Class LongArrays
 java.lang.Object

 it.unimi.dsi.fastutil.longs.LongArrays

public final class LongArrays extends Object
A class providing static methods and objects that do useful things with typespecific arrays.In particular, the
forceCapacity()
,ensureCapacity()
,grow()
,trim()
andsetLength()
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
BinIO
andTextIO
contain several methods make it possible to load and save arrays of primitive types as sequences of elements inDataInput
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 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.
However, if you wish to let the implementation choose an algorithm for you, both
stableSort(long[], int, int)
andunstableSort(long[], int, int)
methods are available, which dynamically chooses an algorithm based on unspecified criteria (but most likely stability, array size, and array element type).All comparisonbased algorithm have an implementation based on a typespecific comparator.
As a general rule, sequential radix sort is significantly faster than quicksort or mergesort, in particular on randomlooking 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 dualpivot parallel sorts in
Arrays
are about 50% faster than the classical singlepivot 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 Also:
Arrays


Field Summary
Fields Modifier and Type Field Description static long[]
DEFAULT_EMPTY_ARRAY
A static, final, empty array to be used as default array in allocations.static long[]
EMPTY_ARRAY
A static, final, empty array.static Hash.Strategy<long[]>
HASH_STRATEGY
A typespecific contentbased hash strategy for arrays.

