Index: pkg/dev_compiler/tool/input_sdk/lib/internal/sort.dart |
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-// Copyright (c) 2011, 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. |
- |
-part of dart._internal; |
- |
-/** |
- * Dual-Pivot Quicksort algorithm. |
- * |
- * This class implements the dual-pivot quicksort algorithm as presented in |
- * Vladimir Yaroslavskiy's paper. |
- * |
- * Some improvements have been copied from Android's implementation. |
- */ |
-class Sort { |
- // When a list has less then [:_INSERTION_SORT_THRESHOLD:] elements it will |
- // be sorted by an insertion sort. |
- static const int _INSERTION_SORT_THRESHOLD = 32; |
- |
- /** |
- * Sorts all elements of the given list [:a:] according to the given |
- * [:compare:] function. |
- * |
- * The [:compare:] function takes two arguments [:x:] and [:y:] and returns |
- * -1 if [:x < y:], |
- * 0 if [:x == y:], and |
- * 1 if [:x > y:]. |
- * |
- * The function's behavior must be consistent. It must not return different |
- * results for the same values. |
- */ |
- static void sort/*<E>*/(List/*<E>*/ a, int compare(dynamic /*=E*/ a, dynamic /*=E*/ b)) { |
- _doSort(a, 0, a.length - 1, compare); |
- } |
- |
- /** |
- * Sorts all elements in the range [:from:] (inclusive) to [:to:] (exclusive) |
- * of the given list [:a:]. |
- * |
- * If the given range is invalid an "OutOfRange" error is raised. |
- * TODO(floitsch): do we want an error? |
- * |
- * See [:sort:] for requirements of the [:compare:] function. |
- */ |
- static void sortRange/*<E>*/(List/*<E>*/ a, int from, int to, int compare(dynamic /*=E*/ a, dynamic /*=E*/ b)) { |
- if ((from < 0) || (to > a.length) || (to < from)) { |
- throw "OutOfRange"; |
- } |
- _doSort(a, from, to - 1, compare); |
- } |
- |
- /** |
- * Sorts the list in the interval [:left:] to [:right:] (both inclusive). |
- */ |
- static void _doSort/*<E>*/(List/*<E>*/ a, int left, int right, int compare(dynamic /*=E*/ a, dynamic /*=E*/ b)) { |
- if ((right - left) <= _INSERTION_SORT_THRESHOLD) { |
- _insertionSort(a, left, right, compare); |
- } else { |
- _dualPivotQuicksort(a, left, right, compare); |
- } |
- } |
- |
- static void _insertionSort/*<E>*/(List/*<E>*/ a, int left, int right, int compare(dynamic /*=E*/ a, dynamic /*=E*/ b)) { |
- for (int i = left + 1; i <= right; i++) { |
- var el = a[i]; |
- int j = i; |
- while ((j > left) && (compare(a[j - 1], el) > 0)) { |
- a[j] = a[j - 1]; |
- j--; |
- } |
- a[j] = el; |
- } |
- } |
- |
- static void _dualPivotQuicksort/*<E>*/(List/*<E>*/ a, |
- int left, int right, |
- int compare(dynamic /*=E*/ a, dynamic /*=E*/ b)) { |
- assert(right - left > _INSERTION_SORT_THRESHOLD); |
- |
- // Compute the two pivots by looking at 5 elements. |
- int sixth = (right - left + 1) ~/ 6; |
- int index1 = left + sixth; |
- int index5 = right - sixth; |
- int index3 = (left + right) ~/ 2; // The midpoint. |
- int index2 = index3 - sixth; |
- int index4 = index3 + sixth; |
- |
- var el1 = a[index1]; |
- var el2 = a[index2]; |
- var el3 = a[index3]; |
- var el4 = a[index4]; |
- var el5 = a[index5]; |
- |
- // Sort the selected 5 elements using a sorting network. |
- if (compare(el1, el2) > 0) { var t = el1; el1 = el2; el2 = t; } |
- if (compare(el4, el5) > 0) { var t = el4; el4 = el5; el5 = t; } |
- if (compare(el1, el3) > 0) { var t = el1; el1 = el3; el3 = t; } |
- if (compare(el2, el3) > 0) { var t = el2; el2 = el3; el3 = t; } |
- if (compare(el1, el4) > 0) { var t = el1; el1 = el4; el4 = t; } |
