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/*
* Copyright (C) 2002-2016 Sebastiano Vigna
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
*
* For the sorting and binary search code:
*
* Copyright (C) 1999 CERN - European Organization for Nuclear Research.
*
* Permission to use, copy, modify, distribute and sell this software and
* its documentation for any purpose is hereby granted without fee,
* provided that the above copyright notice appear in all copies and that
* both that copyright notice and this permission notice appear in
* supporting documentation. CERN makes no representations about the
* suitability of this software for any purpose. It is provided "as is"
* without expressed or implied warranty.
*/
package PACKAGE;
import it.unimi.dsi.fastutil.Arrays;
import it.unimi.dsi.fastutil.Hash;
import java.util.Random;
import java.util.concurrent.ForkJoinPool;
import java.util.concurrent.RecursiveAction;
#if ! KEY_CLASS_Integer
import it.unimi.dsi.fastutil.ints.IntArrays;
#endif
#if KEYS_PRIMITIVE
#if ! KEY_CLASS_Boolean
import java.util.concurrent.Callable;
import java.util.concurrent.ExecutorCompletionService;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.LinkedBlockingQueue;
import java.util.concurrent.atomic.AtomicInteger;
#endif
/** A class providing static methods and objects that do useful things with type-specific arrays.
*
* In particular, the 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 {@link it.unimi.dsi.fastutil.io.BinIO} and {@link it.unimi.dsi.fastutil.io.TextIO}
* contain several methods make it possible to load and save arrays of primitive types as sequences
* of elements in {@link java.io.DataInput} format (i.e., not as objects) or as sequences of lines of text.
*
*
Sorting
*
* There are several sorting methods available. The main theme is that of letting you choose
* the sorting algorithm you prefer (i.e., trading stability of mergesort for no memory allocation in quicksort).
* Several algorithms provide a parallel version, that will use the {@linkplain Runtime#availableProcessors() number of cores available}.
* Some algorithms also provide an explicit indirect sorting facility, which makes it possible
* to sort an array using the values in another array as comparator.
*
*
All comparison-based algorithm have an implementation based on a type-specific comparator.
*
*
As a general rule, sequential radix sort is significantly faster than quicksort or mergesort, in particular
* on random-looking data. In
* the parallel case, up to a few cores parallel radix sort is still the fastest, but at some point quicksort
* exploits parallelism better.
*
*
If you are fine with not knowing exactly which algorithm will be run (in particular, not knowing exactly whether a support array will be allocated),
* the dual-pivot parallel sorts in {@link java.util.Arrays}
* are about 50% faster than the classical single-pivot implementation used here.
*
*
In any case, if sorting time is important I suggest that you benchmark your sorting load
* with your data distribution and on your architecture.
*
* @see java.util.Arrays
*/
public class ARRAYS {
#else
import java.util.Comparator;
/** A class providing static methods and objects that do useful things with type-specific arrays.
*
* In particular, the 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.
*
*
Warning: if your array is not of type {@code Object[]},
* {@link #ensureCapacity(Object[],int,int)} and {@link #grow(Object[],int,int)}
* will use {@linkplain java.lang.reflect.Array#newInstance(Class,int) reflection}
* to preserve your array type. Reflection is significantly slower than using new.
* This phenomenon is particularly
* evident in the first growth phases of an array reallocated with doubling (or similar) logic.
*
*
Sorting
*
* There are several sorting methods available. The main theme is that of letting you choose
* the sorting algorithm you prefer (i.e., trading stability of mergesort for no memory allocation in quicksort).
* Several algorithms provide a parallel version, that will use the {@linkplain Runtime#availableProcessors() number of cores available}.
*
*
All comparison-based algorithm have an implementation based on a type-specific comparator.
*
*
If you are fine with not knowing exactly which algorithm will be run (in particular, not knowing exactly whether a support array will be allocated),
* the dual-pivot parallel sorts in {@link java.util.Arrays}
* are about 50% faster than the classical single-pivot implementation used here.
*
*
In any case, if sorting time is important I suggest that you benchmark your sorting load
* with your data distribution and on your architecture.
*
* @see java.util.Arrays
*/
public class ARRAYS {
#endif
private ARRAYS() {}
/** A static, final, empty array. */
public final static KEY_TYPE[] EMPTY_ARRAY = {};
#if KEY_CLASS_Object
/** Creates a new array using a the given one as prototype.
*
*
This method returns a new array of the given length whose element
* are of the same class as of those of prototype. In case
* of an empty array, it tries to return {@link #EMPTY_ARRAY}, if possible.
*
* @param prototype an array that will be used to type the new one.
* @param length the length of the new array.
* @return a new array of given type and length.
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
private static K[] newArray( final K[] prototype, final int length ) {
final Class klass = prototype.getClass();
if ( klass == Object[].class ) return (K[])( length == 0 ? EMPTY_ARRAY : new Object[ length ] );
return (K[])java.lang.reflect.Array.newInstance( klass.getComponentType(), length );
}
#endif
/** 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.
*
* @param array an array.
* @param length the new minimum length for this array.
* @return 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 KEY_GENERIC KEY_GENERIC_TYPE[] ensureCapacity( final KEY_GENERIC_TYPE[] array, final int length ) {
if ( length > array.length ) {
final KEY_GENERIC_TYPE t[] =
#if KEY_CLASS_Object
newArray( array, length );
#else
new KEY_TYPE[ length ];
#endif
System.arraycopy( array, 0, t, 0, array.length );
return t;
}
return array;
}
/** Ensures that an array can contain the given number of entries, preserving just a part of the array.
*
* @param array an array.
* @param length the new minimum length for this array.
* @param preserve the number of elements of the array that must be preserved in case a new allocation is necessary.
* @return 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 KEY_GENERIC KEY_GENERIC_TYPE[] ensureCapacity( final KEY_GENERIC_TYPE[] array, final int length, final int preserve ) {
if ( length > array.length ) {
final KEY_GENERIC_TYPE t[] =
#if KEY_CLASS_Object
newArray( array, length );
#else
new KEY_TYPE[ length ];
#endif
System.arraycopy( array, 0, t, 0, preserve );
return t;
}
return array;
}
/** Grows the given array to the maximum between the given length and
* the current length multiplied by two, 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.
*
* @param array an array.
* @param length the new minimum length for this array.
* @return 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 KEY_GENERIC KEY_GENERIC_TYPE[] grow( final KEY_GENERIC_TYPE[] array, final int length ) {
if ( length > array.length ) {
final int newLength = (int)Math.max( Math.min( 2L * array.length, Arrays.MAX_ARRAY_SIZE ), length );
final KEY_GENERIC_TYPE t[] =
#if KEY_CLASS_Object
newArray( array, newLength );
#else
new KEY_TYPE[ newLength ];
#endif
System.arraycopy( array, 0, t, 0, array.length );
return t;
}
return array;
}
/** Grows the given array to the maximum between the given length and
* the current length multiplied by two, 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.
*
* @param array an array.
* @param length the new minimum length for this array.
* @param preserve the number of elements of the array that must be preserved in case a new allocation is necessary.
* @return 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 KEY_GENERIC KEY_GENERIC_TYPE[] grow( final KEY_GENERIC_TYPE[] array, final int length, final int preserve ) {
if ( length > array.length ) {
final int newLength = (int)Math.max( Math.min( 2L * array.length, Arrays.MAX_ARRAY_SIZE ), length );
final KEY_GENERIC_TYPE t[] =
#if KEY_CLASS_Object
newArray( array, newLength );
#else
new KEY_TYPE[ newLength ];
#endif
System.arraycopy( array, 0, t, 0, preserve );
return t;
}
return array;
}
/** Trims the given array to the given length.
*
* @param array an array.
* @param length the new maximum length for the array.
* @return 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 KEY_GENERIC KEY_GENERIC_TYPE[] trim( final KEY_GENERIC_TYPE[] array, final int length ) {
if ( length >= array.length ) return array;
final KEY_GENERIC_TYPE t[] =
#if KEY_CLASS_Object
newArray( array, length );
#else
length == 0 ? EMPTY_ARRAY : new KEY_TYPE[ length ];
#endif
System.arraycopy( array, 0, t, 0, length );
return t;
}
/** Sets the length of the given array.
*
* @param array an array.
* @param length the new length for the array.
* @return 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 KEY_GENERIC KEY_GENERIC_TYPE[] setLength( final KEY_GENERIC_TYPE[] array, final int length ) {
if ( length == array.length ) return array;
if ( length < array.length ) return trim( array, length );
return ensureCapacity( array, length );
}
/** Returns a copy of a portion of an array.
*
* @param array an array.
* @param offset the first element to copy.
* @param length the number of elements to copy.
* @return a new array containing length elements of array starting at offset.
*/
public static KEY_GENERIC KEY_GENERIC_TYPE[] copy( final KEY_GENERIC_TYPE[] array, final int offset, final int length ) {
ensureOffsetLength( array, offset, length );
final KEY_GENERIC_TYPE[] a =
#if KEY_CLASS_Object
newArray( array, length );
#else
length == 0 ? EMPTY_ARRAY : new KEY_TYPE[ length ];
#endif
System.arraycopy( array, offset, a, 0, length );
return a;
}
/** Returns a copy of an array.
*
* @param array an array.
* @return a copy of array.
*/
public static KEY_GENERIC KEY_GENERIC_TYPE[] copy( final KEY_GENERIC_TYPE[] array ) {
return array.clone();
}
/** Fills the given array with the given value.
*
* @param array an array.
* @param value the new value for all elements of the array.
* @deprecated Please use the corresponding {@link java.util.Arrays} method.
*/
@Deprecated
public static KEY_GENERIC void fill( final KEY_GENERIC_TYPE[] array, final KEY_GENERIC_TYPE value ) {
int i = array.length;
while( i-- != 0 ) array[ i ] = value;
}
/** Fills a portion of the given array with the given value.
*
* @param array an array.
* @param from the starting index of the portion to fill (inclusive).
* @param to the end index of the portion to fill (exclusive).
* @param value the new value for all elements of the specified portion of the array.
* @deprecated Please use the corresponding {@link java.util.Arrays} method.
*/
@Deprecated
public static KEY_GENERIC void fill( final KEY_GENERIC_TYPE[] array, final int from, int to, final KEY_GENERIC_TYPE value ) {
ensureFromTo( array, from, to );
if ( from == 0 ) while( to-- != 0 ) array[ to ] = value;
else for( int i = from; i < to; i++ ) array[ i ] = value;
}
/** Returns true if the two arrays are elementwise equal.
*
* @param a1 an array.
* @param a2 another array.
* @return true if the two arrays are of the same length, and their elements are equal.
* @deprecated Please use the corresponding {@link java.util.Arrays} method, which is intrinsified in recent JVMs.
*/
@Deprecated
public static KEY_GENERIC boolean equals( final KEY_GENERIC_TYPE[] a1, final KEY_GENERIC_TYPE a2[] ) {
int i = a1.length;
if ( i != a2.length ) return false;
while( i-- != 0 ) if (! KEY_EQUALS( a1[ i ], a2[ i ] ) ) return false;
return true;
}
/** Ensures that a range given by its first (inclusive) and last (exclusive) elements fits an array.
*
*
This method may be used whenever an array range check is needed.
*
* @param a an array.
* @param from a start index (inclusive).
* @param to an end index (exclusive).
* @throws IllegalArgumentException if from is greater than to.
* @throws ArrayIndexOutOfBoundsException if from or to are greater than the array length or negative.