Method Summary
Modifier and Type Method Description static int
binarySearch(long[] a, int from, int to, long key)
Searches a range of the specified array for the specified value using the binary search algorithm.static int
binarySearch(long[] a, int from, int to, long key, LongComparator c)
Searches a range of the specified array for the specified value using the binary search algorithm and a specified comparator.static int
binarySearch(long[] a, long key)
Searches an array for the specified value using the binary search algorithm.static int
binarySearch(long[] a, long key, LongComparator c)
Searches an array for the specified value using the binary search algorithm and a specified comparator.static long[]
copy(long[] array)
Returns a copy of an array.static long[]
copy(long[] array, int offset, int length)
Returns a copy of a portion of an array.static long[]
ensureCapacity(long[] array, int length)
Ensures that an array can contain the given number of entries.static long[]
ensureCapacity(long[] array, int length, int preserve)
Ensures that an array can contain the given number of entries, preserving just a part of the array.static void
ensureFromTo(long[] a, int from, int to)
Ensures that a range given by its first (inclusive) and last (exclusive) elements fits an array.static void
ensureOffsetLength(long[] a, int offset, int length)
Ensures that a range given by an offset and a length fits an array.static void
ensureSameLength(long[] a, long[] b)
Ensures that two arrays are of the same length.static boolean
equals(long[] a1, long[] a2)
Deprecated.Please use the correspondingArrays
method, which is intrinsified in recent JVMs.static void
fill(long[] array, int from, int to, long value)
Deprecated.Please use the correspondingArrays
method.static void
fill(long[] array, long value)
Deprecated.Please use the correspondingArrays
method.static long[]
forceCapacity(long[] array, int length, int preserve)
Forces an array to contain the given number of entries, preserving just a part of the array.static long[]
grow(long[] array, int 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.static long[]
grow(long[] array, int length, int preserve)
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.static void
mergeSort(long[] a)
Sorts an array according to the natural ascending order using mergesort.static void
mergeSort(long[] a, int from, int to)
Sorts the specified range of elements according to the natural ascending order using mergesort.static void
mergeSort(long[] a, int from, int to, long[] supp)
Sorts the specified range of elements according to the natural ascending order using mergesort, using a given prefilled support array.static void
mergeSort(long[] a, int from, int to, LongComparator comp)
Sorts the specified range of elements according to the order induced by the specified comparator using mergesort.static void
mergeSort(long[] a, int from, int to, LongComparator comp, long[] supp)
Sorts the specified range of elements according to the order induced by the specified comparator using mergesort, using a given prefilled support array.static void
mergeSort(long[] a, LongComparator comp)
Sorts an array according to the order induced by the specified comparator using mergesort.static void
parallelQuickSort(long[] x)
Sorts an array according to the natural ascending order using a parallel quicksort.static void
parallelQuickSort(long[] x, int from, int to)
Sorts the specified range of elements according to the natural ascending order using a parallel quicksort.static void
parallelQuickSort(long[] x, int from, int to, LongComparator comp)
Sorts the specified range of elements according to the order induced by the specified comparator using a parallel quicksort.static void
parallelQuickSort(long[] x, long[] y)
Sorts two arrays according to the natural lexicographical ascending order using a parallel quicksort.static void
parallelQuickSort(long[] x, long[] y, int from, int to)
Sorts the specified range of elements of two arrays according to the natural lexicographical ascending order using a parallel quicksort.static void
parallelQuickSort(long[] x, LongComparator comp)
Sorts an array according to the order induced by the specified comparator using a parallel quicksort.static void
parallelQuickSortIndirect(int[] perm, long[] x)
Sorts an array according to the natural ascending order using a parallel indirect quicksort.static void
parallelQuickSortIndirect(int[] perm, long[] x, int from, int to)
Sorts the specified range of elements according to the natural ascending order using a parallel indirect quicksort.static void
parallelRadixSort(long[] a)
Sorts the specified array using parallel radix sort.static void
parallelRadixSort(long[] a, int from, int to)
Sorts the specified range of an array using parallel radix sort.static void
parallelRadixSort(long[] a, long[] b)
Sorts two arrays using a parallel radix sort.static void
parallelRadixSort(long[] a, long[] b, int from, int to)
Sorts the specified range of elements of two arrays using a parallel radix sort.static void
parallelRadixSortIndirect(int[] perm, long[] a, boolean stable)
Sorts the specified array using parallel indirect radix sort.static void
parallelRadixSortIndirect(int[] perm, long[] a, int from, int to, boolean stable)
Sorts the specified range of an array using parallel indirect radix sort.static void
quickSort(long[] x)
Sorts an array according to the natural ascending order using quicksort.static void
quickSort(long[] x, int from, int to)
Sorts the specified range of elements according to the natural ascending order using quicksort.static void
quickSort(long[] x, int from, int to, LongComparator comp)
Sorts the specified range of elements according to the order induced by the specified comparator using quicksort.static void
quickSort(long[] x, long[] y)
Sorts two arrays according to the natural lexicographical ascending order using quicksort.static void
quickSort(long[] x, long[] y, int from, int to)
Sorts the specified range of elements of two arrays according to the natural lexicographical ascending order using quicksort.static void
quickSort(long[] x, LongComparator comp)
Sorts an array according to the order induced by the specified comparator using quicksort.static void
quickSortIndirect(int[] perm, long[] x)
Sorts an array according to the natural ascending order using indirect quicksort.static void
quickSortIndirect(int[] perm, long[] x, int from, int to)
Sorts the specified range of elements according to the natural ascending order using indirect quicksort.static void
radixSort(long[] a)
Sorts the specified array using radix sort.static void
radixSort(long[][] a)
Sorts the specified array of arrays lexicographically using radix sort.static void
radixSort(long[][] a, int from, int to)
Sorts the specified array of arrays lexicographically using radix sort.static void
radixSort(long[] a, int from, int to)
Sorts the specified range of an array using radix sort.static void
radixSort(long[] a, long[] b)
Sorts the specified pair of arrays lexicographically using radix sort.static void
radixSort(long[] a, long[] b, int from, int to)
Sorts the specified range of elements of two arrays using radix sort.static void
radixSortIndirect(int[] perm, long[] a, boolean stable)
Sorts the specified array using indirect radix sort.static void
radixSortIndirect(int[] perm, long[] a, int from, int to, boolean stable)
Sorts the specified array using indirect radix sort.static void
radixSortIndirect(int[] perm, long[] a, long[] b, boolean stable)
Sorts the specified pair of arrays lexicographically using indirect radix sort.static void
radixSortIndirect(int[] perm, long[] a, long[] b, int from, int to, boolean stable)
Sorts the specified pair of arrays lexicographically using indirect radix sort.static long[]
reverse(long[] a)
Reverses the order of the elements in the specified array.static long[]
reverse(long[] a, int from, int to)
Reverses the order of the elements in the specified array fragment.static long[]
setLength(long[] array, int length)
Sets the length of the given array.static long[]
shuffle(long[] a, int from, int to, Random random)
Shuffles the specified array fragment using the specified pseudorandom number generator.static long[]
shuffle(long[] a, Random random)
Shuffles the specified array using the specified pseudorandom number generator.static void
stabilize(int[] perm, long[] x)
Stabilizes a permutation.static void
stabilize(int[] perm, long[] x, int from, int to)
Stabilizes a permutation.static void
stableSort(long[] a)
Sorts the specified range of elements according to the natural ascending order potentially dynamically choosing an appropriate algorithm given the type and size of the array.static void
stableSort(long[] a, int from, int to)
Sorts an array according to the natural ascending order, potentially dynamically choosing an appropriate algorithm given the type and size of the array.static void
stableSort(long[] a, int from, int to, LongComparator comp)
Sorts the specified range of elements according to the order induced by the specified comparator, potentially dynamically choosing an appropriate algorithm given the type and size of the array.static void
stableSort(long[] a, LongComparator comp)
Sorts an array according to the order induced by the specified comparator, potentially dynamically choosing an appropriate algorithm given the type and size of the array.static void
swap(long[] x, int a, int b)
Swaps two elements of an anrray.static void
swap(long[] x, int a, int b, int n)
Swaps two sequences of elements of an array.static long[]
trim(long[] array, int length)
Trims the given array to the given length.static void
unstableSort(long[] a)
Sorts the specified range of elements according to the natural ascending order potentially dynamically choosing an appropriate algorithm given the type and size of the array.static void
unstableSort(long[] a, int from, int to)
Sorts an array according to the natural ascending order, potentially dynamically choosing an appropriate algorithm given the type and size of the array.static void
unstableSort(long[] a, int from, int to, LongComparator comp)
Sorts the specified range of elements according to the order induced by the specified comparator, potentially dynamically choosing an appropriate algorithm given the type and size of the array.static void
unstableSort(long[] a, LongComparator comp)
Sorts an array according to the order induced by the specified comparator, potentially dynamically choosing an appropriate algorithm given the type and size of the array.