- if (compare(el3, el4) > 0) { var t = el3; el3 = el4; el4 = t; } |
- if (compare(el2, el5) > 0) { var t = el2; el2 = el5; el5 = t; } |
- if (compare(el2, el3) > 0) { var t = el2; el2 = el3; el3 = t; } |
- if (compare(el4, el5) > 0) { var t = el4; el4 = el5; el5 = t; } |
- |
- var pivot1 = el2; |
- var pivot2 = el4; |
- |
- // el2 and el4 have been saved in the pivot variables. They will be written |
- // back, once the partioning is finished. |
- a[index1] = el1; |
- a[index3] = el3; |
- a[index5] = el5; |
- |
- a[index2] = a[left]; |
- a[index4] = a[right]; |
- |
- int less = left + 1; // First element in the middle partition. |
- int great = right - 1; // Last element in the middle partition. |
- |
- bool pivots_are_equal = (compare(pivot1, pivot2) == 0); |
- if (pivots_are_equal) { |
- var pivot = pivot1; |
- // Degenerated case where the partioning becomes a dutch national flag |
- // problem. |
- // |
- // [ | < pivot | == pivot | unpartitioned | > pivot | ] |
- // ^ ^ ^ ^ ^ |
- // left less k great right |
- // |
- // a[left] and a[right] are undefined and are filled after the |
- // partitioning. |
- // |
- // Invariants: |
- // 1) for x in ]left, less[ : x < pivot. |
- // 2) for x in [less, k[ : x == pivot. |
- // 3) for x in ]great, right[ : x > pivot. |
- for (int k = less; k <= great; k++) { |
- var ak = a[k]; |
- int comp = compare(ak, pivot); |
- if (comp == 0) continue; |
- if (comp < 0) { |
- if (k != less) { |
- a[k] = a[less]; |
- a[less] = ak; |
- } |
- less++; |
- } else { |
- // comp > 0. |
- // |
- // Find the first element <= pivot in the range [k - 1, great] and |
- // put [:ak:] there. We know that such an element must exist: |
- // When k == less, then el3 (which is equal to pivot) lies in the |
- // interval. Otherwise a[k - 1] == pivot and the search stops at k-1. |
- // Note that in the latter case invariant 2 will be violated for a |
- // short amount of time. The invariant will be restored when the |
- // pivots are put into their final positions. |
- while (true) { |
- comp = compare(a[great], pivot); |
- if (comp > 0) { |
- great--; |
- // This is the only location in the while-loop where a new |
- // iteration is started. |
- continue; |
- } else if (comp < 0) { |
- // Triple exchange. |
- a[k] = a[less]; |
- a[less++] = a[great]; |
- a[great--] = ak; |
- break; |
- } else { |
- // comp == 0; |
- a[k] = a[great]; |
- a[great--] = ak; |
- // Note: if great < k then we will exit the outer loop and fix |
- // invariant 2 (which we just violated). |
- break; |
- } |
- } |
- } |
- } |
- } else { |
- // We partition the list into three parts: |
- // 1. < pivot1 |
- // 2. >= pivot1 && <= pivot2 |
- // 3. > pivot2 |
- // |
- // During the loop we have: |
- // [ | < pivot1 | >= pivot1 && <= pivot2 | unpartitioned | > pivot2 | ] |
- // ^ ^ ^ ^ ^ |
- // left less k great right |
- // |
- // a[left] and a[right] are undefined and are filled after the |
- // partitioning. |
- // |
- // Invariants: |
- // 1. for x in ]left, less[ : x < pivot1 |
- // 2. for x in [less, k[ : pivot1 <= x && x <= pivot2 |
- // 3. for x in ]great, right[ : x > pivot2 |
- for (int k = less; k <= great; k++) { |
- var ak = a[k]; |
- int comp_pivot1 = compare(ak, pivot1); |
- if (comp_pivot1 < 0) { |
- if (k != less) { |
- a[k] = a[less]; |
- a[less] = ak; |
- } |
- less++; |
- } else { |
- int comp_pivot2 = compare(ak, pivot2); |
- if (comp_pivot2 > 0) { |
- while (true) { |
- int comp = compare(a[great], pivot2); |
- if (comp > 0) { |
- great--; |
- if (great < k) break; |