*/
public static KEY_GENERIC void ensureFromTo( final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
Arrays.ensureFromTo( a.length, from, to );
}
/** Ensures that a range given by an offset and a length fits an array.
*
*
This method may be used whenever an array range check is needed.
*
* @param a an array.
* @param offset a start index.
* @param length a length (the number of elements in the range).
* @throws IllegalArgumentException if length is negative.
* @throws ArrayIndexOutOfBoundsException if offset is negative or offset+length is greater than the array length.
*/
public static KEY_GENERIC void ensureOffsetLength( final KEY_GENERIC_TYPE[] a, final int offset, final int length ) {
Arrays.ensureOffsetLength( a.length, offset, length );
}
/** Ensures that two arrays are of the same length.
*
* @param a an array.
* @param b another array.
* @throws IllegalArgumentException if the two argument arrays are not of the same length.
*/
public static KEY_GENERIC void ensureSameLength( final KEY_GENERIC_TYPE[] a, final KEY_GENERIC_TYPE[] b ) {
if ( a.length != b.length ) throw new IllegalArgumentException( "Array size mismatch: " + a.length + " != " + b.length );
}
private static final int QUICKSORT_NO_REC = 16;
private static final int PARALLEL_QUICKSORT_NO_FORK = 8192;
private static final int QUICKSORT_MEDIAN_OF_9 = 128;
private static final int MERGESORT_NO_REC = 16;
/** Swaps two elements of an anrray.
*
* @param x an array.
* @param a a position in {@code x}.
* @param b another position in {@code x}.
*/
public static KEY_GENERIC void swap( final KEY_GENERIC_TYPE x[], final int a, final int b ) {
final KEY_GENERIC_TYPE t = x[ a ];
x[ a ] = x[ b ];
x[ b ] = t;
}
/** Swaps two sequences of elements of an array.
*
* @param x an array.
* @param a a position in {@code x}.
* @param b another position in {@code x}.
* @param n the number of elements to exchange starting at {@code a} and {@code b}.
*/
public static KEY_GENERIC void swap( final KEY_GENERIC_TYPE[] x, int a, int b, final int n ) {
for( int i = 0; i < n; i++, a++, b++ ) swap( x, a, b );
}
private static KEY_GENERIC int med3( final KEY_GENERIC_TYPE x[], final int a, final int b, final int c, KEY_COMPARATOR KEY_GENERIC comp ) {
final int ab = comp.compare( x[ a ], x[ b ] );
final int ac = comp.compare( x[ a ], x[ c ] );
final int bc = comp.compare( x[ b ], x[ c ] );
return ( ab < 0 ?
( bc < 0 ? b : ac < 0 ? c : a ) :
( bc > 0 ? b : ac > 0 ? c : a ) );
}
private static KEY_GENERIC void selectionSort( final KEY_GENERIC_TYPE[] a, final int from, final int to, final KEY_COMPARATOR KEY_GENERIC comp ) {
for( int i = from; i < to - 1; i++ ) {
int m = i;
for( int j = i + 1; j < to; j++ ) if ( comp.compare( a[ j ], a[ m ] ) < 0 ) m = j;
if ( m != i ) {
final KEY_GENERIC_TYPE u = a[ i ];
a[ i ] = a[ m ];
a[ m ] = u;
}
}
}
private static KEY_GENERIC void insertionSort( final KEY_GENERIC_TYPE[] a, final int from, final int to, final KEY_COMPARATOR KEY_GENERIC comp ) {
for ( int i = from; ++i < to; ) {
KEY_GENERIC_TYPE t = a[ i ];
int j = i;
for ( KEY_GENERIC_TYPE u = a[ j - 1 ]; comp.compare( t, u ) < 0; u = a[ --j - 1 ] ) {
a[ j ] = u;
if ( from == j - 1 ) {
--j;
break;
}
}
a[ j ] = t;
}
}
/** Sorts the specified range of elements according to the order induced by the specified
* comparator using quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
Note that this implementation does not allocate any object, contrarily to the implementation
* used to sort primitive types in {@link java.util.Arrays}, which switches to mergesort on large inputs.
*
* @param x the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param comp the comparator to determine the sorting order.
*
*/
public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x, final int from, final int to, final KEY_COMPARATOR KEY_GENERIC comp ) {
final int len = to - from;
// Selection sort on smallest arrays
if ( len < QUICKSORT_NO_REC ) {
selectionSort( x, from, to, comp );
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
if ( len > QUICKSORT_MEDIAN_OF_9 ) { // Big arrays, pseudomedian of 9
int s = len / 8;
l = med3( x, l, l + s, l + 2 * s, comp );
m = med3( x, m - s, m, m + s, comp );
n = med3( x, n - 2 * s, n - s, n, comp );
}
m = med3( x, l, m, n, comp ); // Mid-size, med of 3
final KEY_GENERIC_TYPE v = x[ m ];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while( true ) {
int comparison;
while ( b <= c && ( comparison = comp.compare( x[ b ], v ) ) <= 0 ) {
if ( comparison == 0 ) swap( x, a++, b );
b++;
}
while ( c >= b && ( comparison = comp.compare( x[ c ], v ) ) >=0 ) {
if ( comparison == 0 ) swap( x, c, d-- );
c--;
}
if ( b > c ) break;
swap( x, b++, c-- );
}
// Swap partition elements back to middle
int s;
s = Math.min( a - from, b - a );
swap( x, from, b - s, s );
s = Math.min( d - c, to - d - 1 );
swap( x, b, to - s, s );
// Recursively sort non-partition-elements
if ( ( s = b - a ) > 1 ) quickSort( x, from, from + s, comp );
if ( ( s = d - c ) > 1 ) quickSort( x, to - s, to, comp );
}
/** Sorts an array according to the order induced by the specified
* comparator using quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
Note that this implementation does not allocate any object, contrarily to the implementation
* used to sort primitive types in {@link java.util.Arrays}, which switches to mergesort on large inputs.
*
* @param x the array to be sorted.
* @param comp the comparator to determine the sorting order.
*
*/
public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x, final KEY_COMPARATOR KEY_GENERIC comp ) {
quickSort( x, 0, x.length, comp );
}
protected static class ForkJoinQuickSortComp KEY_GENERIC extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final int from;
private final int to;
private final KEY_GENERIC_TYPE[] x;
private final KEY_COMPARATOR KEY_GENERIC comp;
public ForkJoinQuickSortComp( final KEY_GENERIC_TYPE[] x , final int from , final int to, final KEY_COMPARATOR KEY_GENERIC comp ) {
this.from = from;
this.to = to;
this.x = x;
this.comp = comp;
}
@Override
protected void compute() {
final KEY_GENERIC_TYPE[] x = this.x;
final int len = to - from;
if ( len < PARALLEL_QUICKSORT_NO_FORK ) {
quickSort( x, from, to, comp );
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
int s = len / 8;
l = med3( x, l, l + s, l + 2 * s, comp );
m = med3( x, m - s, m, m + s, comp );
n = med3( x, n - 2 * s, n - s, n, comp );
m = med3( x, l, m, n, comp );
final KEY_GENERIC_TYPE v = x[ m ];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while ( true ) {
int comparison;
while ( b <= c && ( comparison = comp.compare( x[ b ], v ) ) <= 0 ) {
if ( comparison == 0 ) swap( x, a++, b );
b++;
}
while ( c >= b && ( comparison = comp.compare( x[ c ], v ) ) >= 0 ) {
if ( comparison == 0 ) swap( x, c, d-- );
c--;
}
if ( b > c ) break;
swap( x, b++, c-- );
}
// Swap partition elements back to middle
int t;
s = Math.min( a - from, b - a );
swap( x, from, b - s, s );
s = Math.min( d - c, to - d - 1 );
swap( x, b, to - s, s );
// Recursively sort non-partition-elements
s = b - a;
t = d - c;
if ( s > 1 && t > 1 ) invokeAll( new ForkJoinQuickSortComp KEY_GENERIC( x, from, from + s, comp ), new ForkJoinQuickSortComp KEY_GENERIC( x, to - t, to, comp ) );
else if ( s > 1 ) invokeAll( new ForkJoinQuickSortComp KEY_GENERIC( x, from, from + s, comp ) );
else invokeAll( new ForkJoinQuickSortComp KEY_GENERIC( x, to - t, to, comp ) );
}
}
/** Sorts the specified range of elements according to the order induced by the specified
* comparator using a parallel quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param comp the comparator to determine the sorting order.
*/
public static KEY_GENERIC void parallelQuickSort( final KEY_GENERIC_TYPE[] x, final int from, final int to, final KEY_COMPARATOR KEY_GENERIC comp ) {
if ( to - from < PARALLEL_QUICKSORT_NO_FORK ) quickSort( x, from, to, comp );
else {
final ForkJoinPool pool = new ForkJoinPool( Runtime.getRuntime().availableProcessors() );
pool.invoke( new ForkJoinQuickSortComp KEY_GENERIC( x, from, to, comp ) );
pool.shutdown();
}
}
/** Sorts an array according to the order induced by the specified
* comparator using a parallel quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x the array to be sorted.
* @param comp the comparator to determine the sorting order.
*/
public static KEY_GENERIC void parallelQuickSort( final KEY_GENERIC_TYPE[] x, final KEY_COMPARATOR KEY_GENERIC comp ) {
parallelQuickSort( x, 0, x.length, comp );
}
SUPPRESS_WARNINGS_KEY_UNCHECKED
private static KEY_GENERIC int med3( final KEY_GENERIC_TYPE x[], final int a, final int b, final int c ) {
final int ab = KEY_CMP( x[ a ], x[ b ] );
final int ac = KEY_CMP( x[ a ], x[ c ] );
final int bc = KEY_CMP( x[ b ], x[ c ] );
return ( ab < 0 ?
( bc < 0 ? b : ac < 0 ? c : a ) :
( bc > 0 ? b : ac > 0 ? c : a ) );
}
SUPPRESS_WARNINGS_KEY_UNCHECKED
private static KEY_GENERIC void selectionSort( final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
for( int i = from; i < to - 1; i++ ) {
int m = i;
for( int j = i + 1; j < to; j++ ) if ( KEY_LESS( a[ j ], a[ m ] ) ) m = j;
if ( m != i ) {
final KEY_GENERIC_TYPE u = a[ i ];
a[ i ] = a[ m ];
a[ m ] = u;
}
}
}
SUPPRESS_WARNINGS_KEY_UNCHECKED
private static KEY_GENERIC void insertionSort( final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
for ( int i = from; ++i < to; ) {
KEY_GENERIC_TYPE t = a[ i ];
int j = i;
for ( KEY_GENERIC_TYPE u = a[ j - 1 ]; KEY_LESS( t, u ); u = a[ --j - 1 ] ) {
a[ j ] = u;
if ( from == j - 1 ) {
--j;
break;
}
}
a[ j ] = t;
}
}
/** Sorts the specified range of elements according to the natural ascending order using quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
Note that this implementation does not allocate any object, contrarily to the implementation
* used to sort primitive types in {@link java.util.Arrays}, which switches to mergesort on large inputs.
