public final class LongArrays
extends java.lang.Object
In particular, the forceCapacity()
, ensureCapacity()
,
grow()
, trim()
and 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 BinIO
and
TextIO
contain several methods make it
possible to load and save arrays of primitive types as sequences of elements
in DataInput
format (i.e., not as objects) or as sequences of
lines of text.
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.
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.
Arrays
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.

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 corresponding
Arrays method,
which is intrinsified in recent JVMs. 
static void 
fill(long[] array,
int from,
int to,
long value) 
Deprecated.
Please use the corresponding
Arrays method. 
static void 
fill(long[] array,
long value) 
Deprecated.
Please use the corresponding
Arrays 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,
java.util.Random random) 
Shuffles the specified array fragment using the specified pseudorandom number
generator.

static long[] 
shuffle(long[] a,
java.util.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 
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.

public static final long[] EMPTY_ARRAY
public static final long[] DEFAULT_EMPTY_ARRAY
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.ArrayList
public static final Hash.Strategy<long[]> HASH_STRATEGY
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.
public static long[] forceCapacity(long[] array, int length, int preserve)
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.length
entries whose first preserve
entries are the same as those of array
.public static long[] ensureCapacity(long[] array, int length)
If you cannot foresee whether this array will need again to be enlarged, you
should probably use grow()
instead.
array
 an array.length
 the new minimum length for this array.array
, if it contains length
entries or more;
otherwise, an array with length
entries whose first
array.length
entries are the same as those of array
.public static long[] ensureCapacity(long[] array, int length, int preserve)
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.array
, if it can contain length
entries or more;
otherwise, an array with length
entries whose first
preserve
entries are the same as those of array
.public static long[] grow(long[] array, int length)
If you want complete control on the array growth, you should probably use
ensureCapacity()
instead.
array
 an array.length
 the new minimum length for this array.array
, if it can contain length
entries; otherwise,
an array with max(length
,array.length
/φ) entries
whose first array.length
entries are the same as those of
array
.public static long[] grow(long[] array, int length, int preserve)
If you want complete control on the array growth, you should probably use
ensureCapacity()
instead.
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.array
, if it can contain length
entries; otherwise,
an array with max(length
,array.length
/φ) entries
whose first preserve
entries are the same as those of
array
.public static long[] trim(long[] array, int length)
array
 an array.length
 the new maximum length for the array.array
, if it contains length
entries or less;
otherwise, an array with length
entries whose entries are the
same as the first length
entries of array
.public static long[] setLength(long[] array, int length)
array
 an array.length
 the new length for the array.array
, if it contains exactly length
entries;
otherwise, if it contains more than length
entries,
an array with length
entries whose entries are the same as
the first length
entries of array
; otherwise, an
array with length
entries whose first array.length
entries are the same as those of array
.public static long[] copy(long[] array, int offset, int length)
array
 an array.offset
 the first element to copy.length
 the number of elements to copy.length
elements of array
starting at offset
.public static long[] copy(long[] array)
array
 an array.array
.@Deprecated public static void fill(long[] array, long value)
Arrays
method.array
 an array.value
 the new value for all elements of the array.@Deprecated public static void fill(long[] array, int from, int to, long value)
Arrays
method.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.@Deprecated public static boolean equals(long[] a1, long[] a2)
Arrays
method,
which is intrinsified in recent JVMs.a1
 an array.a2
 another array.public static void ensureFromTo(long[] a, int from, int to)
This method may be used whenever an array range check is needed.
a
 an array.from
 a start index (inclusive).to
 an end index (exclusive).java.lang.IllegalArgumentException
 if from
is greater than to
.java.lang.ArrayIndexOutOfBoundsException
 if from
or to
are greater than the array length
or negative.public static void ensureOffsetLength(long[] a, int offset, int length)
This method may be used whenever an array range check is needed.
a
 an array.offset
 a start index.length
 a length (the number of elements in the range).java.lang.IllegalArgumentException
 if length
is negative.java.lang.ArrayIndexOutOfBoundsException
 if offset
is negative or offset
+length
is
greater than the array length.public static void ensureSameLength(long[] a, long[] b)
a
 an array.b
 another array.java.lang.IllegalArgumentException
 if the two argument arrays are not of the same length.public static void swap(long[] x, int a, int b)
x
 an array.a
 a position in x
.b
 another position in x
.public static void swap(long[] x, int a, int b, int n)
x
 an array.a
 a position in x
.b
 another position in x
.n
 the number of elements to exchange starting at a
and
b
.public static void quickSort(long[] x, int from, int to, LongComparator comp)
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.
