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 // Copyright (c) 2013, the Dart project authors. Please see the AUTHORS file // for details. All rights reserved. Use of this source code is governed by a // BSD-style license that can be found in the LICENSE file. import "dart:math" as math; import "utils.dart"; /// Returns a position of the [value] in [sortedList], if it is there. /// /// If the list isn't sorted according to the [compare] function, the result /// is unpredictable. /// /// If [compare] is omitted, this defaults to calling [Comparable.compareTo] on /// the objects. If any object is not [Comparable], this throws a [CastError]. /// /// Returns -1 if [value] is not in the list by default. int binarySearch(List sortedList, T value, {int compare(T a, T b)}) { compare ??= defaultCompare(); int min = 0; int max = sortedList.length; while (min < max) { int mid = min + ((max - min) >> 1); var element = sortedList[mid]; int comp = compare(element, value); if (comp == 0) return mid; if (comp < 0) { min = mid + 1; } else { max = mid; } } return -1; } /// Returns the first position in [sortedList] that does not compare less than /// [value]. /// /// If the list isn't sorted according to the [compare] function, the result /// is unpredictable. /// /// If [compare] is omitted, this defaults to calling [Comparable.compareTo] on /// the objects. If any object is not [Comparable], this throws a [CastError]. /// /// Returns [sortedList.length] if all the items in [sortedList] compare less /// than [value]. int lowerBound(List sortedList, T value, {int compare(T a, T b)}) { compare ??= defaultCompare(); int min = 0; int max = sortedList.length; while (min < max) { int mid = min + ((max - min) >> 1); var element = sortedList[mid]; int comp = compare(element, value); if (comp < 0) { min = mid + 1; } else { max = mid; } } return min; } /// Shuffles a list randomly. /// /// A sub-range of a list can be shuffled by providing [start] and [end]. void shuffle(List list, [int start = 0, int end]) { var random = math.Random(); if (end == null) end = list.length; int length = end - start; while (length > 1) { int pos = random.nextInt(length); length--; var tmp1 = list[start + pos]; list[start + pos] = list[start + length]; list[start + length] = tmp1; } } /// Reverses a list, or a part of a list, in-place. void reverse(List list, [int start = 0, int end]) { if (end == null) end = list.length; _reverse(list, start, end); } /// Internal helper function that assumes valid arguments. void _reverse(List list, int start, int end) { for (int i = start, j = end - 1; i < j; i++, j--) { var tmp = list[i]; list[i] = list[j]; list[j] = tmp; } } /// Sort a list between [start] (inclusive) and [end] (exclusive) using /// insertion sort. /// /// If [compare] is omitted, this defaults to calling [Comparable.compareTo] on /// the objects. If any object is not [Comparable], this throws a [CastError]. /// /// Insertion sort is a simple sorting algorithm. For `n` elements it does on /// the order of `n * log(n)` comparisons but up to `n` squared moves. The /// sorting is performed in-place, without using extra memory. /// /// For short lists the many moves have less impact than the simple algorithm, /// and it is often the favored sorting algorithm for short lists. /// /// This insertion sort is stable: Equal elements end up in the same order /// as they started in. void insertionSort(List list, {int compare(T a, T b), int start = 0, int end}) { // If the same method could have both positional and named optional // parameters, this should be (list, [start, end], {compare}). compare ??= defaultCompare(); end ??= list.length; for (int pos = start + 1; pos < end; pos++) { int min = start; int max = pos; var element = list[pos]; while (min < max) { int mid = min + ((max - min) >> 1); int comparison = compare(element, list[mid]); if (comparison < 0) { max = mid; } else { min = mid + 1; } } list.setRange(min + 1, pos + 1, list, min); list[min] = element; } } /// Limit below which merge sort defaults to insertion sort. const int _MERGE_SORT_LIMIT = 32; /// Sorts a list between [start] (inclusive) and [end] (exclusive) using the /// merge sort algorithm. /// /// If [compare] is omitted, this defaults to calling [Comparable.compareTo] on /// the objects. If any object is not [Comparable], this throws a [CastError]. /// /// Merge-sorting works by splitting the job into two parts, sorting each /// recursively, and then merging the two sorted parts. /// /// This takes on the order of `n * log(n)` comparisons and moves to sort /// `n` elements, but requires extra space of about the same size as the list /// being sorted. /// /// This merge sort is stable: Equal elements end up in the same order /// as they started in. void mergeSort(List list, {int start = 0, int end, int compare(T a, T b)}) { end ??