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/*
* Copyright (C) 2002-2017 Sebastiano Vigna
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
*
* For the sorting and binary search code:
*
* Copyright (C) 1999 CERN - European Organization for Nuclear Research.
*
* Permission to use, copy, modify, distribute and sell this software and
* its documentation for any purpose is hereby granted without fee,
* provided that the above copyright notice appear in all copies and that
* both that copyright notice and this permission notice appear in
* supporting documentation. CERN makes no representations about the
* suitability of this software for any purpose. It is provided "as is"
* without expressed or implied warranty.
*/
package it.unimi.dsi.fastutil.ints;
import it.unimi.dsi.fastutil.Arrays;
import it.unimi.dsi.fastutil.Hash;
import java.util.Random;
import java.util.concurrent.ForkJoinPool;
import java.util.concurrent.RecursiveAction;
import java.util.concurrent.ExecutorCompletionService;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.LinkedBlockingQueue;
import java.util.concurrent.atomic.AtomicInteger;
/**
* A class providing static methods and objects that do useful things with
* type-specific arrays.
*
*
* In particular, the {@code forceCapacity()}, {@code ensureCapacity()},
* {@code grow()}, {@code trim()} and {@code setLength()} methods allow to
* handle arrays much like array lists. This can be very useful when efficiency
* (or syntactic simplicity) reasons make array lists unsuitable.
*
*
* Note that {@link it.unimi.dsi.fastutil.io.BinIO} and
* {@link it.unimi.dsi.fastutil.io.TextIO} contain several methods make it
* possible to load and save arrays of primitive types as sequences of elements
* in {@link java.io.DataInput} format (i.e., not as objects) or as sequences of
* lines of text.
*
*
Sorting
*
*
* There are several sorting methods available. The main theme is that of
* letting you choose the sorting algorithm you prefer (i.e., trading stability
* of mergesort for no memory allocation in quicksort). Several algorithms
* provide a parallel version, that will use the
* {@linkplain Runtime#availableProcessors() number of cores available}. Some
* algorithms also provide an explicit indirect sorting facility, which
* makes it possible to sort an array using the values in another array as
* comparator.
*
*
* All comparison-based algorithm have an implementation based on a
* type-specific comparator.
*
*
* As a general rule, sequential radix sort is significantly faster than
* quicksort or mergesort, in particular on random-looking data. In the parallel
* case, up to a few cores parallel radix sort is still the fastest, but at some
* point quicksort exploits parallelism better.
*
*
* If you are fine with not knowing exactly which algorithm will be run (in
* particular, not knowing exactly whether a support array will be allocated),
* the dual-pivot parallel sorts in {@link java.util.Arrays} are about 50%
* faster than the classical single-pivot implementation used here.
*
*
* In any case, if sorting time is important I suggest that you benchmark your
* sorting load with your data distribution and on your architecture.
*
* @see java.util.Arrays
*/
public final class IntArrays {
private IntArrays() {
}
/** A static, final, empty array. */
public static final int[] EMPTY_ARRAY = {};
/**
* A static, final, empty array to be used as default array in allocations. An
* object distinct from {@link #EMPTY_ARRAY} makes it possible to have different
* behaviors depending on whether the user required an empty allocation, or we
* are just lazily delaying allocation.
*
* @see java.util.ArrayList
*/
public static final int[] DEFAULT_EMPTY_ARRAY = {};
/**
* Forces an array to contain the given number of entries, preserving just a
* part of the array.
*
* @param array
* an array.
* @param length
* the new minimum length for this array.
* @param preserve
* the number of elements of the array that must be preserved in case
* a new allocation is necessary.
* @return an array with {@code length} entries whose first {@code preserve}
* entries are the same as those of {@code array}.
*/
public static int[] forceCapacity(final int[] array, final int length, final int preserve) {
final int t[] = new int[length];
System.arraycopy(array, 0, t, 0, preserve);
return t;
}
/**
* Ensures that an array can contain the given number of entries.
*
*
* If you cannot foresee whether this array will need again to be enlarged, you
* should probably use {@code grow()} instead.
*
* @param array
* an array.
* @param length
* the new minimum length for this array.
* @return {@code array}, if it contains {@code length} entries or more;
* otherwise, an array with {@code length} entries whose first
* {@code array.length} entries are the same as those of {@code array}.
*/
public static int[] ensureCapacity(final int[] array, final int length) {
return ensureCapacity(array, length, array.length);
}
/**
* Ensures that an array can contain the given number of entries, preserving
* just a part of the array.
*
* @param array
* an array.
* @param length
* the new minimum length for this array.
* @param preserve
* the number of elements of the array that must be preserved in case
* a new allocation is necessary.
* @return {@code array}, if it can contain {@code length} entries or more;
* otherwise, an array with {@code length} entries whose first
* {@code preserve} entries are the same as those of {@code array}.
*/
public static int[] ensureCapacity(final int[] array, final int length, final int preserve) {
return length > array.length ? forceCapacity(array, length, preserve) : array;
}
/**
* Grows the given array to the maximum between the given length and the current
* length increased by 50%, provided that the given length is larger than the
* current length.
*
*
* If you want complete control on the array growth, you should probably use
* {@code ensureCapacity()} instead.
*
* @param array
* an array.
* @param length
* the new minimum length for this array.
* @return {@code array}, if it can contain {@code length} entries; otherwise,
* an array with max({@code length},{@code array.length}/φ) entries
* whose first {@code array.length} entries are the same as those of
* {@code array}.
*/
public static int[] grow(final int[] array, final int length) {
return grow(array, length, array.length);
}
/**
* Grows the given array to the maximum between the given length and the current
* length increased by 50%, provided that the given length is larger than the
* current length, preserving just a part of the array.
*
*
* If you want complete control on the array growth, you should probably use
* {@code ensureCapacity()} instead.
*
* @param array
* an array.
* @param length
* the new minimum length for this array.
* @param preserve
* the number of elements of the array that must be preserved in case
* a new allocation is necessary.
* @return {@code array}, if it can contain {@code length} entries; otherwise,
* an array with max({@code length},{@code array.length}/φ) entries
* whose first {@code preserve} entries are the same as those of
* {@code array}.
*/
public static int[] grow(final int[] array, final int length, final int preserve) {
if (length > array.length) {
final int newLength = (int) Math
.max(Math.min((long) array.length + (array.length >> 1), Arrays.MAX_ARRAY_SIZE), length);
final int t[] = new int[newLength];
System.arraycopy(array, 0, t, 0, preserve);
return t;
}
return array;
}
/**
* Trims the given array to the given length.
*
* @param array
* an array.
* @param length
* the new maximum length for the array.
* @return {@code array}, if it contains {@code length} entries or less;
* otherwise, an array with {@code length} entries whose entries are the
* same as the first {@code length} entries of {@code array}.
*
*/
public static int[] trim(final int[] array, final int length) {
if (length >= array.length)
return array;
final int t[] = length == 0 ? EMPTY_ARRAY : new int[length];
System.arraycopy(array, 0, t, 0, length);
return t;
}
/**
* Sets the length of the given array.
*
* @param array
* an array.
* @param length
* the new length for the array.
* @return {@code array}, if it contains exactly {@code length} entries;
* otherwise, if it contains more than {@code length} entries,
* an array with {@code length} entries whose entries are the same as
* the first {@code length} entries of {@code array}; otherwise, an
* array with {@code length} entries whose first {@code array.length}
* entries are the same as those of {@code array}.
*
*/
public static int[] setLength(final int[] array, final int length) {
if (length == array.length)
return array;
if (length < array.length)
return trim(array, length);
return ensureCapacity(array, length);
}
/**
* Returns a copy of a portion of an array.
*
* @param array
* an array.
* @param offset
* the first element to copy.
* @param length
* the number of elements to copy.
* @return a new array containing {@code length} elements of {@code array}
* starting at {@code offset}.
*/
public static int[] copy(final int[] array, final int offset, final int length) {
ensureOffsetLength(array, offset, length);
final int[] a = length == 0 ? EMPTY_ARRAY : new int[length];
System.arraycopy(array, offset, a, 0, length);
return a;
}
/**
* Returns a copy of an array.
*
* @param array
* an array.
* @return a copy of {@code array}.
*/
public static int[] copy(final int[] array) {
return array.clone();
}
/**
* Fills the given array with the given value.
*
* @param array
* an array.
* @param value
* the new value for all elements of the array.
* @deprecated Please use the corresponding {@link java.util.Arrays} method.
*/
@Deprecated
public static void fill(final int[] array, final int value) {
int i = array.length;
while (i-- != 0)
array[i] = value;
}
/**
* Fills a portion of the given array with the given value.
*
* @param array
* an array.
* @param from
* the starting index of the portion to fill (inclusive).
* @param to
* the end index of the portion to fill (exclusive).
* @param value
* the new value for all elements of the specified portion of the
* array.
* @deprecated Please use the corresponding {@link java.util.Arrays} method.
*/
@Deprecated
public static void fill(final int[] array, final int from, int to, final int value) {
ensureFromTo(array, from, to);
if (from == 0)
while (to-- != 0)
array[to] = value;
else
for (int i = from; i < to; i++)
array[i] = value;
}
/**
* Returns true if the two arrays are elementwise equal.
*
* @param a1
* an array.
* @param a2
* another array.
* @return true if the two arrays are of the same length, and their elements are
* equal.
* @deprecated Please use the corresponding {@link java.util.Arrays} method,
* which is intrinsified in recent JVMs.
*/
@Deprecated
public static boolean equals(final int[] a1, final int a2[]) {
int i = a1.length;
if (i != a2.length)
return false;
while (i-- != 0)
if (!((a1[i]) == (a2[i])))
return false;
return true;
}
/**
* Ensures that a range given by its first (inclusive) and last (exclusive)
* elements fits an array.
*
*
* This method may be used whenever an array range check is needed.
*
* @param a
* an array.
* @param from
* a start index (inclusive).
* @param to
* an end index (exclusive).
* @throws IllegalArgumentException
* if {@code from} is greater than {@code to}.
