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1 // Copyright (c) 2013, the Dart project authors. Please see the AUTHORS file | 1 // Copyright (c) 2013, the Dart project authors. Please see the AUTHORS file |
2 // for details. All rights reserved. Use of this source code is governed by a | 2 // for details. All rights reserved. Use of this source code is governed by a |
3 // BSD-style license that can be found in the LICENSE file. | 3 // BSD-style license that can be found in the LICENSE file. |
4 | 4 |
5 /** | 5 @deprecated |
6 * Operations on collections. | |
7 */ | |
8 library dart.collection_helpers.algorithms; | 6 library dart.collection_helpers.algorithms; |
9 | 7 |
10 import "dart:math" show Random; | 8 export "package:collection/algorithms.dart"; |
11 | |
12 /** Version of [binarySearch] optimized for comparable keys */ | |
13 int _comparableBinarySearch(List<Comparable> list, Comparable key) { | |
14 int min = 0; | |
15 int max = list.length; | |
16 while (min < max) { | |
17 int mid = min + ((max - min) >> 1); | |
18 var element = list[mid]; | |
19 int comp = element.compareTo(key); | |
20 if (comp == 0) return mid; | |
21 if (comp < 0) { | |
22 min = mid + 1; | |
23 } else { | |
24 max = mid; | |
25 } | |
26 } | |
27 return -1; | |
28 } | |
29 | |
30 /** | |
31 * Returns a position of the [key] in [sortedList], if it is there. | |
32 * | |
33 * If the list isn't sorted according to the [compare] function, the result | |
34 * is unpredictable. | |
35 * | |
36 * If [compare] is omitted, it defaults to calling [Comparable.compareTo] on | |
37 * the objects. | |
38 * | |
39 * Returns -1 if [key] is not in the list by default. | |
40 */ | |
41 int binarySearch(List sortedList, var key, | |
42 { int compare(var a, var b) }) { | |
43 if (compare == null) { | |
44 return _comparableBinarySearch(sortedList, key); | |
45 } | |
46 int min = 0; | |
47 int max = sortedList.length; | |
48 while (min < max) { | |
49 int mid = min + ((max - min) >> 1); | |
50 var element = sortedList[mid]; | |
51 int comp = compare(element, key); | |
52 if (comp == 0) return mid; | |
53 if (comp < 0) { | |
54 min = mid + 1; | |
55 } else { | |
56 max = mid; | |
57 } | |
58 } | |
59 return -1; | |
60 } | |
61 | |
62 | |
63 /** | |
64 * Shuffles a list randomly. | |
65 * | |
66 * A sub-range of a list can be shuffled by providing [start] and [end]. | |
67 */ | |
68 void shuffle(List list, [int start = 0, int end = null]) { | |
69 Random random = new Random(); | |
70 if (end == null) end = list.length; | |
71 int length = end - start; | |
72 while (length > 1) { | |
73 int pos = random.nextInt(length); | |
74 length--; | |
75 var tmp1 = list[start + pos]; | |
76 list[start + pos] = list[start + length]; | |
77 list[start + length] = tmp1; | |
78 } | |
79 } | |
80 | |
81 | |
82 /** | |
83 * Reverses a list, or a part of a list, in-place. | |
84 */ | |
85 void reverse(List list, [int start = 0, int end = null]) { | |
86 if (end == null) end = list.length; | |
87 _reverse(list, start, end); | |
88 } | |
89 | |
90 // Internal helper function that assumes valid arguments. | |
91 void _reverse(List list, int start, int end) { | |
92 for (int i = start, j = end - 1; i < j; i++, j--) { | |
93 var tmp = list[i]; | |
94 list[i] = list[j]; | |
95 list[j] = tmp; | |
96 } | |
97 } | |
98 | |
99 /** | |
100 * Sort a list using insertion sort. | |
101 * | |
102 * Insertion sort is a simple sorting algorithm. For `n` elements it does on | |
103 * the order of `n * log(n)` comparisons but up to `n` squared moves. The | |
104 * sorting is performed in-place, without using extra memory. | |
105 * | |
106 * For short lists the many moves have less impact than the simple algorithm, | |
107 * and it is often the favored sorting algorithm for short lists. | |
108 * | |