Field Detail

EMPTY_ARRAY
public static final long[] EMPTY_ARRAY
A static, final, empty array.

DEFAULT_EMPTY_ARRAY
public static final long[] DEFAULT_EMPTY_ARRAY
A static, final, empty array to be used as default array in allocations. An object distinct fromEMPTY_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 Also:
ArrayList

HASH_STRATEGY
public static final Hash.Strategy<long[]> HASH_STRATEGY
A typespecific contentbased 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
null
correctly, and it is serializable.


Method Detail

forceCapacity
public static long[] forceCapacity(long[] array, int length, int preserve)
Forces an array to contain the given number of entries, preserving just a part of the array. Parameters:
array
 an array.length
 the new minimum length for this array.preserve
 the number of elements of the array that must be preserved in case a new allocation is necessary. Returns:
 an array with
length
entries whose firstpreserve
entries are the same as those ofarray
.

ensureCapacity
public static long[] ensureCapacity(long[] array, int length)
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
grow()
instead. Parameters:
array
 an array.length
 the new minimum length for this array. Returns:
array
, if it containslength
entries or more; otherwise, an array withlength
entries whose firstarray.length
entries are the same as those ofarray
.

ensureCapacity
public static long[] ensureCapacity(long[] array, int length, int preserve)
Ensures that an array can contain the given number of entries, preserving just a part of the array. Parameters:
array
 an array.length
 the new minimum length for this array.preserve
 the number of elements of the array that must be preserved in case a new allocation is necessary. Returns:
array
, if it can containlength
entries or more; otherwise, an array withlength
entries whose firstpreserve
entries are the same as those ofarray
.

grow
public static long[] grow(long[] array, int 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.If you want complete control on the array growth, you should probably use
ensureCapacity()
instead. Parameters:
array
 an array.length
 the new minimum length for this array. Returns:
array
, if it can containlength
entries; otherwise, an array with max(length
,array.length
/φ) entries whose firstarray.length
entries are the same as those ofarray
.

