/*

* Copyright (c) 2009, 2011, Oracle and/or its affiliates. All rights reserved.

* ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*/

package java.util;

/**

* This class implements the Dual-Pivot Quicksort algorithm by

* Vladimir Yaroslavskiy, Jon Bentley, and Josh Bloch. The 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.

*

* @author Vladimir Yaroslavskiy

* @author Jon Bentley

* @author Josh Bloch

*

* @version 2011.02.11 m765.827.12i:5\7pm

* @since 1.7

*/

final class DualPivotQuicksort {

/**

* Prevents instantiation.

*/

private DualPivotQuicksort() {}

/*

* Tuning parameters.

*/

/**

* The maximum number of runs in merge sort.

*/

private static final int MAX_RUN_COUNT = 67;

/**

* The maximum length of run in merge sort.

*/

private static final int MAX_RUN_LENGTH = 33;

/**

* If the length of an array to be sorted is less than this

* constant, Quicksort is used in preference to merge sort.

*/

private static final int QUICKSORT_THRESHOLD = 286;

/**

* If the length of an array to be sorted is less than this

* constant, insertion sort is used in preference to Quicksort.

*/

private static final int INSERTION_SORT_THRESHOLD = 47;

/**

* If the length of a byte array to be sorted is greater than this

* constant, counting sort is used in preference to insertion sort.

*/

private static final int COUNTING_SORT_THRESHOLD_FOR_BYTE = 29;

/**

* If the length of a short or char array to be sorted is greater

* than this constant, counting sort is used in preference to Quicksort.

*/

private static final int COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR = 3200;

/*

* Sorting methods for seven primitive types.

*/

/**

* Sorts the specified array.

*

* @param a the array to be sorted

*/

public static void sort(int[] a) {

sort(a, 0, a.length - 1);

}

/**

* Sorts the specified range of the array.

*

* @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

*/

public static void sort(int[] a, int left, int right) {

// 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) {

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; ) {

int 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]; ) {

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

if (run[count] == right++) { // The last run contains one element

run[++count] = right;

} else if (count == 1) { // The array is already sorted

return;

}

/*

* Create temporary array, which is used for merging.

* Implementation note: variable "right" is increased by 1.

*/

int[] b; byte odd = 0;

for (int n = 1; (n <<= 1) < count; odd ^= 1);

if (odd == 0) {

b = a; a = new int[b.length];

for (int i = left - 1; ++i < right; a[i] = b[i]);

} else {

b = new int[a.length];

}

// Merging

for (int last; count > 1; count = last) {

for (int k = (last = 0) + 2; k <= count; k += 2) {

int hi = run[k], mi = run[k - 1];

for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {

if (q >= hi || p < mi && a[p] <= a[q]) {

b[i] = a[p++];

} else {

b[i] = a[q++];

}

}

run[++last] = hi;

}

if ((count & 1) != 0) {

for (int i = right, lo = run[count - 1]; --i >= lo;

b[i] = a[i]

);

run[++last] = right;

}

int[] t = a; a = b; b = t;

}

}

/**

* 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(int[] 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) {

int ai = a[i + 1];

while (ai < a[j]) {

a[j + 1] = a[j];

if (j-- == left) {

break;

}

}

a[j + 1] = ai;

}

} else {

/*

* Skip the longest 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) {

int 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;

}

int 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]) { int t = a[e2]; a[e2] = a[e1]; a[e1] = t; }

if (a[e3] < a[e2]) { int 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]) { int 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]) { int 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.

*/

int pivot1 = a[e2];

int 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; ) {

int 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; ) {

int 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.

*/

int 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) {

if (a[k] == pivot) {

continue;

}

int 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);

}

}

/**

* Sorts the specified array.

*

* @param a the array to be sorted

*/

public static void sort(long[] a) {

sort(a, 0, a.length - 1);

}

/**

* Sorts the specified range of the array.

*

* @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

*/

public static void sort(long[] a, int left, int right) {

// 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) {

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; ) {

long 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]; ) {

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

if (run[count] == right++) { // The last run contains one element

run[++count] = right;

} else if (count == 1) { // The array is already sorted

return;

}

/*

* Create temporary array, which is used for merging.

* Implementation note: variable "right" is increased by 1.

*/

long[] b; byte odd = 0;

for (int n = 1; (n <<= 1) < count; odd ^= 1);

if (odd == 0) {

b = a; a = new long[b.length];

for (int i = left - 1; ++i < right; a[i] = b[i]);

} else {

b = new long[a.length];

}

// Merging

for (int last; count > 1; count = last) {

for (int k = (last = 0) + 2; k <= count; k += 2) {

int hi = run[k], mi = run[k - 1];

for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {

if (q >= hi || p < mi && a[p] <= a[q]) {

b[i] = a[p++];

} else {

b[i] = a[q++];

}

}

run[++last] = hi;

}

if ((count & 1) != 0) {

for (int i = right, lo = run[count - 1]; --i >= lo;

b[i] = a[i]

);

run[++last] = right;

}

long[] t = a; a = b; b = t;

}

}

/**

* 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(long[] 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) {

long ai = a[i + 1];

while (ai < a[j]) {

a[j + 1] = a[j];

if (j-- == left) {

break;

}

}

a[j + 1] = ai;

}

} else {

/*

* Skip the longest 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) {

long 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;

}

long 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]) { long t = a[e2]; a[e2] = a[e1]; a[e1] = t; }

if (a[e3] < a[e2]) { long 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]) { long 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]) { long 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.

*/

long pivot1 = a[e2];

long 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; ) {

long 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; ) {

long 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.

*/

long 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) {

if (a[k] == pivot) {

continue;

}

long 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);

}

}

/**

* Sorts the specified array.

*

* @param a the array to be sorted

*/

public static void sort(short[] a) {

sort(a, 0, a.length - 1);

}

/**

* Sorts the specified range of the array.

*

* @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

*/

public static void sort(short[] a, int left, int right) {

// Use counting sort on large arrays

if (right - left > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {

int[] count = new int[NUM_SHORT_VALUES];

for (int i = left - 1; ++i <= right;

count[a[i] - Short.MIN_VALUE]++

);

for (int i = NUM_SHORT_VALUES, k = right + 1; k > left; ) {

while (count[--i] == 0);

short value = (short) (i + Short.MIN_VALUE);

int s = count[i];

do {