1// Heap implementation -*- C++ -*-
2
3// Copyright (C) 2001-2021 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library. This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25/*
26 *
27 * Copyright (c) 1994
28 * Hewlett-Packard Company
29 *
30 * Permission to use, copy, modify, distribute and sell this software
31 * and its documentation for any purpose is hereby granted without fee,
32 * provided that the above copyright notice appear in all copies and
33 * that both that copyright notice and this permission notice appear
34 * in supporting documentation. Hewlett-Packard Company makes no
35 * representations about the suitability of this software for any
36 * purpose. It is provided "as is" without express or implied warranty.
37 *
38 * Copyright (c) 1997
39 * Silicon Graphics Computer Systems, Inc.
40 *
41 * Permission to use, copy, modify, distribute and sell this software
42 * and its documentation for any purpose is hereby granted without fee,
43 * provided that the above copyright notice appear in all copies and
44 * that both that copyright notice and this permission notice appear
45 * in supporting documentation. Silicon Graphics makes no
46 * representations about the suitability of this software for any
47 * purpose. It is provided "as is" without express or implied warranty.
48 */
49
50/** @file bits/stl_heap.h
51 * This is an internal header file, included by other library headers.
52 * Do not attempt to use it directly. @headername{queue}
53 */
54
55#ifndef _STL_HEAP_H
56#define _STL_HEAP_H 1
57
58#include <debug/debug.h>
59#include <bits/move.h>
60#include <bits/predefined_ops.h>
61
62namespace std _GLIBCXX_VISIBILITY(default)
63{
64_GLIBCXX_BEGIN_NAMESPACE_VERSION
65
66 /**
67 * @defgroup heap_algorithms Heap
68 * @ingroup sorting_algorithms
69 */
70
71 template<typename _RandomAccessIterator, typename _Distance,
72 typename _Compare>
73 _GLIBCXX20_CONSTEXPR
74 _Distance
75 __is_heap_until(_RandomAccessIterator __first, _Distance __n,
76 _Compare& __comp)
77 {
78 _Distance __parent = 0;
79 for (_Distance __child = 1; __child < __n; ++__child)
80 {
81 if (__comp(__first + __parent, __first + __child))
82 return __child;
83 if ((__child & 1) == 0)
84 ++__parent;
85 }
86 return __n;
87 }
88
89 // __is_heap, a predicate testing whether or not a range is a heap.
90 // This function is an extension, not part of the C++ standard.
91 template<typename _RandomAccessIterator, typename _Distance>
92 _GLIBCXX20_CONSTEXPR
93 inline bool
94 __is_heap(_RandomAccessIterator __first, _Distance __n)
95 {
96 __gnu_cxx::__ops::_Iter_less_iter __comp;
97 return std::__is_heap_until(__first, __n, __comp) == __n;
98 }
99
100 template<typename _RandomAccessIterator, typename _Compare,
101 typename _Distance>
102 _GLIBCXX20_CONSTEXPR
103 inline bool
104 __is_heap(_RandomAccessIterator __first, _Compare __comp, _Distance __n)
105 {
106 typedef __decltype(__comp) _Cmp;
107 __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
108 return std::__is_heap_until(__first, __n, __cmp) == __n;
109 }
110
111 template<typename _RandomAccessIterator>
112 _GLIBCXX20_CONSTEXPR
113 inline bool
114 __is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
115 { return std::__is_heap(__first, std::distance(__first, __last)); }
116
117 template<typename _RandomAccessIterator, typename _Compare>
118 _GLIBCXX20_CONSTEXPR
119 inline bool
120 __is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
121 _Compare __comp)
122 {
123 return std::__is_heap(__first, _GLIBCXX_MOVE(__comp),
124 std::distance(__first, __last));
125 }
126
127 // Heap-manipulation functions: push_heap, pop_heap, make_heap, sort_heap,
128 // + is_heap and is_heap_until in C++0x.
