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/*
* Copyright (C) 2009-2024 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.
*
*
*
* Copyright (C) 1999 CERN - European Organization for Nuclear Research.
*
* Permission to use, copy, modify, distribute and sell this software and
* its documentation for any purpose is hereby granted without fee,
* provided that the above copyright notice appear in all copies and that
* both that copyright notice and this permission notice appear in
* supporting documentation. CERN makes no representations about the
* suitability of this software for any purpose. It is provided "as is"
* without expressed or implied warranty.
*/
package it.unimi.dsi.fastutil.ints;
import java.util.Arrays;
import java.util.Random;
import java.util.concurrent.ForkJoinPool;
import java.util.concurrent.ForkJoinTask;
import java.util.concurrent.RecursiveAction;
import it.unimi.dsi.fastutil.BigArrays;
import it.unimi.dsi.fastutil.Hash;
import static it.unimi.dsi.fastutil.BigArrays.ensureLength;
import static it.unimi.dsi.fastutil.BigArrays.start;
import static it.unimi.dsi.fastutil.BigArrays.segment;
import static it.unimi.dsi.fastutil.BigArrays.displacement;
import static it.unimi.dsi.fastutil.BigArrays.SEGMENT_MASK;
import static it.unimi.dsi.fastutil.BigArrays.SEGMENT_SHIFT;
import static it.unimi.dsi.fastutil.BigArrays.SEGMENT_SIZE;
import java.util.concurrent.atomic.AtomicIntegerArray;
import it.unimi.dsi.fastutil.bytes.ByteBigArrays;
/**
* A class providing static methods and objects that do useful things with {@linkplain BigArrays big
* arrays}.
*
*
* Note that {@link it.unimi.dsi.fastutil.io.BinIO} and {@link it.unimi.dsi.fastutil.io.TextIO}
* contain several methods that make it possible to load and save big 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.
*
*
Parallel operations
Some algorithms provide a parallel version that will by default use
* the {@linkplain ForkJoinPool#commonPool() common pool}, but this can be overridden by calling the
* function in a task already in the {@link ForkJoinPool} that the operation should run in. For
* example, something along the lines of
* "{@code poolToParallelSortIn.invoke(() -> parallelQuickSort(arrayToSort))}" will run the parallel
* sort in {@code poolToParallelSortIn} instead of the default pool.
*
* @see BigArrays
*/
public final class IntBigArrays {
private IntBigArrays() {
}
/** A static, final, empty big array. */
public static final int[][] EMPTY_BIG_ARRAY = {};
/**
* A static, final, empty big array to be used as default big array in allocations. An object
* distinct from {@link #EMPTY_BIG_ARRAY} makes it possible to have different behaviors depending on
* whether the user required an empty allocation, or we are just lazily delaying allocation.
*
* @see java.util.ArrayList
*/
public static final int[][] DEFAULT_EMPTY_BIG_ARRAY = {};
/**
* Returns the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @return the element of the big array at the specified position.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int get(final int[][] array, final long index) {
return array[segment(index)][displacement(index)];
}
/**
* Sets the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @param value the new value for the array element at the specified position.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void set(final int[][] array, final long index, int value) {
array[segment(index)][displacement(index)] = value;
}
/**
* Swaps the element of the given big array of specified indices.
*
* @param array a big array.
* @param first a position in the big array.
* @param second a position in the big array.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void swap(final int[][] array, final long first, final long second) {
final int t = array[segment(first)][displacement(first)];
array[segment(first)][displacement(first)] = array[segment(second)][displacement(second)];
array[segment(second)][displacement(second)] = t;
}
/**
* Adds the specified increment the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @param incr the increment
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void add(final int[][] array, final long index, int incr) {
array[segment(index)][displacement(index)] += incr;
}
/**
* Multiplies by the specified factor the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @param factor the factor
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void mul(final int[][] array, final long index, int factor) {
array[segment(index)][displacement(index)] *= factor;
}
/**
* Increments the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void incr(final int[][] array, final long index) {
array[segment(index)][displacement(index)]++;
}
/**
* Decrements the element of the given big array of specified index.
*
* @param array a big array.
* @param index a position in the big array.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void decr(final int[][] array, final long index) {
array[segment(index)][displacement(index)]--;
}
/**
* Returns the length of the given big array.
*
* @param array a big array.
* @return the length of the given big array.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static long length(final int[][] array) {
final int length = array.length;
return length == 0 ? 0 : start(length - 1) + array[length - 1].length;
}
/**
* Copies a big array from the specified source big array, beginning at the specified position, to
* the specified position of the destination big array. Handles correctly overlapping regions of the
* same big array.
*
* @param srcArray the source big array.
* @param srcPos the starting position in the source big array.
* @param destArray the destination big array.
* @param destPos the starting position in the destination data.
* @param length the number of elements to be copied.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void copy(final int[][] srcArray, final long srcPos, final int[][] destArray, final long destPos, long length) {
BigArrays.copy(srcArray, srcPos, destArray, destPos, length);
}
/**
* Copies a big array from the specified source big array, beginning at the specified position, to
* the specified position of the destination array.
*
* @param srcArray the source big array.
* @param srcPos the starting position in the source big array.
* @param destArray the destination array.
* @param destPos the starting position in the destination data.
* @param length the number of elements to be copied.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void copyFromBig(final int[][] srcArray, final long srcPos, final int[] destArray, int destPos, int length) {
BigArrays.copyFromBig(srcArray, srcPos, destArray, destPos, length);
}
/**
* Copies an array from the specified source array, beginning at the specified position, to the
* specified position of the destination big array.
*
* @param srcArray the source array.
* @param srcPos the starting position in the source array.
