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/* Generic definitions */
/* Assertions (useful to generate conditional code) */
/* Current type and class (and size, if applicable) */
/* Value methods */
/* Interfaces (keys) */
/* Interfaces (values) */
/* Abstract implementations (keys) */
/* Abstract implementations (values) */
/* Static containers (keys) */
/* Static containers (values) */
/* Implementations */
/* Synchronized wrappers */
/* Unmodifiable wrappers */
/* Other wrappers */
/* Methods (keys) */
/* Methods (values) */
/* Methods (keys/values) */
/* Methods that have special names depending on keys (but the special names depend on values) */
/* Equality */
/* Object/Reference-only definitions (keys) */
/* Primitive-type-only definitions (keys) */
/* Object/Reference-only definitions (values) */
/*
* Copyright (C) 2009-2016 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.
*
*
*
* 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 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 it.unimi.dsi.fastutil.bytes.ByteBigArrays;
/**
* A class providing static methods and objects that do useful things with
* {@linkplain BigArrays big arrays}.
*
*
* In particular, the ensureCapacity(), grow(),
* trim() and setLength() methods allow to handle big
* arrays much like array lists.
*
*
* 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.
*
* @see BigArrays
*/
public class IntBigArrays {
private IntBigArrays() {
}
/** A static, final, empty big array. */
public final static int[][] 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.
*/
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.
*/
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.
*/
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
*/
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
*/
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.
*/
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.
*/
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.
*/
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.
*/
public static void copy(final int[][] srcArray, final long srcPos,
final int[][] destArray, final long destPos, long length) {
if (destPos <= srcPos) {
int srcSegment = segment(srcPos);
int destSegment = segment(destPos);
int srcDispl = displacement(srcPos);
int destDispl = displacement(destPos);
int l;
while (length > 0) {
l = (int) Math.min(length, Math.min(srcArray[srcSegment].length
- srcDispl, destArray[destSegment].length - destDispl));
System.arraycopy(srcArray[srcSegment], srcDispl,
destArray[destSegment], destDispl, l);
if ((srcDispl += l) == SEGMENT_SIZE) {
srcDispl = 0;
srcSegment++;
}
if ((destDispl += l) == SEGMENT_SIZE) {
destDispl = 0;
destSegment++;
}
length -= l;
}
} else {
int srcSegment = segment(srcPos + length);
int destSegment = segment(destPos + length);
int srcDispl = displacement(srcPos + length);
int destDispl = displacement(destPos + length);
int l;
while (length > 0) {
if (srcDispl == 0) {
srcDispl = SEGMENT_SIZE;
srcSegment--;
}
if (destDispl == 0) {
destDispl = SEGMENT_SIZE;
destSegment--;
}
l = (int) Math.min(length, Math.min(srcDispl, destDispl));
System.arraycopy(srcArray[srcSegment], srcDispl - l,
destArray[destSegment], destDispl - l, l);
srcDispl -= l;
destDispl -= l;
length -= l;
}
}
}
/**
* 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.
*/
public static void copyFromBig(final int[][] srcArray, final long srcPos,
final int[] destArray, int destPos, int length) {
int srcSegment = segment(srcPos);
int srcDispl = displacement(srcPos);
int l;
while (length > 0) {
l = Math.min(srcArray[srcSegment].length - srcDispl, length);
System.arraycopy(srcArray[srcSegment], srcDispl, destArray,
destPos, l);
if ((srcDispl += l) == SEGMENT_SIZE) {
srcDispl = 0;
srcSegment++;
}
destPos += l;
length -= l;
}
}
/**
* 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.
*/
public static void copyToBig(final int[] srcArray, int srcPos,
final int[][] destArray, final long destPos, long length) {
int destSegment = segment(destPos);
int destDispl = displacement(destPos);
int l;
while (length > 0) {
l = (int) Math.min(destArray[destSegment].length - destDispl,
length);
System.arraycopy(srcArray, srcPos, destArray[destSegment],
destDispl, l);
if ((destDispl += l) == SEGMENT_SIZE) {
destDispl = 0;
destSegment++;
}
srcPos += l;
length -= l;
}
}
/**
* 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;
}
/**
* 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
* array.
*/
public static int[][] wrap(final int[] array) {
if (array.length == 0)
return EMPTY_BIG_ARRAY;
if (array.length <= SEGMENT_SIZE)
return new int[][]{array};
final int[][] bigArray = newBigArray(array.length);
for (int i = 0; i < bigArray.length; i++)
System.arraycopy(array, (int) start(i), bigArray[i], 0,
bigArray[i].length);
return bigArray;
}
/**
* 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 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 array, if it contains length entries or
* more; otherwise, a big array with length entries
* whose first length(array) entries are the same as
* those of array.
*/
public static int[][] ensureCapacity(final int[][] array, final long length) {
return ensureCapacity(array, length, length(array));
}
/**
* 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 array, if it can contain length entries
* or more; otherwise, a big array with length entries
* whose first preserve entries are the same as those
* of array.