129
130 template<typename _RandomAccessIterator, typename _Distance, typename _Tp,
131 typename _Compare>
132 _GLIBCXX20_CONSTEXPR
133 void
134 __push_heap(_RandomAccessIterator __first,
135 _Distance __holeIndex, _Distance __topIndex, _Tp __value,
136 _Compare& __comp)
137 {
138 _Distance __parent = (__holeIndex - 1) / 2;
139 while (__holeIndex > __topIndex && __comp(__first + __parent, __value))
140 {
141 *(__first + __holeIndex) = _GLIBCXX_MOVE(*(__first + __parent));
142 __holeIndex = __parent;
143 __parent = (__holeIndex - 1) / 2;
144 }
145 *(__first + __holeIndex) = _GLIBCXX_MOVE(__value);
146 }
147
148 /**
149 * @brief Push an element onto a heap.
150 * @param __first Start of heap.
151 * @param __last End of heap + element.
152 * @ingroup heap_algorithms
153 *
154 * This operation pushes the element at last-1 onto the valid heap
155 * over the range [__first,__last-1). After completion,
156 * [__first,__last) is a valid heap.
157 */
158 template<typename _RandomAccessIterator>
159 _GLIBCXX20_CONSTEXPR
160 inline void
161 push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
162 {
163 typedef typename iterator_traits<_RandomAccessIterator>::value_type
164 _ValueType;
165 typedef typename iterator_traits<_RandomAccessIterator>::difference_type
166 _DistanceType;
167
168 // concept requirements
169 __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
170 _RandomAccessIterator>)
171 __glibcxx_function_requires(_LessThanComparableConcept<_ValueType>)
172 __glibcxx_requires_valid_range(__first, __last);
173 __glibcxx_requires_irreflexive(__first, __last);
174 __glibcxx_requires_heap(__first, __last - 1);
175
176 __gnu_cxx::__ops::_Iter_less_val __comp;
177 _ValueType __value = _GLIBCXX_MOVE(*(__last - 1));
178 std::__push_heap(__first, _DistanceType((__last - __first) - 1),
179 _DistanceType(0), _GLIBCXX_MOVE(__value), __comp);
180 }
181
182 /**
183 * @brief Push an element onto a heap using comparison functor.
184 * @param __first Start of heap.
185 * @param __last End of heap + element.
186 * @param __comp Comparison functor.
187 * @ingroup heap_algorithms
188 *
189 * This operation pushes the element at __last-1 onto the valid
190 * heap over the range [__first,__last-1). After completion,
191 * [__first,__last) is a valid heap. Compare operations are
192 * performed using comp.
193 */
194 template<typename _RandomAccessIterator, typename _Compare>
195 _GLIBCXX20_CONSTEXPR
196 inline void
197 push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
198 _Compare __comp)
199 {
200 typedef typename iterator_traits<_RandomAccessIterator>::value_type
201 _ValueType;
202 typedef typename iterator_traits<_RandomAccessIterator>::difference_type
203 _DistanceType;
204
205 // concept requirements
206 __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
207 _RandomAccessIterator>)
208 __glibcxx_requires_valid_range(__first, __last);
209 __glibcxx_requires_irreflexive_pred(__first, __last, __comp);
210 __glibcxx_requires_heap_pred(__first, __last - 1, __comp);
211
212 __decltype(__gnu_cxx::__ops::__iter_comp_val(_GLIBCXX_MOVE(__comp)))
213 __cmp(_GLIBCXX_MOVE(__comp));
214 _ValueType __value = _GLIBCXX_MOVE(*(__last - 1));
215 std::__push_heap(__first, _DistanceType((__last - __first) - 1),
216 _DistanceType(0), _GLIBCXX_MOVE(__value), __cmp);
217 }
218
219 template<typename _RandomAccessIterator, typename _Distance,
220 typename _Tp, typename _Compare>
221 _GLIBCXX20_CONSTEXPR
222 void
223 __adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
224 _Distance __len, _Tp __value, _Compare __comp)
225 {
226 const _Distance __topIndex = __holeIndex;
227 _Distance __secondChild = __holeIndex;
228 while (__secondChild < (__len - 1) / 2)
229 {
230 __secondChild = 2 * (__secondChild + 1);
231 if (__comp(__first + __secondChild,
232 __first + (__secondChild - 1)))
233 __secondChild--;
234 *(__first + __holeIndex) = _GLIBCXX_MOVE(*(__first + __secondChild));
235 __holeIndex = __secondChild;
236 }
237 if ((__len & 1) == 0 && __secondChild == (__len - 2) / 2)
238 {
239 __secondChild = 2 * (__secondChild + 1);