* @throws ArrayIndexOutOfBoundsException
* if {@code from} or {@code to} are greater than the array length
* or negative.
*/
public static void ensureFromTo(final int[] a, final int from, final int to) {
Arrays.ensureFromTo(a.length, from, to);
}
/**
* Ensures that a range given by an offset and a length fits an array.
*
*
* This method may be used whenever an array range check is needed.
*
* @param a
* an array.
* @param offset
* a start index.
* @param length
* a length (the number of elements in the range).
* @throws IllegalArgumentException
* if {@code length} is negative.
* @throws ArrayIndexOutOfBoundsException
* if {@code offset} is negative or {@code offset}+{@code length} is
* greater than the array length.
*/
public static void ensureOffsetLength(final int[] a, final int offset, final int length) {
Arrays.ensureOffsetLength(a.length, offset, length);
}
/**
* Ensures that two arrays are of the same length.
*
* @param a
* an array.
* @param b
* another array.
* @throws IllegalArgumentException
* if the two argument arrays are not of the same length.
*/
public static void ensureSameLength(final int[] a, final int[] b) {
if (a.length != b.length)
throw new IllegalArgumentException("Array size mismatch: " + a.length + " != " + b.length);
}
private static final int QUICKSORT_NO_REC = 16;
private static final int PARALLEL_QUICKSORT_NO_FORK = 8192;
private static final int QUICKSORT_MEDIAN_OF_9 = 128;
private static final int MERGESORT_NO_REC = 16;
/**
* Swaps two elements of an anrray.
*
* @param x
* an array.
* @param a
* a position in {@code x}.
* @param b
* another position in {@code x}.
*/
public static void swap(final int x[], final int a, final int b) {
final int t = x[a];
x[a] = x[b];
x[b] = t;
}
/**
* Swaps two sequences of elements of an array.
*
* @param x
* an array.
* @param a
* a position in {@code x}.
* @param b
* another position in {@code x}.
* @param n
* the number of elements to exchange starting at {@code a} and
* {@code b}.
*/
public static void swap(final int[] x, int a, int b, final int n) {
for (int i = 0; i < n; i++, a++, b++)
swap(x, a, b);
}
private static int med3(final int x[], final int a, final int b, final int c, IntComparator comp) {
final int ab = comp.compare(x[a], x[b]);
final int ac = comp.compare(x[a], x[c]);
final int bc = comp.compare(x[b], x[c]);
return (ab < 0 ? (bc < 0 ? b : ac < 0 ? c : a) : (bc > 0 ? b : ac > 0 ? c : a));
}
private static void selectionSort(final int[] a, final int from, final int to, final IntComparator comp) {
for (int i = from; i < to - 1; i++) {
int m = i;
for (int j = i + 1; j < to; j++)
if (comp.compare(a[j], a[m]) < 0)
m = j;
if (m != i) {
final int u = a[i];
a[i] = a[m];
a[m] = u;
}
}
}
private static void insertionSort(final int[] a, final int from, final int to, final IntComparator comp) {
for (int i = from; ++i < to;) {
int t = a[i];
int j = i;
for (int u = a[j - 1]; comp.compare(t, u) < 0; u = a[--j - 1]) {
a[j] = u;
if (from == j - 1) {
--j;
break;
}
}
a[j] = t;
}
}
/**
* Sorts the specified range of elements according to the order induced by the
* specified comparator using quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* Note that this implementation does not allocate any object, contrarily to the
* implementation used to sort primitive types in {@link java.util.Arrays},
* which switches to mergesort on large inputs.
*
* @param x
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
* @param comp
* the comparator to determine the sorting order.
*
*/
public static void quickSort(final int[] x, final int from, final int to, final IntComparator comp) {
final int len = to - from;
// Selection sort on smallest arrays
if (len < QUICKSORT_NO_REC) {
selectionSort(x, from, to, comp);
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
if (len > QUICKSORT_MEDIAN_OF_9) { // Big arrays, pseudomedian of 9
int s = len / 8;
l = med3(x, l, l + s, l + 2 * s, comp);
m = med3(x, m - s, m, m + s, comp);
n = med3(x, n - 2 * s, n - s, n, comp);
}
m = med3(x, l, m, n, comp); // Mid-size, med of 3
final int v = x[m];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = comp.compare(x[b], v)) <= 0) {
if (comparison == 0)
swap(x, a++, b);
b++;
}
while (c >= b && (comparison = comp.compare(x[c], v)) >= 0) {
if (comparison == 0)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int s;
s = Math.min(a - from, b - a);
swap(x, from, b - s, s);
s = Math.min(d - c, to - d - 1);
swap(x, b, to - s, s);
// Recursively sort non-partition-elements
if ((s = b - a) > 1)
quickSort(x, from, from + s, comp);
if ((s = d - c) > 1)
quickSort(x, to - s, to, comp);
}
/**
* Sorts an array according to the order induced by the specified comparator
* using quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* Note that this implementation does not allocate any object, contrarily to the
* implementation used to sort primitive types in {@link java.util.Arrays},
* which switches to mergesort on large inputs.
*
* @param x
* the array to be sorted.
* @param comp
* the comparator to determine the sorting order.
*
*/
public static void quickSort(final int[] x, final IntComparator comp) {
quickSort(x, 0, x.length, comp);
}
protected static class ForkJoinQuickSortComp extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final int from;
private final int to;
private final int[] x;
private final IntComparator comp;
public ForkJoinQuickSortComp(final int[] x, final int from, final int to, final IntComparator comp) {
this.from = from;
this.to = to;
this.x = x;
this.comp = comp;
}
@Override
protected void compute() {
final int[] x = this.x;
final int len = to - from;
if (len < PARALLEL_QUICKSORT_NO_FORK) {
quickSort(x, from, to, comp);
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
int s = len / 8;
l = med3(x, l, l + s, l + 2 * s, comp);
m = med3(x, m - s, m, m + s, comp);
n = med3(x, n - 2 * s, n - s, n, comp);
m = med3(x, l, m, n, comp);
final int v = x[m];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = comp.compare(x[b], v)) <= 0) {
if (comparison == 0)
swap(x, a++, b);
b++;
}
while (c >= b && (comparison = comp.compare(x[c], v)) >= 0) {
if (comparison == 0)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int t;
s = Math.min(a - from, b - a);
swap(x, from, b - s, s);
s = Math.min(d - c, to - d - 1);
swap(x, b, to - s, s);
// Recursively sort non-partition-elements
s = b - a;
t = d - c;
if (s > 1 && t > 1)
invokeAll(new ForkJoinQuickSortComp(x, from, from + s, comp),
new ForkJoinQuickSortComp(x, to - t, to, comp));
else if (s > 1)
invokeAll(new ForkJoinQuickSortComp(x, from, from + s, comp));
else
invokeAll(new ForkJoinQuickSortComp(x, to - t, to, comp));
}
}
/**
* Sorts the specified range of elements according to the order induced by the
* specified comparator using a parallel quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
* @param comp
* the comparator to determine the sorting order.
*/
public static void parallelQuickSort(final int[] x, final int from, final int to, final IntComparator comp) {
if (to - from < PARALLEL_QUICKSORT_NO_FORK)
quickSort(x, from, to, comp);
else {
final ForkJoinPool pool = new ForkJoinPool(Runtime.getRuntime().availableProcessors());
pool.invoke(new ForkJoinQuickSortComp(x, from, to, comp));
pool.shutdown();
}
}
/**
* Sorts an array according to the order induced by the specified comparator
* using a parallel quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x
* the array to be sorted.
* @param comp
* the comparator to determine the sorting order.
*/
public static void parallelQuickSort(final int[] x, final IntComparator comp) {
parallelQuickSort(x, 0, x.length, comp);
}
private static int med3(final int x[], final int a, final int b, final int c) {
final int ab = (Integer.compare((x[a]), (x[b])));
final int ac = (Integer.compare((x[a]), (x[c])));
final int bc = (Integer.compare((x[b]), (x[c])));
return (ab < 0 ? (bc < 0 ? b : ac < 0 ? c : a) : (bc > 0 ? b : ac > 0 ? c : a));
}
private static void selectionSort(final int[] a, final int from, final int to) {
for (int i = from; i < to - 1; i++) {
int m = i;
for (int j = i + 1; j < to; j++)
if (((a[j]) < (a[m])))
m = j;
if (m != i) {
final int u = a[i];
a[i] = a[m];
a[m] = u;
}
}
}
private static void insertionSort(final int[] a, final int from, final int to) {
for (int i = from; ++i < to;) {
int t = a[i];
int j = i;
for (int u = a[j - 1]; ((t) < (u)); u = a[--j - 1]) {
a[j] = u;
if (from == j - 1) {
--j;
break;
}
}
a[j] = t;
}
}
/**
* Sorts the specified range of elements according to the natural ascending
* order using quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* Note that this implementation does not allocate any object, contrarily to the
* implementation used to sort primitive types in {@link java.util.Arrays},
* which switches to mergesort on large inputs.
*
* @param x
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void quickSort(final int[] x, final int from, final int to) {
final int len = to - from;
// Selection sort on smallest arrays
if (len < QUICKSORT_NO_REC) {
selectionSort(x, from, to);
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
if (len > QUICKSORT_MEDIAN_OF_9) { // Big arrays, pseudomedian of 9
int s = len / 8;
l = med3(x, l, l + s, l + 2 * s);
m = med3(x, m - s, m, m + s);
n = med3(x, n - 2 * s, n - s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
final int v = x[m];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = (Integer.compare((x[b]), (v)))) <= 0) {
if (comparison == 0)
swap(x, a++, b);
b++;
}
while (c >= b && (comparison = (Integer.compare((x[c]), (v)))) >= 0) {
if (comparison == 0)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int s;
s = Math.min(a - from, b - a);
swap(x, from, b - s, s);
s = Math.min(d - c, to - d - 1);
swap(x, b, to - s, s);
// Recursively sort non-partition-elements
if ((s = b - a) > 1)
quickSort(x, from, from + s);
if ((s = d - c) > 1)
quickSort(x, to - s, to);
}
/**
* Sorts an array according to the natural ascending order using quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* Note that this implementation does not allocate any object, contrarily to the
* implementation used to sort primitive types in {@link java.util.Arrays},
* which switches to mergesort on large inputs.