* @param destArray the destination big array.
* @param destPos the starting position in the destination data.
* @param length the number of elements to be copied.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void copyToBig(final int[] srcArray, int srcPos, final int[][] destArray, final long destPos, long length) {
BigArrays.copyToBig(srcArray, srcPos, destArray, destPos, length);
}
/**
* Creates a new big array.
*
* @param length the length of the new big array.
* @return a new big array of given length.
*/
public static int[][] newBigArray(final long length) {
if (length == 0) return EMPTY_BIG_ARRAY;
ensureLength(length);
final int baseLength = (int)((length + SEGMENT_MASK) >>> SEGMENT_SHIFT);
int[][] base = new int[baseLength][];
final int residual = (int)(length & SEGMENT_MASK);
if (residual != 0) {
for (int i = 0; i < baseLength - 1; i++) base[i] = new int[SEGMENT_SIZE];
base[baseLength - 1] = new int[residual];
} else for (int i = 0; i < baseLength; i++) base[i] = new int[SEGMENT_SIZE];
return base;
}
/** A static, final, empty big atomic array. */
public static final AtomicIntegerArray[] EMPTY_BIG_ATOMIC_ARRAY = {};
/**
* Creates a new big atomic array.
*
* @param length the length of the new big array.
* @return a new big atomic array of given length.
*/
public static AtomicIntegerArray[] newBigAtomicArray(final long length) {
if (length == 0) return EMPTY_BIG_ATOMIC_ARRAY;
ensureLength(length);
final int baseLength = (int)((length + SEGMENT_MASK) >>> SEGMENT_SHIFT);
AtomicIntegerArray[] base = new AtomicIntegerArray[baseLength];
final int residual = (int)(length & SEGMENT_MASK);
if (residual != 0) {
for (int i = 0; i < baseLength - 1; i++) base[i] = new AtomicIntegerArray(SEGMENT_SIZE);
base[baseLength - 1] = new AtomicIntegerArray(residual);
} else for (int i = 0; i < baseLength; i++) base[i] = new AtomicIntegerArray(SEGMENT_SIZE);
return base;
}
/**
* Turns a standard array into a big array.
*
*
* Note that the returned big array might contain as a segment the original array.
*
* @param array an array.
* @return a new big array with the same length and content of {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] wrap(final int[] array) {
return BigArrays.wrap(array);
}
/**
* Ensures that a big array can contain the given number of entries.
*
*
* If you cannot foresee whether this big array will need again to be enlarged, you should probably
* use {@code grow()} instead.
*
*
* Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @return {@code array}, if it contains {@code length} entries or more; otherwise, a big array with
* {@code length} entries whose first {@code length(array)} entries are the same as those of
* {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] ensureCapacity(final int[][] array, final long length) {
return ensureCapacity(array, length, length(array));
}
/**
* Forces a big array to contain the given number of entries, preserving just a part of the big
* array.
*
*
* Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @param preserve the number of elements of the big array that must be preserved in case a new
* allocation is necessary.
* @return a big array with {@code length} entries whose first {@code preserve} entries are the same
* as those of {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] forceCapacity(final int[][] array, final long length, final long preserve) {
return BigArrays.forceCapacity(array, length, preserve);
}
/**
* Ensures that a big array can contain the given number of entries, preserving just a part of the
* big array.
*
*
* Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @param preserve the number of elements of the big array that must be preserved in case a new
* allocation is necessary.
* @return {@code array}, if it can contain {@code length} entries or more; otherwise, a big array
* with {@code length} entries whose first {@code preserve} entries are the same as those of
* {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] ensureCapacity(final int[][] array, final long length, final long preserve) {
return length > length(array) ? forceCapacity(array, length, preserve) : array;
}
/**
* Grows the given big array to the maximum between the given length and the current length
* increased by 50%, provided that the given length is larger than the current length.
*
*
* If you want complete control on the big array growth, you should probably use
* {@code ensureCapacity()} instead.
*
*
* Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @return {@code array}, if it can contain {@code length} entries; otherwise, a big array with
* max({@code length},{@code length(array)}/φ) entries whose first {@code length(array)}
* entries are the same as those of {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] grow(final int[][] array, final long length) {
final long oldLength = length(array);
return length > oldLength ? grow(array, length, oldLength) : array;
}
/**
* Grows the given big array to the maximum between the given length and the current length
* increased by 50%, provided that the given length is larger than the current length, preserving
* just a part of the big array.
*
*
* If you want complete control on the big array growth, you should probably use
* {@code ensureCapacity()} instead.
*
*
* Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new minimum length for this big array.
* @param preserve the number of elements of the big array that must be preserved in case a new
* allocation is necessary.
* @return {@code array}, if it can contain {@code length} entries; otherwise, a big array with
* max({@code length},{@code length(array)}/φ) entries whose first {@code preserve}
* entries are the same as those of {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] grow(final int[][] array, final long length, final long preserve) {
final long oldLength = length(array);
return length > oldLength ? ensureCapacity(array, Math.max(oldLength + (oldLength >> 1), length), preserve) : array;
}
/**
* Trims the given big array to the given length.
*
*
* Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new maximum length for the big array.
* @return {@code array}, if it contains {@code length} entries or less; otherwise, a big array with
* {@code length} entries whose entries are the same as the first {@code length} entries of
* {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] trim(final int[][] array, final long length) {
ensureLength(length);
final long oldLength = length(array);
if (length >= oldLength) return array;
final int baseLength = (int)((length + SEGMENT_MASK) >>> SEGMENT_SHIFT);
final int[][] base = Arrays.copyOf(array, baseLength);
final int residual = (int)(length & SEGMENT_MASK);
if (residual != 0) base[baseLength - 1] = IntArrays.trim(base[baseLength - 1], residual);
return base;
}
/**
* Sets the length of the given big array.