*/
public static int[][] ensureCapacity(final int[][] array,
final long length, final long preserve) {
final long oldLength = length(array);
if (length > oldLength) {
ensureLength(length);
final int valid = array.length
- (array.length == 0 || array.length > 0
&& array[array.length - 1].length == SEGMENT_SIZE
? 0
: 1);
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) {
for (int i = valid; i < baseLength - 1; i++)
base[i] = new int[SEGMENT_SIZE];
base[baseLength - 1] = new int[residual];
} else
for (int i = valid; i < baseLength; i++)
base[i] = new int[SEGMENT_SIZE];
if (preserve - (valid * (long) SEGMENT_SIZE) > 0)
copy(array, valid * (long) SEGMENT_SIZE, base, valid
* (long) SEGMENT_SIZE, preserve
- (valid * (long) SEGMENT_SIZE));
return base;
}
return array;
}
/**
* Grows the given big 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 big array growth, you should probably
* use 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 array, if it can contain length
* entries; otherwise, a big array with max(length,
* length(array)/φ) entries whose first
* length(array) entries are the same as those of
* array.
* */
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 multiplied by two, 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 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 array, if it can contain length
* entries; otherwise, a big array with max(length,
* length(array)/φ) entries whose first
* preserve entries are the same as those of
* array.
* */
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(2 * oldLength, 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 array, if it contains length entries or
* less; otherwise, a big array with length entries
* whose entries are the same as the first length
* entries of array.
*
*/
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 array, if it contains exactly length
* entries; otherwise, if it contains more than
* length entries, a big array with length
* entries whose entries are the same as the first
* length entries of array; otherwise, a
* big array with length entries whose first
* length(array) entries are the same as those of
* array.
*
*/
public static int[][] setLength(final int[][] array, final long length) {
final long oldLength = length(array);
if (length == oldLength)
return array;
if (length < oldLength)
return trim(array, length);
return ensureCapacity(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 length elements of
* array starting at offset.
*/
public static int[][] copy(final int[][] array, final long offset,
final long length) {
ensureOffsetLength(array, offset, length);
final int[][] a = newBigArray(length);
copy(array, offset, a, 0, length);
return a;
}
/**
* Returns a copy of a big array.
*
* @param array
* a big array.
* @return a copy of array.
*/
public static int[][] copy(final int[][] array) {
final int[][] base = array.clone();
for (int i = base.length; i-- != 0;)
base[i] = array[i].clone();
return base;
}
/**
* 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.
*/
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., 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.
*/
public static void fill(final int[][] array, final long from, long to,
final int value) {
final long length = length(array);
BigArrays.ensureFromTo(length, from, to);
int fromSegment = segment(from);
int toSegment = segment(to);
int fromDispl = displacement(from);
int toDispl = displacement(to);
if (fromSegment == toSegment) {
Arrays.fill(array[fromSegment], fromDispl, toDispl, value);
return;
}
if (toDispl != 0)
Arrays.fill(array[toSegment], 0, toDispl, value);
while (--toSegment > fromSegment)
Arrays.fill(array[toSegment], value);
Arrays.fill(array[fromSegment], fromDispl, SEGMENT_SIZE, 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.
*/
public static boolean equals(final int[][] a1, final int a2[][]) {
if (length(a1) != length(a2))
return false;
int i = a1.length, j;
int[] t, u;
while (i-- != 0) {
t = a1[i];
u = a2[i];
j = t.length;
while (j-- != 0)
if (!((t[j]) == (u[j])))
return false;
}
return true;
}
/*
* 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
* a is null.
*
* @param a the big array whose string representation to return.
*
* @return the string representation of a.
*/
public static String toString(final int[][] a) {
if (a == null)
return "null";
final long last = length(a) - 1;
if (last == -1)
return "[]";
final StringBuilder b = new StringBuilder();
b.append('[');
for (long i = 0;; i++) {
b.append(String.valueOf(get(a, i)));
if (i == last)
return b.append(']').toString();
b.append(", ");
}
}
/**
* 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 from is greater than to.
* @throws ArrayIndexOutOfBoundsException
* if from or to are greater than the
* big array length or negative.
*/
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 length is negative.
* @throws ArrayIndexOutOfBoundsException
* if offset is negative or offset+
* length is greater than the big array length.
*/
public static void ensureOffsetLength(final int[][] a, final long offset,
final long length) {
BigArrays.ensureOffsetLength(length(a), offset, length);
}
/** 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;
public int hashCode(final int[][] o) {
return java.util.Arrays.deepHashCode(o);
}
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 null correctly, and it is serializable.