*
* @param x the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x, final int from, final int to ) {
final int len = to - from;
// Selection sort on smallest arrays
if ( len < QUICKSORT_NO_REC ) {
selectionSort( x, from, to );
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
if ( len > QUICKSORT_MEDIAN_OF_9 ) { // Big arrays, pseudomedian of 9
int s = len / 8;
l = med3( x, l, l + s, l + 2 * s );
m = med3( x, m - s, m, m + s );
n = med3( x, n - 2 * s, n - s, n );
}
m = med3( x, l, m, n ); // Mid-size, med of 3
final KEY_GENERIC_TYPE v = x[ m ];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while(true) {
int comparison;
while ( b <= c && ( comparison = KEY_CMP( x[ b ], v ) ) <= 0 ) {
if ( comparison == 0 ) swap( x, a++, b );
b++;
}
while (c >= b && ( comparison = KEY_CMP( x[ c ], v ) ) >=0 ) {
if ( comparison == 0 ) swap( x, c, d-- );
c--;
}
if ( b > c ) break;
swap( x, b++, c-- );
}
// Swap partition elements back to middle
int s;
s = Math.min( a - from, b - a );
swap( x, from, b - s, s );
s = Math.min( d - c, to - d - 1 );
swap( x, b, to - s, s );
// Recursively sort non-partition-elements
if ( ( s = b - a ) > 1 ) quickSort( x, from, from + s );
if ( ( s = d - c ) > 1 ) quickSort( x, to - s, to );
}
/** Sorts an array according to the natural ascending order using quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
Note that this implementation does not allocate any object, contrarily to the implementation
* used to sort primitive types in {@link java.util.Arrays}, which switches to mergesort on large inputs.
*
* @param x the array to be sorted.
*
*/
public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x ) {
quickSort( x, 0, x.length );
}
protected static class ForkJoinQuickSort KEY_GENERIC extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final int from;
private final int to;
private final KEY_GENERIC_TYPE[] x;
public ForkJoinQuickSort( final KEY_GENERIC_TYPE[] x , final int from , final int to ) {
this.from = from;
this.to = to;
this.x = x;
}
@Override
SUPPRESS_WARNINGS_KEY_UNCHECKED
protected void compute() {
final KEY_GENERIC_TYPE[] x = this.x;
final int len = to - from;
if ( len < PARALLEL_QUICKSORT_NO_FORK ) {
quickSort( x, from, to );
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
int s = len / 8;
l = med3( x, l, l + s, l + 2 * s );
m = med3( x, m - s, m, m + s );
n = med3( x, n - 2 * s, n - s, n );
m = med3( x, l, m, n );
final KEY_GENERIC_TYPE v = x[ m ];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while ( true ) {
int comparison;
while ( b <= c && ( comparison = KEY_CMP( x[ b ], v ) ) <= 0 ) {
if ( comparison == 0 ) swap( x, a++, b );
b++;
}
while ( c >= b && ( comparison = KEY_CMP( x[ c ], v ) ) >= 0 ) {
if ( comparison == 0 ) swap( x, c, d-- );
c--;
}
if ( b > c ) break;
swap( x, b++, c-- );
}
// Swap partition elements back to middle
int t;
s = Math.min( a - from, b - a );
swap( x, from, b - s, s );
s = Math.min( d - c, to - d - 1 );
swap( x, b, to - s, s );
// Recursively sort non-partition-elements
s = b - a;
t = d - c;
if ( s > 1 && t > 1 ) invokeAll( new ForkJoinQuickSort KEY_GENERIC( x, from, from + s ), new ForkJoinQuickSort KEY_GENERIC( x, to - t, to ) );
else if ( s > 1 ) invokeAll( new ForkJoinQuickSort KEY_GENERIC( x, from, from + s ) );
else invokeAll( new ForkJoinQuickSort KEY_GENERIC( x, to - t, to ) );
}
}
/** Sorts the specified range of elements according to the natural ascending order using a parallel quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static KEY_GENERIC void parallelQuickSort( final KEY_GENERIC_TYPE[] x, final int from, final int to ) {
if ( to - from < PARALLEL_QUICKSORT_NO_FORK ) quickSort( x, from, to );
else {
final ForkJoinPool pool = new ForkJoinPool( Runtime.getRuntime().availableProcessors() );
pool.invoke( new ForkJoinQuickSort KEY_GENERIC( x, from, to ) );
pool.shutdown();
}
}
/** Sorts an array according to the natural ascending order using a parallel quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x the array to be sorted.
*
*/
public static KEY_GENERIC void parallelQuickSort( final KEY_GENERIC_TYPE[] x ) {
parallelQuickSort( x, 0, x.length );
}
SUPPRESS_WARNINGS_KEY_UNCHECKED
private static KEY_GENERIC int med3Indirect( final int perm[], final KEY_GENERIC_TYPE x[], final int a, final int b, final int c ) {
final KEY_GENERIC_TYPE aa = x[ perm[ a ] ];
final KEY_GENERIC_TYPE bb = x[ perm[ b ] ];
final KEY_GENERIC_TYPE cc = x[ perm[ c ] ];
final int ab = KEY_CMP( aa, bb );
final int ac = KEY_CMP( aa, cc );
final int bc = KEY_CMP( bb, cc );
return ( ab < 0 ?
( bc < 0 ? b : ac < 0 ? c : a ) :
( bc > 0 ? b : ac > 0 ? c : a ) );
}
SUPPRESS_WARNINGS_KEY_UNCHECKED
private static KEY_GENERIC void insertionSortIndirect( final int[] perm, final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
for ( int i = from; ++i < to; ) {
int t = perm[ i ];
int j = i;
for ( int u = perm[ j - 1 ]; KEY_LESS( a[ t ], a[ u ] ); u = perm[ --j - 1 ] ) {
perm[ j ] = u;
if ( from == j - 1 ) {
--j;
break;
}
}
perm[ j ] = t;
}
}
/** Sorts the specified range of elements according to the natural ascending order using indirect quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This method implement an indirect sort. The elements of 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 {@link java.util.Arrays}, which switches to mergesort on large inputs.
*
* @param perm a permutation array indexing {@code x}.
* @param x the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
public static KEY_GENERIC void quickSortIndirect( final int[] perm, final KEY_GENERIC_TYPE[] x, final int from, final int to ) {
final int len = to - from;
// Selection sort on smallest arrays
if ( len < QUICKSORT_NO_REC ) {
insertionSortIndirect( perm, x, from, to );
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
if ( len > QUICKSORT_MEDIAN_OF_9 ) { // Big arrays, pseudomedian of 9
int s = len / 8;
l = med3Indirect( perm, x, l, l + s, l + 2 * s );
m = med3Indirect( perm, x, m - s, m, m + s );
n = med3Indirect( perm, x, n - 2 * s, n - s, n );
}
m = med3Indirect( perm, x, l, m, n ); // Mid-size, med of 3
final KEY_GENERIC_TYPE v = x[ perm[ m ] ];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while(true) {
int comparison;
while ( b <= c && ( comparison = KEY_CMP( x[ perm[ b ] ], v ) ) <= 0 ) {
if ( comparison == 0 ) IntArrays.swap( perm, a++, b );
b++;
}
while (c >= b && ( comparison = KEY_CMP( x[ perm[ c ] ], v ) ) >=0 ) {
if ( comparison == 0 ) IntArrays.swap( perm, c, d-- );
c--;
}
if ( b > c ) break;
IntArrays.swap( perm, b++, c-- );
}
// Swap partition elements back to middle
int s;
s = Math.min( a - from, b - a );
IntArrays.swap( perm, from, b - s, s );
s = Math.min( d - c, to - d - 1 );
IntArrays.swap( perm, b, to - s, s );
// Recursively sort non-partition-elements
if ( ( s = b - a ) > 1 ) quickSortIndirect( perm, x, from, from + s );
if ( ( s = d - c ) > 1 ) quickSortIndirect( perm, x, to - s, to );
}
/** Sorts an array according to the natural ascending order using indirect quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This method implement an indirect sort. The elements of 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 {@link java.util.Arrays}, which switches to mergesort on large inputs.
*
* @param perm a permutation array indexing {@code x}.
* @param x the array to be sorted.
*/
public static KEY_GENERIC void quickSortIndirect( final int perm[], final KEY_GENERIC_TYPE[] x ) {
quickSortIndirect( perm, x, 0, x.length );
}
protected static class ForkJoinQuickSortIndirect KEY_GENERIC extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final int from;
private final int to;
private final int[] perm;
private final KEY_GENERIC_TYPE[] x;
public ForkJoinQuickSortIndirect( final int perm[], final KEY_GENERIC_TYPE[] x , final int from , final int to ) {
this.from = from;
this.to = to;
this.x = x;
this.perm = perm;
}
@Override
SUPPRESS_WARNINGS_KEY_UNCHECKED
protected void compute() {
final KEY_GENERIC_TYPE[] x = this.x;
final int len = to - from;
if ( len < PARALLEL_QUICKSORT_NO_FORK ) {
quickSortIndirect( perm, x, from, to );
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
int s = len / 8;
l = med3Indirect( perm, x, l, l + s, l + 2 * s );
m = med3Indirect( perm, x, m - s, m, m + s );
n = med3Indirect( perm, x, n - 2 * s, n - s, n );
m = med3Indirect( perm, x, l, m, n );
final KEY_GENERIC_TYPE v = x[ perm[ m ] ];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while ( true ) {
int comparison;
while ( b <= c && ( comparison = KEY_CMP( x[ perm[ b ] ], v ) ) <= 0 ) {
if ( comparison == 0 ) IntArrays.swap( perm, a++, b );
b++;
}
while ( c >= b && ( comparison = KEY_CMP( x[ perm[ c ] ], v ) ) >= 0 ) {
if ( comparison == 0 ) IntArrays.swap( perm, c, d-- );
c--;
}
if ( b > c ) break;
IntArrays.swap( perm, b++, c-- );
}
// Swap partition elements back to middle
int t;
s = Math.min( a - from, b - a );
IntArrays.swap( perm, from, b - s, s );
s = Math.min( d - c, to - d - 1 );
IntArrays.swap( perm, b, to - s, s );
// Recursively sort non-partition-elements
s = b - a;
t = d - c;
if ( s > 1 && t > 1 ) invokeAll( new ForkJoinQuickSortIndirect KEY_GENERIC( perm, x, from, from + s ), new ForkJoinQuickSortIndirect KEY_GENERIC( perm, x, to - t, to ) );
else if ( s > 1 ) invokeAll( new ForkJoinQuickSortIndirect KEY_GENERIC( perm, x, from, from + s ) );
else invokeAll( new ForkJoinQuickSortIndirect KEY_GENERIC( perm, x, to - t, to ) );
}
}
/** Sorts the specified range of elements according to the natural ascending order using a parallel indirect quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This method implement an indirect sort. The elements of 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 {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param perm a permutation array indexing {@code x}.
* @param x the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static KEY_GENERIC void parallelQuickSortIndirect( final int[] perm, final KEY_GENERIC_TYPE[] x, final int from, final int to ) {
if ( to - from < PARALLEL_QUICKSORT_NO_FORK ) quickSortIndirect( perm, x, from, to );
else {
final ForkJoinPool pool = new ForkJoinPool( Runtime.getRuntime().availableProcessors() );
pool.invoke( new ForkJoinQuickSortIndirect KEY_GENERIC( perm, x, from, to ) );
pool.shutdown();
}
}
/** Sorts an array according to the natural ascending order using a parallel indirect quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This method implement an indirect sort. The elements of 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 {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param perm a permutation array indexing {@code x}.
* @param x the array to be sorted.
*
*/
public static KEY_GENERIC void parallelQuickSortIndirect( final int perm[], final KEY_GENERIC_TYPE[] x ) {
parallelQuickSortIndirect( perm, x, 0, x.length );
}
/** Stabilizes a permutation.
*
*
This method can be used to stabilize the permutation generated by an indirect sorting, assuming that
* initially the permutation array was in ascending order (e.g., the identity, as usually happens). This method
* scans the permutation, and for each non-singleton block of elements with the same associated values in {@code x},
* permutes them in ascending order. The resulting permutation corresponds to a stable sort.