*
*
* Warning: the returned array might use part of the segments of the original
* array, which must be considered read-only after calling this method.
*
* @param array a big array.
* @param length the new length for the big array.
* @return {@code array}, if it contains exactly {@code length} entries; otherwise, if it contains
* more than {@code length} entries, a big array with {@code length} entries whose
* entries are the same as the first {@code length} entries of {@code array}; otherwise, a
* big array with {@code length} entries whose first {@code length(array)} entries are the
* same as those of {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] setLength(final int[][] array, final long length) {
return BigArrays.setLength(array, length);
}
/**
* Returns a copy of a portion of a big array.
*
* @param array a big array.
* @param offset the first element to copy.
* @param length the number of elements to copy.
* @return a new big array containing {@code length} elements of {@code array} starting at
* {@code offset}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] copy(final int[][] array, final long offset, final long length) {
return BigArrays.copy(array, offset, length);
}
/**
* Returns a copy of a big array.
*
* @param array a big array.
* @return a copy of {@code array}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static int[][] copy(final int[][] array) {
return BigArrays.copy(array);
}
/**
* Fills the given big array with the given value.
*
*
* This method uses a backward loop. It is significantly faster than the corresponding method in
* {@link java.util.Arrays}.
*
* @param array a big array.
* @param value the new value for all elements of the big array.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void fill(final int[][] array, final int value) {
for (int i = array.length; i-- != 0;) Arrays.fill(array[i], value);
}
/**
* Fills a portion of the given big array with the given value.
*
*
* If possible (i.e., {@code from} is 0) this method uses a backward loop. In this case, it is
* significantly faster than the corresponding method in {@link java.util.Arrays}.
*
* @param array a big array.
* @param from the starting index of the portion to fill.
* @param to the end index of the portion to fill.
* @param value the new value for all elements of the specified portion of the big array.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void fill(final int[][] array, final long from, long to, final int value) {
BigArrays.fill(array, from, to, value);
}
/**
* Returns true if the two big arrays are elementwise equal.
*
*
* This method uses a backward loop. It is significantly faster than the corresponding method in
* {@link java.util.Arrays}.
*
* @param a1 a big array.
* @param a2 another big array.
* @return true if the two big arrays are of the same length, and their elements are equal.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static boolean equals(final int[][] a1, final int a2[][]) {
return BigArrays.equals(a1, a2);
}
/* Returns a string representation of the contents of the specified big array.
*
* The string representation consists of a list of the big array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Returns "null" if {@code a} is null.
* @param a the big array whose string representation to return.
* @return the string representation of {@code a}.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static String toString(final int[][] a) {
return BigArrays.toString(a);
}
/**
* Ensures that a range given by its first (inclusive) and last (exclusive) elements fits a big
* array.
*
*
* This method may be used whenever a big array range check is needed.
*
* @param a a big array.
* @param from a start index (inclusive).
* @param to an end index (inclusive).
* @throws IllegalArgumentException if {@code from} is greater than {@code to}.
* @throws ArrayIndexOutOfBoundsException if {@code from} or {@code to} are greater than the big
* array length or negative.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void ensureFromTo(final int[][] a, final long from, final long to) {
BigArrays.ensureFromTo(length(a), from, to);
}
/**
* Ensures that a range given by an offset and a length fits a big array.
*
*
* This method may be used whenever a big array range check is needed.
*
* @param a a big array.
* @param offset a start index.
* @param length a length (the number of elements in the range).
* @throws IllegalArgumentException if {@code length} is negative.
* @throws ArrayIndexOutOfBoundsException if {@code offset} is negative or
* {@code offset}+{@code length} is greater than the big array length.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void ensureOffsetLength(final int[][] a, final long offset, final long length) {
BigArrays.ensureOffsetLength(length(a), offset, length);
}
/**
* Ensures that two big arrays are of the same length.
*
* @param a a big array.
* @param b another big array.
* @throws IllegalArgumentException if the two argument arrays are not of the same length.
* @deprecated Please use the version in {@link it.unimi.dsi.fastutil.BigArrays}.
*/
@Deprecated
public static void ensureSameLength(final int[][] a, final int[][] b) {
if (length(a) != length(b)) throw new IllegalArgumentException("Array size mismatch: " + length(a) + " != " + length(b));
}
/** A type-specific content-based hash strategy for big arrays. */
private static final class BigArrayHashStrategy implements Hash.Strategy, java.io.Serializable {
private static final long serialVersionUID = -7046029254386353129L;
@Override
public int hashCode(final int[][] o) {
return java.util.Arrays.deepHashCode(o);
}
@Override
public boolean equals(final int[][] a, final int[][] b) {
return IntBigArrays.equals(a, b);
}
}
/**
* A type-specific content-based hash strategy for big arrays.
*
*
* This hash strategy may be used in custom hash collections whenever keys are big arrays, and they
* must be considered equal by content. This strategy will handle {@code null} correctly, and it is
* serializable.