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.public static void quickSort(long[] x, LongComparator comp)
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.
x
 the array to be sorted.comp
 the comparator to determine the sorting order.public static void parallelQuickSort(long[] x, int from, int to, LongComparator comp)
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 with
Runtime.availableProcessors()
parallel threads.
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.public static void parallelQuickSort(long[] x, LongComparator comp)
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 with
Runtime.availableProcessors()
parallel threads.
x
 the array to be sorted.comp
 the comparator to determine the sorting order.public static void quickSort(long[] x, int from, int to)
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.
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.public static void quickSort(long[] x)
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.
x
 the array to be sorted.public static void parallelQuickSort(long[] x, int from, int to)
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 with
Runtime.availableProcessors()
parallel threads.
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.public static void parallelQuickSort(long[] x)
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 with
Runtime.availableProcessors()
parallel threads.
x
 the array to be sorted.public static void quickSortIndirect(int[] perm, long[] x, int from, int to)
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 that 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 Arrays
,
which switches to mergesort on large inputs.
perm
 a permutation array indexing x
.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.public static void quickSortIndirect(int[] perm, long[] x)
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 that 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 Arrays
,
which switches to mergesort on large inputs.
perm
 a permutation array indexing x
.x
 the array to be sorted.public static void parallelQuickSortIndirect(int[] perm, long[] x, int from, int to)
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 that x[perm[i]] ≤ x[perm[i + 1]]
.
This implementation uses a ForkJoinPool
executor service with
Runtime.availableProcessors()
parallel threads.
perm
 a permutation array indexing x
.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.public static void parallelQuickSortIndirect(int[] perm, long[] x)
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 that x[perm[i]] ≤ x[perm[i + 1]]
.
This implementation uses a ForkJoinPool
executor service with
Runtime.availableProcessors()
parallel threads.
perm
 a permutation array indexing x
.x
 the array to be sorted.public static void stabilize(int[] perm, long[] x, int from, int to)
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 that x[perm[i]] = x[perm[i + 1]]
implies perm[i] ≤ perm[i + 1]
.
perm
 a permutation array indexing x
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.public static void stabilize(int[] perm, long[] x)
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 that x[perm[i]] = x[perm[i + 1]]
implies perm[i] ≤ perm[i + 1]
.
perm
 a permutation array indexing x
so that it is sorted.x
 the sorted array to be stabilized.public static void quickSort(long[] x, long[] y, int from, int to)
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]
or x[i]
== x[i + 1]
and y[i] ≤ y[i + 1]
.
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.public static void quickSort(long[] x, long[] y)
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]
or x[i]
== x[i + 1]
and y[i] ≤ y[i + 1]
.
x
 the first array to be sorted.y
 the second array to be sorted.public static void parallelQuickSort(long[] x, long[] y, int from, int to)
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]
or x[i]
== x[i + 1]
and y[i] ≤ y[i + 1]
.
This implementation uses a ForkJoinPool
executor service with
Runtime.availableProcessors()
parallel threads.
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.public static void parallelQuickSort(long[] x, long[] y)
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]
or x[i]
== x[i + 1]
and y[i] ≤ y[i + 1]
.
This implementation uses a ForkJoinPool
executor service with
Runtime.availableProcessors()
parallel threads.
x
 the first array to be sorted.y
 the second array to be sorted.public static void mergeSort(long[] a, int from, int to, long[] supp)
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.
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 least to
elements, and whose
entries are identical to those of a
in the specified
range.public static void mergeSort(long[] a, int from, int to)
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.
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.public static void mergeSort(long[] a)
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.
a
 the array to be sorted.public static void mergeSort(long[] a, int from, int to, LongComparator comp, long[] supp)
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.
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 least to
elements, and whose
entries are identical to those of a
in the specified
range.public static void mergeSort(long[] a, int from, int to, LongComparator comp)
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.
