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/* Copyright (c) 2023 LibJ
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* You should have received a copy of The MIT License (MIT) along with this
* program. If not, see
* Implementation note: The sorting algorithm is a Dual-Pivot Quicksort by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch.
* This algorithm offers O(n log(n)) performance on many data sets that cause other quicksorts to degrade to quadratic performance,
* and is typically faster than traditional (one-pivot) Quicksort implementations.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
* @param toIndex the index of the last element, exclusive, to be sorted
* @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or {@code toIndex > a.length}
*/
public static void sort(boolean[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex);
DualPivotQuicksortBoolean.sort(a, fromIndex, toIndex - 1, null, 0, 0);
}
/**
* Sorts the specified range of the array using the given workspace array slice if possible for merging
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
* @param work a workspace array (slice)
* @param workBase origin of usable space in work array
* @param workLen usable size of work array
*/
static void sort(boolean[] a, int left, int right, boolean[] work, int workBase, int workLen) {
// Use Quicksort on small arrays
if (right - left < QUICKSORT_THRESHOLD) {
sort(a, left, right, true);
return;
}
/*
* Index run[i] is the start of i-th run (ascending or descending sequence).
*/
int[] run = new int[MAX_RUN_COUNT + 1];
int count = 0;
run[0] = left;
// Check if the array is nearly sorted
for (int k = left; k < right; run[count] = k) { // [A]
if (!a[k] && a[k + 1]) { // ascending
while (++k <= right && (!a[k - 1] || a[k]));
}
else if (a[k] && !a[k + 1]) { // descending
while (++k <= right && (a[k - 1] || !a[k]));
for (int lo = run[count] - 1, hi = k; ++lo < --hi;) { // [A]
boolean t = a[lo];
a[lo] = a[hi];
a[hi] = t;
}
}
else { // equal
for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k];) { // [A]
if (--m == 0) {
sort(a, left, right, true);
return;
}
}
}
/*
* The array is not highly structured, use Quicksort instead of merge sort.
*/
if (++count == MAX_RUN_COUNT) {
sort(a, left, right, true);
return;
}
}
// Check special cases
// Implementation note: variable "right" is increased by 1.
if (run[count] == right++) { // The last run contains one element
run[++count] = right;
}
else if (count == 1) { // The array is already sorted
return;
}
// Determine alternation base for merge
byte odd = 0;
for (int n = 1; (n <<= 1) < count; odd ^= 1); // [X]
// Use or create temporary array b for merging
boolean[] b; // temp array; alternates with a
int ao, bo; // array offsets from 'left'
int blen = right - left; // space needed for b
if (work == null || workLen < blen || workBase + blen > work.length) {
work = new boolean[blen];
workBase = 0;
}
if (odd == 0) {
System.arraycopy(a, left, work, workBase, blen);
b = a;
bo = 0;
a = work;
ao = workBase - left;
}
else {
b = work;
ao = 0;
bo = workBase - left;
}
// Merging
for (int last; count > 1; count = last) { // [N]
for (int k = (last = 0) + 2; k <= count; k += 2) { // [A]
int hi = run[k], mi = run[k - 1];
for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) { // [X]
if (q >= hi || p < mi && (!a[p + ao] || a[q + ao])) {
b[i + bo] = a[p++ + ao];
}
else {
b[i + bo] = a[q++ + ao];
}
}
run[++last] = hi;
}
if ((count & 1) != 0) {
for (int i = right, lo = run[count - 1]; --i >= lo; b[i + bo] = a[i + ao]); // [A]
run[++last] = right;
}
boolean[] t = a;
a = b;
b = t;
int o = ao;
ao = bo;
bo = o;
}
}
/**
* Sorts the specified range of the array by Dual-Pivot Quicksort.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
* @param leftmost indicates if this part is the leftmost in the range
*/
private static void sort(boolean[] a, int left, int right, boolean leftmost) {
int length = right - left + 1;
// Use insertion sort on tiny arrays
if (length < INSERTION_SORT_THRESHOLD) {
if (leftmost) {
/*
* Traditional (without sentinel) insertion sort, optimized for server VM, is used in case of the leftmost part.