*/
@SuppressWarnings({ "rawtypes" })
public static final Hash.Strategy HASH_STRATEGY = new BigArrayHashStrategy();
private static final int QUICKSORT_NO_REC = 7;
private static final int PARALLEL_QUICKSORT_NO_FORK = 8192;
private static final int MEDIUM = 40;
private static ForkJoinPool getPool() {
// Make sure to update Arrays.drv, BigArrays.drv, and src/it/unimi/dsi/fastutil/Arrays.java as well
ForkJoinPool current = ForkJoinTask.getPool();
return current == null ? ForkJoinPool.commonPool() : current;
}
private static void swap(final int[][] x, long a, long b, final long n) {
for (int i = 0; i < n; i++, a++, b++) BigArrays.swap(x, a, b);
}
private static long med3(final int x[][], final long a, final long b, final long c, IntComparator comp) {
int ab = comp.compare(BigArrays.get(x, a), BigArrays.get(x, b));
int ac = comp.compare(BigArrays.get(x, a), BigArrays.get(x, c));
int bc = comp.compare(BigArrays.get(x, b), BigArrays.get(x, c));
return (ab < 0 ? (bc < 0 ? b : ac < 0 ? c : a) : (bc > 0 ? b : ac > 0 ? c : a));
}
private static void selectionSort(final int[][] a, final long from, final long to, final IntComparator comp) {
for (long i = from; i < to - 1; i++) {
long m = i;
for (long j = i + 1; j < to; j++) if (comp.compare(BigArrays.get(a, j), BigArrays.get(a, m)) < 0) m = j;
if (m != i) BigArrays.swap(a, i, m);
}
}
/**
* 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.
*
* @param x the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param comp the comparator to determine the sorting order.
*/
public static void quickSort(final int[][] x, final long from, final long to, final IntComparator comp) {
final long len = to - from;
// Selection sort on smallest arrays
if (len < QUICKSORT_NO_REC) {
selectionSort(x, from, to, comp);
return;
}
// Choose a partition element, v
long m = from + len / 2; // Small arrays, middle element
if (len > QUICKSORT_NO_REC) {
long l = from;
long n = to - 1;
if (len > MEDIUM) { // Big arrays, pseudomedian of 9
long s = len / 8;
l = med3(x, l, l + s, l + 2 * s, comp);
m = med3(x, m - s, m, m + s, comp);
n = med3(x, n - 2 * s, n - s, n, comp);
}
m = med3(x, l, m, n, comp); // Mid-size, med of 3
}
final int v = BigArrays.get(x, m);
// Establish Invariant: v* (v)* v*
long a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = comp.compare(BigArrays.get(x, b), v)) <= 0) {
if (comparison == 0) BigArrays.swap(x, a++, b);
b++;
}
while (c >= b && (comparison = comp.compare(BigArrays.get(x, c), v)) >= 0) {
if (comparison == 0) BigArrays.swap(x, c, d--);
c--;
}
if (b > c) break;
BigArrays.swap(x, b++, c--);
}
// Swap partition elements back to middle
long s, n = to;
s = Math.min(a - from, b - a);
swap(x, from, b - s, s);
s = Math.min(d - c, n - d - 1);
swap(x, b, n - 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, n - s, n, comp);
}
private static long med3(final int x[][], final long a, final long b, final long c) {
int ab = (Integer.compare((BigArrays.get(x, a)), (BigArrays.get(x, b))));
int ac = (Integer.compare((BigArrays.get(x, a)), (BigArrays.get(x, c))));
int bc = (Integer.compare((BigArrays.get(x, b)), (BigArrays.get(x, c))));
return (ab < 0 ? (bc < 0 ? b : ac < 0 ? c : a) : (bc > 0 ? b : ac > 0 ? c : a));
}
private static void selectionSort(final int[][] a, final long from, final long to) {
for (long i = from; i < to - 1; i++) {
long m = i;
for (long j = i + 1; j < to; j++) if (((BigArrays.get(a, j)) < (BigArrays.get(a, m)))) m = j;
if (m != i) BigArrays.swap(a, i, m);
}
}
/**
* Sorts the specified big 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.
*
* @param x the big array to be sorted.
* @param comp the comparator to determine the sorting order.
*
*/
public static void quickSort(final int[][] x, final IntComparator comp) {
quickSort(x, 0, BigArrays.length(x), comp);
}
/**
* 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.
*
* @param x the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void quickSort(final int[][] x, final long from, final long to) {
final long len = to - from;
// Selection sort on smallest arrays
if (len < QUICKSORT_NO_REC) {
selectionSort(x, from, to);
return;
}
// Choose a partition element, v
long m = from + len / 2; // Small arrays, middle element
if (len > QUICKSORT_NO_REC) {
long l = from;
long n = to - 1;
if (len > MEDIUM) { // Big arrays, pseudomedian of 9
long s = len / 8;
l = med3(x, l, l + s, l + 2 * s);
m = med3(x, m - s, m, m + s);
n = med3(x, n - 2 * s, n - s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
final int v = BigArrays.get(x, m);
// Establish Invariant: v* (v)* v*
long a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = (Integer.compare((BigArrays.get(x, b)), (v)))) <= 0) {
if (comparison == 0) BigArrays.swap(x, a++, b);
b++;
}
while (c >= b && (comparison = (Integer.compare((BigArrays.get(x, c)), (v)))) >= 0) {
if (comparison == 0) BigArrays.swap(x, c, d--);
c--;
}
if (b > c) break;
BigArrays.swap(x, b++, c--);
}
// Swap partition elements back to middle
long s, n = to;
s = Math.min(a - from, b - a);
swap(x, from, b - s, s);
s = Math.min(d - c, n - d - 1);
swap(x, b, n - s, s);
// Recursively sort non-partition-elements
if ((s = b - a) > 1) quickSort(x, from, from + s);
if ((s = d - c) > 1) quickSort(x, n - s, n);
}
/**
* Sorts the specified big 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.
*
* @param x the big array to be sorted.