*
*
Usually combining an unstable indirect sort and this method is more efficient than using a stable sort,
* as most stable sort algorithms require a support array.
*
*
More precisely, assuming that 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 ].
*
* @param perm a permutation array indexing {@code x} so that it is sorted.
* @param x the sorted array to be stabilized.
* @param from the index of the first element (inclusive) to be stabilized.
* @param to the index of the last element (exclusive) to be stabilized.
*/
public static KEY_GENERIC void stabilize( final int perm[], final KEY_GENERIC_TYPE[] x, final int from, final int to ) {
int curr = from;
for( int i = from + 1; i < to; i++ ) {
if ( x[ perm[ i ] ] != x[ perm[ curr ] ] ) {
if ( i - curr > 1 ) IntArrays.parallelQuickSort( perm, curr, i );
curr = i;
}
}
if ( to - curr > 1 ) IntArrays.parallelQuickSort( perm, curr, to );
}
/** Stabilizes a permutation.
*
*
This method can be used to stabilize the permutation generated by an indirect sorting, assuming that
* initially the permutation array was in ascending order (e.g., the identity, as usually happens). This method
* scans the permutation, and for each non-singleton block of elements with the same associated values in {@code x},
* permutes them in ascending order. The resulting permutation corresponds to a stable sort.
*
*
Usually combining an unstable indirect sort and this method is more efficient than using a stable sort,
* as most stable sort algorithms require a support array.
*
*
More precisely, assuming that 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 ].
*
* @param perm a permutation array indexing {@code x} so that it is sorted.
* @param x the sorted array to be stabilized.
*/
public static KEY_GENERIC void stabilize( final int perm[], final KEY_GENERIC_TYPE[] x ) {
stabilize( perm, x, 0, perm.length );
}
SUPPRESS_WARNINGS_KEY_UNCHECKED
private static KEY_GENERIC int med3( final KEY_GENERIC_TYPE x[], final KEY_GENERIC_TYPE[] y, final int a, final int b, final int c ) {
int t;
final int ab = ( t = KEY_CMP( x[ a ], x[ b ] ) ) == 0 ? KEY_CMP( y[ a ], y[ b ] ) : t;
final int ac = ( t = KEY_CMP( x[ a ], x[ c ] ) ) == 0 ? KEY_CMP( y[ a ], y[ c ] ) : t;
final int bc = ( t = KEY_CMP( x[ b ], x[ c ] ) ) == 0 ? KEY_CMP( y[ b ], y[ c ] ) : t;
return ( ab < 0 ?
( bc < 0 ? b : ac < 0 ? c : a ) :
( bc > 0 ? b : ac > 0 ? c : a ) );
}
private static KEY_GENERIC void swap( final KEY_GENERIC_TYPE x[], final KEY_GENERIC_TYPE[] y, final int a, final int b ) {
final KEY_GENERIC_TYPE t = x[ a ];
final KEY_GENERIC_TYPE u = y[ a ];
x[ a ] = x[ b ];
y[ a ] = y[ b ];
x[ b ] = t;
y[ b ] = u;
}
private static KEY_GENERIC void swap( final KEY_GENERIC_TYPE[] x, final KEY_GENERIC_TYPE[] y, int a, int b, final int n ) {
for ( int i = 0; i < n; i++, a++, b++ ) swap( x, y, a, b );
}
SUPPRESS_WARNINGS_KEY_UNCHECKED
private static KEY_GENERIC void selectionSort( final KEY_GENERIC_TYPE[] a, final KEY_GENERIC_TYPE[] b, final int from, final int to ) {
for( int i = from; i < to - 1; i++ ) {
int m = i, u;
for( int j = i + 1; j < to; j++ )
if ( ( u = KEY_CMP( a[ j ], a[ m ] ) ) < 0 || u == 0 && KEY_LESS( b[ j ], b[ m ] ) ) m = j;
if ( m != i ) {
KEY_GENERIC_TYPE t = a[ i ];
a[ i ] = a[ m ];
a[ m ] = t;
t = b[ i ];
b[ i ] = b[ m ];
b[ m ] = t;
}
}
}
/** Sorts the specified range of elements of two arrays according to the natural lexicographical
* ascending order using quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This method implements a lexicographical sorting of the arguments. Pairs of
* elements in the same position in the two provided arrays will be considered a single key, and
* permuted accordingly. In the end, either x[ i ] < x[ i + 1 ] or x[ i ]
* == x[ i + 1 ] and y[ i ] ≤ y[ i + 1 ].
*
* @param x the first array to be sorted.
* @param y the second array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x, final KEY_GENERIC_TYPE[] y, final int from, final int to ) {
final int len = to - from;
if ( len < QUICKSORT_NO_REC ) {
selectionSort( x, y, from, to );
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
if ( len > QUICKSORT_MEDIAN_OF_9 ) { // Big arrays, pseudomedian of 9
int s = len / 8;
l = med3( x, y, l, l + s, l + 2 * s );
m = med3( x, y, m - s, m, m + s );
n = med3( x, y, n - 2 * s, n - s, n );
}
m = med3( x, y, l, m, n ); // Mid-size, med of 3
final KEY_GENERIC_TYPE v = x[ m ], w = y[ m ];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while ( true ) {
int comparison, t;
while ( b <= c && ( comparison = ( t = KEY_CMP( x[ b ], v ) ) == 0 ? KEY_CMP( y[ b ], w ) : t ) <= 0 ) {
if ( comparison == 0 ) swap( x, y, a++, b );
b++;
}
while ( c >= b && ( comparison = ( t = KEY_CMP( x[ c ], v ) ) == 0 ? KEY_CMP( y[ c ], w ) : t ) >= 0 ) {
if ( comparison == 0 ) swap( x, y, c, d-- );
c--;
}
if ( b > c ) break;
swap( x, y, b++, c-- );
}
// Swap partition elements back to middle
int s;
s = Math.min( a - from, b - a );
swap( x, y, from, b - s, s );
s = Math.min( d - c, to - d - 1 );
swap( x, y, b, to - s, s );
// Recursively sort non-partition-elements
if ( ( s = b - a ) > 1 ) quickSort( x, y, from, from + s );
if ( ( s = d - c ) > 1 ) quickSort( x, y, to - s, to );
}
/** Sorts two arrays according to the natural lexicographical ascending order using quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This method implements a lexicographical sorting of the arguments. Pairs of
* elements in the same position in the two provided arrays will be considered a single key, and
* permuted accordingly. In the end, either x[ i ] < x[ i + 1 ] or x[ i ]
* == x[ i + 1 ] and y[ i ] ≤ y[ i + 1 ].
*
* @param x the first array to be sorted.
* @param y the second array to be sorted.
*/
public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x, final KEY_GENERIC_TYPE[] y ) {
ensureSameLength( x, y );
quickSort( x, y, 0, x.length );
}
protected static class ForkJoinQuickSort2 KEY_GENERIC extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final int from;
private final int to;
private final KEY_GENERIC_TYPE[] x, y;
public ForkJoinQuickSort2( final KEY_GENERIC_TYPE[] x, final KEY_GENERIC_TYPE[] y, final int from , final int to ) {
this.from = from;
this.to = to;
this.x = x;
this.y = y;
}
@Override
SUPPRESS_WARNINGS_KEY_UNCHECKED
protected void compute() {
final KEY_GENERIC_TYPE[] x = this.x;
final KEY_GENERIC_TYPE[] y = this.y;
final int len = to - from;
if ( len < PARALLEL_QUICKSORT_NO_FORK ) {
quickSort( x, y, from, to );
return;
}
// Choose a partition element, v
int m = from + len / 2;
int l = from;
int n = to - 1;
int s = len / 8;
l = med3( x, y, l, l + s, l + 2 * s );
m = med3( x, y, m - s, m, m + s );
n = med3( x, y, n - 2 * s, n - s, n );
m = med3( x, y, l, m, n );
final KEY_GENERIC_TYPE v = x[ m ], w = y[ m ];
// Establish Invariant: v* (v)* v*
int a = from, b = a, c = to - 1, d = c;
while ( true ) {
int comparison, t;
while ( b <= c && ( comparison = ( t = KEY_CMP( x[ b ], v ) ) == 0 ? KEY_CMP( y[ b ], w ) : t ) <= 0 ) {
if ( comparison == 0 ) swap( x, y, a++, b );
b++;
}
while ( c >= b && ( comparison = ( t = KEY_CMP( x[ c ], v ) ) == 0 ? KEY_CMP( y[ c ], w ) : t ) >= 0 ) {
if ( comparison == 0 ) swap( x, y, c, d-- );
c--;
}
if ( b > c ) break;
swap( x, y, b++, c-- );
}
// Swap partition elements back to middle
int t;
s = Math.min( a - from, b - a );
swap( x, y, from, b - s, s );
s = Math.min( d - c, to - d - 1 );
swap( x, y, b, to - s, s );
s = b - a;
t = d - c;
// Recursively sort non-partition-elements
if ( s > 1 && t > 1 ) invokeAll( new ForkJoinQuickSort2 KEY_GENERIC( x, y, from, from + s ), new ForkJoinQuickSort2 KEY_GENERIC( x, y, to - t, to ) );
else if ( s > 1 ) invokeAll( new ForkJoinQuickSort2 KEY_GENERIC( x, y, from, from + s ) );
else invokeAll( new ForkJoinQuickSort2 KEY_GENERIC( x, y, to - t, to ) );
}
}
/** Sorts the specified range of elements of two arrays according to the natural lexicographical
* ascending order using a parallel quicksort.
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This method implements a lexicographical sorting of the arguments. Pairs of
* elements in the same position in the two provided arrays will be considered a single key, and
* permuted accordingly. In the end, either x[ i ] < x[ i + 1 ] or x[ i ]
* == x[ i + 1 ] and y[ i ] ≤ y[ i + 1 ].
*
*
This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x the first array to be sorted.
* @param y the second array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static KEY_GENERIC void parallelQuickSort( final KEY_GENERIC_TYPE[] x, final KEY_GENERIC_TYPE[] y, final int from, final int to ) {
if ( to - from < PARALLEL_QUICKSORT_NO_FORK ) quickSort( x, y, from, to );
final ForkJoinPool pool = new ForkJoinPool( Runtime.getRuntime().availableProcessors() );
pool.invoke( new ForkJoinQuickSort2 KEY_GENERIC( x, y, from, to ) );
pool.shutdown();
}
/** Sorts two arrays according to the natural lexicographical
* ascending order using a parallel quicksort.
*
*
The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages
* 1249−1265, 1993.
*
*
This method implements a lexicographical sorting of the arguments. Pairs of
* elements in the same position in the two provided arrays will be considered a single key, and
* permuted accordingly. In the end, either x[ i ] < x[ i + 1 ] or x[ i ]
* == x[ i + 1 ] and y[ i ] ≤ y[ i + 1 ].
*
*
This implementation uses a {@link ForkJoinPool} executor service with
* {@link Runtime#availableProcessors()} parallel threads.
*
* @param x the first array to be sorted.
* @param y the second array to be sorted.
*/
public static KEY_GENERIC void parallelQuickSort( final KEY_GENERIC_TYPE[] x, final KEY_GENERIC_TYPE[] y ) {
ensureSameLength( x, y );
parallelQuickSort( x, y, 0, x.length );
}
/** Sorts the specified range of elements according to the natural ascending order using mergesort, using a given pre-filled support array.