*
* @param x
* the array to be sorted.
*
*/
public static void quickSort(final int[] x) {
quickSort(x, 0, x.length);
}
protected static class ForkJoinQuickSort extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final int from;
private final int to;
private final int[] x;
public ForkJoinQuickSort(final int[] x, final int from, final int to) {
this.from = from;
this.to = to;
this.x = x;
}
@Override
protected void compute() {
final int[] x = this.x;
final int len = to - from;
if (len < PARALLEL_QUICKSORT_NO_FORK) {
quickSort(x, from, to);
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
int s = len / 8;
l = med3(x, l, l + s, l + 2 * s);
m = med3(x, m - s, m, m + s);
n = med3(x, n - 2 * s, n - s, n);
m = med3(x, l, m, n);
final int v = x[m];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = (Integer.compare((x[b]), (v)))) <= 0) {
if (comparison == 0)
swap(x, a++, b);
b++;
}
while (c >= b && (comparison = (Integer.compare((x[c]), (v)))) >= 0) {
if (comparison == 0)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int t;
s = Math.min(a - from, b - a);
swap(x, from, b - s, s);
s = Math.min(d - c, to - d - 1);
swap(x, b, to - s, s);
// Recursively sort non-partition-elements
s = b - a;
t = d - c;
if (s > 1 && t > 1)
invokeAll(new ForkJoinQuickSort(x, from, from + s), new ForkJoinQuickSort(x, to - t, to));
else if (s > 1)
invokeAll(new ForkJoinQuickSort(x, from, from + s));
else
invokeAll(new ForkJoinQuickSort(x, to - t, to));
}
}
/**
* Sorts the specified range of elements according to the natural ascending
* order using a parallel quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void parallelQuickSort(final int[] x, final int from, final int to) {
if (to - from < PARALLEL_QUICKSORT_NO_FORK)
quickSort(x, from, to);
else {
final ForkJoinPool pool = new ForkJoinPool(Runtime.getRuntime().availableProcessors());
pool.invoke(new ForkJoinQuickSort(x, from, to));
pool.shutdown();
}
}
/**
* Sorts an array according to the natural ascending order using a parallel
* quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x
* the array to be sorted.
*
*/
public static void parallelQuickSort(final int[] x) {
parallelQuickSort(x, 0, x.length);
}
private static int med3Indirect(final int perm[], final int x[], final int a, final int b, final int c) {
final int aa = x[perm[a]];
final int bb = x[perm[b]];
final int cc = x[perm[c]];
final int ab = (Integer.compare((aa), (bb)));
final int ac = (Integer.compare((aa), (cc)));
final int bc = (Integer.compare((bb), (cc)));
return (ab < 0 ? (bc < 0 ? b : ac < 0 ? c : a) : (bc > 0 ? b : ac > 0 ? c : a));
}
private static void insertionSortIndirect(final int[] perm, final int[] a, final int from, final int to) {
for (int i = from; ++i < to;) {
int t = perm[i];
int j = i;
for (int u = perm[j - 1]; ((a[t]) < (a[u])); u = perm[--j - 1]) {
perm[j] = u;
if (from == j - 1) {
--j;
break;
}
}
perm[j] = t;
}
}
/**
* Sorts the specified range of elements according to the natural ascending
* order using indirect quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code x[perm[i]] ≤ x[perm[i + 1]]}.
*
*
* Note that this implementation does not allocate any object, contrarily to the
* implementation used to sort primitive types in {@link java.util.Arrays},
* which switches to mergesort on large inputs.
*
* @param perm
* a permutation array indexing {@code x}.
* @param x
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void quickSortIndirect(final int[] perm, final int[] x, final int from, final int to) {
final int len = to - from;
// Selection sort on smallest arrays
if (len < QUICKSORT_NO_REC) {
insertionSortIndirect(perm, x, from, to);
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
if (len > QUICKSORT_MEDIAN_OF_9) { // Big arrays, pseudomedian of 9
int s = len / 8;
l = med3Indirect(perm, x, l, l + s, l + 2 * s);
m = med3Indirect(perm, x, m - s, m, m + s);
n = med3Indirect(perm, x, n - 2 * s, n - s, n);
}
m = med3Indirect(perm, x, l, m, n); // Mid-size, med of 3
final int v = x[perm[m]];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = (Integer.compare((x[perm[b]]), (v)))) <= 0) {
if (comparison == 0)
IntArrays.swap(perm, a++, b);
b++;
}
while (c >= b && (comparison = (Integer.compare((x[perm[c]]), (v)))) >= 0) {
if (comparison == 0)
IntArrays.swap(perm, c, d--);
c--;
}
if (b > c)
break;
IntArrays.swap(perm, b++, c--);
}
// Swap partition elements back to middle
int s;
s = Math.min(a - from, b - a);
IntArrays.swap(perm, from, b - s, s);
s = Math.min(d - c, to - d - 1);
IntArrays.swap(perm, b, to - s, s);
// Recursively sort non-partition-elements
if ((s = b - a) > 1)
quickSortIndirect(perm, x, from, from + s);
if ((s = d - c) > 1)
quickSortIndirect(perm, x, to - s, to);
}
/**
* Sorts an array according to the natural ascending order using indirect
* quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code x[perm[i]] ≤ x[perm[i + 1]]}.
*
*
* Note that this implementation does not allocate any object, contrarily to the
* implementation used to sort primitive types in {@link java.util.Arrays},
* which switches to mergesort on large inputs.
*
* @param perm
* a permutation array indexing {@code x}.
* @param x
* the array to be sorted.
*/
public static void quickSortIndirect(final int perm[], final int[] x) {
quickSortIndirect(perm, x, 0, x.length);
}
protected static class ForkJoinQuickSortIndirect extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final int from;
private final int to;
private final int[] perm;
private final int[] x;
public ForkJoinQuickSortIndirect(final int perm[], final int[] x, final int from, final int to) {
this.from = from;
this.to = to;
this.x = x;
this.perm = perm;
}
@Override
protected void compute() {
final int[] x = this.x;
final int len = to - from;
if (len < PARALLEL_QUICKSORT_NO_FORK) {
quickSortIndirect(perm, x, from, to);
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
int s = len / 8;
l = med3Indirect(perm, x, l, l + s, l + 2 * s);
m = med3Indirect(perm, x, m - s, m, m + s);
n = med3Indirect(perm, x, n - 2 * s, n - s, n);
m = med3Indirect(perm, x, l, m, n);
final int v = x[perm[m]];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = (Integer.compare((x[perm[b]]), (v)))) <= 0) {
if (comparison == 0)
IntArrays.swap(perm, a++, b);
b++;
}
while (c >= b && (comparison = (Integer.compare((x[perm[c]]), (v)))) >= 0) {
if (comparison == 0)
IntArrays.swap(perm, c, d--);
c--;
}
if (b > c)
break;
IntArrays.swap(perm, b++, c--);
}
// Swap partition elements back to middle
int t;
s = Math.min(a - from, b - a);
IntArrays.swap(perm, from, b - s, s);
s = Math.min(d - c, to - d - 1);
IntArrays.swap(perm, b, to - s, s);
// Recursively sort non-partition-elements
s = b - a;
t = d - c;
if (s > 1 && t > 1)
invokeAll(new ForkJoinQuickSortIndirect(perm, x, from, from + s),
new ForkJoinQuickSortIndirect(perm, x, to - t, to));
else if (s > 1)
invokeAll(new ForkJoinQuickSortIndirect(perm, x, from, from + s));
else
invokeAll(new ForkJoinQuickSortIndirect(perm, x, to - t, to));
}
}
/**
* Sorts the specified range of elements according to the natural ascending
* order using a parallel indirect quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code x[perm[i]] ≤ x[perm[i + 1]]}.
*
*
* This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param perm
* a permutation array indexing {@code x}.
* @param x
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void parallelQuickSortIndirect(final int[] perm, final int[] x, final int from, final int to) {
if (to - from < PARALLEL_QUICKSORT_NO_FORK)
quickSortIndirect(perm, x, from, to);
else {
final ForkJoinPool pool = new ForkJoinPool(Runtime.getRuntime().availableProcessors());
pool.invoke(new ForkJoinQuickSortIndirect(perm, x, from, to));
pool.shutdown();
}
}
/**
* Sorts an array according to the natural ascending order using a parallel
* indirect quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code x[perm[i]] ≤ x[perm[i + 1]]}.
*
*
* This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param perm
* a permutation array indexing {@code x}.
* @param x
* the array to be sorted.
*
*/
public static void parallelQuickSortIndirect(final int perm[], final int[] x) {
parallelQuickSortIndirect(perm, x, 0, x.length);
}
/**
* Stabilizes a permutation.
*
*
* This method can be used to stabilize the permutation generated by an indirect
* sorting, assuming that initially the permutation array was in ascending order
* (e.g., the identity, as usually happens). This method scans the permutation,
* and for each non-singleton block of elements with the same associated values
* in {@code x}, permutes them in ascending order. The resulting permutation
* corresponds to a stable sort.
*
*
* Usually combining an unstable indirect sort and this method is more efficient
* than using a stable sort, as most stable sort algorithms require a support
* array.
*
*
* More precisely, assuming that {@code x[perm[i]] ≤ x[perm[i + 1]]}, after
* stabilization we will also have that {@code x[perm[i]] = x[perm[i + 1]]}
* implies {@code perm[i] ≤ perm[i + 1]}.
*
* @param perm
* a permutation array indexing {@code x} so that it is sorted.
* @param x
* the sorted array to be stabilized.
* @param from
* the index of the first element (inclusive) to be stabilized.
* @param to
* the index of the last element (exclusive) to be stabilized.
*/
public static void stabilize(final int perm[], final int[] x, final int from, final int to) {
int curr = from;
for (int i = from + 1; i < to; i++) {
if (x[perm[i]] != x[perm[curr]]) {
if (i - curr > 1)
IntArrays.parallelQuickSort(perm, curr, i);
curr = i;
}
}
if (to - curr > 1)
IntArrays.parallelQuickSort(perm, curr, to);
}
/**
* Stabilizes a permutation.