*/
public static void quickSort(final int[][] x) {
quickSort(x, 0, BigArrays.length(x));
}
protected static class ForkJoinQuickSort extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final long from;
private final long to;
private final int[][] x;
public ForkJoinQuickSort(final int[][] x, final long from, final long to) {
this.from = from;
this.to = to;
this.x = x;
}
@Override
protected void compute() {
final int[][] x = this.x;
final long len = to - from;
if (len < PARALLEL_QUICKSORT_NO_FORK) {
quickSort(x, from, to);
return;
}
// Choose a partition element, v
long m = from + len / 2;
long l = from;
long n = to - 1;
long s = len / 8;
l = med3(x, l, l + s, l + 2 * s);
m = med3(x, m - s, m, m + s);
n = med3(x, n - 2 * s, n - s, n);
m = med3(x, l, m, n);
final int v = BigArrays.get(x, m);
// Establish Invariant: v* (v)* v*
long a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = (Integer.compare((BigArrays.get(x, b)), (v)))) <= 0) {
if (comparison == 0) BigArrays.swap(x, a++, b);
b++;
}
while (c >= b && (comparison = (Integer.compare((BigArrays.get(x, c)), (v)))) >= 0) {
if (comparison == 0) BigArrays.swap(x, c, d--);
c--;
}
if (b > c) break;
BigArrays.swap(x, b++, c--);
}
// Swap partition elements back to middle
long t;
s = Math.min(a - from, b - a);
swap(x, from, b - s, s);
s = Math.min(d - c, to - d - 1);
swap(x, b, to - s, s);
// Recursively sort non-partition-elements
s = b - a;
t = d - c;
if (s > 1 && t > 1) invokeAll(new ForkJoinQuickSort(x, from, from + s), new ForkJoinQuickSort(x, to - t, to));
else if (s > 1) invokeAll(new ForkJoinQuickSort(x, from, from + s));
else invokeAll(new ForkJoinQuickSort(x, to - t, to));
}
}
/**
* Sorts the specified range of elements according to the natural ascending order using a parallel
* quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas McIlroy,
* “Engineering a Sort Function”, Software: Practice and Experience, 23(11),
* pages 1249−1265, 1993.
*
* @param x the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void parallelQuickSort(final int[][] x, final long from, final long to) {
ForkJoinPool pool = getPool();
if (to - from < PARALLEL_QUICKSORT_NO_FORK || pool.getParallelism() == 1) quickSort(x, from, to);
else {
pool.invoke(new ForkJoinQuickSort(x, from, to));
}
}
/**
* Sorts a big 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.
*
* @param x the big array to be sorted.
*/
public static void parallelQuickSort(final int[][] x) {
parallelQuickSort(x, 0, BigArrays.length(x));
}
protected static class ForkJoinQuickSortComp extends RecursiveAction {
private static final long serialVersionUID = 1L;
private final long from;
private final long to;
private final int[][] x;
private final IntComparator comp;
public ForkJoinQuickSortComp(final int[][] x, final long from, final long to, final IntComparator comp) {
this.from = from;
this.to = to;
this.x = x;
this.comp = comp;
}
@Override
protected void compute() {
final int[][] x = this.x;
final long len = to - from;
if (len < PARALLEL_QUICKSORT_NO_FORK) {
quickSort(x, from, to, comp);
return;
}
// Choose a partition element, v
long m = from + len / 2;
long l = from;
long n = to - 1;
long s = len / 8;
l = med3(x, l, l + s, l + 2 * s, comp);
m = med3(x, m - s, m, m + s, comp);
n = med3(x, n - 2 * s, n - s, n, comp);
m = med3(x, l, m, n, comp);
final int v = BigArrays.get(x, m);
// Establish Invariant: v* (v)* v*
long a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c && (comparison = comp.compare(BigArrays.get(x, b), v)) <= 0) {
if (comparison == 0) BigArrays.swap(x, a++, b);
b++;
}
while (c >= b && (comparison = comp.compare(BigArrays.get(x, c), v)) >= 0) {
if (comparison == 0) BigArrays.swap(x, c, d--);
c--;
}
if (b > c) break;
BigArrays.swap(x, b++, c--);
}
// Swap partition elements back to middle
long t;
s = Math.min(a - from, b - a);
swap(x, from, b - s, s);
s = Math.min(d - c, to - d - 1);
swap(x, b, to - s, s);
// Recursively sort non-partition-elements
s = b - a;
t = d - c;
if (s > 1 && t > 1) invokeAll(new ForkJoinQuickSortComp(x, from, from + s, comp), new ForkJoinQuickSortComp(x, to - t, to, comp));
else if (s > 1) invokeAll(new ForkJoinQuickSortComp(x, from, from + s, comp));
else invokeAll(new ForkJoinQuickSortComp(x, to - t, to, comp));
}
}
/**
* Sorts the specified range of elements according to the order induced by the specified comparator
* using a parallel quicksort.
*
*
* The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas McIlroy,
* “Engineering a Sort Function”, Software: Practice and Experience, 23(11),
* pages 1249−1265, 1993.
*
* @param x the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
* @param comp the comparator to determine the sorting order.
*/
public static void parallelQuickSort(final int[][] x, final long from, final long to, final IntComparator comp) {
ForkJoinPool pool = getPool();
if (to - from < PARALLEL_QUICKSORT_NO_FORK || pool.getParallelism() == 1) quickSort(x, from, to, comp);
else {
pool.invoke(new ForkJoinQuickSortComp(x, from, to, comp));
}
}
/**
* Sorts a big 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.
*
* @param x the big array to be sorted.
* @param comp the comparator to determine the sorting order.