240 *(__first + __holeIndex) = _GLIBCXX_MOVE(*(__first
241 + (__secondChild - 1)));
242 __holeIndex = __secondChild - 1;
243 }
244 __decltype(__gnu_cxx::__ops::__iter_comp_val(_GLIBCXX_MOVE(__comp)))
245 __cmp(_GLIBCXX_MOVE(__comp));
246 std::__push_heap(__first, __holeIndex, __topIndex,
247 _GLIBCXX_MOVE(__value), __cmp);
248 }
249
250 template<typename _RandomAccessIterator, typename _Compare>
251 _GLIBCXX20_CONSTEXPR
252 inline void
253 __pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
254 _RandomAccessIterator __result, _Compare& __comp)
255 {
256 typedef typename iterator_traits<_RandomAccessIterator>::value_type
257 _ValueType;
258 typedef typename iterator_traits<_RandomAccessIterator>::difference_type
259 _DistanceType;
260
261 _ValueType __value = _GLIBCXX_MOVE(*__result);
262 *__result = _GLIBCXX_MOVE(*__first);
263 std::__adjust_heap(__first, _DistanceType(0),
264 _DistanceType(__last - __first),
265 _GLIBCXX_MOVE(__value), __comp);
266 }
267
268 /**
269 * @brief Pop an element off a heap.
270 * @param __first Start of heap.
271 * @param __last End of heap.
272 * @pre [__first, __last) is a valid, non-empty range.
273 * @ingroup heap_algorithms
274 *
275 * This operation pops the top of the heap. The elements __first
276 * and __last-1 are swapped and [__first,__last-1) is made into a
277 * heap.
278 */
279 template<typename _RandomAccessIterator>
280 _GLIBCXX20_CONSTEXPR
281 inline void
282 pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
283 {
284 // concept requirements
285 __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
286 _RandomAccessIterator>)
287 __glibcxx_function_requires(_LessThanComparableConcept<
288 typename iterator_traits<_RandomAccessIterator>::value_type>)
289 __glibcxx_requires_non_empty_range(__first, __last);
290 __glibcxx_requires_valid_range(__first, __last);
291 __glibcxx_requires_irreflexive(__first, __last);
292 __glibcxx_requires_heap(__first, __last);
293
294 if (__last - __first > 1)
295 {
296 --__last;
297 __gnu_cxx::__ops::_Iter_less_iter __comp;
298 std::__pop_heap(__first, __last, __last, __comp);
299 }
300 }
301
302 /**
303 * @brief Pop an element off a heap using comparison functor.
304 * @param __first Start of heap.
305 * @param __last End of heap.
306 * @param __comp Comparison functor to use.
307 * @ingroup heap_algorithms
308 *
309 * This operation pops the top of the heap. The elements __first
310 * and __last-1 are swapped and [__first,__last-1) is made into a
311 * heap. Comparisons are made using comp.
312 */
313 template<typename _RandomAccessIterator, typename _Compare>
314 _GLIBCXX20_CONSTEXPR
315 inline void
316 pop_heap(_RandomAccessIterator __first,
317 _RandomAccessIterator __last, _Compare __comp)
318 {
319 // concept requirements
320 __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
321 _RandomAccessIterator>)
322 __glibcxx_requires_valid_range(__first, __last);
323 __glibcxx_requires_irreflexive_pred(__first, __last, __comp);
324 __glibcxx_requires_non_empty_range(__first, __last);
325 __glibcxx_requires_heap_pred(__first, __last, __comp);
326
327 if (__last - __first > 1)
328 {
329 typedef __decltype(__comp) _Cmp;
330 __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
331 --__last;
332 std::__pop_heap(__first, __last, __last, __cmp);
333 }
334 }
335
336 template<typename _RandomAccessIterator, typename _Compare>
337 _GLIBCXX20_CONSTEXPR
338 void
339 __make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
340 _Compare& __comp)
341 {
342 typedef typename iterator_traits<_RandomAccessIterator>::value_type
343 _ValueType;
344 typedef typename iterator_traits<_RandomAccessIterator>::difference_type
345 _DistanceType;
346
347 if (__last - __first < 2)
348 return;
349
350 const _DistanceType __len = __last - __first;
351 _DistanceType __parent = (__len - 2) / 2;
352 while (true)
353 {
354 _ValueType __value = _GLIBCXX_MOVE(*(__first + __parent));
355 std::__adjust_heap(__first, __parent, __len, _GLIBCXX_MOVE(__value),
356 __comp);
357 if (__parent == 0)
358 return;
359 __parent--;
360 }
361 }
362
363 /**
364 * @brief Construct a heap over a range.