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.public static void mergeSort(long[] a, LongComparator comp)
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.
a
 the array to be sorted.comp
 the comparator to determine the sorting order.public static int binarySearch(long[] a, int from, int to, long key)
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.((<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.Arrays
public static int binarySearch(long[] a, long key)
a
 the array to be searched.key
 the value to be searched for.((<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.Arrays
public static int binarySearch(long[] a, int from, int to, long key, LongComparator c)
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.((<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.Arrays
public static int binarySearch(long[] a, long key, LongComparator c)
a
 the array to be searched.key
 the value to be searched for.c
 a comparator.((<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.Arrays
public static void radixSort(long[] a)
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.
a
 the array to be sorted.public static void radixSort(long[] a, int from, int to)
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.
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.public static void parallelRadixSort(long[] a, int from, int to)
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.
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.public static void parallelRadixSort(long[] a)
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.
a
 the array to be sorted.public static void radixSortIndirect(int[] perm, long[] a, boolean stable)
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 that a[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).
perm
 a permutation array indexing a
.a
 the array to be sorted.stable
 whether the sorting algorithm should be stable.public static void radixSortIndirect(int[] perm, long[] a, int from, int to, boolean stable)
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 that a[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).
perm
 a permutation array indexing a
.a
 the array to be sorted.from
 the index of the first element of perm
(inclusive) to be
permuted.to
 the index of the last element of perm
(exclusive) to be
permuted.stable
 whether the sorting algorithm should be stable.public static void parallelRadixSortIndirect(int[] perm, long[] a, int from, int to, boolean stable)
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 that a[perm[i]] ≤ a[perm[i + 1]]
.
This implementation uses a pool of Runtime.availableProcessors()
threads.
perm
 a permutation array indexing a
.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.public static void parallelRadixSortIndirect(int[] perm, long[] a, boolean stable)
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 that a[perm[i]] ≤ a[perm[i + 1]]
.
This implementation uses a pool of Runtime.availableProcessors()
threads.
perm
 a permutation array indexing a
.a
 the array to be sorted.stable
 whether the sorting algorithm should be stable.public static void radixSort(long[] a, long[] b)
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]
or a[i] == a[i + 1]
and
b[i] ≤ b[i + 1]
.
a
 the first array to be sorted.b
 the second array to be sorted.public static void radixSort(long[] a, long[] b, int from, int to)
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]
or a[i] == a[i + 1]
and
b[i] ≤ b[i + 1]
.
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.public static void parallelRadixSort(long[] a, long[] b, int from, int to)
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]
or a[i] == a[i + 1]
and
b[i] ≤ b[i + 1]
.
This implementation uses a pool of Runtime.availableProcessors()
threads.
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.public static void parallelRadixSort(long[] a, long[] b)
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]
or a[i] == a[i + 1]
and
b[i] ≤ b[i + 1]
.
This implementation uses a pool of Runtime.availableProcessors()
threads.
a
 the first array to be sorted.b
 the second array to be sorted.public static void radixSortIndirect(int[] perm, long[] a, long[] b, boolean stable)
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 that a[perm[i]] ≤ a[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).
perm
 a permutation array indexing a
.a
 the array to be sorted.b
 the second array to be sorted.stable
 whether the sorting algorithm should be stable.public static void radixSortIndirect(int[] perm, long[] a, long[] b, int from, int to, boolean stable)
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 that a[perm[i]] ≤ a[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).
perm
 a permutation array indexing a
.a
 the array to be sorted.b
 the second array to be sorted.from
 the index of the first element of perm
(inclusive) to be
permuted.to
 the index of the last element of perm
(exclusive) to be
permuted.stable
 whether the sorting algorithm should be stable.public static void radixSort(long[][] a)
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.
a
 an array containing arrays of equal length to be sorted
lexicographically in parallel.public static void radixSort(long[][] a, int from, int to)
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.
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.public static long[] shuffle(long[] a, int from, int to, java.util.Random random)
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.a
.public static long[] shuffle(long[] a, java.util.Random random)
a
 the array to be shuffled.random
 a pseudorandom number generator.a
.public static long[] reverse(long[] a)
a
 the array to be reversed.a
.public static long[] reverse(long[] a, int from, int to)
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.a
.