*/
public static void parallelQuickSort(final int[][] x, final IntComparator comp) {
parallelQuickSort(x, 0, BigArrays.length(x), comp);
}
/**
* Searches a range of the specified big 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 big 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 big array; otherwise,
* (-(insertion point) - 1). The insertion point is defined as
* the the point at which the value would be inserted into the big array: the index of the
* first element greater than the key, or the length of the big array, if all elements in
* the big 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 long binarySearch(final int[][] a, long from, long to, final int key) {
int midVal;
to--;
while (from <= to) {
final long mid = (from + to) >>> 1;
midVal = BigArrays.get(a, mid);
if (midVal < key) from = mid + 1;
else if (midVal > key) to = mid - 1;
else return mid;
}
return -(from + 1);
}
/**
* Searches a big 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 big array to be searched.
* @param key the value to be searched for.
* @return index of the search key, if it is contained in the big array; otherwise,
* (-(insertion point) - 1). The insertion point is defined as
* the the point at which the value would be inserted into the big array: the index of the
* first element greater than the key, or the length of the big array, if all elements in
* the big 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 long binarySearch(final int[][] a, final int key) {
return binarySearch(a, 0, BigArrays.length(a), key);
}
/**
* Searches a range of the specified big 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 big 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 big array; otherwise,
* (-(insertion point) - 1). The insertion point is defined as
* the the point at which the value would be inserted into the big array: the index of the
* first element greater than the key, or the length of the big array, if all elements in
* the big 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 long binarySearch(final int[][] a, long from, long to, final int key, final IntComparator c) {
int midVal;
to--;
while (from <= to) {
final long mid = (from + to) >>> 1;
midVal = BigArrays.get(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 a big 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 big 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 big array; otherwise,
* (-(insertion point) - 1). The insertion point is defined as
* the the point at which the value would be inserted into the big array: the index of the
* first element greater than the key, or the length of the big array, if all elements in
* the big 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 long binarySearch(final int[][] a, final int key, final IntComparator c) {
return binarySearch(a, 0, BigArrays.length(a), key, c);
}
/** The size of a digit used during radix sort (must be a power of 2). */
private static final int DIGIT_BITS = 8;
/** The mask to extract a digit of {@link #DIGIT_BITS} bits. */
private static final int DIGIT_MASK = (1 << DIGIT_BITS) - 1;
/** The number of digits per element. */
private static final int DIGITS_PER_ELEMENT = Integer.SIZE / DIGIT_BITS;
/**
* This method fixes negative numbers so that the combination exponent/significand is
* lexicographically sorted.
*/
/**
* Sorts the specified big 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), and further improved using the digit-oracle idea described by Juha
* Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”,
* String Processing and Information Retrieval, 15th International Symposium, volume 5280 of
* Lecture Notes in Computer Science, pages 3−14, Springer (2008).
*
* @implSpec This implementation is significantly faster than quicksort already at small sizes (say,
* more than 10000 elements), but it can only sort in ascending order. It will allocate a
* support array of bytes with the same number of elements as the array to be sorted.
*
* @param a the big array to be sorted.
*/
public static void radixSort(final int[][] a) {
radixSort(a, 0, BigArrays.length(a));
}
/**
* Sorts the specified big 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), and further improved using the digit-oracle idea described by Juha
* Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”,
* String Processing and Information Retrieval, 15th International Symposium, volume 5280 of
* Lecture Notes in Computer Science, pages 3−14, Springer (2008).
*
* @implSpec This implementation is significantly faster than quicksort already at small sizes (say,
* more than 10000 elements), but it can only sort in ascending order. It will allocate a
* support array of bytes with the same number of elements as the array to be sorted.
*
* @param a the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void radixSort(final int[][] a, final long from, final long to) {
final int maxLevel = DIGITS_PER_ELEMENT - 1;
final int stackSize = ((1 << DIGIT_BITS) - 1) * (DIGITS_PER_ELEMENT - 1) + 1;
final long[] offsetStack = new long[stackSize];
int offsetPos = 0;
final long[] lengthStack = new long[stackSize];
int lengthPos = 0;
final int[] levelStack = new int[stackSize];
int levelPos = 0;
offsetStack[offsetPos++] = from;
lengthStack[lengthPos++] = to - from;
levelStack[levelPos++] = 0;
final long[] count = new long[1 << DIGIT_BITS];
final long[] pos = new long[1 << DIGIT_BITS];
final byte[][] digit = ByteBigArrays.newBigArray(to - from);
while (offsetPos > 0) {
final long first = offsetStack[--offsetPos];
final long length = lengthStack[--lengthPos];
final int level = levelStack[--levelPos];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
if (length < MEDIUM) {
selectionSort(a, first, first + length);
continue;
}
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 (long i = length; i-- != 0;) BigArrays.set(digit, i, (byte)((((BigArrays.get(a, first + i)) >>> shift) & DIGIT_MASK) ^ signMask));
for (long i = length; i-- != 0;) count[BigArrays.get(digit, i) & 0xFF]++;
// Compute cumulative distribution and push non-singleton keys on stack.
int lastUsed = -1;
long p = 0;
for (int i = 0; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0) {
lastUsed = i;
if (level < maxLevel && count[i] > 1) {
// System.err.println(" Pushing " + new StackEntry(first + pos[i - 1], first + pos[i], level +
// 1));
offsetStack[offsetPos++] = p + first;
lengthStack[lengthPos++] = count[i];
levelStack[levelPos++] = level + 1;
}
}
pos[i] = (p += count[i]);
}
// When all slots are OK, the last slot is necessarily OK.