365 * @param __first Start of heap.
366 * @param __last End of heap.
367 * @ingroup heap_algorithms
368 *
369 * This operation makes the elements in [__first,__last) into a heap.
370 */
371 template<typename _RandomAccessIterator>
372 _GLIBCXX20_CONSTEXPR
373 inline void
374 make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
375 {
376 // concept requirements
377 __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
378 _RandomAccessIterator>)
379 __glibcxx_function_requires(_LessThanComparableConcept<
380 typename iterator_traits<_RandomAccessIterator>::value_type>)
381 __glibcxx_requires_valid_range(__first, __last);
382 __glibcxx_requires_irreflexive(__first, __last);
383
384 __gnu_cxx::__ops::_Iter_less_iter __comp;
385 std::__make_heap(__first, __last, __comp);
386 }
387
388 /**
389 * @brief Construct a heap over a range using comparison functor.
390 * @param __first Start of heap.
391 * @param __last End of heap.
392 * @param __comp Comparison functor to use.
393 * @ingroup heap_algorithms
394 *
395 * This operation makes the elements in [__first,__last) into a heap.
396 * Comparisons are made using __comp.
397 */
398 template<typename _RandomAccessIterator, typename _Compare>
399 _GLIBCXX20_CONSTEXPR
400 inline void
401 make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
402 _Compare __comp)
403 {
404 // concept requirements
405 __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
406 _RandomAccessIterator>)
407 __glibcxx_requires_valid_range(__first, __last);
408 __glibcxx_requires_irreflexive_pred(__first, __last, __comp);
409
410 typedef __decltype(__comp) _Cmp;
411 __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
412 std::__make_heap(__first, __last, __cmp);
413 }
414
415 template<typename _RandomAccessIterator, typename _Compare>
416 _GLIBCXX20_CONSTEXPR
417 void
418 __sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
419 _Compare& __comp)
420 {
421 while (__last - __first > 1)
422 {
423 --__last;
424 std::__pop_heap(__first, __last, __last, __comp);
425 }
426 }
427
428 /**
429 * @brief Sort a heap.
430 * @param __first Start of heap.
431 * @param __last End of heap.
432 * @ingroup heap_algorithms
433 *
434 * This operation sorts the valid heap in the range [__first,__last).
435 */
436 template<typename _RandomAccessIterator>
437 _GLIBCXX20_CONSTEXPR
438 inline void
439 sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
440 {
441 // concept requirements
442 __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
443 _RandomAccessIterator>)
444 __glibcxx_function_requires(_LessThanComparableConcept<
445 typename iterator_traits<_RandomAccessIterator>::value_type>)
446 __glibcxx_requires_valid_range(__first, __last);
447 __glibcxx_requires_irreflexive(__first, __last);
448 __glibcxx_requires_heap(__first, __last);
449
450 __gnu_cxx::__ops::_Iter_less_iter __comp;
451 std::__sort_heap(__first, __last, __comp);
452 }
453
454 /**
455 * @brief Sort a heap using comparison functor.
456 * @param __first Start of heap.
457 * @param __last End of heap.
458 * @param __comp Comparison functor to use.
459 * @ingroup heap_algorithms
460 *
461 * This operation sorts the valid heap in the range [__first,__last).
462 * Comparisons are made using __comp.
463 */
464 template<typename _RandomAccessIterator, typename _Compare>
465 _GLIBCXX20_CONSTEXPR
466 inline void
467 sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
468 _Compare __comp)
469 {
470 // concept requirements
471 __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
472 _RandomAccessIterator>)
473 __glibcxx_requires_valid_range(__first, __last);
474 __glibcxx_requires_irreflexive_pred(__first, __last, __comp);
475 __glibcxx_requires_heap_pred(__first, __last, __comp);
476
477 typedef __decltype(__comp) _Cmp;
478 __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
479 std::__sort_heap(__first, __last, __cmp);
480 }
481
482#if __cplusplus >= 201103L
483 /**
484 * @brief Search the end of a heap.