*/
for (int i = left, j = i; i < right; j = ++i) { // [A]
boolean ai = a[i + 1];
while (!ai && a[j]) {
a[j + 1] = a[j];
if (j-- == left) {
break;
}
}
a[j + 1] = ai;
}
}
else {
/*
* Skip the booleanest ascending sequence.
*/
do {
if (left >= right) {
return;
}
}
while (a[++left] || !a[left - 1]);
/*
* Every element from adjoining part plays the role of sentinel, therefore this allows us to avoid the left range check on each
* iteration. Moreover, we use the more optimized algorithm, so called pair insertion sort, which is faster (in the context of
* Quicksort) than traditional implementation of insertion sort.
*/
for (int k = left; ++left <= right; k = ++left) { // [A]
boolean a1 = a[k], a2 = a[left];
if (!a1 && a2) {
a2 = a1;
a1 = a[left];
}
while (!a1 && a[--k]) {
a[k + 2] = a[k];
}
a[++k + 1] = a1;
while (!a2 && a[--k]) {
a[k + 1] = a[k];
}
a[k + 1] = a2;
}
boolean last = a[right];
while (!last && a[--right]) {
a[right + 1] = a[right];
}
a[right + 1] = last;
}
return;
}
// Inexpensive approximation of length / 7
int seventh = (length >> 3) + (length >> 6) + 1;
/*
* Sort five evenly spaced elements around (and including) the center element in the range. These elements will be used for pivot
* selection as described below. The choice for spacing these elements was empirically determined to work well on a wide variety of
* inputs.
*/
int e3 = (left + right) >>> 1; // The midpoint
int e2 = e3 - seventh;
int e1 = e2 - seventh;
int e4 = e3 + seventh;
int e5 = e4 + seventh;
// Sort these elements using insertion sort
if (!a[e2] && a[e1]) { boolean t = a[e2]; a[e2] = a[e1]; a[e1] = t; }
if (!a[e3] && a[e2]) {
boolean t = a[e3];
a[e3] = a[e2];
a[e2] = t;
if (!t && a[e1]) { a[e2] = a[e1]; a[e1] = t; }
}
if (!a[e4] && a[e3]) {
boolean t = a[e4];
a[e4] = a[e3];
a[e3] = t;
if (!t && a[e2]) {
a[e3] = a[e2];
a[e2] = t;
if (!t && a[e1]) { a[e2] = a[e1]; a[e1] = t; }
}
}
if (!a[e5] && a[e4]) {
boolean t = a[e5];
a[e5] = a[e4];
a[e4] = t;
if (!t && a[e3]) {
a[e4] = a[e3];
a[e3] = t;
if (!t && a[e2]) {
a[e3] = a[e2];
a[e2] = t;
if (!t && a[e1]) { a[e2] = a[e1]; a[e1] = t; }
}
}
}
// Pointers
int less = left; // The index of the first element of center part
int great = right; // The index before the first element of right part
if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
/*
* Use the second and fourth of the five sorted elements as pivots. These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*/
boolean pivot1 = a[e2];
boolean pivot2 = a[e4];
/*
* The first and the last elements to be sorted are moved to the locations formerly occupied by the pivots. When partitioning is
* complete, the pivots are swapped back into their final positions, and excluded from subsequent sorting.
*/
a[e2] = a[left];
a[e4] = a[right];
/*
* Skip elements, which are less or greater than pivot values.
*/
while (!a[++less] && pivot1);
while (a[--great] && !pivot2);
/*
* Partitioning: left part center part right part +--------------------------------------------------------------+ | < pivot1 |
* pivot1 <= && <= pivot2 | ? | > pivot2 | +--------------------------------------------------------------+ ^ ^ ^ | | | less k great
* Invariants: all in (left, less) < pivot1 pivot1 <= all in [less, k) <= pivot2 all in (great, right) > pivot2 Pointer k is the
* first index of ?-part.
*/
outer:
for (int k = less - 1; ++k <= great;) { // [A]
boolean ak = a[k];
if (!ak && pivot1) { // Move a[k] to left part
a[k] = a[less];
/*
* Here and below we use "a[i] = b; i++;" instead of "a[i++] = b;" due to performance issue.