grow
public static long[] grow(long[] array, int length, int preserve)
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
ensureCapacity()
instead. Parameters:
array
 an array.length
 the new minimum length for this array.preserve
 the number of elements of the array that must be preserved in case a new allocation is necessary. Returns:
array
, if it can containlength
entries; otherwise, an array with max(length
,array.length
/φ) entries whose firstpreserve
entries are the same as those ofarray
.

trim
public static long[] trim(long[] array, int length)
Trims the given array to the given length. Parameters:
array
 an array.length
 the new maximum length for the array. Returns:
array
, if it containslength
entries or less; otherwise, an array withlength
entries whose entries are the same as the firstlength
entries ofarray
.

setLength
public static long[] setLength(long[] array, int length)
Sets the length of the given array. Parameters:
array
 an array.length
 the new length for the array. Returns:
array
, if it contains exactlylength
entries; otherwise, if it contains more thanlength
entries, an array withlength
entries whose entries are the same as the firstlength
entries ofarray
; otherwise, an array withlength
entries whose firstarray.length
entries are the same as those ofarray
.

copy
public static long[] copy(long[] array, int offset, int length)
Returns a copy of a portion of an array. Parameters:
array
 an array.offset
 the first element to copy.length
 the number of elements to copy. Returns:
 a new array containing
length
elements ofarray
starting atoffset
.

copy
public static long[] copy(long[] array)
Returns a copy of an array. Parameters:
array
 an array. Returns:
 a copy of
array
.

fill
@Deprecated public static void fill(long[] array, long value)
Deprecated.Please use the correspondingArrays
method.Fills the given array with the given value. Parameters:
array
 an array.value
 the new value for all elements of the array.

fill
@Deprecated public static void fill(long[] array, int from, int to, long value)
Deprecated.Please use the correspondingArrays
method.Fills a portion of the given array with the given value. Parameters:
array
 an array.from
 the starting index of the portion to fill (inclusive).to
 the end index of the portion to fill (exclusive).value
 the new value for all elements of the specified portion of the array.

equals
@Deprecated public static boolean equals(long[] a1, long[] a2)
Deprecated.Please use the correspondingArrays
method, which is intrinsified in recent JVMs.Returns true if the two arrays are elementwise equal. Parameters:
a1
 an array.a2
 another array. Returns:
 true if the two arrays are of the same length, and their elements are equal.

ensureFromTo
public static void ensureFromTo(long[] a, int from, int to)
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.
 Parameters:
a
 an array.from
 a start index (inclusive).to
 an end index (exclusive). Throws:
IllegalArgumentException
 iffrom
is greater thanto
.ArrayIndexOutOfBoundsException
 iffrom
orto
are greater than the array length or negative.

ensureOffsetLength
public static void ensureOffsetLength(long[] a, int offset, int length)
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.
 Parameters:
a
 an array.offset
 a start index.length
 a length (the number of elements in the range). Throws:
IllegalArgumentException
 iflength
is negative.ArrayIndexOutOfBoundsException
 ifoffset
is negative oroffset
+length
is greater than the array length.

ensureSameLength
public static void ensureSameLength(long[] a, long[] b)
Ensures that two arrays are of the same length. Parameters:
a
 an array.b
 another array. Throws:
IllegalArgumentException
 if the two argument arrays are not of the same length.

swap
public static void swap(long[] x, int a, int b)
Swaps two elements of an anrray. Parameters:
x
 an array.a
 a position inx
.b
 another position inx
.

swap
public static void swap(long[] x, int a, int b, int n)
Swaps two sequences of elements of an array. Parameters:
x
 an array.a
 a position inx
.b
 another position inx
.n
 the number of elements to exchange starting ata
andb
.

quickSort
public static void quickSort(long[] x, int from, int to, LongComparator comp)
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
Arrays
, which switches to mergesort on large inputs. Parameters:
x
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.comp
 the comparator to determine the sorting order.

quickSort
public static void quickSort(long[] x, LongComparator 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
Arrays
, which switches to mergesort on large inputs. Parameters:
x
 the array to be sorted.comp
 the comparator to determine the sorting order.