109 * This insertion sort is stable: Equal elements end up in the same order | |
110 * as they started in. | |
111 */ | |
112 void insertionSort(List list, | |
113 { int compare(a, b), | |
114 int start: 0, | |
115 int end: null }) { | |
116 // If the same method could have both positional and named optional | |
117 // parameters, this should be (list, [start, end], {compare}). | |
118 if (end == null) end = list.length; | |
119 if (compare == null) compare = Comparable.compare; | |
120 _insertionSort(list, compare, start, end, start + 1); | |
121 } | |
122 | |
123 /** | |
124 * Internal helper function that assumes arguments correct. | |
125 * | |
126 * Assumes that the elements up to [sortedUntil] (not inclusive) are | |
127 * already sorted. The [sortedUntil] values should always be at least | |
128 * `start + 1`. | |
129 */ | |
130 void _insertionSort(List list, int compare(a, b), int start, int end, | |
131 int sortedUntil) { | |
132 for (int pos = sortedUntil; pos < end; pos++) { | |
133 int min = start; | |
134 int max = pos; | |
135 var element = list[pos]; | |
136 while (min < max) { | |
137 int mid = min + ((max - min) >> 1); | |
138 int comparison = compare(element, list[mid]); | |
139 if (comparison < 0) { | |
140 max = mid; | |
141 } else { | |
142 min = mid + 1; | |
143 } | |
144 } | |
145 list.setRange(min + 1, pos + 1, list, min); | |
146 list[min] = element; | |
147 } | |
148 } | |
149 | |
150 /** Limit below which merge sort defaults to insertion sort. */ | |
151 const int _MERGE_SORT_LIMIT = 32; | |
152 | |
153 /** | |
154 * Sorts a list, or a range of a list, using the merge sort algorithm. | |
155 * | |
156 * Merge-sorting works by splitting the job into two parts, sorting each | |
157 * recursively, and then merging the two sorted parts. | |
158 * | |
159 * This takes on the order of `n * log(n)` comparisons and moves to sort | |
160 * `n` elements, but requires extra space of about the same size as the list | |
161 * being sorted. | |
162 * | |
163 * This merge sort is stable: Equal elements end up in the same order | |
164 * as they started in. | |
165 */ | |
166 void mergeSort(List list, {int start: 0, int end: null, int compare(a, b)}) { | |
167 if (end == null) end = list.length; | |
168 if (compare == null) compare = Comparable.compare; | |
169 int length = end - start; | |
170 if (length < 2) return; | |
171 if (length < _MERGE_SORT_LIMIT) { | |
172 _insertionSort(list, compare, start, end, start + 1); | |
173 return; | |
174 } | |
175 // Special case the first split instead of directly calling | |
176 // _mergeSort, because the _mergeSort requires its target to | |
177 // be different from its source, and it requires extra space | |
178 // of the same size as the list to sort. | |
179 // This split allows us to have only half as much extra space, | |
180 // and it ends up in the original place. | |
181 int middle = start + ((end - start) >> 1); | |
182 int firstLength = middle - start; | |
183 int secondLength = end - middle; | |
184 // secondLength is always the same as firstLength, or one greater. | |
185 List scratchSpace = new List(secondLength); | |
186 _mergeSort(list, compare, middle, end, scratchSpace, 0); | |
187 int firstTarget = end - firstLength; | |
188 _mergeSort(list, compare, start, middle, list, firstTarget); | |
189 _merge(compare, | |
190 list, firstTarget, end, | |
191 scratchSpace, 0, secondLength, | |
192 list, start); | |
193 } | |
194 | |
195 /** | |
196 * Performs an insertion sort into a potentially different list than the | |
197 * one containing the original values. | |
198 * | |
199 * It will work in-place as well. | |
200 */ | |
201 void _movingInsertionSort(List list, int compare(a, b), int start, int end, | |
202 List target, int targetOffset) { | |
203 int length = end - start; | |