*
*
This sort is guaranteed to be stable: equal elements will not be reordered as a result
* of the sort. Moreover, no support arrays will be allocated.
* @param a the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param supp a support array containing at least to elements, and whose entries are identical to those
* of {@code a} in the specified range.
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], final int from, final int to, final KEY_GENERIC_TYPE supp[] ) {
int len = to - from;
// Insertion sort on smallest arrays
if ( len < MERGESORT_NO_REC ) {
insertionSort( a, from, to );
return;
}
// Recursively sort halves of a into supp
final int mid = ( from + to ) >>> 1;
mergeSort( supp, from, mid, a );
mergeSort( supp, mid, to, a );
// If list is already sorted, just copy from supp to a. This is an
// optimization that results in faster sorts for nearly ordered lists.
if ( KEY_LESSEQ( supp[ mid - 1 ], supp[ mid ] ) ) {
System.arraycopy( supp, from, a, from, len );
return;
}
// Merge sorted halves (now in supp) into a
for( int i = from, p = from, q = mid; i < to; i++ ) {
if ( q >= to || p < mid && KEY_LESSEQ( supp[ p ], supp[ q ] ) ) a[ i ] = supp[ p++ ];
else a[ i ] = supp[ q++ ];
}
}
/** Sorts the specified range of elements according to the natural ascending order using mergesort.
*
*
This sort is guaranteed to be stable: equal elements will not be reordered as a result
* of the sort. An array as large as a will be allocated by this method.
* @param a the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], final int from, final int to ) {
mergeSort( a, from, to, a.clone() );
}
/** Sorts an array according to the natural ascending order using mergesort.
*
*
This sort is guaranteed to be stable: equal elements will not be reordered as a result
* of the sort. An array as large as a will be allocated by this method.
* @param a the array to be sorted.
*/
public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[] ) {
mergeSort( a, 0, a.length );
}
/** Sorts the specified range of elements according to the order induced by the specified
* comparator using mergesort, using a given pre-filled support array.
*
*
This sort is guaranteed to be stable: equal elements will not be reordered as a result
* of the sort. Moreover, no support arrays will be allocated.
* @param a the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param comp the comparator to determine the sorting order.
* @param supp a support array containing at least to elements, and whose entries are identical to those
* of {@code a} in the specified range.
*/
public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], final int from, final int to, KEY_COMPARATOR KEY_GENERIC comp, final KEY_GENERIC_TYPE supp[] ) {
int len = to - from;
// Insertion sort on smallest arrays
if ( len < MERGESORT_NO_REC ) {
insertionSort( a, from, to, comp );
return;
}
// Recursively sort halves of a into supp
final int mid = ( from + to ) >>> 1;
mergeSort( supp, from, mid, comp, a );
mergeSort( supp, mid, to, comp, a );
// If list is already sorted, just copy from supp to a. This is an
// optimization that results in faster sorts for nearly ordered lists.
if ( comp.compare( supp[ mid - 1 ], supp[ mid ] ) <= 0 ) {
System.arraycopy( supp, from, a, from, len );
return;
}
// Merge sorted halves (now in supp) into a
for( int i = from, p = from, q = mid; i < to; i++ ) {
if ( q >= to || p < mid && comp.compare( supp[ p ], supp[ q ] ) <= 0 ) a[ i ] = supp[ p++ ];
else a[ i ] = supp[ q++ ];
}
}
/** Sorts the specified range of elements according to the order induced by the specified
* comparator using mergesort.
*
*
This sort is guaranteed to be stable: equal elements will not be reordered as a result
* of the sort. An array as large as a will be allocated by this method.
*
* @param a the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param comp the comparator to determine the sorting order.
*/
public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], final int from, final int to, KEY_COMPARATOR KEY_GENERIC comp ) {
mergeSort( a, from, to, comp, a.clone() );
}
/** Sorts an array according to the order induced by the specified
* comparator using mergesort.
*
*
This sort is guaranteed to be stable: equal elements will not be reordered as a result
* of the sort. An array as large as a will be allocated by this method.
* @param a the array to be sorted.
* @param comp the comparator to determine the sorting order.
*/
public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], KEY_COMPARATOR KEY_GENERIC comp ) {
mergeSort( a, 0, a.length, comp );
}
#if ! KEY_CLASS_Boolean
/**
* Searches a range of the specified array for the specified value using
* the binary search algorithm. The range must be sorted prior to making this call.
* If it is not sorted, the results are undefined. If the range contains multiple elements with
* the specified value, there is no guarantee which one will be found.
*
* @param a the array to be searched.
* @param from the index of the first element (inclusive) to be searched.
* @param to the index of the last element (exclusive) to be searched.
* @param key the value to be searched for.
* @return index of the search key, if it is contained in the array;
* otherwise, (-(insertion point) - 1). The insertion
* point is defined as the the point at which the value would
* be inserted into the array: the index of the first
* element greater than the key, or the length of the array, if all
* elements in the array are less than the specified key. Note
* that this guarantees that the return value will be ≥ 0 if
* and only if the key is found.
* @see java.util.Arrays
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
public static KEY_GENERIC int binarySearch( final KEY_GENERIC_TYPE[] a, int from, int to, final KEY_GENERIC_TYPE key ) {
KEY_GENERIC_TYPE midVal;
to--;
while (from <= to) {
final int mid = (from + to) >>> 1;
midVal = a[ mid ];
#if KEYS_PRIMITIVE
if (midVal < key) from = mid + 1;
else if (midVal > key) to = mid - 1;
else return mid;
#else
final int cmp = ((Comparable KEY_SUPER_GENERIC)midVal).compareTo( key );
if ( cmp < 0 ) from = mid + 1;
else if (cmp > 0) to = mid - 1;
else return mid;
#endif
}
return -( from + 1 );
}
/**
* Searches an array for the specified value using
* the binary search algorithm. The range must be sorted prior to making this call.
* If it is not sorted, the results are undefined. If the range contains multiple elements with
* the specified value, there is no guarantee which one will be found.
*
* @param a the array to be searched.
* @param key the value to be searched for.
* @return index of the search key, if it is contained in the array;
* otherwise, (-(insertion point) - 1). The insertion
* point is defined as the the point at which the value would
* be inserted into the array: the index of the first
* element greater than the key, or the length of the array, if all
* elements in the array are less than the specified key. Note
* that this guarantees that the return value will be ≥ 0 if
* and only if the key is found.
* @see java.util.Arrays
*/
public static KEY_GENERIC int binarySearch( final KEY_GENERIC_TYPE[] a, final KEY_GENERIC_TYPE key ) {
return binarySearch( a, 0, a.length, key );
}
/**
* Searches a range of the specified array for the specified value using
* the binary search algorithm and a specified comparator. The range must be sorted following the comparator prior to making this call.
* If it is not sorted, the results are undefined. If the range contains multiple elements with
* the specified value, there is no guarantee which one will be found.
*
* @param a the array to be searched.
* @param from the index of the first element (inclusive) to be searched.
* @param to the index of the last element (exclusive) to be searched.
* @param key the value to be searched for.
* @param c a comparator.
* @return index of the search key, if it is contained in the array;
* otherwise, (-(insertion point) - 1). The insertion
* point is defined as the the point at which the value would
* be inserted into the array: the index of the first
* element greater than the key, or the length of the array, if all
* elements in the array are less than the specified key. Note
* that this guarantees that the return value will be ≥ 0 if
* and only if the key is found.
* @see java.util.Arrays
*/
public static KEY_GENERIC int binarySearch( final KEY_GENERIC_TYPE[] a, int from, int to, final KEY_GENERIC_TYPE key, final KEY_COMPARATOR KEY_GENERIC c ) {
KEY_GENERIC_TYPE midVal;
to--;
while (from <= to) {
final int mid = (from + to) >>> 1;
midVal = a[ mid ];
final int cmp = c.compare( midVal, key );
if ( cmp < 0 ) from = mid + 1;
else if (cmp > 0) to = mid - 1;
else return mid; // key found
}
return -( from + 1 );
}
/**
* Searches an array for the specified value using
* the binary search algorithm and a specified comparator. The range must be sorted following the comparator prior to making this call.
* If it is not sorted, the results are undefined. If the range contains multiple elements with
* the specified value, there is no guarantee which one will be found.
*
* @param a the array to be searched.
* @param key the value to be searched for.
* @param c a comparator.
* @return index of the search key, if it is contained in the array;
* otherwise, (-(insertion point) - 1). The insertion
* point is defined as the the point at which the value would
* be inserted into the array: the index of the first
* element greater than the key, or the length of the array, if all
* elements in the array are less than the specified key. Note
* that this guarantees that the return value will be ≥ 0 if
* and only if the key is found.
* @see java.util.Arrays
*/
public static KEY_GENERIC int binarySearch( final KEY_GENERIC_TYPE[] a, final KEY_GENERIC_TYPE key, final KEY_COMPARATOR KEY_GENERIC c ) {
return binarySearch( a, 0, a.length, key, c );
}
#if KEYS_PRIMITIVE
/** The size of a digit used during radix sort (must be a power of 2). */
private static final int DIGIT_BITS = 8;
/** The mask to extract a digit of {@link #DIGIT_BITS} bits. */
private static final int DIGIT_MASK = ( 1 << DIGIT_BITS ) - 1;
/** The number of digits per element. */
private static final int DIGITS_PER_ELEMENT = KEY_CLASS.SIZE / DIGIT_BITS;
private static final int RADIXSORT_NO_REC = 1024;
private static final int PARALLEL_RADIXSORT_NO_FORK = 1024;
/** This method fixes negative numbers so that the combination exponent/significand is lexicographically sorted. */
#if KEY_CLASS_Double
private static final long fixDouble( final double d ) {
final long l = Double.doubleToLongBits( d );
return l >= 0 ? l : l ^ 0x7FFFFFFFFFFFFFFFL;
}
#elif KEY_CLASS_Float
private static final int fixFloat( final float f ) {
final int i = Float.floatToIntBits( f );
return i >= 0 ? i : i ^ 0x7FFFFFFF;
}
#endif
/** Sorts the specified array using radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This implementation is significantly faster than quicksort
* already at small sizes (say, more than 10000 elements), but it can only
* sort in ascending order.
*
* @param a the array to be sorted.
*/
public static void radixSort( final KEY_TYPE[] a ) {
radixSort( a, 0, a.length );
}
/** Sorts the specified range of an array using radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This implementation is significantly faster than quicksort
* already at small sizes (say, more than 10000 elements), but it can only
* sort in ascending order.