parallelQuickSort
public static void parallelQuickSort(long[] x, int from, int to, LongComparator 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
ForkJoinPool
executor service withRuntime.availableProcessors()
parallel threads. Parameters:
x
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.comp
 the comparator to determine the sorting order.

parallelQuickSort
public static void parallelQuickSort(long[] x, LongComparator comp)
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
ForkJoinPool
executor service withRuntime.availableProcessors()
parallel threads. Parameters:
x
 the array to be sorted.comp
 the comparator to determine the sorting order.

quickSort
public static void quickSort(long[] x, int from, int to)
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
Arrays
, which switches to mergesort on large inputs. Parameters:
x
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

quickSort
public static void quickSort(long[] x)
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
Arrays
, which switches to mergesort on large inputs. Parameters:
x
 the array to be sorted.

parallelQuickSort
public static void parallelQuickSort(long[] x, int from, int 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
ForkJoinPool
executor service withRuntime.availableProcessors()
parallel threads. Parameters:
x
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

parallelQuickSort
public static void parallelQuickSort(long[] x)
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
ForkJoinPool
executor service withRuntime.availableProcessors()
parallel threads. Parameters:
x
 the array to be sorted.

quickSortIndirect
public static void quickSortIndirect(int[] perm, long[] x, int from, int to)
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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thatx[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
Arrays
, which switches to mergesort on large inputs. Parameters:
perm
 a permutation array indexingx
.x
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

quickSortIndirect
public static void quickSortIndirect(int[] perm, long[] x)
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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thatx[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
Arrays
, which switches to mergesort on large inputs. Parameters:
perm
 a permutation array indexingx
.x
 the array to be sorted.

parallelQuickSortIndirect
public static void parallelQuickSortIndirect(int[] perm, long[] x, int from, int 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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thatx[perm[i]] ≤ x[perm[i + 1]]
.This implementation uses a
ForkJoinPool
executor service withRuntime.availableProcessors()
parallel threads. Parameters:
perm
 a permutation array indexingx
.x
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

parallelQuickSortIndirect
public static void parallelQuickSortIndirect(int[] perm, long[] x)
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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thatx[perm[i]] ≤ x[perm[i + 1]]
.This implementation uses a
ForkJoinPool
executor service withRuntime.availableProcessors()
parallel threads. Parameters:
perm
 a permutation array indexingx
.x
 the array to be sorted.

stabilize
public static void stabilize(int[] perm, long[] x, int from, int 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 nonsingleton block of elements with the same associated values in
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
x[perm[i]] ≤ x[perm[i + 1]]
, after stabilization we will also have thatx[perm[i]] = x[perm[i + 1]]
impliesperm[i] ≤ perm[i + 1]
. Parameters:
perm
 a permutation array indexingx
so that it is sorted.x
 the sorted array to be stabilized.from
 the index of the first element (inclusive) to be stabilized.to
 the index of the last element (exclusive) to be stabilized.

stabilize
public static void stabilize(int[] perm, long[] x)
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 nonsingleton block of elements with the same associated values in
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
x[perm[i]] ≤ x[perm[i + 1]]
, after stabilization we will also have thatx[perm[i]] = x[perm[i + 1]]
impliesperm[i] ≤ perm[i + 1]
. Parameters:
perm
 a permutation array indexingx
so that it is sorted.x
 the sorted array to be stabilized.

quickSort
public static void quickSort(long[] x, long[] y, int from, int to)
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
x[i] < x[i + 1]
orx[i] == x[i + 1]
andy[i] ≤ y[i + 1]
. Parameters:
x
 the first array to be sorted.y
 the second array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

quickSort
public static void quickSort(long[] x, long[] y)
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
x[i] < x[i + 1]
orx[i] == x[i + 1]
andy[i] ≤ y[i + 1]
. Parameters:
x
 the first array to be sorted.y
 the second array to be sorted.