204 if (length == 0) return; | |
205 target[targetOffset] = list[start]; | |
206 for (int i = 1; i < length; i++) { | |
207 var element = list[start + i]; | |
208 int min = targetOffset; | |
209 int max = targetOffset + i; | |
210 while (min < max) { | |
211 int mid = min + ((max - min) >> 1); | |
212 if (compare(element, target[mid]) < 0) { | |
213 max = mid; | |
214 } else { | |
215 min = mid + 1; | |
216 } | |
217 } | |
218 target.setRange(min + 1, targetOffset + i + 1, | |
219 target, min); | |
220 target[min] = element; | |
221 } | |
222 } | |
223 | |
224 /** | |
225 * Sorts [list] from [start] to [end] into [target] at [targetOffset]. | |
226 * | |
227 * The `target` list must be able to contain the range from `start` to `end` | |
228 * after `targetOffset`. | |
229 * | |
230 * Allows target to be the same list as [list], as long as it's not | |
231 * overlapping the `start..end` range. | |
232 */ | |
233 void _mergeSort(List list, int compare(a, b), int start, int end, | |
234 List target, int targetOffset) { | |
235 int length = end - start; | |
236 if (length < _MERGE_SORT_LIMIT) { | |
237 _movingInsertionSort(list, compare, start, end, target, targetOffset); | |
238 return; | |
239 } | |
240 int middle = start + (length >> 1); | |
241 int firstLength = middle - start; | |
242 int secondLength = end - middle; | |
243 // Here secondLength >= firstLength (differs by at most one). | |
244 int targetMiddle = targetOffset + firstLength; | |
245 // Sort the second half into the end of the target area. | |
246 _mergeSort(list, compare, middle, end, | |
247 target, targetMiddle); | |
248 // Sort the first half into the end of the source area. | |
249 _mergeSort(list, compare, start, middle, | |
250 list, middle); | |
251 // Merge the two parts into the target area. | |
252 _merge(compare, | |
253 list, middle, middle + firstLength, | |
254 target, targetMiddle, targetMiddle + secondLength, | |
255 target, targetOffset); | |
256 } | |
257 | |
258 /** | |
259 * Merges two lists into a target list. | |
260 * | |
261 * One of the input lists may be positioned at the end of the target | |
262 * list. | |
263 * | |
264 * For equal object, elements from [firstList] are always preferred. | |
265 * This allows the merge to be stable if the first list contains elements | |
266 * that started out earlier than the ones in [secondList] | |
267 */ | |
268 void _merge(int compare(a, b), | |
269 List firstList, int firstStart, int firstEnd, | |
270 List secondList, int secondStart, int secondEnd, | |
271 List target, int targetOffset) { | |
272 // No empty lists reaches here. | |
273 assert(firstStart < firstEnd); | |
274 assert(secondStart < secondEnd); | |
275 int cursor1 = firstStart; | |
276 int cursor2 = secondStart; | |
277 var firstElement = firstList[cursor1++]; | |
278 var secondElement = secondList[cursor2++]; | |
279 while (true) { | |
280 if (compare(firstElement, secondElement) <= 0) { | |
281 target[targetOffset++] = firstElement; | |
282 if (cursor1 == firstEnd) break; // Flushing second list after loop. | |
283 firstElement = firstList[cursor1++]; | |
284 } else { | |
285 target[targetOffset++] = secondElement; | |
286 if (cursor2 != secondEnd) { | |
287 secondElement = secondList[cursor2++]; | |
288 continue; | |
289 } | |
290 // Second list empties first. Flushing first list here. | |
291 target[targetOffset++] = firstElement; | |
292 target.setRange(targetOffset, targetOffset + (firstEnd - cursor1), | |
293 firstList, cursor1); | |
294 return; | |
295 } | |
296 } | |
297 // First list empties first. Reached by break above. | |
298 target[targetOffset++] = secondElement; | |
299 target.setRange(targetOffset, targetOffset + (secondEnd - cursor2), | |
300 secondList, cursor2); | |
301 } | |
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