*
*
* This method can be used to stabilize the permutation generated by an indirect
* sorting, assuming that initially the permutation array was in ascending order
* (e.g., the identity, as usually happens). This method scans the permutation,
* and for each non-singleton block of elements with the same associated values
* in {@code x}, permutes them in ascending order. The resulting permutation
* corresponds to a stable sort.
*
*
* Usually combining an unstable indirect sort and this method is more efficient
* than using a stable sort, as most stable sort algorithms require a support
* array.
*
*
* More precisely, assuming that {@code x[perm[i]] ≤ x[perm[i + 1]]}, after
* stabilization we will also have that {@code x[perm[i]] = x[perm[i + 1]]}
* implies {@code perm[i] ≤ perm[i + 1]}.
*
* @param perm
* a permutation array indexing {@code x} so that it is sorted.
* @param x
* the sorted array to be stabilized.
*/
public static void stabilize(final int perm[], final int[] x) {
stabilize(perm, x, 0, perm.length);
}
private static int med3(final int x[], final int[] y, final int a, final int b, final int c) {
int t;
final int ab = (t = (Integer.compare((x[a]), (x[b])))) == 0 ? (Integer.compare((y[a]), (y[b]))) : t;
final int ac = (t = (Integer.compare((x[a]), (x[c])))) == 0 ? (Integer.compare((y[a]), (y[c]))) : t;
final int bc = (t = (Integer.compare((x[b]), (x[c])))) == 0 ? (Integer.compare((y[b]), (y[c]))) : t;
return (ab < 0 ? (bc < 0 ? b : ac < 0 ? c : a) : (bc > 0 ? b : ac > 0 ? c : a));
}
private static void swap(final int x[], final int[] y, final int a, final int b) {
final int t = x[a];
final int u = y[a];
x[a] = x[b];
y[a] = y[b];
x[b] = t;
y[b] = u;
}
private static void swap(final int[] x, final int[] y, int a, int b, final int n) {
for (int i = 0; i < n; i++, a++, b++)
swap(x, y, a, b);
}
private static void selectionSort(final int[] a, final int[] b, final int from, final int to) {
for (int i = from; i < to - 1; i++) {
int m = i, u;
for (int j = i + 1; j < to; j++)
if ((u = (Integer.compare((a[j]), (a[m])))) < 0 || u == 0 && ((b[j]) < (b[m])))
m = j;
if (m != i) {
int t = a[i];
a[i] = a[m];
a[m] = t;
t = b[i];
b[i] = b[m];
b[m] = t;
}
}
}
/**
* Sorts the specified range of elements of two arrays according to the natural
* lexicographical ascending order using quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This method implements a lexicographical sorting of the arguments.
* Pairs of elements in the same position in the two provided arrays will be
* considered a single key, and permuted accordingly. In the end, either
* {@code x[i] < x[i + 1]} or x[i]
* == x[i + 1] and {@code y[i] ≤ y[i + 1]}.
*
* @param x
* the first array to be sorted.
* @param y
* the second array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void quickSort(final int[] x, final int[] y, final int from, final int to) {
final int len = to - from;
if (len < QUICKSORT_NO_REC) {
selectionSort(x, y, from, to);
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
if (len > QUICKSORT_MEDIAN_OF_9) { // Big arrays, pseudomedian of 9
int s = len / 8;
l = med3(x, y, l, l + s, l + 2 * s);
m = med3(x, y, m - s, m, m + s);
n = med3(x, y, n - 2 * s, n - s, n);
}
m = med3(x, y, l, m, n); // Mid-size, med of 3
final int v = x[m], w = y[m];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison, t;
while (b <= c && (comparison = (t = (Integer.compare((x[b]), (v)))) == 0
? (Integer.compare((y[b]), (w)))
: t) <= 0) {
if (comparison == 0)
swap(x, y, a++, b);
b++;
}
while (c >= b && (comparison = (t = (Integer.compare((x[c]), (v)))) == 0
? (Integer.compare((y[c]), (w)))
: t) >= 0) {
if (comparison == 0)
swap(x, y, c, d--);
c--;
}
if (b > c)
break;
swap(x, y, b++, c--);
}
// Swap partition elements back to middle
int s;
s = Math.min(a - from, b - a);
swap(x, y, from, b - s, s);
s = Math.min(d - c, to - d - 1);
swap(x, y, b, to - s, s);
// Recursively sort non-partition-elements
if ((s = b - a) > 1)
quickSort(x, y, from, from + s);
if ((s = d - c) > 1)
quickSort(x, y, to - s, to);
}
/**
* Sorts two arrays according to the natural lexicographical ascending order
* using quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This method implements a lexicographical sorting of the arguments.
* Pairs of elements in the same position in the two provided arrays will be
* considered a single key, and permuted accordingly. In the end, either
* {@code x[i] < x[i + 1]} or x[i]
* == x[i + 1] and {@code y[i] ≤ y[i + 1]}.
*
* @param x
* the first array to be sorted.
* @param y
* the second array to be sorted.
*/
public static void quickSort(final int[] x, final int[] y) {
ensureSameLength(x, y);
quickSort(x, y, 0, x.length);
}
protected static class ForkJoinQuickSort2 extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final int from;
private final int to;
private final int[] x, y;
public ForkJoinQuickSort2(final int[] x, final int[] y, final int from, final int to) {
this.from = from;
this.to = to;
this.x = x;
this.y = y;
}
@Override
protected void compute() {
final int[] x = this.x;
final int[] y = this.y;
final int len = to - from;
if (len < PARALLEL_QUICKSORT_NO_FORK) {
quickSort(x, y, from, to);
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
int s = len / 8;
l = med3(x, y, l, l + s, l + 2 * s);
m = med3(x, y, m - s, m, m + s);
n = med3(x, y, n - 2 * s, n - s, n);
m = med3(x, y, l, m, n);
final int v = x[m], w = y[m];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison, t;
while (b <= c && (comparison = (t = (Integer.compare((x[b]), (v)))) == 0
? (Integer.compare((y[b]), (w)))
: t) <= 0) {
if (comparison == 0)
swap(x, y, a++, b);
b++;
}
while (c >= b && (comparison = (t = (Integer.compare((x[c]), (v)))) == 0
? (Integer.compare((y[c]), (w)))
: t) >= 0) {
if (comparison == 0)
swap(x, y, c, d--);
c--;
}
if (b > c)
break;
swap(x, y, b++, c--);
}
// Swap partition elements back to middle
int t;
s = Math.min(a - from, b - a);
swap(x, y, from, b - s, s);
s = Math.min(d - c, to - d - 1);
swap(x, y, b, to - s, s);
s = b - a;
t = d - c;
// Recursively sort non-partition-elements
if (s > 1 && t > 1)
invokeAll(new ForkJoinQuickSort2(x, y, from, from + s), new ForkJoinQuickSort2(x, y, to - t, to));
else if (s > 1)
invokeAll(new ForkJoinQuickSort2(x, y, from, from + s));
else
invokeAll(new ForkJoinQuickSort2(x, y, to - t, to));
}
}
/**
* Sorts the specified range of elements of two arrays according to the natural
* lexicographical ascending order using a parallel quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This method implements a lexicographical sorting of the arguments.
* Pairs of elements in the same position in the two provided arrays will be
* considered a single key, and permuted accordingly. In the end, either
* {@code x[i] < x[i + 1]} or x[i]
* == x[i + 1] and {@code y[i] ≤ y[i + 1]}.
*
*
* This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x
* the first array to be sorted.
* @param y
* the second array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void parallelQuickSort(final int[] x, final int[] y, final int from, final int to) {
if (to - from < PARALLEL_QUICKSORT_NO_FORK)
quickSort(x, y, from, to);
final ForkJoinPool pool = new ForkJoinPool(Runtime.getRuntime().availableProcessors());
pool.invoke(new ForkJoinQuickSort2(x, y, from, to));
pool.shutdown();
}
/**
* Sorts two arrays according to the natural lexicographical ascending order
* using a parallel quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M.
* Douglas McIlroy, “Engineering a Sort Function”, Software:
* Practice and Experience, 23(11), pages 1249−1265, 1993.
*
*
* This method implements a lexicographical sorting of the arguments.
* Pairs of elements in the same position in the two provided arrays will be
* considered a single key, and permuted accordingly. In the end, either
* {@code x[i] < x[i + 1]} or x[i]
* == x[i + 1] and {@code y[i] ≤ y[i + 1]}.
*
*
* This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x
* the first array to be sorted.
* @param y
* the second array to be sorted.
*/
public static void parallelQuickSort(final int[] x, final int[] y) {
ensureSameLength(x, y);
parallelQuickSort(x, y, 0, x.length);
}
/**
* Sorts the specified range of elements according to the natural ascending
* order using mergesort, using a given pre-filled support array.
*
*
* This sort is guaranteed to be stable: equal elements will not be
* reordered as a result of the sort. Moreover, no support arrays will be
* allocated.
*
* @param a
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
* @param supp
* a support array containing at least {@code to} elements, and whose
* entries are identical to those of {@code a} in the specified
* range.
*/
public static void mergeSort(final int a[], final int from, final int to, final int supp[]) {
int len = to - from;
// Insertion sort on smallest arrays
if (len < MERGESORT_NO_REC) {
insertionSort(a, from, to);
return;
}
// Recursively sort halves of a into supp
final int mid = (from + to) >>> 1;
mergeSort(supp, from, mid, a);
mergeSort(supp, mid, to, a);
// If list is already sorted, just copy from supp to a. This is an
// optimization that results in faster sorts for nearly ordered lists.
if (((supp[mid - 1]) <= (supp[mid]))) {
System.arraycopy(supp, from, a, from, len);
return;
}
// Merge sorted halves (now in supp) into a
for (int i = from, p = from, q = mid; i < to; i++) {
if (q >= to || p < mid && ((supp[p]) <= (supp[q])))
a[i] = supp[p++];
else
a[i] = supp[q++];
}
}
/**
* Sorts the specified range of elements according to the natural ascending
* order using mergesort.