= list.length; compare ??= defaultCompare(); int length = end - start; if (length < 2) return; if (length < _MERGE_SORT_LIMIT) { insertionSort(list, compare: compare, start: start, end: end); return; } // Special case the first split instead of directly calling // _mergeSort, because the _mergeSort requires its target to // be different from its source, and it requires extra space // of the same size as the list to sort. // This split allows us to have only half as much extra space, // and it ends up in the original place. int middle = start + ((end - start) >> 1); int firstLength = middle - start; int secondLength = end - middle; // secondLength is always the same as firstLength, or one greater. var scratchSpace = List(secondLength); _mergeSort(list, compare, middle, end, scratchSpace, 0); int firstTarget = end - firstLength; _mergeSort(list, compare, start, middle, list, firstTarget); _merge(compare, list, firstTarget, end, scratchSpace, 0, secondLength, list, start); } /// Performs an insertion sort into a potentially different list than the /// one containing the original values. /// /// It will work in-place as well. void _movingInsertionSort(List list, int compare(T a, T b), int start, int end, List target, int targetOffset) { int length = end - start; if (length == 0) return; target[targetOffset] = list[start]; for (int i = 1; i < length; i++) { var element = list[start + i]; int min = targetOffset; int max = targetOffset + i; while (min < max) { int mid = min + ((max - min) >> 1); if (compare(element, target[mid]) < 0) { max = mid; } else { min = mid + 1; } } target.setRange(min + 1, targetOffset + i + 1, target, min); target[min] = element; } } /// Sorts [list] from [start] to [end] into [target] at [targetOffset]. /// /// The `target` list must be able to contain the range from `start` to `end` /// after `targetOffset`. /// /// Allows target to be the same list as [list], as long as it's not /// overlapping the `start..end` range. void _mergeSort(List list, int compare(T a, T b), int start, int end, List target, int targetOffset) { int length = end - start; if (length < _MERGE_SORT_LIMIT) { _movingInsertionSort(list, compare, start, end, target, targetOffset); return; } int middle = start + (length >> 1); int firstLength = middle - start; int secondLength = end - middle; // Here secondLength >= firstLength (differs by at most one). int targetMiddle = targetOffset + firstLength; // Sort the second half into the end of the target area. _mergeSort(list, compare, middle, end, target, targetMiddle); // Sort the first half into the end of the source area. _mergeSort(list, compare, start, middle, list, middle); // Merge the two parts into the target area. _merge(compare, list, middle, middle + firstLength, target, targetMiddle, targetMiddle + secondLength, target, targetOffset); } /// Merges two lists into a target list. /// /// One of the input lists may be positioned at the end of the target /// list. /// /// For equal object, elements from [firstList] are always preferred. /// This allows the merge to be stable if the first list contains elements /// that started out earlier than the ones in [secondList] void _merge( int compare(T a, T b), List firstList, int firstStart, int firstEnd, List secondList, int secondStart, int secondEnd, List target, int targetOffset) { // No empty lists reaches here. assert(firstStart < firstEnd); assert(secondStart < secondEnd); int cursor1 = firstStart; int cursor2 = secondStart; var firstElement = firstList[cursor1++]; var secondElement = secondList[cursor2++]; while (true) { if (compare(firstElement, secondElement) <= 0) { target[targetOffset++] = firstElement; if (cursor1 == firstEnd) break; // Flushing second list after loop. firstElement = firstList[cursor1++]; } else { target[targetOffset++] = secondElement; if (cursor2 != secondEnd) { secondElement = secondList[cursor2++]; continue; } // Second list empties first. Flushing first list here. target[targetOffset++] = firstElement; target.setRange(targetOffset, targetOffset + (firstEnd - cursor1), firstList, cursor1); return; } } // First list empties first. Reached by break above. target[targetOffset++] = secondElement; target.setRange( targetOffset, targetOffset + (secondEnd - cursor2), secondList, cursor2); }