parallelQuickSort
public static void parallelQuickSort(long[] x, long[] y, int from, int 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
x[i] < x[i + 1]
orx[i] == x[i + 1]
andy[i] ≤ y[i + 1]
.This implementation uses a
ForkJoinPool
executor service withRuntime.availableProcessors()
parallel threads. Parameters:
x
 the first array to be sorted.y
 the second array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

parallelQuickSort
public static void parallelQuickSort(long[] x, long[] y)
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
x[i] < x[i + 1]
orx[i] == x[i + 1]
andy[i] ≤ y[i + 1]
.This implementation uses a
ForkJoinPool
executor service withRuntime.availableProcessors()
parallel threads. Parameters:
x
 the first array to be sorted.y
 the second array to be sorted.

unstableSort
public static void unstableSort(long[] a, int from, int to)
Sorts an array according to the natural ascending order, potentially dynamically choosing an appropriate algorithm given the type and size of the array. The sort will be stable unless it is provable that it would be impossible for there to be any difference between a stable and unstable sort for the given type, in which case stability is meaningless and thus unspecified. Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted. Since:
 8.3.0

unstableSort
public static void unstableSort(long[] a)
Sorts the specified range of elements according to the natural ascending order potentially dynamically choosing an appropriate algorithm given the type and size of the array. No assurance is made of the stability of the sort. Parameters:
a
 the array to be sorted. Since:
 8.3.0

unstableSort
public static void unstableSort(long[] a, int from, int to, LongComparator comp)
Sorts the specified range of elements according to the order induced by the specified comparator, potentially dynamically choosing an appropriate algorithm given the type and size of the array. No assurance is made of the stability of the sort. Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.comp
 the comparator to determine the sorting order. Since:
 8.3.0

unstableSort
public static void unstableSort(long[] a, LongComparator comp)
Sorts an array according to the order induced by the specified comparator, potentially dynamically choosing an appropriate algorithm given the type and size of the array. No assurance is made of the stability of the sort. Parameters:
a
 the array to be sorted.comp
 the comparator to determine the sorting order. Since:
 8.3.0

mergeSort
public static void mergeSort(long[] a, int from, int to, long[] supp)
Sorts the specified range of elements according to the natural ascending order using mergesort, using a given prefilled 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.
 Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.supp
 a support array containing at leastto
elements, and whose entries are identical to those ofa
in the specified range.

mergeSort
public static void mergeSort(long[] a, int from, int to)
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
a
will be allocated by this method. Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

mergeSort
public static void mergeSort(long[] a)
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
a
will be allocated by this method. Parameters:
a
 the array to be sorted.

mergeSort
public static void mergeSort(long[] a, int from, int to, LongComparator comp, long[] supp)
Sorts the specified range of elements according to the order induced by the specified comparator using mergesort, using a given prefilled 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.
 Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.comp
 the comparator to determine the sorting order.supp
 a support array containing at leastto
elements, and whose entries are identical to those ofa
in the specified range.

mergeSort
public static void mergeSort(long[] a, int from, int to, LongComparator comp)
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
a
will be allocated by this method. Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.comp
 the comparator to determine the sorting order.

mergeSort
public static void mergeSort(long[] a, LongComparator comp)
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
a
will be allocated by this method. Parameters:
a
 the array to be sorted.comp
 the comparator to determine the sorting order.

stableSort
public static void stableSort(long[] a, int from, int to)
Sorts an array according to the natural ascending order, potentially dynamically choosing an appropriate algorithm given the type and size of the array. The sort will be stable unless it is provable that it would be impossible for there to be any difference between a stable and unstable sort for the given type, in which case stability is meaningless and thus unspecified.An array as large as
a
may be allocated by this method. Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted. Since:
 8.3.0

stableSort
public static void stableSort(long[] a)
Sorts the specified range of elements according to the natural ascending order potentially dynamically choosing an appropriate algorithm given the type and size of the array. The sort will be stable unless it is provable that it would be impossible for there to be any difference between a stable and unstable sort for the given type, in which case stability is meaningless and thus unspecified.An array as large as
a
may be allocated by this method. Parameters:
a
 the array to be sorted. Since:
 8.3.0

stableSort
public static void stableSort(long[] a, int from, int to, LongComparator comp)
Sorts the specified range of elements according to the order induced by the specified comparator, potentially dynamically choosing an appropriate algorithm given the type and size of the array. The sort will be stable unless it is provable that it would be impossible for there to be any difference between a stable and unstable sort for the given type, in which case stability is meaningless and thus unspecified.An array as large as
a
may be allocated by this method. Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.comp
 the comparator to determine the sorting order. Since:
 8.3.0