*
*
* This sort is guaranteed to be stable: equal elements will not be
* reordered as a result of the sort. An array as large as {@code a} will be
* allocated by this method.
*
* @param a
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void mergeSort(final int a[], final int from, final int to) {
mergeSort(a, from, to, a.clone());
}
/**
* Sorts an array according to the natural ascending order using mergesort.
*
*
* This sort is guaranteed to be stable: equal elements will not be
* reordered as a result of the sort. An array as large as {@code a} will be
* allocated by this method.
*
* @param a
* the array to be sorted.
*/
public static void mergeSort(final int a[]) {
mergeSort(a, 0, a.length);
}
/**
* Sorts the specified range of elements according to the order induced by the
* specified comparator using mergesort, using a given pre-filled support array.
*
*
* This sort is guaranteed to be stable: equal elements will not be
* reordered as a result of the sort. Moreover, no support arrays will be
* allocated.
*
* @param a
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
* @param comp
* the comparator to determine the sorting order.
* @param supp
* a support array containing at least {@code to} elements, and whose
* entries are identical to those of {@code a} in the specified
* range.
*/
public static void mergeSort(final int a[], final int from, final int to, IntComparator comp, final int supp[]) {
int len = to - from;
// Insertion sort on smallest arrays
if (len < MERGESORT_NO_REC) {
insertionSort(a, from, to, comp);
return;
}
// Recursively sort halves of a into supp
final int mid = (from + to) >>> 1;
mergeSort(supp, from, mid, comp, a);
mergeSort(supp, mid, to, comp, a);
// If list is already sorted, just copy from supp to a. This is an
// optimization that results in faster sorts for nearly ordered lists.
if (comp.compare(supp[mid - 1], supp[mid]) <= 0) {
System.arraycopy(supp, from, a, from, len);
return;
}
// Merge sorted halves (now in supp) into a
for (int i = from, p = from, q = mid; i < to; i++) {
if (q >= to || p < mid && comp.compare(supp[p], supp[q]) <= 0)
a[i] = supp[p++];
else
a[i] = supp[q++];
}
}
/**
* Sorts the specified range of elements according to the order induced by the
* specified comparator using mergesort.
*
*
* This sort is guaranteed to be stable: equal elements will not be
* reordered as a result of the sort. An array as large as {@code a} will be
* allocated by this method.
*
* @param a
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
* @param comp
* the comparator to determine the sorting order.
*/
public static void mergeSort(final int a[], final int from, final int to, IntComparator comp) {
mergeSort(a, from, to, comp, a.clone());
}
/**
* Sorts an array according to the order induced by the specified comparator
* using mergesort.
*
*
* This sort is guaranteed to be stable: equal elements will not be
* reordered as a result of the sort. An array as large as {@code a} will be
* allocated by this method.
*
* @param a
* the array to be sorted.
* @param comp
* the comparator to determine the sorting order.
*/
public static void mergeSort(final int a[], IntComparator comp) {
mergeSort(a, 0, a.length, comp);
}
/**
* Searches a range of the specified array for the specified value using the
* binary search algorithm. The range must be sorted prior to making this call.
* If it is not sorted, the results are undefined. If the range contains
* multiple elements with the specified value, there is no guarantee which one
* will be found.
*
* @param a
* the array to be searched.
* @param from
* the index of the first element (inclusive) to be searched.
* @param to
* the index of the last element (exclusive) to be searched.
* @param key
* the value to be searched for.
* @return index of the search key, if it is contained in the array; otherwise,
* {@code (-(insertion point) - 1)}. The insertion point
* is defined as the the point at which the value would be inserted into
* the array: the index of the first element greater than the key, or
* the length of the array, if all elements in the array are less than
* the specified key. Note that this guarantees that the return value
* will be ≥ 0 if and only if the key is found.
* @see java.util.Arrays
*/
public static int binarySearch(final int[] a, int from, int to, final int key) {
int midVal;
to--;
while (from <= to) {
final int mid = (from + to) >>> 1;
midVal = a[mid];
if (midVal < key)
from = mid + 1;
else if (midVal > key)
to = mid - 1;
else
return mid;
}
return -(from + 1);
}
/**
* Searches an array for the specified value using the binary search algorithm.
* The range must be sorted prior to making this call. If it is not sorted, the
* results are undefined. If the range contains multiple elements with the
* specified value, there is no guarantee which one will be found.
*
* @param a
* the array to be searched.
* @param key
* the value to be searched for.
* @return index of the search key, if it is contained in the array; otherwise,
* {@code (-(insertion point) - 1)}. The insertion point
* is defined as the the point at which the value would be inserted into
* the array: the index of the first element greater than the key, or
* the length of the array, if all elements in the array are less than
* the specified key. Note that this guarantees that the return value
* will be ≥ 0 if and only if the key is found.
* @see java.util.Arrays
*/
public static int binarySearch(final int[] a, final int key) {
return binarySearch(a, 0, a.length, key);
}
/**
* Searches a range of the specified array for the specified value using the
* binary search algorithm and a specified comparator. The range must be sorted
* following the comparator prior to making this call. If it is not sorted, the
* results are undefined. If the range contains multiple elements with the
* specified value, there is no guarantee which one will be found.
*
* @param a
* the array to be searched.
* @param from
* the index of the first element (inclusive) to be searched.
* @param to
* the index of the last element (exclusive) to be searched.
* @param key
* the value to be searched for.
* @param c
* a comparator.
* @return index of the search key, if it is contained in the array; otherwise,
* {@code (-(insertion point) - 1)}. The insertion point
* is defined as the the point at which the value would be inserted into
* the array: the index of the first element greater than the key, or
* the length of the array, if all elements in the array are less than
* the specified key. Note that this guarantees that the return value
* will be ≥ 0 if and only if the key is found.
* @see java.util.Arrays
*/
public static int binarySearch(final int[] a, int from, int to, final int key, final IntComparator c) {
int midVal;
to--;
while (from <= to) {
final int mid = (from + to) >>> 1;
midVal = a[mid];
final int cmp = c.compare(midVal, key);
if (cmp < 0)
from = mid + 1;
else if (cmp > 0)
to = mid - 1;
else
return mid; // key found
}
return -(from + 1);
}
/**
* Searches an array for the specified value using the binary search algorithm
* and a specified comparator. The range must be sorted following the comparator
* prior to making this call. If it is not sorted, the results are undefined. If
* the range contains multiple elements with the specified value, there is no
* guarantee which one will be found.
*
* @param a
* the array to be searched.
* @param key
* the value to be searched for.
* @param c
* a comparator.
* @return index of the search key, if it is contained in the array; otherwise,
* {@code (-(insertion point) - 1)}. The insertion point
* is defined as the the point at which the value would be inserted into
* the array: the index of the first element greater than the key, or
* the length of the array, if all elements in the array are less than
* the specified key. Note that this guarantees that the return value
* will be ≥ 0 if and only if the key is found.
* @see java.util.Arrays
*/
public static int binarySearch(final int[] a, final int key, final IntComparator c) {
return binarySearch(a, 0, a.length, key, c);
}
/** The size of a digit used during radix sort (must be a power of 2). */
private static final int DIGIT_BITS = 8;
/** The mask to extract a digit of {@link #DIGIT_BITS} bits. */
private static final int DIGIT_MASK = (1 << DIGIT_BITS) - 1;
/** The number of digits per element. */
private static final int DIGITS_PER_ELEMENT = Integer.SIZE / DIGIT_BITS;
private static final int RADIXSORT_NO_REC = 1024;
private static final int PARALLEL_RADIXSORT_NO_FORK = 1024;
/**
* This method fixes negative numbers so that the combination
* exponent/significand is lexicographically sorted.
*/
/**
* Sorts the specified array using radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This implementation is significantly faster than quicksort already at small
* sizes (say, more than 10000 elements), but it can only sort in ascending
* order.
*
* @param a
* the array to be sorted.
*/
public static void radixSort(final int[] a) {
radixSort(a, 0, a.length);
}
/**
* Sorts the specified range of an array using radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This implementation is significantly faster than quicksort already at small
* sizes (say, more than 10000 elements), but it can only sort in ascending
* order.
*
* @param a
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void radixSort(final int[] a, final int from, final int to) {
if (to - from < RADIXSORT_NO_REC) {
quickSort(a, from, to);
return;
}
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final int stackSize = ((1 << DIGIT_BITS) - 1) * (DIGITS_PER_ELEMENT - 1) + 1;
int stackPos = 0;
final int[] offsetStack = new int[stackSize];
final int[] lengthStack = new int[stackSize];
final int[] levelStack = new int[stackSize];
offsetStack[stackPos] = from;
lengthStack[stackPos] = to - from;
levelStack[stackPos++] = 0;
final int[] count = new int[1 << DIGIT_BITS];
final int[] pos = new int[1 << DIGIT_BITS];
while (stackPos > 0) {
final int first = offsetStack[--stackPos];
final int length = lengthStack[stackPos];
final int level = levelStack[stackPos];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the shift
// that extract the
// right byte from a
// key
// Count keys.
for (int i = first + length; i-- != first;)
count[((a[i]) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
for (int i = 0, p = first; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0)
lastUsed = i;
pos[i] = (p += count[i]);
}
final int end = first + length - count[lastUsed];
// i moves through the start of each block
for (int i = first, c = -1, d; i <= end; i += count[c], count[c] = 0) {
int t = a[i];
c = ((t) >>> shift & DIGIT_MASK ^ signMask);
if (i < end) { // When all slots are OK, the last slot is necessarily OK.
while ((d = --pos[c]) > i) {
final int z = t;
t = a[d];
a[d] = z;
c = ((t) >>> shift & DIGIT_MASK ^ signMask);
}
a[i] = t;
}
if (level < maxLevel && count[c] > 1) {
if (count[c] < RADIXSORT_NO_REC)
quickSort(a, i, i + count[c]);
else {
offsetStack[stackPos] = i;
lengthStack[stackPos] = count[c];
levelStack[stackPos++] = level + 1;
}
}
}
}
}
protected static final class Segment {
protected final int offset, length, level;
protected Segment(final int offset, final int length, final int level) {
this.offset = offset;
this.length = length;
this.level = level;
}
@Override
public String toString() {
return "Segment [offset=" + offset + ", length=" + length + ", level=" + level + "]";
}
}
protected static final Segment POISON_PILL = new Segment(-1, -1, -1);
/**
* Sorts the specified range of an array using parallel radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This implementation uses a pool of {@link Runtime#availableProcessors()}
* threads.