*
* @param a the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void radixSort( final KEY_TYPE[] a, final int from, final int to ) {
if ( to - from < RADIXSORT_NO_REC ) {
quickSort( a, from, to );
return;
}
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( DIGITS_PER_ELEMENT - 1 ) + 1;
int stackPos = 0;
final int[] offsetStack = new int[ stackSize ];
final int[] lengthStack = new int[ stackSize ];
final int[] levelStack = new int[ stackSize ];
offsetStack[ stackPos ] = from;
lengthStack[ stackPos ] = to - from;
levelStack[ stackPos++ ] = 0;
final int[] count = new int[ 1 << DIGIT_BITS ];
final int[] pos = new int[ 1 << DIGIT_BITS ];
while( stackPos > 0 ) {
final int first = offsetStack[ --stackPos ];
final int length = lengthStack[ stackPos ];
final int level = levelStack[ stackPos ];
#if KEY_CLASS_Character
final int signMask = 0;
#else
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( int i = first + length; i-- != first; ) count[ INT( KEY2LEXINT( a[ i ] ) >>> shift & DIGIT_MASK ^ signMask ) ]++;
// Compute cumulative distribution
int lastUsed = -1;
for ( int i = 0, p = first; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) lastUsed = i;
pos[ i ] = ( p += count[ i ] );
}
final int end = first + length - count[ lastUsed ];
// i moves through the start of each block
for( int i = first, c = -1, d; i <= end; i += count[ c ], count[ c ] = 0 ) {
KEY_TYPE t = a[ i ];
c = INT( KEY2LEXINT( t ) >>> shift & DIGIT_MASK ^ signMask );
if ( i < end ) { // When all slots are OK, the last slot is necessarily OK.
while ( ( d = --pos[ c ] ) > i ) {
final KEY_TYPE z = t;
t = a[ d ];
a[ d ] = z;
c = INT( KEY2LEXINT( t ) >>> shift & DIGIT_MASK ^ signMask );
}
a[ i ] = t;
}
if ( level < maxLevel && count[ c ] > 1 ) {
if ( count[ c ] < RADIXSORT_NO_REC ) quickSort( a, i, i + count[ c ] );
else {
offsetStack[ stackPos ] = i;
lengthStack[ stackPos ] = count[ c ];
levelStack[ stackPos++ ] = level + 1;
}
}
}
}
}
protected final static class Segment {
protected final int offset, length, level;
protected Segment( final int offset, final int length, final int level ) {
this.offset = offset;
this.length = length;
this.level = level;
}
@Override
public String toString() {
return "Segment [offset=" + offset + ", length=" + length + ", level=" + level + "]";
}
}
protected final static Segment POISON_PILL = new Segment( -1, -1, -1 );
/** Sorts the specified range of an array using parallel radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This implementation uses a pool of {@link Runtime#availableProcessors()} threads.
*
* @param a the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void parallelRadixSort( final KEY_TYPE[] a, final int from, final int to ) {
if ( to - from < PARALLEL_RADIXSORT_NO_FORK ) {
quickSort( a, from, to );
return;
}
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final LinkedBlockingQueue queue = new LinkedBlockingQueue();
queue.add( new Segment( from, to - from, 0 ) );
final AtomicInteger queueSize = new AtomicInteger( 1 );
final int numberOfThreads = Runtime.getRuntime().availableProcessors();
final ExecutorService executorService = Executors.newFixedThreadPool( numberOfThreads, Executors.defaultThreadFactory() );
final ExecutorCompletionService executorCompletionService = new ExecutorCompletionService( executorService );
for( int i = numberOfThreads; i-- != 0; ) executorCompletionService.submit( new Callable() {
public Void call() throws Exception {
final int[] count = new int[ 1 << DIGIT_BITS ];
final int[] pos = new int[ 1 << DIGIT_BITS ];
for(;;) {
if ( queueSize.get() == 0 ) for( int i = numberOfThreads; i-- != 0; ) queue.add( POISON_PILL );
final Segment segment = queue.take();
if ( segment == POISON_PILL ) return null;
final int first = segment.offset;
final int length = segment.length;
final int level = segment.level;
#if KEY_CLASS_Character
final int signMask = 0;
#else
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( int i = first + length; i-- != first; ) count[ INT( KEY2LEXINT( a[ i ] ) >>> shift & DIGIT_MASK ^ signMask ) ]++;
// Compute cumulative distribution
int lastUsed = -1;
for( int i = 0, p = first; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) lastUsed = i;
pos[ i ] = ( p += count[ i ] );
}
final int end = first + length - count[ lastUsed ];
// i moves through the start of each block
for( int i = first, c = -1, d; i <= end; i += count[ c ], count[ c ] = 0 ) {
KEY_TYPE t = a[ i ];
c = INT( KEY2LEXINT( t ) >>> shift & DIGIT_MASK ^ signMask );
if ( i < end ) {
while( ( d = --pos[ c ] ) > i ) {
final KEY_TYPE z = t;
t = a[ d ];
a[ d ] = z;
c = INT( KEY2LEXINT( t ) >>> shift & DIGIT_MASK ^ signMask );
}
a[ i ] = t;
}
if ( level < maxLevel && count[ c ] > 1 ) {
if ( count[ c ] < PARALLEL_RADIXSORT_NO_FORK ) quickSort( a, i, i + count[ c ] );
else {
queueSize.incrementAndGet();
queue.add( new Segment( i, count[ c ], level + 1 ) );
}
}
}
queueSize.decrementAndGet();
}
}
} );
Throwable problem = null;
for( int i = numberOfThreads; i-- != 0; )
try {
executorCompletionService.take().get();
}
catch( Exception e ) {
problem = e.getCause(); // We keep only the last one. They will be logged anyway.
}
executorService.shutdown();
if ( problem != null ) throw ( problem instanceof RuntimeException ) ? (RuntimeException)problem : new RuntimeException( problem );
}
/** Sorts the specified array using parallel radix sort.
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This implementation uses a pool of {@link Runtime#availableProcessors()} threads.
*
* @param a the array to be sorted.
*/
public static void parallelRadixSort( final KEY_TYPE[] a ) {
parallelRadixSort( a, 0, a.length );
}
/** Sorts the specified array using indirect radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implement an indirect sort. The elements of 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).
*
* @param perm a permutation array indexing a.
* @param a the array to be sorted.
* @param stable whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect( final int[] perm, final KEY_TYPE[] a, final boolean stable ) {
radixSortIndirect( perm, a, 0, perm.length, stable );
}
/** Sorts the specified array using indirect radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implement an indirect sort. The elements of 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).
*
* @param perm a permutation array indexing a.
* @param a the array to be sorted.
* @param from the index of the first element of perm (inclusive) to be permuted.
* @param to the index of the last element of perm (exclusive) to be permuted.
* @param stable whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect( final int[] perm, final KEY_TYPE[] a, final int from, final int to, final boolean stable ) {
if ( to - from < RADIXSORT_NO_REC ) {
insertionSortIndirect( perm, a, from, to );
return;
}
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( DIGITS_PER_ELEMENT - 1 ) + 1;
int stackPos = 0;
final int[] offsetStack = new int[ stackSize ];
final int[] lengthStack = new int[ stackSize ];
final int[] levelStack = new int[ stackSize ];
offsetStack[ stackPos ] = from;
lengthStack[ stackPos ] = to - from;
levelStack[ stackPos++ ] = 0;
final int[] count = new int[ 1 << DIGIT_BITS ];
final int[] pos = new int[ 1 << DIGIT_BITS ];
final int[] support = stable ? new int[ perm.length ] : null;
while( stackPos > 0 ) {
final int first = offsetStack[ --stackPos ];
final int length = lengthStack[ stackPos ];
final int level = levelStack[ stackPos ];
#if KEY_CLASS_Character
final int signMask = 0;
#else
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( int i = first + length; i-- != first; ) count[ INT( KEY2LEXINT( a[ perm[ i ] ] ) >>> shift & DIGIT_MASK ^ signMask ) ]++;
// Compute cumulative distribution
int lastUsed = -1;
for ( int i = 0, p = stable ? 0 : first; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) lastUsed = i;
pos[ i ] = ( p += count[ i ] );
}
if ( stable ) {
for( int i = first + length; i-- != first; ) support[ --pos[ INT( KEY2LEXINT( a[ perm[ i ] ] ) >>> shift & DIGIT_MASK ^ signMask ) ] ] = perm[ i ];
System.arraycopy( support, 0, perm, first, length );
for( int i = 0, p = first; i <= lastUsed; i++ ) {
if ( level < maxLevel && count[ i ] > 1 ) {
if ( count[ i ] < RADIXSORT_NO_REC ) insertionSortIndirect( perm, a, p, p + count[ i ] );
else {
offsetStack[ stackPos ] = p;
lengthStack[ stackPos ] = count[ i ];
levelStack[ stackPos++ ] = level + 1;
}
}
p += count[ i ];
}
java.util.Arrays.fill( count, 0 );
}
else {
final int end = first + length - count[ lastUsed ];
// i moves through the start of each block
for( int i = first, c = -1, d; i <= end; i += count[ c ], count[ c ] = 0 ) {
int t = perm[ i ];
c = INT( KEY2LEXINT( a[ t ] ) >>> shift & DIGIT_MASK ^ signMask );
if ( i < end ) { // When all slots are OK, the last slot is necessarily OK.
while( ( d = --pos[ c ] ) > i ) {
final int z = t;
t = perm[ d ];
perm[ d ] = z;
c = INT( KEY2LEXINT( a[ t ] ) >>> shift & DIGIT_MASK ^ signMask );
}
perm[ i ] = t;
}
if ( level < maxLevel && count[ c ] > 1 ) {
if ( count[ c ] < RADIXSORT_NO_REC ) insertionSortIndirect( perm, a, i, i + count[ c ] );
else {
offsetStack[ stackPos ] = i;
lengthStack[ stackPos ] = count[ c ];
levelStack[ stackPos++ ] = level + 1;
}
}
}
}
}
}
/** Sorts the specified range of an array using parallel indirect radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implement an indirect sort. The elements of 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 {@link Runtime#availableProcessors()} threads.
*
* @param perm a permutation array indexing a.
* @param a the array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param stable whether the sorting algorithm should be stable.
*/
public static void parallelRadixSortIndirect( final int perm[], final KEY_TYPE[] a, final int from, final int to, final boolean stable ) {
if ( to - from < PARALLEL_RADIXSORT_NO_FORK ) {
radixSortIndirect( perm, a, from, to, stable );
return;
}
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final LinkedBlockingQueue queue = new LinkedBlockingQueue();
queue.add( new Segment( from, to - from, 0 ) );
final AtomicInteger queueSize = new AtomicInteger( 1 );
final int numberOfThreads = Runtime.getRuntime().availableProcessors();
final ExecutorService executorService = Executors.newFixedThreadPool( numberOfThreads, Executors.defaultThreadFactory() );
final ExecutorCompletionService executorCompletionService = new ExecutorCompletionService( executorService );
final int[] support = stable ? new int[ perm.length ] : null;
for( int i = numberOfThreads; i-- != 0; ) executorCompletionService.submit( new Callable() {
public Void call() throws Exception {
final int[] count = new int[ 1 << DIGIT_BITS ];
final int[] pos = new int[ 1 << DIGIT_BITS ];
for(;;) {
if ( queueSize.get() == 0 ) for( int i = numberOfThreads; i-- != 0; ) queue.add( POISON_PILL );
final Segment segment = queue.take();
if ( segment == POISON_PILL ) return null;
final int first = segment.offset;
final int length = segment.length;
final int level = segment.level;
#if KEY_CLASS_Character
final int signMask = 0;
#else
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( int i = first + length; i-- != first; ) count[ INT( KEY2LEXINT( a[ perm[ i ] ] ) >>> shift & DIGIT_MASK ^ signMask ) ]++;
// Compute cumulative distribution
int lastUsed = -1;
for ( int i = 0, p = first; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) lastUsed = i;
pos[ i ] = ( p += count[ i ] );
}
if ( stable ) {
for( int i = first + length; i-- != first; ) support[ --pos[ INT( KEY2LEXINT( a[ perm[ i ] ] ) >>> shift & DIGIT_MASK ^ signMask ) ] ] = perm[ i ];
System.arraycopy( support, first, perm, first, length );
for( int i = 0, p = first; i <= lastUsed; i++ ) {
if ( level < maxLevel && count[ i ] > 1 ) {
if ( count[ i ] < PARALLEL_RADIXSORT_NO_FORK ) radixSortIndirect( perm, a, p, p + count[ i ], stable );
else {
queueSize.incrementAndGet();
queue.add( new Segment( p, count[ i ], level + 1 ) );
}
}
p += count[ i ];
}
java.util.Arrays.fill( count, 0 );
}
else {
final int end = first + length - count[ lastUsed ];
// i moves through the start of each block
for( int i = first, c = -1, d; i <= end; i += count[ c ], count[ c ] = 0 ) {
int t = perm[ i ];
c = INT( KEY2LEXINT( a[ t ] ) >>> shift & DIGIT_MASK ^ signMask );
if ( i < end ) { // When all slots are OK, the last slot is necessarily OK.
while( ( d = --pos[ c ] ) > i ) {
final int z = t;
t = perm[ d ];
perm[ d ] = z;
c = INT( KEY2LEXINT( a[ t ] ) >>> shift & DIGIT_MASK ^ signMask );
}
perm[ i ] = t;
}
if ( level < maxLevel && count[ c ] > 1 ) {
if ( count[ c ] < PARALLEL_RADIXSORT_NO_FORK ) radixSortIndirect( perm, a, i, i + count[ c ], stable );
else {
queueSize.incrementAndGet();
queue.add( new Segment( i, count[ c ], level + 1 ) );
}
}
}
}
queueSize.decrementAndGet();
}
}
} );
Throwable problem = null;
for( int i = numberOfThreads; i-- != 0; )
try {
executorCompletionService.take().get();
}
catch( Exception e ) {
problem = e.getCause(); // We keep only the last one. They will be logged anyway.