485 * @param __first Start of range.
486 * @param __last End of range.
487 * @return An iterator pointing to the first element not in the heap.
488 * @ingroup heap_algorithms
489 *
490 * This operation returns the last iterator i in [__first, __last) for which
491 * the range [__first, i) is a heap.
492 */
493 template<typename _RandomAccessIterator>
494 _GLIBCXX20_CONSTEXPR
495 inline _RandomAccessIterator
496 is_heap_until(_RandomAccessIterator __first, _RandomAccessIterator __last)
497 {
498 // concept requirements
499 __glibcxx_function_requires(_RandomAccessIteratorConcept<
500 _RandomAccessIterator>)
501 __glibcxx_function_requires(_LessThanComparableConcept<
502 typename iterator_traits<_RandomAccessIterator>::value_type>)
503 __glibcxx_requires_valid_range(__first, __last);
504 __glibcxx_requires_irreflexive(__first, __last);
505
506 __gnu_cxx::__ops::_Iter_less_iter __comp;
507 return __first +
508 std::__is_heap_until(__first, std::distance(__first, __last), __comp);
509 }
510
511 /**
512 * @brief Search the end of a heap using comparison functor.
513 * @param __first Start of range.
514 * @param __last End of range.
515 * @param __comp Comparison functor to use.
516 * @return An iterator pointing to the first element not in the heap.
517 * @ingroup heap_algorithms
518 *
519 * This operation returns the last iterator i in [__first, __last) for which
520 * the range [__first, i) is a heap. Comparisons are made using __comp.
521 */
522 template<typename _RandomAccessIterator, typename _Compare>
523 _GLIBCXX20_CONSTEXPR
524 inline _RandomAccessIterator
525 is_heap_until(_RandomAccessIterator __first, _RandomAccessIterator __last,
526 _Compare __comp)
527 {
528 // concept requirements
529 __glibcxx_function_requires(_RandomAccessIteratorConcept<
530 _RandomAccessIterator>)
531 __glibcxx_requires_valid_range(__first, __last);
532 __glibcxx_requires_irreflexive_pred(__first, __last, __comp);
533
534 typedef __decltype(__comp) _Cmp;
535 __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
536 return __first
537 + std::__is_heap_until(__first, std::distance(__first, __last), __cmp);
538 }
539
540 /**
541 * @brief Determines whether a range is a heap.
542 * @param __first Start of range.
543 * @param __last End of range.
544 * @return True if range is a heap, false otherwise.
545 * @ingroup heap_algorithms
546 */
547 template<typename _RandomAccessIterator>
548 _GLIBCXX20_CONSTEXPR
549 inline bool
550 is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
551 { return std::is_heap_until(__first, __last) == __last; }
552
553 /**
554 * @brief Determines whether a range is a heap using comparison functor.
555 * @param __first Start of range.
556 * @param __last End of range.
557 * @param __comp Comparison functor to use.
558 * @return True if range is a heap, false otherwise.
559 * @ingroup heap_algorithms
560 */
561 template<typename _RandomAccessIterator, typename _Compare>
562 _GLIBCXX20_CONSTEXPR
563 inline bool
564 is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
565 _Compare __comp)
566 {
567 // concept requirements
568 __glibcxx_function_requires(_RandomAccessIteratorConcept<
569 _RandomAccessIterator>)
570 __glibcxx_requires_valid_range(__first, __last);
571 __glibcxx_requires_irreflexive_pred(__first, __last, __comp);
572
573 const auto __dist = std::distance(__first, __last);
574 typedef __decltype(__comp) _Cmp;
575 __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(_GLIBCXX_MOVE(__comp));
576 return std::__is_heap_until(__first, __dist, __cmp) == __dist;
577 }
578#endif
579
580_GLIBCXX_END_NAMESPACE_VERSION
581} // namespace
582
583#endif /* _STL_HEAP_H */
584