max()) const
Search a sub-tree for the element nearest to a given point.
Definition: kdtree.hpp:240
void InsertRecursive(const T &element, size_t node_idx, int level)
Insert one element in the tree somewhere below node_idx.
Definition: kdtree.hpp:124
void Rebuild()
Reconstruct the tree with the same elements, letting it be fully balanced.
Definition: kdtree.hpp:388
std::pair< T, DistT > node_distance
A data element and its distance to a searched-for point.
Definition: kdtree.hpp:229
void Insert(const T &element)
Insert a single element in the tree.
Definition: kdtree.hpp:398
Kdtree(TxyFunc xyfunc)
Construct a new Kdtree with the given xyfunc.
Definition: kdtree.hpp:353
void CheckInvariant()
Verify the invariant for the entire tree, does nothing unless KDTREE_DEBUG is defined.
Definition: kdtree.hpp:344
std::vector< node > nodes
Pool of all nodes in the tree.
Definition: kdtree.hpp:47
bool IsUnbalanced()
Check if the entire tree is in need of rebuilding.
Definition: kdtree.hpp:311
TxyFunc xyfunc
Functor to extract a coordinate from an element.
Definition: kdtree.hpp:50
static node_distance SelectNearestNodeDistance(const node_distance &a, const node_distance &b)
Ordering function for node_distance objects, elements with equal distance are ordered by less-than co...
Definition: kdtree.hpp:231
void Remove(const T &element)
Remove a single element from the tree, if it exists.
Definition: kdtree.hpp:417
static const size_t INVALID_NODE
Index value indicating no-such-node.
Definition: kdtree.hpp:45
void CheckInvariant(size_t node_idx, int level, CoordT min_x, CoordT max_x, CoordT min_y, CoordT max_y)
Verify that the invariant is true for a sub-tree, assert if not.
Definition: kdtree.hpp:319
size_t root
Index of root node.
Definition: kdtree.hpp:49
size_t RemoveRecursive(const T &element, size_t node_idx, int level)
Find and remove one element from the tree.
Definition: kdtree.hpp:184
size_t BuildSubtree(It begin, It end, int level)
Construct a subtree from elements between begin and end iterators, return index of root.
Definition: kdtree.hpp:78
size_t AddNode(const T &element)
Create one new node in the tree, return its index in the pool.
Definition: kdtree.hpp:54
T FindNearest(CoordT x, CoordT y) const
Find the element closest to given coordinate, in Manhattan distance.
Definition: kdtree.hpp:441
std::vector< T > FreeSubtree(size_t node_idx)
Free all children of the given node.
Definition: kdtree.hpp:153
CoordT SelectSplitCoord(It begin, It end, int level)
Find a coordinate value to split a range of elements at.
Definition: kdtree.hpp:69
std::vector< T > FindContained(CoordT x1, CoordT y1, CoordT x2, CoordT y2) const
Find all items contained within the given rectangle.
Definition: kdtree.hpp:475
void Clear()
Clear the tree.
Definition: kdtree.hpp:377
size_t CountValue(const T &element, size_t node_idx) const
Debugging function, counts number of occurrences of an element regardless of its correct position in ...
Definition: kdtree.hpp:298
size_t unbalanced
Number approximating how unbalanced the tree might be.
Definition: kdtree.hpp:51
constexpr T abs(const T a)
Returns the absolute value of (scalar) variable.
Definition: math_func.hpp:23
Type of a node in the tree.
Definition: kdtree.hpp:37
T element
Element stored at node.
Definition: kdtree.hpp:38
size_t left
Index of node to the left, INVALID_NODE if none.
Definition: kdtree.hpp:39
size_t right
Index of node to the right, INVALID_NODE if none.
Definition: kdtree.hpp:40