*
* @param a
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void parallelRadixSort(final int[] a, final int from, final int to) {
if (to - from < PARALLEL_RADIXSORT_NO_FORK) {
quickSort(a, from, to);
return;
}
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final LinkedBlockingQueue queue = new LinkedBlockingQueue<>();
queue.add(new Segment(from, to - from, 0));
final AtomicInteger queueSize = new AtomicInteger(1);
final int numberOfThreads = Runtime.getRuntime().availableProcessors();
final ExecutorService executorService = Executors.newFixedThreadPool(numberOfThreads,
Executors.defaultThreadFactory());
final ExecutorCompletionService executorCompletionService = new ExecutorCompletionService<>(
executorService);
for (int j = numberOfThreads; j-- != 0;)
executorCompletionService.submit(() -> {
final int[] count = new int[1 << DIGIT_BITS];
final int[] pos = new int[1 << DIGIT_BITS];
for (;;) {
if (queueSize.get() == 0)
for (int i = numberOfThreads; i-- != 0;)
queue.add(POISON_PILL);
final Segment segment = queue.take();
if (segment == POISON_PILL)
return null;
final int first = segment.offset;
final int length = segment.length;
final int level = segment.level;
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the
// shift
// that
// extract
// the right
// byte from
// a key
// Count keys.
for (int i = first + length; i-- != first;)
count[((a[i]) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
for (int i = 0, p = first; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0)
lastUsed = i;
pos[i] = (p += count[i]);
}
final int end = first + length - count[lastUsed];
// i moves through the start of each block
for (int i = first, c = -1, d; i <= end; i += count[c], count[c] = 0) {
int t = a[i];
c = ((t) >>> shift & DIGIT_MASK ^ signMask);
if (i < end) {
while ((d = --pos[c]) > i) {
final int z = t;
t = a[d];
a[d] = z;
c = ((t) >>> shift & DIGIT_MASK ^ signMask);
}
a[i] = t;
}
if (level < maxLevel && count[c] > 1) {
if (count[c] < PARALLEL_RADIXSORT_NO_FORK)
quickSort(a, i, i + count[c]);
else {
queueSize.incrementAndGet();
queue.add(new Segment(i, count[c], level + 1));
}
}
}
queueSize.decrementAndGet();
}
});
Throwable problem = null;
for (int i = numberOfThreads; i-- != 0;)
try {
executorCompletionService.take().get();
} catch (Exception e) {
problem = e.getCause(); // We keep only the last one. They will be logged anyway.
}
executorService.shutdown();
if (problem != null)
throw (problem instanceof RuntimeException) ? (RuntimeException) problem : new RuntimeException(problem);
}
/**
* Sorts the specified array using parallel radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This implementation uses a pool of {@link Runtime#availableProcessors()}
* threads.
*
* @param a
* the array to be sorted.
*/
public static void parallelRadixSort(final int[] a) {
parallelRadixSort(a, 0, a.length);
}
/**
* Sorts the specified array using indirect radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code a[perm[i]] ≤ a[perm[i + 1]]}.
*
*
* This implementation will allocate, in the stable case, a support array as
* large as {@code perm} (note that the stable version is slightly faster).
*
* @param perm
* a permutation array indexing {@code a}.
* @param a
* the array to be sorted.
* @param stable
* whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect(final int[] perm, final int[] a, final boolean stable) {
radixSortIndirect(perm, a, 0, perm.length, stable);
}
/**
* Sorts the specified array using indirect radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code a[perm[i]] ≤ a[perm[i + 1]]}.
*
*
* This implementation will allocate, in the stable case, a support array as
* large as {@code perm} (note that the stable version is slightly faster).
*
* @param perm
* a permutation array indexing {@code a}.
* @param a
* the array to be sorted.
* @param from
* the index of the first element of {@code perm} (inclusive) to be
* permuted.
* @param to
* the index of the last element of {@code perm} (exclusive) to be
* permuted.
* @param stable
* whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect(final int[] perm, final int[] a, final int from, final int to,
final boolean stable) {
if (to - from < RADIXSORT_NO_REC) {
insertionSortIndirect(perm, a, from, to);
return;
}
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final int stackSize = ((1 << DIGIT_BITS) - 1) * (DIGITS_PER_ELEMENT - 1) + 1;
int stackPos = 0;
final int[] offsetStack = new int[stackSize];
final int[] lengthStack = new int[stackSize];
final int[] levelStack = new int[stackSize];
offsetStack[stackPos] = from;
lengthStack[stackPos] = to - from;
levelStack[stackPos++] = 0;
final int[] count = new int[1 << DIGIT_BITS];
final int[] pos = new int[1 << DIGIT_BITS];
final int[] support = stable ? new int[perm.length] : null;
while (stackPos > 0) {
final int first = offsetStack[--stackPos];
final int length = lengthStack[stackPos];
final int level = levelStack[stackPos];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the shift
// that extract the
// right byte from a
// key
// Count keys.
for (int i = first + length; i-- != first;)
count[((a[perm[i]]) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
for (int i = 0, p = stable ? 0 : first; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0)
lastUsed = i;
pos[i] = (p += count[i]);
}
if (stable) {
for (int i = first + length; i-- != first;)
support[--pos[((a[perm[i]]) >>> shift & DIGIT_MASK ^ signMask)]] = perm[i];
System.arraycopy(support, 0, perm, first, length);
for (int i = 0, p = first; i <= lastUsed; i++) {
if (level < maxLevel && count[i] > 1) {
if (count[i] < RADIXSORT_NO_REC)
insertionSortIndirect(perm, a, p, p + count[i]);
else {
offsetStack[stackPos] = p;
lengthStack[stackPos] = count[i];
levelStack[stackPos++] = level + 1;
}
}
p += count[i];
}
java.util.Arrays.fill(count, 0);
} else {
final int end = first + length - count[lastUsed];
// i moves through the start of each block
for (int i = first, c = -1, d; i <= end; i += count[c], count[c] = 0) {
int t = perm[i];
c = ((a[t]) >>> shift & DIGIT_MASK ^ signMask);
if (i < end) { // When all slots are OK, the last slot is necessarily OK.
while ((d = --pos[c]) > i) {
final int z = t;
t = perm[d];
perm[d] = z;
c = ((a[t]) >>> shift & DIGIT_MASK ^ signMask);
}
perm[i] = t;
}
if (level < maxLevel && count[c] > 1) {
if (count[c] < RADIXSORT_NO_REC)
insertionSortIndirect(perm, a, i, i + count[c]);
else {
offsetStack[stackPos] = i;
lengthStack[stackPos] = count[c];
levelStack[stackPos++] = level + 1;
}
}
}
}
}
}
/**
* Sorts the specified range of an array using parallel indirect radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code a[perm[i]] ≤ a[perm[i + 1]]}.
*
*
* This implementation uses a pool of {@link Runtime#availableProcessors()}
* threads.
*
* @param perm
* a permutation array indexing {@code a}.
* @param a
* the array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
* @param stable
* whether the sorting algorithm should be stable.
*/
public static void parallelRadixSortIndirect(final int perm[], final int[] a, final int from, final int to,
final boolean stable) {
if (to - from < PARALLEL_RADIXSORT_NO_FORK) {
radixSortIndirect(perm, a, from, to, stable);
return;
}
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final LinkedBlockingQueue queue = new LinkedBlockingQueue<>();
queue.add(new Segment(from, to - from, 0));
final AtomicInteger queueSize = new AtomicInteger(1);
final int numberOfThreads = Runtime.getRuntime().availableProcessors();
final ExecutorService executorService = Executors.newFixedThreadPool(numberOfThreads,
Executors.defaultThreadFactory());
final ExecutorCompletionService executorCompletionService = new ExecutorCompletionService<>(
executorService);
final int[] support = stable ? new int[perm.length] : null;
for (int j = numberOfThreads; j-- != 0;)
executorCompletionService.submit(() -> {
final int[] count = new int[1 << DIGIT_BITS];
final int[] pos = new int[1 << DIGIT_BITS];
for (;;) {
if (queueSize.get() == 0)
for (int i = numberOfThreads; i-- != 0;)
queue.add(POISON_PILL);
final Segment segment = queue.take();
if (segment == POISON_PILL)
return null;
final int first = segment.offset;
final int length = segment.length;
final int level = segment.level;
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the
// shift
// that
// extract
// the right
// byte from
// a key
// Count keys.
for (int i = first + length; i-- != first;)
count[((a[perm[i]]) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
for (int i = 0, p = first; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0)
lastUsed = i;
pos[i] = (p += count[i]);
}
if (stable) {
for (int i = first + length; i-- != first;)
support[--pos[((a[perm[i]]) >>> shift & DIGIT_MASK ^ signMask)]] = perm[i];
System.arraycopy(support, first, perm, first, length);
for (int i = 0, p = first; i <= lastUsed; i++) {
if (level < maxLevel && count[i] > 1) {
if (count[i] < PARALLEL_RADIXSORT_NO_FORK)
radixSortIndirect(perm, a, p, p + count[i], stable);
else {
queueSize.incrementAndGet();
queue.add(new Segment(p, count[i], level + 1));
}
}
p += count[i];
}
java.util.Arrays.fill(count, 0);
} else {
final int end = first + length - count[lastUsed];
// i moves through the start of each block
for (int i = first, c = -1, d; i <= end; i += count[c], count[c] = 0) {
int t = perm[i];
c = ((a[t]) >>> shift & DIGIT_MASK ^ signMask);
if (i < end) { // When all slots are OK, the last slot is necessarily OK.
while ((d = --pos[c]) > i) {
final int z = t;
t = perm[d];
perm[d] = z;
c = ((a[t]) >>> shift & DIGIT_MASK ^ signMask);
}
perm[i] = t;
}
if (level < maxLevel && count[c] > 1) {
if (count[c] < PARALLEL_RADIXSORT_NO_FORK)
radixSortIndirect(perm, a, i, i + count[c], stable);
else {
queueSize.incrementAndGet();
queue.add(new Segment(i, count[c], level + 1));
}
}
}
}
queueSize.decrementAndGet();
}
});
Throwable problem = null;
for (int i = numberOfThreads; i-- != 0;)
try {
executorCompletionService.take().get();
} catch (Exception e) {
problem = e.getCause(); // We keep only the last one. They will be logged anyway.