stableSort
public static void stableSort(long[] a, LongComparator comp)
Sorts an array according to the order induced by the specified comparator, potentially dynamically choosing an appropriate algorithm given the type and size of the array. The sort will be stable unless it is provable that it would be impossible for there to be any difference between a stable and unstable sort for the given type, in which case stability is meaningless and thus unspecified.An array as large as
a
may be allocated by this method. Parameters:
a
 the array to be sorted.comp
 the comparator to determine the sorting order. Since:
 8.3.0

binarySearch
public static int binarySearch(long[] a, int from, int to, long key)
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. Parameters:
a
 the array to be searched.from
 the index of the first element (inclusive) to be searched.to
 the index of the last element (exclusive) to be searched.key
 the value to be searched for. Returns:
 index of the search key, if it is contained in the array; otherwise,
((<i>insertion point</i>)  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 Also:
Arrays

binarySearch
public static int binarySearch(long[] a, long key)
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. Parameters:
a
 the array to be searched.key
 the value to be searched for. Returns:
 index of the search key, if it is contained in the array; otherwise,
((<i>insertion point</i>)  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 Also:
Arrays

binarySearch
public static int binarySearch(long[] a, int from, int to, long key, LongComparator c)
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. Parameters:
a
 the array to be searched.from
 the index of the first element (inclusive) to be searched.to
 the index of the last element (exclusive) to be searched.key
 the value to be searched for.c
 a comparator. Returns:
 index of the search key, if it is contained in the array; otherwise,
((<i>insertion point</i>)  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 Also:
Arrays

binarySearch
public static int binarySearch(long[] a, long key, LongComparator c)
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. Parameters:
a
 the array to be searched.key
 the value to be searched for.c
 a comparator. Returns:
 index of the search key, if it is contained in the array; otherwise,
((<i>insertion point</i>)  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 Also:
Arrays

radixSort
public static void radixSort(long[] a)
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 5000 elements), but it can only sort in ascending order.
 Parameters:
a
 the array to be sorted.

radixSort
public static void radixSort(long[] a, int from, int to)
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 5000 elements), but it can only sort in ascending order.
 Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

parallelRadixSort
public static void parallelRadixSort(long[] a, int from, int to)
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
Runtime.availableProcessors()
threads. Parameters:
a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

parallelRadixSort
public static void parallelRadixSort(long[] a)
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
Runtime.availableProcessors()
threads. Parameters:
a
 the array to be sorted.

radixSortIndirect
public static void radixSortIndirect(int[] perm, long[] a, boolean 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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thata[perm[i]] ≤ a[perm[i + 1]]
.This implementation will allocate, in the stable case, a support array as large as
perm
(note that the stable version is slightly faster). Parameters:
perm
 a permutation array indexinga
.a
 the array to be sorted.stable
 whether the sorting algorithm should be stable.

radixSortIndirect
public static void radixSortIndirect(int[] perm, long[] a, int from, int to, boolean 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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thata[perm[i]] ≤ a[perm[i + 1]]
.This implementation will allocate, in the stable case, a support array as large as
perm
(note that the stable version is slightly faster). Parameters:
perm
 a permutation array indexinga
.a
 the array to be sorted.from
 the index of the first element ofperm
(inclusive) to be permuted.to
 the index of the last element ofperm
(exclusive) to be permuted.stable
 whether the sorting algorithm should be stable.

parallelRadixSortIndirect
public static void parallelRadixSortIndirect(int[] perm, long[] a, int from, int to, boolean stable)
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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thata[perm[i]] ≤ a[perm[i + 1]]
.This implementation uses a pool of
Runtime.availableProcessors()
threads. Parameters:
perm
 a permutation array indexinga
.a
 the array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.stable
 whether the sorting algorithm should be stable.

parallelRadixSortIndirect
public static void parallelRadixSortIndirect(int[] perm, long[] a, boolean stable)
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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thata[perm[i]] ≤ a[perm[i + 1]]
.This implementation uses a pool of
Runtime.availableProcessors()
threads. Parameters:
perm
 a permutation array indexinga
.a
 the array to be sorted.stable
 whether the sorting algorithm should be stable.