final long end = length - count[lastUsed];
count[lastUsed] = 0;
// i moves through the start of each block
int c = -1;
for (long i = 0, d; i < end; i += count[c], count[c] = 0) {
int t = BigArrays.get(a, i + first);
c = BigArrays.get(digit, i) & 0xFF;
while ((d = --pos[c]) > i) {
final int z = t;
final int zz = c;
t = BigArrays.get(a, d + first);
c = BigArrays.get(digit, d) & 0xFF;
BigArrays.set(a, d + first, z);
BigArrays.set(digit, d, (byte)zz);
}
BigArrays.set(a, i + first, t);
}
}
}
private static void selectionSort(final int[][] a, final int[][] b, final long from, final long to) {
for (long i = from; i < to - 1; i++) {
long m = i;
for (long j = i + 1; j < to; j++) if (((BigArrays.get(a, j)) < (BigArrays.get(a, m))) || ((BigArrays.get(a, j)) == (BigArrays.get(a, m))) && ((BigArrays.get(b, j)) < (BigArrays.get(b, m)))) m = j;
if (m != i) {
int t = BigArrays.get(a, i);
BigArrays.set(a, i, BigArrays.get(a, m));
BigArrays.set(a, m, t);
t = BigArrays.get(b, i);
BigArrays.set(b, i, BigArrays.get(b, m));
BigArrays.set(b, m, t);
}
}
}
/**
* Sorts the specified pair of big 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), and further improved using the digit-oracle idea described by Juha
* Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”,
* String Processing and Information Retrieval, 15th International Symposium, volume 5280 of
* Lecture Notes in Computer Science, pages 3−14, Springer (2008).
*
*
* This method implements a lexicographical sorting of the arguments. Pairs of elements in
* the same position in the two provided arrays will be considered a single key, and permuted
* accordingly. In the end, either {@code a[i] < a[i + 1]} or {@code a[i] == a[i + 1]} and
* {@code b[i] <= b[i + 1]}.
*
* @implSpec This implementation is significantly faster than quicksort already at small sizes (say,
* more than 10000 elements), but it can only sort in ascending order. It will allocate a
* support array of bytes with the same number of elements as the arrays to be sorted.
*
* @param a the first big array to be sorted.
* @param b the second big array to be sorted.
*/
public static void radixSort(final int[][] a, final int[][] b) {
radixSort(a, b, 0, BigArrays.length(a));
}
/**
* Sorts the specified pair of big 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), and further improved using the digit-oracle idea described by Juha
* Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”,
* String Processing and Information Retrieval, 15th International Symposium, volume 5280 of
* Lecture Notes in Computer Science, pages 3−14, Springer (2008).
*
*
* This method implements a lexicographical sorting of the arguments. Pairs of elements in
* the same position in the two provided arrays will be considered a single key, and permuted
* accordingly. In the end, either {@code a[i] < a[i + 1]} or {@code a[i] == a[i + 1]} and
* {@code b[i] <= b[i + 1]}.
*
* @implSpec This implementation is significantly faster than quicksort already at small sizes (say,
* more than 10000 elements), but it can only sort in ascending order. It will allocate a
* support array of bytes with the same number of elements as the arrays to be sorted.
*
* @param a the first big array to be sorted.
* @param b the second big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
public static void radixSort(final int[][] a, final int[][] b, final long from, final long to) {
final int layers = 2;
if (BigArrays.length(a) != BigArrays.length(b)) throw new IllegalArgumentException("Array size mismatch.");
final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
final int stackSize = ((1 << DIGIT_BITS) - 1) * (layers * DIGITS_PER_ELEMENT - 1) + 1;
final long[] offsetStack = new long[stackSize];
int offsetPos = 0;
final long[] lengthStack = new long[stackSize];
int lengthPos = 0;
final int[] levelStack = new int[stackSize];
int levelPos = 0;
offsetStack[offsetPos++] = from;
lengthStack[lengthPos++] = to - from;
levelStack[levelPos++] = 0;
final long[] count = new long[1 << DIGIT_BITS];
final long[] pos = new long[1 << DIGIT_BITS];
final byte[][] digit = ByteBigArrays.newBigArray(to - from);
while (offsetPos > 0) {
final long first = offsetStack[--offsetPos];
final long length = lengthStack[--lengthPos];
final int level = levelStack[--levelPos];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
if (length < MEDIUM) {
selectionSort(a, b, first, first + length);
continue;
}
final int[][] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the shift
// that extract the
// right byte from a
// key
// Count keys.
for (long i = length; i-- != 0;) BigArrays.set(digit, i, (byte)((((BigArrays.get(k, first + i)) >>> shift) & DIGIT_MASK) ^ signMask));
for (long i = length; i-- != 0;) count[BigArrays.get(digit, i) & 0xFF]++;
// Compute cumulative distribution and push non-singleton keys on stack.
int lastUsed = -1;
long p = 0;
for (int i = 0; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0) {
lastUsed = i;
if (level < maxLevel && count[i] > 1) {
offsetStack[offsetPos++] = p + first;
lengthStack[lengthPos++] = count[i];
levelStack[levelPos++] = level + 1;
}
}
pos[i] = (p += count[i]);
}
// When all slots are OK, the last slot is necessarily OK.
final long end = length - count[lastUsed];
count[lastUsed] = 0;
// i moves through the start of each block
int c = -1;
for (long i = 0, d; i < end; i += count[c], count[c] = 0) {
int t = BigArrays.get(a, i + first);
int u = BigArrays.get(b, i + first);
c = BigArrays.get(digit, i) & 0xFF;
while ((d = --pos[c]) > i) {
int z = t;
final int zz = c;
t = BigArrays.get(a, d + first);
BigArrays.set(a, d + first, z);
z = u;
u = BigArrays.get(b, d + first);
BigArrays.set(b, d + first, z);
c = BigArrays.get(digit, d) & 0xFF;
BigArrays.set(digit, d, (byte)zz);
}
BigArrays.set(a, i + first, t);
BigArrays.set(b, i + first, u);
}
}
}
private static final int RADIXSORT_NO_REC = 1024;
private static void insertionSortIndirect(final long[][] perm, final int[][] a, final int[][] b, final long from, final long to) {
for (long i = from; ++i < to;) {
long t = BigArrays.get(perm, i);
long j = i;
for (long u = BigArrays.get(perm, j - 1); ((BigArrays.get(a, t)) < (BigArrays.get(a, u))) || ((BigArrays.get(a, t)) == (BigArrays.get(a, u))) && ((BigArrays.get(b, t)) < (BigArrays.get(b, u))); u = BigArrays.get(perm, --j - 1)) {
BigArrays.set(perm, j, u);
if (from == j - 1) {
--j;
break;
}
}
BigArrays.set(perm, j, t);
}
}
/**
* Sorts the specified pair of arrays lexicographically using indirect radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M.