}
executorService.shutdown();
if (problem != null)
throw (problem instanceof RuntimeException) ? (RuntimeException) problem : new RuntimeException(problem);
}
/**
* Sorts the specified array using parallel indirect radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code a[perm[i]] ≤ a[perm[i + 1]]}.
*
*
* This implementation uses a pool of {@link Runtime#availableProcessors()}
* threads.
*
* @param perm
* a permutation array indexing {@code a}.
* @param a
* the array to be sorted.
* @param stable
* whether the sorting algorithm should be stable.
*/
public static void parallelRadixSortIndirect(final int perm[], final int[] a, final boolean stable) {
parallelRadixSortIndirect(perm, a, 0, a.length, stable);
}
/**
* Sorts the specified pair of arrays lexicographically using radix sort.
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implements a lexicographical sorting of the arguments.
* Pairs of elements in the same position in the two provided arrays will be
* considered a single key, and permuted accordingly. In the end, either
* {@code a[i] < a[i + 1]} or {@code a[i] == a[i + 1]} and
* {@code b[i] ≤ b[i + 1]}.
*
* @param a
* the first array to be sorted.
* @param b
* the second array to be sorted.
*/
public static void radixSort(final int[] a, final int[] b) {
ensureSameLength(a, b);
radixSort(a, b, 0, a.length);
}
/**
* Sorts the specified range of elements of two arrays using radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implements a lexicographical sorting of the arguments.
* Pairs of elements in the same position in the two provided arrays will be
* considered a single key, and permuted accordingly. In the end, either
* {@code a[i] < a[i + 1]} or {@code a[i] == a[i + 1]} and
* {@code b[i] ≤ b[i + 1]}.
*
* @param a
* the first array to be sorted.
* @param b
* the second array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void radixSort(final int[] a, final int[] b, final int from, final int to) {
if (to - from < RADIXSORT_NO_REC) {
selectionSort(a, b, from, to);
return;
}
final int layers = 2;
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
final int stackSize = ((1 << DIGIT_BITS) - 1) * (layers * DIGITS_PER_ELEMENT - 1) + 1;
int stackPos = 0;
final int[] offsetStack = new int[stackSize];
final int[] lengthStack = new int[stackSize];
final int[] levelStack = new int[stackSize];
offsetStack[stackPos] = from;
lengthStack[stackPos] = to - from;
levelStack[stackPos++] = 0;
final int[] count = new int[1 << DIGIT_BITS];
final int[] pos = new int[1 << DIGIT_BITS];
while (stackPos > 0) {
final int first = offsetStack[--stackPos];
final int length = lengthStack[stackPos];
final int level = levelStack[stackPos];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int[] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the shift
// that extract the
// right byte from a
// key
// Count keys.
for (int i = first + length; i-- != first;)
count[((k[i]) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
for (int i = 0, p = first; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0)
lastUsed = i;
pos[i] = (p += count[i]);
}
final int end = first + length - count[lastUsed];
// i moves through the start of each block
for (int i = first, c = -1, d; i <= end; i += count[c], count[c] = 0) {
int t = a[i];
int u = b[i];
c = ((k[i]) >>> shift & DIGIT_MASK ^ signMask);
if (i < end) { // When all slots are OK, the last slot is necessarily OK.
while ((d = --pos[c]) > i) {
c = ((k[d]) >>> shift & DIGIT_MASK ^ signMask);
int z = t;
t = a[d];
a[d] = z;
z = u;
u = b[d];
b[d] = z;
}
a[i] = t;
b[i] = u;
}
if (level < maxLevel && count[c] > 1) {
if (count[c] < RADIXSORT_NO_REC)
selectionSort(a, b, i, i + count[c]);
else {
offsetStack[stackPos] = i;
lengthStack[stackPos] = count[c];
levelStack[stackPos++] = level + 1;
}
}
}
}
}
/**
* Sorts the specified range of elements of two arrays using a parallel radix
* sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implements a lexicographical sorting of the arguments.
* Pairs of elements in the same position in the two provided arrays will be
* considered a single key, and permuted accordingly. In the end, either
* {@code a[i] < a[i + 1]} or {@code a[i] == a[i + 1]} and
* {@code b[i] ≤ b[i + 1]}.
*
*
* This implementation uses a pool of {@link Runtime#availableProcessors()}
* threads.
*
* @param a
* the first array to be sorted.
* @param b
* the second array to be sorted.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void parallelRadixSort(final int[] a, final int[] b, final int from, final int to) {
if (to - from < PARALLEL_RADIXSORT_NO_FORK) {
quickSort(a, b, from, to);
return;
}
final int layers = 2;
if (a.length != b.length)
throw new IllegalArgumentException("Array size mismatch.");
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
final LinkedBlockingQueue queue = new LinkedBlockingQueue<>();
queue.add(new Segment(from, to - from, 0));
final AtomicInteger queueSize = new AtomicInteger(1);
final int numberOfThreads = Runtime.getRuntime().availableProcessors();
final ExecutorService executorService = Executors.newFixedThreadPool(numberOfThreads,
Executors.defaultThreadFactory());
final ExecutorCompletionService executorCompletionService = new ExecutorCompletionService<>(
executorService);
for (int j = numberOfThreads; j-- != 0;)
executorCompletionService.submit(() -> {
final int[] count = new int[1 << DIGIT_BITS];
final int[] pos = new int[1 << DIGIT_BITS];
for (;;) {
if (queueSize.get() == 0)
for (int i = numberOfThreads; i-- != 0;)
queue.add(POISON_PILL);
final Segment segment = queue.take();
if (segment == POISON_PILL)
return null;
final int first = segment.offset;
final int length = segment.length;
final int level = segment.level;
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int[] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS;
// Count keys.
for (int i = first + length; i-- != first;)
count[((k[i]) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
for (int i = 0, p = first; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0)
lastUsed = i;
pos[i] = (p += count[i]);
}
final int end = first + length - count[lastUsed];
for (int i = first, c = -1, d; i <= end; i += count[c], count[c] = 0) {
int t = a[i];
int u = b[i];
c = ((k[i]) >>> shift & DIGIT_MASK ^ signMask);
if (i < end) { // When all slots are OK, the last slot is necessarily OK.
while ((d = --pos[c]) > i) {
c = ((k[d]) >>> shift & DIGIT_MASK ^ signMask);
final int z = t;
final int w = u;
t = a[d];
u = b[d];
a[d] = z;
b[d] = w;
}
a[i] = t;
b[i] = u;
}
if (level < maxLevel && count[c] > 1) {
if (count[c] < PARALLEL_RADIXSORT_NO_FORK)
quickSort(a, b, i, i + count[c]);
else {
queueSize.incrementAndGet();
queue.add(new Segment(i, count[c], level + 1));
}
}
}
queueSize.decrementAndGet();
}
});
Throwable problem = null;
for (int i = numberOfThreads; i-- != 0;)
try {
executorCompletionService.take().get();
} catch (Exception e) {
problem = e.getCause(); // We keep only the last one. They will be logged anyway.
}
executorService.shutdown();
if (problem != null)
throw (problem instanceof RuntimeException) ? (RuntimeException) problem : new RuntimeException(problem);
}
/**
* Sorts two arrays using a parallel radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implements a lexicographical sorting of the arguments.
* Pairs of elements in the same position in the two provided arrays will be
* considered a single key, and permuted accordingly. In the end, either
* {@code a[i] < a[i + 1]} or {@code a[i] == a[i + 1]} and
* {@code b[i] ≤ b[i + 1]}.
*
*
* This implementation uses a pool of {@link Runtime#availableProcessors()}
* threads.
*
* @param a
* the first array to be sorted.
* @param b
* the second array to be sorted.
*/
public static void parallelRadixSort(final int[] a, final int[] b) {
ensureSameLength(a, b);
parallelRadixSort(a, b, 0, a.length);
}
private static void insertionSortIndirect(final int[] perm, final int[] a, final int[] b, final int from,
final int to) {
for (int i = from; ++i < to;) {
int t = perm[i];
int j = i;
for (int u = perm[j - 1]; ((a[t]) < (a[u])) || ((a[t]) == (a[u])) && ((b[t]) < (b[u])); u = perm[--j - 1]) {
perm[j] = u;
if (from == j - 1) {
--j;
break;
}
}
perm[j] = t;
}
}
/**
* Sorts the specified pair of arrays lexicographically using indirect radix
* sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code a[perm[i]] ≤ a[perm[i + 1]]} or
* {@code a[perm[i]] == a[perm[i + 1]]} and
* {@code b[perm[i]] ≤ b[perm[i + 1]]}.
*
*
* This implementation will allocate, in the stable case, a further support
* array as large as {@code perm} (note that the stable version is slightly
* faster).
*
* @param perm
* a permutation array indexing {@code a}.
* @param a
* the array to be sorted.
* @param b
* the second array to be sorted.
* @param stable
* whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect(final int[] perm, final int[] a, final int[] b, final boolean stable) {
ensureSameLength(a, b);
radixSortIndirect(perm, a, b, 0, a.length, stable);
}
/**
* Sorts the specified pair of arrays lexicographically using indirect radix
* sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implement an indirect sort. The elements of {@code perm}
* (which must be exactly the numbers in the interval {@code [0..perm.length)})
* will be permuted so that {@code a[perm[i]] ≤ a[perm[i + 1]]} or
* {@code a[perm[i]] == a[perm[i + 1]]} and
* {@code b[perm[i]] ≤ b[perm[i + 1]]}.