*/
@SuppressWarnings({"rawtypes"})
public final static Hash.Strategy HASH_STRATEGY = new BigArrayHashStrategy();
private static final int SMALL = 7;
private static final int MEDIUM = 40;
private static void vecSwap(final int[][] x, long a, long b, final long n) {
for (int i = 0; i < n; i++, a++, b++)
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(get(x, a), get(x, b));
int ac = comp.compare(get(x, a), get(x, c));
int bc = comp.compare(get(x, b), 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(IntBigArrays.get(a, j), IntBigArrays.get(a, m)) < 0)
m = j;
if (m != i)
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 < SMALL) {
selectionSort(x, from, to, comp);
return;
}
// Choose a partition element, v
long m = from + len / 2; // Small arrays, middle element
if (len > SMALL) {
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 = 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(get(x, b), v)) <= 0) {
if (comparison == 0)
swap(x, a++, b);
b++;
}
while (c >= b && (comparison = comp.compare(get(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
long s, n = to;
s = Math.min(a - from, b - a);
vecSwap(x, from, b - s, s);
s = Math.min(d - c, n - d - 1);
vecSwap(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((get(x, a)), (get(x, b))));
int ac = (Integer.compare((get(x, a)), (get(x, c))));
int bc = (Integer.compare((get(x, b)), (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 (((IntBigArrays.get(a, j)) < (IntBigArrays.get(a, m))))
m = j;
if (m != i)
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, IntBigArrays.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 < SMALL) {
selectionSort(x, from, to);
return;
}
// Choose a partition element, v
long m = from + len / 2; // Small arrays, middle element
if (len > SMALL) {
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 = 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((get(x, b)), (v)))) <= 0) {
if (comparison == 0)
swap(x, a++, b);
b++;
}
while (c >= b
&& (comparison = (Integer.compare((get(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
long s, n = to;
s = Math.min(a - from, b - a);
vecSwap(x, from, b - s, s);
s = Math.min(d - c, n - d - 1);
vecSwap(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, IntBigArrays.length(x));
}
/**
* 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 = 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, IntBigArrays.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 = 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, IntBigArrays.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).
*
*
* 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, IntBigArrays.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).
*
*
* 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;)
ByteBigArrays
.set(digit,
i,
(byte) ((((IntBigArrays.get(a, first + i)) >>> shift) & DIGIT_MASK) ^ signMask));
for (long i = length; i-- != 0;)
count[ByteBigArrays.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 = IntBigArrays.get(a, i + first);
c = ByteBigArrays.get(digit, i) & 0xFF;
while ((d = --pos[c]) > i) {
final int z = t;
final int zz = c;
t = IntBigArrays.get(a, d + first);
c = ByteBigArrays.get(digit, d) & 0xFF;
IntBigArrays.set(a, d + first, z);
ByteBigArrays.set(digit, d, (byte) zz);
}
IntBigArrays.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 (((IntBigArrays.get(a, j)) < (IntBigArrays.get(a, m)))
|| ((IntBigArrays.get(a, j)) == (IntBigArrays.get(a, m)))
&& ((IntBigArrays.get(b, j)) < (IntBigArrays.get(b, m))))
m = j;
if (m != i) {
int t = IntBigArrays.get(a, i);
IntBigArrays.set(a, i, IntBigArrays.get(a, m));
IntBigArrays.set(a, m, t);
t = IntBigArrays.get(b, i);
IntBigArrays.set(b, i, IntBigArrays.get(b, m));
IntBigArrays.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 a[ i ] < a[ i + 1 ] or
* a[ i ] == a[ i + 1 ] and
* b[ i ] <= b[ i + 1 ].
*
*
* 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, IntBigArrays.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 a[ i ] < a[ i + 1 ] or
* a[ i ] == a[ i + 1 ] and
* b[ i ] <= b[ i + 1 ].
*
*
* 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 (IntBigArrays.length(a) != IntBigArrays.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;)
ByteBigArrays
.set(digit,
i,
(byte) ((((IntBigArrays.get(k, first + i)) >>> shift) & DIGIT_MASK) ^ signMask));
for (long i = length; i-- != 0;)
count[ByteBigArrays.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 = IntBigArrays.get(a, i + first);
int u = IntBigArrays.get(b, i + first);
c = ByteBigArrays.get(digit, i) & 0xFF;
while ((d = --pos[c]) > i) {
int z = t;
final int zz = c;
t = IntBigArrays.get(a, d + first);
IntBigArrays.set(a, d + first, z);
z = u;
u = IntBigArrays.get(b, d + first);
IntBigArrays.set(b, d + first, z);
c = ByteBigArrays.get(digit, d) & 0xFF;
ByteBigArrays.set(digit, d, (byte) zz);
}
IntBigArrays.set(a, i + first, t);
IntBigArrays.set(b, i + first, u);
}
}
}
/**
* 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 (please use a XorShift* generator).
* @return a.
*/
public static int[][] shuffle(final int[][] a, final long from,
final long to, final Random random) {
for (long i = to - from; i-- != 0;) {
final long p = (random.nextLong() & 0x7FFFFFFFFFFFFFFFL) % (i + 1);
final int t = get(a, from + i);
set(a, from + i, get(a, from + p));
set(a, from + p, t);
}
return a;
}
/**
* 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 (please use a XorShift* generator).
* @return a.
*/
public static int[][] shuffle(final int[][] a, final Random random) {
for (long i = length(a); i-- != 0;) {
final long p = (random.nextLong() & 0x7FFFFFFFFFFFFFFFL) % (i + 1);
final int t = get(a, i);
set(a, i, get(a, p));
set(a, p, t);
}
return a;
}
}