*/
a[less] = ak;
++less;
}
else if (ak && !pivot2) { // Move a[k] to right part
while (a[great] && !pivot2) {
if (great-- == k) {
break outer;
}
}
if (!a[great] && pivot1) { // a[great] <= pivot2
a[k] = a[less];
a[less] = a[great];
++less;
}
else { // pivot1 <= a[great] <= pivot2
a[k] = a[great];
}
/*
* Here and below we use "a[i] = b; i--;" instead of "a[i--] = b;" due to performance issue.
*/
a[great] = ak;
--great;
}
}
// Swap pivots into their final positions
a[left] = a[less - 1];
a[less - 1] = pivot1;
a[right] = a[great + 1];
a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivots
sort(a, left, less - 2, leftmost);
sort(a, great + 2, right, false);
/*
* If center part is too large (comprises > 4/7 of the array), swap internal pivot values to ends.
*/
if (less < e1 && e5 < great) {
/*
* Skip elements, which are equal to pivot values.
*/
while (a[less] == pivot1) {
++less;
}
while (a[great] == pivot2) {
--great;
}
/*
* Partitioning: left part center part right part +----------------------------------------------------------+ | == pivot1 | pivot1
* < && < pivot2 | ? | == pivot2 | +----------------------------------------------------------+ ^ ^ ^ | | | less k great Invariants:
* all in (*, less) == pivot1 pivot1 < all in [less, k) < pivot2 all in (great, *) == pivot2 Pointer k is the first index of ?-part.
*/
outer:
for (int k = less - 1; ++k <= great;) { // [A]
boolean ak = a[k];
if (ak == pivot1) { // Move a[k] to left part
a[k] = a[less];
a[less] = ak;
++less;
}
else if (ak == pivot2) { // Move a[k] to right part
while (a[great] == pivot2) {
if (great-- == k) {
break outer;
}
}
if (a[great] == pivot1) { // a[great] < pivot2
a[k] = a[less];
/*
* Even though a[great] equals to pivot1, the assignment a[less] = pivot1 may be incorrect, if a[great] and pivot1 are
* floating-point zeros of different signs. Therefore in float and double sorting methods we have to use more accurate assignment
* a[less] = a[great].
*/
a[less] = pivot1;
++less;
}
else { // pivot1 < a[great] < pivot2
a[k] = a[great];
}
a[great] = ak;
--great;
}
}
}
// Sort center part recursively
sort(a, less, great, false);
}
else { // Partitioning with one pivot
/*
* Use the third of the five sorted elements as pivot. This value is inexpensive approximation of the median.
*/
boolean pivot = a[e3];
/*
* Partitioning degenerates to the traditional 3-way (or "Dutch National Flag") schema: left part center part right part
* +-------------------------------------------------+ | < pivot | == pivot | ? | > pivot |
* +-------------------------------------------------+ ^ ^ ^ | | | less k great Invariants: all in (left, less) < pivot all in
* [less, k) == pivot all in (great, right) > pivot Pointer k is the first index of ?-part.
*/
for (int k = less; k <= great; ++k) { // [A]
if (a[k] == pivot) {
continue;
}
boolean ak = a[k];
if (!ak && pivot) { // Move a[k] to left part
a[k] = a[less];
a[less] = ak;
++less;
}
else { // a[k] > pivot - Move a[k] to right part
while (a[great] && !pivot) {
--great;
}
if (!a[great] && pivot) { // a[great] <= pivot
a[k] = a[less];
a[less] = a[great];
++less;
}
else { // a[great] == pivot
/*
* Even though a[great] equals to pivot, the assignment a[k] = pivot may be incorrect, if a[great] and pivot are floating-point
* zeros of different signs. Therefore in float and double sorting methods we have to use more accurate assignment a[k] = a[great].
*/
a[k] = pivot;
}
a[great] = ak;
--great;
}
}
/*
* Sort left and right parts recursively. All elements from center part are equal and, therefore, already sorted.
*/
sort(a, left, less - 1, leftmost);
sort(a, great + 1, right, false);
}
}
}