*
*
* This implementation will allocate, in the stable case, a further support
* array as large as {@code perm} (note that the stable version is slightly
* faster).
*
* @param perm
* a permutation array indexing {@code a}.
* @param a
* the array to be sorted.
* @param b
* the second array to be sorted.
* @param from
* the index of the first element of {@code perm} (inclusive) to be
* permuted.
* @param to
* the index of the last element of {@code perm} (exclusive) to be
* permuted.
* @param stable
* whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect(final int[] perm, final int[] a, final int[] b, final int from, final int to,
final boolean stable) {
if (to - from < RADIXSORT_NO_REC) {
insertionSortIndirect(perm, a, b, from, to);
return;
}
final int layers = 2;
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
final int stackSize = ((1 << DIGIT_BITS) - 1) * (layers * DIGITS_PER_ELEMENT - 1) + 1;
int stackPos = 0;
final int[] offsetStack = new int[stackSize];
final int[] lengthStack = new int[stackSize];
final int[] levelStack = new int[stackSize];
offsetStack[stackPos] = from;
lengthStack[stackPos] = to - from;
levelStack[stackPos++] = 0;
final int[] count = new int[1 << DIGIT_BITS];
final int[] pos = new int[1 << DIGIT_BITS];
final int[] support = stable ? new int[perm.length] : null;
while (stackPos > 0) {
final int first = offsetStack[--stackPos];
final int length = lengthStack[stackPos];
final int level = levelStack[stackPos];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int[] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the shift
// that extract the
// right byte from a
// key
// Count keys.
for (int i = first + length; i-- != first;)
count[((k[perm[i]]) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
for (int i = 0, p = stable ? 0 : first; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0)
lastUsed = i;
pos[i] = (p += count[i]);
}
if (stable) {
for (int i = first + length; i-- != first;)
support[--pos[((k[perm[i]]) >>> shift & DIGIT_MASK ^ signMask)]] = perm[i];
System.arraycopy(support, 0, perm, first, length);
for (int i = 0, p = first; i < 1 << DIGIT_BITS; i++) {
if (level < maxLevel && count[i] > 1) {
if (count[i] < RADIXSORT_NO_REC)
insertionSortIndirect(perm, a, b, p, p + count[i]);
else {
offsetStack[stackPos] = p;
lengthStack[stackPos] = count[i];
levelStack[stackPos++] = level + 1;
}
}
p += count[i];
}
java.util.Arrays.fill(count, 0);
} else {
final int end = first + length - count[lastUsed];
// i moves through the start of each block
for (int i = first, c = -1, d; i <= end; i += count[c], count[c] = 0) {
int t = perm[i];
c = ((k[t]) >>> shift & DIGIT_MASK ^ signMask);
if (i < end) { // When all slots are OK, the last slot is necessarily OK.
while ((d = --pos[c]) > i) {
final int z = t;
t = perm[d];
perm[d] = z;
c = ((k[t]) >>> shift & DIGIT_MASK ^ signMask);
}
perm[i] = t;
}
if (level < maxLevel && count[c] > 1) {
if (count[c] < RADIXSORT_NO_REC)
insertionSortIndirect(perm, a, b, i, i + count[c]);
else {
offsetStack[stackPos] = i;
lengthStack[stackPos] = count[c];
levelStack[stackPos++] = level + 1;
}
}
}
}
}
}
private static void selectionSort(final int[][] a, final int from, final int to, final int level) {
final int layers = a.length;
final int firstLayer = level / DIGITS_PER_ELEMENT;
for (int i = from; i < to - 1; i++) {
int m = i;
for (int j = i + 1; j < to; j++) {
for (int p = firstLayer; p < layers; p++) {
if (a[p][j] < a[p][m]) {
m = j;
break;
} else if (a[p][j] > a[p][m])
break;
}
}
if (m != i) {
for (int p = layers; p-- != 0;) {
final int u = a[p][i];
a[p][i] = a[p][m];
a[p][m] = u;
}
}
}
}
/**
* Sorts the specified array of arrays lexicographically using radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implements a lexicographical sorting of the provided
* arrays. Tuples of elements in the same position will be considered a single
* key, and permuted accordingly.
*
* @param a
* an array containing arrays of equal length to be sorted
* lexicographically in parallel.
*/
public static void radixSort(final int[][] a) {
radixSort(a, 0, a[0].length);
}
/**
* Sorts the specified array of arrays lexicographically using radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy,
* Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”,
* Computing Systems, 6(1), pages 5−27 (1993).
*
*
* This method implements a lexicographical sorting of the provided
* arrays. Tuples of elements in the same position will be considered a single
* key, and permuted accordingly.
*
* @param a
* an array containing arrays of equal length to be sorted
* lexicographically in parallel.
* @param from
* the index of the first element (inclusive) to be sorted.
* @param to
* the index of the last element (exclusive) to be sorted.
*/
public static void radixSort(final int[][] a, final int from, final int to) {
if (to - from < RADIXSORT_NO_REC) {
selectionSort(a, from, to, 0);
return;
}
final int layers = a.length;
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
for (int p = layers, l = a[0].length; p-- != 0;)
if (a[p].length != l)
throw new IllegalArgumentException(
"The array of index " + p + " has not the same length of the array of index 0.");
final int stackSize = ((1 << DIGIT_BITS) - 1) * (layers * DIGITS_PER_ELEMENT - 1) + 1;
int stackPos = 0;
final int[] offsetStack = new int[stackSize];
final int[] lengthStack = new int[stackSize];
final int[] levelStack = new int[stackSize];
offsetStack[stackPos] = from;
lengthStack[stackPos] = to - from;
levelStack[stackPos++] = 0;
final int[] count = new int[1 << DIGIT_BITS];
final int[] pos = new int[1 << DIGIT_BITS];
final int[] t = new int[layers];
while (stackPos > 0) {
final int first = offsetStack[--stackPos];
final int length = lengthStack[stackPos];
final int level = levelStack[stackPos];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int[] k = a[level / DIGITS_PER_ELEMENT]; // This is the key array
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the shift
// that extract the
// right byte from a
// key
// Count keys.
for (int i = first + length; i-- != first;)
count[((k[i]) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
for (int i = 0, p = first; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0)
lastUsed = i;
pos[i] = (p += count[i]);
}
final int end = first + length - count[lastUsed];
// i moves through the start of each block
for (int i = first, c = -1, d; i <= end; i += count[c], count[c] = 0) {
for (int p = layers; p-- != 0;)
t[p] = a[p][i];
c = ((k[i]) >>> shift & DIGIT_MASK ^ signMask);
if (i < end) { // When all slots are OK, the last slot is necessarily OK.
while ((d = --pos[c]) > i) {
c = ((k[d]) >>> shift & DIGIT_MASK ^ signMask);
for (int p = layers; p-- != 0;) {
final int u = t[p];
t[p] = a[p][d];
a[p][d] = u;
}
}
for (int p = layers; p-- != 0;)
a[p][i] = t[p];
}
if (level < maxLevel && count[c] > 1) {
if (count[c] < RADIXSORT_NO_REC)
selectionSort(a, i, i + count[c], level + 1);
else {
offsetStack[stackPos] = i;
lengthStack[stackPos] = count[c];
levelStack[stackPos++] = level + 1;
}
}
}
}
}
/**
* Shuffles the specified array fragment using the specified pseudorandom number
* generator.
*
* @param a
* the array to be shuffled.
* @param from
* the index of the first element (inclusive) to be shuffled.
* @param to
* the index of the last element (exclusive) to be shuffled.
* @param random
* a pseudorandom number generator.
* @return {@code a}.
*/
public static int[] shuffle(final int[] a, final int from, final int to, final Random random) {
for (int i = to - from; i-- != 0;) {
final int p = random.nextInt(i + 1);
final int t = a[from + i];
a[from + i] = a[from + p];
a[from + p] = t;
}
return a;
}
/**
* Shuffles the specified array using the specified pseudorandom number
* generator.
*
* @param a
* the array to be shuffled.
* @param random
* a pseudorandom number generator.
* @return {@code a}.
*/
public static int[] shuffle(final int[] a, final Random random) {
for (int i = a.length; i-- != 0;) {
final int p = random.nextInt(i + 1);
final int t = a[i];
a[i] = a[p];
a[p] = t;
}
return a;
}
/**
* Reverses the order of the elements in the specified array.
*
* @param a
* the array to be reversed.
* @return {@code a}.
*/
public static int[] reverse(final int[] a) {
final int length = a.length;
for (int i = length / 2; i-- != 0;) {
final int t = a[length - i - 1];
a[length - i - 1] = a[i];
a[i] = t;
}
return a;
}
/**
* Reverses the order of the elements in the specified array fragment.
*
* @param a
* the array to be reversed.
* @param from
* the index of the first element (inclusive) to be reversed.
* @param to
* the index of the last element (exclusive) to be reversed.
* @return {@code a}.
*/
public static int[] reverse(final int[] a, final int from, final int to) {
final int length = to - from;
for (int i = length / 2; i-- != 0;) {
final int t = a[from + length - i - 1];
a[from + length - i - 1] = a[from + i];
a[from + i] = t;
}
return a;
}
/** A type-specific content-based hash strategy for arrays. */
private static final class ArrayHashStrategy implements Hash.Strategy, java.io.Serializable {
private static final long serialVersionUID = -7046029254386353129L;
@Override
public int hashCode(final int[] o) {
return java.util.Arrays.hashCode(o);
}
@Override
public boolean equals(final int[] a, final int[] b) {
return java.util.Arrays.equals(a, b);
}
}
/**
* A type-specific content-based hash strategy for arrays.
*
*
* This hash strategy may be used in custom hash collections whenever keys are
* arrays, and they must be considered equal by content. This strategy will
* handle {@code null} correctly, and it is serializable.
*/
public static final Hash.Strategy HASH_STRATEGY = new ArrayHashStrategy();
}