- // This is the only location inside the loop where a new |
- // iteration is started. |
- continue; |
- } else { |
- // a[great] <= pivot2. |
- comp = compare(a[great], pivot1); |
- if (comp < 0) { |
- // Triple exchange. |
- a[k] = a[less]; |
- a[less++] = a[great]; |
- a[great--] = ak; |
- } else { |
- // a[great] >= pivot1. |
- a[k] = a[great]; |
- a[great--] = ak; |
- } |
- break; |
- } |
- } |
- } |
- } |
- } |
- } |
- |
- // Move pivots into their final positions. |
- // We shrunk the list from both sides (a[left] and a[right] have |
- // meaningless values in them) and now we move elements from the first |
- // and third partition into these locations so that we can store the |
- // pivots. |
- a[left] = a[less - 1]; |
- a[less - 1] = pivot1; |
- a[right] = a[great + 1]; |
- a[great + 1] = pivot2; |
- |
- // The list is now partitioned into three partitions: |
- // [ < pivot1 | >= pivot1 && <= pivot2 | > pivot2 ] |
- // ^ ^ ^ ^ |
- // left less great right |
- |
- // Recursive descent. (Don't include the pivot values.) |
- _doSort(a, left, less - 2, compare); |
- _doSort(a, great + 2, right, compare); |
- |
- if (pivots_are_equal) { |
- // All elements in the second partition are equal to the pivot. No |
- // need to sort them. |
- return; |
- } |
- |
- // In theory it should be enough to call _doSort recursively on the second |
- // partition. |
- // The Android source however removes the pivot elements from the recursive |
- // call if the second partition is too large (more than 2/3 of the list). |
- if (less < index1 && great > index5) { |
- while (compare(a[less], pivot1) == 0) { less++; } |
- while (compare(a[great], pivot2) == 0) { great--; } |
- |
- // Copy paste of the previous 3-way partitioning with adaptions. |
- // |
- // We partition the list into three parts: |
- // 1. == pivot1 |
- // 2. > pivot1 && < pivot2 |
- // 3. == pivot2 |
- // |
- // During the loop we have: |
- // [ == pivot1 | > pivot1 && < pivot2 | unpartitioned | == pivot2 ] |
- // ^ ^ ^ |
- // less k great |
- // |
- // Invariants: |
- // 1. for x in [ *, less[ : x == pivot1 |
- // 2. for x in [less, k[ : pivot1 < x && x < pivot2 |
- // 3. for x in ]great, * ] : x == pivot2 |
- for (int k = less; k <= great; k++) { |
- var ak = a[k]; |
- int comp_pivot1 = compare(ak, pivot1); |
- if (comp_pivot1 == 0) { |
- if (k != less) { |
- a[k] = a[less]; |
- a[less] = ak; |
- } |
- less++; |
- } else { |
- int comp_pivot2 = compare(ak, pivot2); |
- if (comp_pivot2 == 0) { |
- while (true) { |
- int comp = compare(a[great], pivot2); |
- if (comp == 0) { |
- great--; |
- if (great < k) break; |
- // This is the only location inside the loop where a new |
- // iteration is started. |
- continue; |
- } else { |
- // a[great] < pivot2. |
- comp = compare(a[great], pivot1); |
- if (comp < 0) { |
- // Triple exchange. |
- a[k] = a[less]; |
- a[less++] = a[great]; |
- a[great--] = ak; |
- } else { |
- // a[great] == pivot1. |
- a[k] = a[great]; |
- a[great--] = ak; |
- } |
- break; |
- } |
- } |
- } |
- } |
- } |
- // The second partition has now been cleared of pivot elements and looks |
- // as follows: |
- // [ * | > pivot1 && < pivot2 | * ] |
- // ^ ^ |
- // less great |
- // Sort the second partition using recursive descent. |
- _doSort(a, less, great, compare); |
- } else { |
- // The second partition looks as follows: |
- // [ * | >= pivot1 && <= pivot2 | * ] |
- // ^ ^ |
- // less great |
- // Simply sort it by recursive descent. |
- _doSort(a, less, great, compare); |
- } |
- } |
-} |