radixSort
public static void radixSort(long[] a, long[] b)
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
a[i] < a[i + 1]
ora[i] == a[i + 1]
andb[i] ≤ b[i + 1]
. Parameters:
a
 the first array to be sorted.b
 the second array to be sorted.

radixSort
public static void radixSort(long[] a, long[] b, int from, int to)
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
a[i] < a[i + 1]
ora[i] == a[i + 1]
andb[i] ≤ b[i + 1]
. Parameters:
a
 the first array to be sorted.b
 the second array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

parallelRadixSort
public static void parallelRadixSort(long[] a, long[] b, int from, int to)
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
a[i] < a[i + 1]
ora[i] == a[i + 1]
andb[i] ≤ b[i + 1]
.This implementation uses a pool of
Runtime.availableProcessors()
threads. Parameters:
a
 the first array to be sorted.b
 the second array to be sorted.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

parallelRadixSort
public static void parallelRadixSort(long[] a, long[] b)
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
a[i] < a[i + 1]
ora[i] == a[i + 1]
andb[i] ≤ b[i + 1]
.This implementation uses a pool of
Runtime.availableProcessors()
threads. Parameters:
a
 the first array to be sorted.b
 the second array to be sorted.

radixSortIndirect
public static void radixSortIndirect(int[] perm, long[] a, long[] b, boolean 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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thata[perm[i]] ≤ a[perm[i + 1]]
ora[perm[i]] == a[perm[i + 1]]
andb[perm[i]] ≤ b[perm[i + 1]]
.This implementation will allocate, in the stable case, a further support array as large as
perm
(note that the stable version is slightly faster). Parameters:
perm
 a permutation array indexinga
.a
 the array to be sorted.b
 the second array to be sorted.stable
 whether the sorting algorithm should be stable.

radixSortIndirect
public static void radixSortIndirect(int[] perm, long[] a, long[] b, int from, int to, boolean 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
perm
(which must be exactly the numbers in the interval[0..perm.length)
) will be permuted so thata[perm[i]] ≤ a[perm[i + 1]]
ora[perm[i]] == a[perm[i + 1]]
andb[perm[i]] ≤ b[perm[i + 1]]
.This implementation will allocate, in the stable case, a further support array as large as
perm
(note that the stable version is slightly faster). Parameters:
perm
 a permutation array indexinga
.a
 the array to be sorted.b
 the second array to be sorted.from
 the index of the first element ofperm
(inclusive) to be permuted.to
 the index of the last element ofperm
(exclusive) to be permuted.stable
 whether the sorting algorithm should be stable.

radixSort
public static void radixSort(long[][] a)
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.
 Parameters:
a
 an array containing arrays of equal length to be sorted lexicographically in parallel.

radixSort
public static void radixSort(long[][] a, int from, int to)
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.
 Parameters:
a
 an array containing arrays of equal length to be sorted lexicographically in parallel.from
 the index of the first element (inclusive) to be sorted.to
 the index of the last element (exclusive) to be sorted.

shuffle
public static long[] shuffle(long[] a, int from, int to, Random random)
Shuffles the specified array fragment using the specified pseudorandom number generator. Parameters:
a
 the array to be shuffled.from
 the index of the first element (inclusive) to be shuffled.to
 the index of the last element (exclusive) to be shuffled.random
 a pseudorandom number generator. Returns:
a
.

shuffle
public static long[] shuffle(long[] a, Random random)
Shuffles the specified array using the specified pseudorandom number generator. Parameters:
a
 the array to be shuffled.random
 a pseudorandom number generator. Returns:
a
.

reverse
public static long[] reverse(long[] a)
Reverses the order of the elements in the specified array. Parameters:
a
 the array to be reversed. Returns:
a
.

reverse
public static long[] reverse(long[] a, int from, int to)
Reverses the order of the elements in the specified array fragment. Parameters:
a
 the array to be reversed.from
 the index of the first element (inclusive) to be reversed.to
 the index of the last element (exclusive) to be reversed. Returns:
a
.