* Douglas McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages
* 5−27 (1993).
*
*
* This method implement an indirect sort. The elements of {@code perm} (which must be
* exactly the numbers in the interval {@code [0..length(perm))}) will be permuted so that
* {@code a[perm[i]] ≤ a[perm[i + 1]]} or {@code a[perm[i]] == a[perm[i + 1]]} and
* {@code b[perm[i]] ≤ b[perm[i + 1]]}.
*
* @implSpec This implementation will allocate, in the stable case, a further support array as large
* as {@code perm} (note that the stable version is slightly faster).
*
* @param perm a permutation array indexing {@code a}.
* @param a the array to be sorted.
* @param b the second array to be sorted.
* @param stable whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect(final long[][] perm, final int[][] a, final int[][] b, final boolean stable) {
ensureSameLength(a, b);
radixSortIndirect(perm, a, b, 0, BigArrays.length(a), stable);
}
/**
* Sorts the specified pair of arrays lexicographically using indirect radix sort.
*
*
* The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M.
* Douglas McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages
* 5−27 (1993).
*
*
* This method implement an indirect sort. The elements of {@code perm} (which must be
* exactly the numbers in the interval {@code [0..length(perm))}) will be permuted so that
* {@code a[perm[i]] ≤ a[perm[i + 1]]} or {@code a[perm[i]] == a[perm[i + 1]]} and
* {@code b[perm[i]] ≤ b[perm[i + 1]]}.
*
* @implSpec This implementation will allocate, in the stable case, a further support array as large
* as {@code perm} (note that the stable version is slightly faster).
*
* @param perm a permutation array indexing {@code a}.
* @param a the array to be sorted.
* @param b the second array to be sorted.
* @param from the index of the first element of {@code perm} (inclusive) to be permuted.
* @param to the index of the last element of {@code perm} (exclusive) to be permuted.
* @param stable whether the sorting algorithm should be stable.
*/
public static void radixSortIndirect(final long[][] perm, final int[][] a, final int[][] b, final long from, final long 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 long[] offsetStack = new long[stackSize];
final long[] lengthStack = new long[stackSize];
final int[] levelStack = new int[stackSize];
offsetStack[stackPos] = from;
lengthStack[stackPos] = to - from;
levelStack[stackPos++] = 0;
final long[] count = new long[1 << DIGIT_BITS];
final long[] pos = new long[1 << DIGIT_BITS];
final long[][] support = stable ? it.unimi.dsi.fastutil.longs.LongBigArrays.newBigArray(BigArrays.length(perm)) : null;
while (stackPos > 0) {
final long first = offsetStack[--stackPos];
final long length = lengthStack[stackPos];
final int level = levelStack[stackPos];
final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
final int[][] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
final int shift = (DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT) * DIGIT_BITS; // This is the shift
// that extract the
// right byte from a
// key
// Count keys.
for (long i = first + length; i-- != first;) count[((BigArrays.get(k, BigArrays.get(perm, i))) >>> shift & DIGIT_MASK ^ signMask)]++;
// Compute cumulative distribution
int lastUsed = -1;
long p = stable ? 0 : first;
for (int i = 0; i < 1 << DIGIT_BITS; i++) {
if (count[i] != 0) lastUsed = i;
pos[i] = (p += count[i]);
}
if (stable) {
for (long i = first + length; i-- != first;) BigArrays.set(support, --pos[((BigArrays.get(k, BigArrays.get(perm, i))) >>> shift & DIGIT_MASK ^ signMask)], BigArrays.get(perm, i));
BigArrays.copy(support, 0, perm, first, length);
p = first;
for (int i = 0; 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 long end = first + length - count[lastUsed];
// i moves through the start of each block
int c = -1;
for (long i = first, d; i <= end; i += count[c], count[c] = 0) {
long t = BigArrays.get(perm, i);
c = ((BigArrays.get(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 long z = t;
t = BigArrays.get(perm, d);
BigArrays.set(perm, d, z);
c = ((BigArrays.get(k, t)) >>> shift & DIGIT_MASK ^ signMask);
}
BigArrays.set(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;
}
}
}
}
}
}
/**
* Shuffles the specified big array fragment using the specified pseudorandom number generator.
*
* @param a the big array to be shuffled.
* @param from the index of the first element (inclusive) to be shuffled.
* @param to the index of the last element (exclusive) to be shuffled.
* @param random a pseudorandom number generator.
* @return {@code a}.
*/
public static int[][] shuffle(final int[][] a, final long from, final long to, final Random random) {
return BigArrays.shuffle(a, from, to, random);
}
/**
* Shuffles the specified big array using the specified pseudorandom number generator.
*
* @param a the big array to be shuffled.
* @param random a pseudorandom number generator.
* @return {@code a}.
*/
public static int[][] shuffle(final int[][] a, final Random random) {
return BigArrays.shuffle(a, random);
}
}