}
executorService.shutdown();
if ( problem != null ) throw ( problem instanceof RuntimeException ) ? (RuntimeException)problem : new RuntimeException( problem );
}
/** Sorts the specified array using parallel indirect radix sort.
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implement an indirect sort. The elements of 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 {@link Runtime#availableProcessors()} threads.
*
* @param perm a permutation array indexing a.
* @param a the array to be sorted.
* @param stable whether the sorting algorithm should be stable.
*/
public static void parallelRadixSortIndirect( final int perm[], final KEY_TYPE[] a, final boolean stable ) {
parallelRadixSortIndirect( perm, a, 0, a.length, stable );
}
/** Sorts the specified pair of arrays lexicographically using radix sort.
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implements a lexicographical sorting of the arguments. Pairs of elements
* in the same position in the two provided arrays will be considered a single key, and permuted
* accordingly. In the end, either a[ i ] < a[ i + 1 ] or a[ i ] == a[ i + 1 ] and b[ i ] ≤ b[ i + 1 ].
*
* @param a the first array to be sorted.
* @param b the second array to be sorted.
*/
public static void radixSort( final KEY_TYPE[] a, final KEY_TYPE[] b ) {
ensureSameLength( a, b );
radixSort( a, b, 0, a.length );
}
/** Sorts the specified range of elements of two arrays using radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implements a lexicographical sorting of the arguments. Pairs of elements
* in the same position in the two provided arrays will be considered a single key, and permuted
* accordingly. In the end, either a[ i ] < a[ i + 1 ] or a[ i ] == a[ i + 1 ] and b[ i ] ≤ b[ i + 1 ].
*
* @param a the first array to be sorted.
* @param b the second array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void radixSort( final KEY_TYPE[] a, final KEY_TYPE[] b, final int from, final int to ) {
if ( to - from < RADIXSORT_NO_REC ) {
selectionSort( a, b, from, to );
return;
}
final int layers = 2;
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( layers * DIGITS_PER_ELEMENT - 1 ) + 1;
int stackPos = 0;
final int[] offsetStack = new int[ stackSize ];
final int[] lengthStack = new int[ stackSize ];
final int[] levelStack = new int[ stackSize ];
offsetStack[ stackPos ] = from;
lengthStack[ stackPos ] = to - from;
levelStack[ stackPos++ ] = 0;
final int[] count = new int[ 1 << DIGIT_BITS ];
final int[] pos = new int[ 1 << DIGIT_BITS ];
while( stackPos > 0 ) {
final int first = offsetStack[ --stackPos ];
final int length = lengthStack[ stackPos ];
final int level = levelStack[ stackPos ];
#if KEY_CLASS_Character
final int signMask = 0;
#else
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
final KEY_TYPE[] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( int i = first + length; i-- != first; ) count[ INT( KEY2LEXINT( k[ i ] ) >>> shift & DIGIT_MASK ^ signMask ) ]++;
// Compute cumulative distribution
int lastUsed = -1;
for ( int i = 0, p = first; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) lastUsed = i;
pos[ i ] = ( p += count[ i ] );
}
final int end = first + length - count[ lastUsed ];
// i moves through the start of each block
for( int i = first, c = -1, d; i <= end; i += count[ c ], count[ c ] = 0 ) {
KEY_TYPE t = a[ i ];
KEY_TYPE u = b[ i ];
c = INT( KEY2LEXINT( k[ i ] ) >>> shift & DIGIT_MASK ^ signMask );
if ( i < end ) { // When all slots are OK, the last slot is necessarily OK.
while( ( d = --pos[ c ] ) > i ) {
c = INT( KEY2LEXINT( k[ d ] ) >>> shift & DIGIT_MASK ^ signMask );
KEY_TYPE z = t;
t = a[ d ];
a[ d ] = z;
z = u;
u = b[ d ];
b[ d ] = z;
}
a[ i ] = t;
b[ i ] = u;
}
if ( level < maxLevel && count[ c ] > 1 ) {
if ( count[ c ] < RADIXSORT_NO_REC ) selectionSort( a, b, i, i + count[ c ] );
else {
offsetStack[ stackPos ] = i;
lengthStack[ stackPos ] = count[ c ];
levelStack[ stackPos++ ] = level + 1;
}
}
}
}
}
/** Sorts the specified range of elements of two arrays using a parallel radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implements a lexicographical sorting of the arguments. Pairs of elements
* in the same position in the two provided arrays will be considered a single key, and permuted
* accordingly. In the end, either a[ i ] < a[ i + 1 ] or a[ i ] == a[ i + 1 ] and b[ i ] ≤ b[ i + 1 ].
*
*
This implementation uses a pool of {@link Runtime#availableProcessors()} threads.
*
* @param a the first array to be sorted.
* @param b the second array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void parallelRadixSort( final KEY_TYPE[] a, final KEY_TYPE[] b, final int from, final int to ) {
if ( to - from < PARALLEL_RADIXSORT_NO_FORK ) {
quickSort( a, b, from, to );
return;
}
final int layers = 2;
if ( a.length != b.length ) throw new IllegalArgumentException( "Array size mismatch." );
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
final LinkedBlockingQueue queue = new LinkedBlockingQueue();
queue.add( new Segment( from, to - from, 0 ) );
final AtomicInteger queueSize = new AtomicInteger( 1 );
final int numberOfThreads = Runtime.getRuntime().availableProcessors();
final ExecutorService executorService = Executors.newFixedThreadPool( numberOfThreads, Executors.defaultThreadFactory() );
final ExecutorCompletionService executorCompletionService = new ExecutorCompletionService( executorService );
for ( int i = numberOfThreads; i-- != 0; )
executorCompletionService.submit( new Callable() {
public Void call() throws Exception {
final int[] count = new int[ 1 << DIGIT_BITS ];
final int[] pos = new int[ 1 << DIGIT_BITS ];
for ( ;; ) {
if ( queueSize.get() == 0 ) for ( int i = numberOfThreads; i-- != 0; )
queue.add( POISON_PILL );
final Segment segment = queue.take();
if ( segment == POISON_PILL ) return null;
final int first = segment.offset;
final int length = segment.length;
final int level = segment.level;
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final KEY_TYPE[] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS;
// Count keys.
for ( int i = first + length; i-- != first; )
count[ INT( KEY2LEXINT( k[ i ] ) >>> shift & DIGIT_MASK ^ signMask ) ]++;
// Compute cumulative distribution
int lastUsed = -1;
for ( int i = 0, p = first; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) lastUsed = i;
pos[ i ] = ( p += count[ i ] );
}
final int end = first + length - count[ lastUsed ];
for ( int i = first, c = -1, d; i <= end; i += count[ c ], count[ c ] = 0 ) {
KEY_TYPE t = a[ i ];
KEY_TYPE u = b[ i ];
c = INT( KEY2LEXINT( k[ i ] ) >>> shift & DIGIT_MASK ^ signMask );
if ( i < end ) { // When all slots are OK, the last slot is necessarily OK.
while ( ( d = --pos[ c ] ) > i ) {
c = INT( KEY2LEXINT( k[ d ] ) >>> shift & DIGIT_MASK ^ signMask );
final KEY_TYPE z = t;
final KEY_TYPE w = u;
t = a[ d ];
u = b[ d ];
a[ d ] = z;
b[ d ] = w;
}
a[ i ] = t;
b[ i ] = u;
}
if ( level < maxLevel && count[ c ] > 1 ) {
if ( count[ c ] < PARALLEL_RADIXSORT_NO_FORK ) quickSort( a, b, i, i + count[ c ] );
else {
queueSize.incrementAndGet();
queue.add( new Segment( i, count[ c ], level + 1 ) );
}
}
}
queueSize.decrementAndGet();
}
}
} );
Throwable problem = null;
for ( int i = numberOfThreads; i-- != 0; )
try {
executorCompletionService.take().get();
}
catch ( Exception e ) {
problem = e.getCause(); // We keep only the last one. They will be logged anyway.
}
executorService.shutdown();
if ( problem != null ) throw ( problem instanceof RuntimeException ) ? (RuntimeException)problem : new RuntimeException( problem );
}
/** Sorts two arrays using a parallel radix sort.
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implements a lexicographical sorting of the arguments. Pairs of elements
* in the same position in the two provided arrays will be considered a single key, and permuted
* accordingly. In the end, either a[ i ] < a[ i + 1 ] or a[ i ] == a[ i + 1 ] and b[ i ] ≤ b[ i + 1 ].
*
*
This implementation uses a pool of {@link Runtime#availableProcessors()} threads.
*
* @param a the first array to be sorted.
* @param b the second array to be sorted.
*/
public static void parallelRadixSort( final KEY_TYPE[] a, final KEY_TYPE[] b ) {
ensureSameLength( a, b );
parallelRadixSort( a, b, 0, a.length );
}
private static KEY_GENERIC void insertionSortIndirect( final int[] perm, final KEY_TYPE[] a, final KEY_TYPE[] b, final int from, final int to ) {
for ( int i = from; ++i < to; ) {
int t = perm[ i ];
int j = i;
for ( int u = perm[ j - 1 ]; KEY_LESS( a[ t ], a[ u ] ) || KEY_CMP_EQ( a[ t ], a[ u ] ) && KEY_LESS( b[ t ], b[ u ] ); u = perm[ --j - 1 ] ) {
perm[ j ] = u;
if ( from == j - 1 ) {
--j;
break;
}
}
perm[ j ] = t;
}
}
/** Sorts the specified pair of arrays lexicographically using indirect radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implement an indirect sort. The elements of 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).
*
* @param perm a permutation array indexing a.
* @param a the array to be sorted.
* @param b the second array to be sorted.
* @param stable whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect( final int[] perm, final KEY_TYPE[] a, final KEY_TYPE[] b, final boolean stable ) {
ensureSameLength( a, b );
radixSortIndirect( perm, a, b, 0, a.length, stable );
}
/** Sorts the specified pair of arrays lexicographically using indirect radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implement an indirect sort. The elements of 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).
*
* @param perm a permutation array indexing a.
* @param a the array to be sorted.
* @param b the second array to be sorted.
* @param from the index of the first element of perm (inclusive) to be permuted.
* @param to the index of the last element of perm (exclusive) to be permuted.
* @param stable whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect( final int[] perm, final KEY_TYPE[] a, final KEY_TYPE[] b, final int from, final int to, final boolean stable ) {
if ( to - from < RADIXSORT_NO_REC ) {
insertionSortIndirect( perm, a, b, from, to );
return;
}
final int layers = 2;
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( layers * DIGITS_PER_ELEMENT - 1 ) + 1;
int stackPos = 0;
final int[] offsetStack = new int[ stackSize ];
final int[] lengthStack = new int[ stackSize ];
final int[] levelStack = new int[ stackSize ];
offsetStack[ stackPos ] = from;
lengthStack[ stackPos ] = to - from;
levelStack[ stackPos++ ] = 0;
final int[] count = new int[ 1 << DIGIT_BITS ];
final int[] pos = new int[ 1 << DIGIT_BITS ];
final int[] support = stable ? new int[ perm.length ] : null;
while( stackPos > 0 ) {
final int first = offsetStack[ --stackPos ];
final int length = lengthStack[ stackPos ];
final int level = levelStack[ stackPos ];
#if KEY_CLASS_Character
final int signMask = 0;
#else
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
final KEY_TYPE[] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( int i = first + length; i-- != first; ) count[ INT( KEY2LEXINT( k[ perm[ i ] ] ) >>> shift & DIGIT_MASK ^ signMask ) ]++;
// Compute cumulative distribution
int lastUsed = -1;
for ( int i = 0, p = stable ? 0 : first; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) lastUsed = i;
pos[ i ] = ( p += count[ i ] );
}
if ( stable ) {
for( int i = first + length; i-- != first; ) support[ --pos[ INT( KEY2LEXINT( k[ perm[ i ] ] ) >>> shift & DIGIT_MASK ^ signMask ) ] ] = perm[ i ];
System.arraycopy( support, 0, perm, first, length );
for( int i = 0, p = first; i < 1 << DIGIT_BITS; i++ ) {
if ( level < maxLevel && count[ i ] > 1 ) {
if ( count[ i ] < RADIXSORT_NO_REC ) insertionSortIndirect( perm, a, b, p, p + count[ i ] );
else {
offsetStack[ stackPos ] = p;
lengthStack[ stackPos ] = count[ i ];
levelStack[ stackPos++ ] = level + 1;
}
}
p += count[ i ];
}
java.util.Arrays.fill( count, 0 );
}
else {
final int end = first + length - count[ lastUsed ];
// i moves through the start of each block
for( int i = first, c = -1, d; i <= end; i += count[ c ], count[ c ] = 0 ) {
int t = perm[ i ];
c = INT( KEY2LEXINT( k[ t ] ) >>> shift & DIGIT_MASK ^ signMask );
if ( i < end ) { // When all slots are OK, the last slot is necessarily OK.
while( ( d = --pos[ c ] ) > i ) {
final int z = t;
t = perm[ d ];
perm[ d ] = z;
c = INT( KEY2LEXINT( k[ t ] ) >>> shift & DIGIT_MASK ^ signMask );
}
perm[ i ] = t;
}
if ( level < maxLevel && count[ c ] > 1 ) {
if ( count[ c ] < RADIXSORT_NO_REC ) insertionSortIndirect( perm, a, b, i, i + count[ c ] );
else {
offsetStack[ stackPos ] = i;
lengthStack[ stackPos ] = count[ c ];
levelStack[ stackPos++ ] = level + 1;
}
}
}
}
}
}
private static void selectionSort( final KEY_TYPE[][] a, final int from, final int to, final int level ) {
final int layers = a.length;
final int firstLayer = level / DIGITS_PER_ELEMENT;
for( int i = from; i < to - 1; i++ ) {
int m = i;
for( int j = i + 1; j < to; j++ ) {
for( int p = firstLayer; p < layers; p++ ) {
if ( a[ p ][ j ] < a[ p ][ m ] ) {
m = j;
break;
}
else if ( a[ p ][ j ] > a[ p ][ m ] ) break;
}
}
if ( m != i ) {
for( int p = layers; p-- != 0; ) {
final KEY_TYPE u = a[ p ][ i ];
a[ p ][ i ] = a[ p ][ m ];
a[ p ][ m ] = u;
}
}
}
}
/** Sorts the specified array of arrays lexicographically using radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implements a lexicographical sorting of the provided arrays. Tuples of elements
* in the same position will be considered a single key, and permuted
* accordingly.
*
* @param a an array containing arrays of equal length to be sorted lexicographically in parallel.
*/
public static void radixSort( final KEY_TYPE[][] a ) {
radixSort( a, 0, a[ 0 ].length );
}
/** Sorts the specified array of arrays lexicographically using radix sort.
*
*
The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
* McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993).
*
*
This method implements a lexicographical sorting of the provided arrays. Tuples of elements
* in the same position will be considered a single key, and permuted
* accordingly.
*
* @param a an array containing arrays of equal length to be sorted lexicographically in parallel.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void radixSort( final KEY_TYPE[][] a, final int from, final int to ) {
if ( to - from < RADIXSORT_NO_REC ) {
selectionSort( a, from, to, 0 );
return;
}
final int layers = a.length;
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
for( int p = layers, l = a[ 0 ].length; p-- != 0; ) if ( a[ p ].length != l ) throw new IllegalArgumentException( "The array of index " + p + " has not the same length of the array of index 0." );
final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( layers * DIGITS_PER_ELEMENT - 1 ) + 1;
int stackPos = 0;
final int[] offsetStack = new int[ stackSize ];
final int[] lengthStack = new int[ stackSize ];
final int[] levelStack = new int[ stackSize ];
offsetStack[ stackPos ] = from;
lengthStack[ stackPos ] = to - from;
levelStack[ stackPos++ ] = 0;
final int[] count = new int[ 1 << DIGIT_BITS ];
final int[] pos = new int[ 1 << DIGIT_BITS ];
final KEY_TYPE[] t = new KEY_TYPE[ layers ];
while( stackPos > 0 ) {
final int first = offsetStack[ --stackPos ];
final int length = lengthStack[ stackPos ];
final int level = levelStack[ stackPos ];
#if KEY_CLASS_Character
final int signMask = 0;
#else
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
final KEY_TYPE[] k = a[ level / DIGITS_PER_ELEMENT ]; // This is the key array
final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key
// Count keys.
for( int i = first + length; i-- != first; ) count[ INT( KEY2LEXINT( k[ i ] ) >>> shift & DIGIT_MASK ^ signMask ) ]++;
// Compute cumulative distribution
int lastUsed = -1;
for ( int i = 0, p = first; i < 1 << DIGIT_BITS; i++ ) {
if ( count[ i ] != 0 ) lastUsed = i;
pos[ i ] = ( p += count[ i ] );
}
final int end = first + length - count[ lastUsed ];
// i moves through the start of each block
for( int i = first, c = -1, d; i <= end; i += count[ c ], count[ c ] = 0 ) {
for( int p = layers; p-- != 0; ) t[ p ] = a[ p ][ i ];
c = INT( KEY2LEXINT( k[ i ] ) >>> shift & DIGIT_MASK ^ signMask );
if ( i < end ) { // When all slots are OK, the last slot is necessarily OK.
while( ( d = --pos[ c ] ) > i ) {
c = INT( KEY2LEXINT( k[ d ] ) >>> shift & DIGIT_MASK ^ signMask );
for( int p = layers; p-- != 0; ) {
final KEY_TYPE u = t[ p ];
t[ p ] = a[ p ][ d ];
a[ p ][ d ] = u;
}
}
for( int p = layers; p-- != 0; ) a[ p ][ i ] = t[ p ];
}
if ( level < maxLevel && count[ c ] > 1 ) {
if ( count[ c ] < RADIXSORT_NO_REC ) selectionSort( a, i, i + count[ c ], level + 1 );
else {
offsetStack[ stackPos ] = i;
lengthStack[ stackPos ] = count[ c ];
levelStack[ stackPos++ ] = level + 1;
}
}
}
}
}
#endif
#endif
/** Shuffles the specified array fragment using the specified pseudorandom number generator.
*
* @param a the array to be shuffled.
* @param from the index of the first element (inclusive) to be shuffled.
* @param to the index of the last element (exclusive) to be shuffled.
* @param random a pseudorandom number generator (please use a XorShift* generator).
* @return a.
*/
public static KEY_GENERIC KEY_GENERIC_TYPE[] shuffle( final KEY_GENERIC_TYPE[] a, final int from, final int to, final Random random ) {
for( int i = to - from; i-- != 0; ) {
final int p = random.nextInt( i + 1 );
final KEY_GENERIC_TYPE t = a[ from + i ];
a[ from + i ] = a[ from + p ];
a[ from + p ] = t;
}
return a;
}
/** Shuffles the specified array using the specified pseudorandom number generator.
*
* @param a the array to be shuffled.
* @param random a pseudorandom number generator (please use a XorShift* generator).
* @return a.
*/
public static KEY_GENERIC KEY_GENERIC_TYPE[] shuffle( final KEY_GENERIC_TYPE[] a, final Random random ) {
for( int i = a.length; i-- != 0; ) {
final int p = random.nextInt( i + 1 );
final KEY_GENERIC_TYPE t = a[ i ];
a[ i ] = a[ p ];
a[ p ] = t;
}
return a;
}
/** Reverses the order of the elements in the specified array.
*
* @param a the array to be reversed.
* @return a.
*/
public static KEY_GENERIC KEY_GENERIC_TYPE[] reverse( final KEY_GENERIC_TYPE[] a ) {
final int length = a.length;
for( int i = length / 2; i-- != 0; ) {
final KEY_GENERIC_TYPE t = a[ length - i - 1 ];
a[ length - i - 1 ] = a[ i ];
a[ i ] = t;
}
return a;
}
/** Reverses the order of the elements in the specified array fragment.
*
* @param a the array to be reversed.
* @param from the index of the first element (inclusive) to be reversed.
* @param to the index of the last element (exclusive) to be reversed.
* @return a.
*/
public static KEY_GENERIC KEY_GENERIC_TYPE[] reverse( final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
final int length = to - from;
for( int i = length / 2; i-- != 0; ) {
final KEY_GENERIC_TYPE t = a[ from + length - i - 1 ];
a[ from + length - i - 1 ] = a[ from + i ];
a[ from + i ] = t;
}
return a;
}
/** A type-specific content-based hash strategy for arrays. */
private static final class ArrayHashStrategy KEY_GENERIC implements Hash.Strategy, java.io.Serializable {
private static final long serialVersionUID = -7046029254386353129L;
public int hashCode( final KEY_GENERIC_TYPE[] o ) {
return java.util.Arrays.hashCode( o );
}
public boolean equals( final KEY_GENERIC_TYPE[] a, final KEY_GENERIC_TYPE[] b ) {
return java.util.Arrays.equals( a, b );
}
}
/** A type-specific content-based hash strategy for arrays.
*
* This hash strategy may be used in custom hash collections whenever keys are
* arrays, and they must be considered equal by content. This strategy
* will handle null correctly, and it is serializable.
*/
#if KEYS_PRIMITIVE
public final static Hash.Strategy HASH_STRATEGY = new ArrayHashStrategy();
#else
@SuppressWarnings({"rawtypes"})
public final static Hash.Strategy HASH_STRATEGY = new ArrayHashStrategy();
#endif
}