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/*
* Copyright 2004-2011 H2 Group. Multiple-Licensed under the H2 License,
* Version 1.0, and under the Eclipse Public License, Version 1.0
* (http://h2database.com/html/license.html).
* Initial Developer: H2 Group
*/
package org.h2.dev.sort;
import java.util.Comparator;
/**
* A stable quicksort implementation that uses O(log(n)) memory. It normally
* runs in O(n*log(n)*log(n)), but at most in O(n^2).
*
* @param <T> the element type
*/
public class InPlaceStableQuicksort<T> {
/**
* The minimum size of the temporary array. It is used to speed up sorting
* small blocks.
*/
private static final int TEMP_SIZE = 1024;
/**
* Blocks smaller than this number are sorted using binary insertion sort.
* This usually speeds up sorting.
*/
private static final int INSERTION_SORT_SIZE = 16;
/**
* The data array to sort.
*/
private T[] data;
/**
* The comparator.
*/
private Comparator<T> comp;
/**
* The temporary array.
*/
private T[] temp;
/**
* Sort an array using the given comparator.
*
* @param data the data array to sort
* @param comp the comparator
*/
public static <T> void sort(T[] data, Comparator<T> comp) {
new InPlaceStableQuicksort<T>().sortArray(data, comp);
}
/**
* Sort an array using the given comparator.
*
* @param d the data array to sort
* @param c the comparator
*/
public void sortArray(T[] d, Comparator<T> c) {
this.data = d;
this.comp = c;
int len = Math.max((int) (100 * Math.log(d.length)), TEMP_SIZE);
len = Math.min(d.length, len);
@SuppressWarnings("unchecked")
T[] t = (T[]) new Object[len];
this.temp = t;
quicksort(0, d.length - 1);
}
/**
* Sort a block using the quicksort algorithm.
*
* @param from the index of the first entry to sort
* @param to the index of the last entry to sort
*/
private void quicksort(int from, int to) {
while (to > from) {
if (to - from < INSERTION_SORT_SIZE) {
binaryInsertionSort(from, to);
return;
}
T pivot = selectPivot(from, to);
int second = partition(pivot, from, to);
if (second > to) {
pivot = selectPivot(from, to);
pivot = data[to];
second = partition(pivot, from, to);
if (second > to) {
second--;
}
}
quicksort(from, second - 1);
from = second;
}
}
/**
* Sort a block using the binary insertion sort algorithm.
*
* @param from the index of the first entry to sort
* @param to the index of the last entry to sort
*/
private void binaryInsertionSort(int from, int to) {
for (int i = from + 1; i <= to; i++) {
T x = data[i];
int ins = binarySearch(x, from, i - 1);
for (int j = i - 1; j >= ins; j--) {
data[j + 1] = data[j];
}
data[ins] = x;
}
}
/**
* Find the index of the element that is larger than x.
*
* @param x the element to search
* @param from the index of the first entry
* @param to the index of the last entry
* @return the position
*/
private int binarySearch(T x, int from, int to) {
while (from <= to) {
int m = (from + to) >>> 1;
if (comp.compare(x, data[m]) >= 0) {
from = m + 1;
} else {
to = m - 1;
}
}
return from;
}
/**
* Move all elements that are bigger than the pivot to the end of the list,
* and return the partitioning index. The partitioning index is the start
* index of the range where all elements are larger than the pivot. If the
* partitioning index is larger than the 'to' index, then all elements are
* smaller or equal to the pivot.
*
* @param pivot the pivot
* @param from the index of the first element
* @param to the index of the last element
* @return the the first element of the second partition
*/
private int partition(T pivot, int from, int to) {
if (to - from < temp.length) {
return partitionSmall(pivot, from, to);
}
int m = (from + to + 1) / 2;
int m1 = partition(pivot, from, m - 1);
int m2 = partition(pivot, m, to);
swapBlocks(m1, m, m2 - 1);
return m1 + m2 - m;
}
/**
* Partition a small block using the temporary array. This will speed up
* partitioning.
*
* @param pivot the pivot
* @param from the index of the first element
* @param to the index of the last element
* @return the the first element of the second partition
*/
private int partitionSmall(T pivot, int from, int to) {
int tempIndex = 0, dataIndex = from;
for (int i = from; i <= to; i++) {
T x = data[i];
if (comp.compare(x, pivot) <= 0) {
if (tempIndex > 0) {
data[dataIndex] = x;
}
dataIndex++;
} else {
temp[tempIndex++] = x;
}
}
if (tempIndex > 0) {
System.arraycopy(temp, 0, data, dataIndex, tempIndex);
}
return dataIndex;
}
/**
* Swap the elements of two blocks in the data array. Both blocks are next
* to each other (the second block starts just after the first block ends).
*
* @param from the index of the first element in the first block
* @param second the index of the first element in the second block
* @param to the index of the last element in the second block
*/
private void swapBlocks(int from, int second, int to) {
int len1 = second - from, len2 = to - second + 1;
if (len1 == 0 || len2 == 0) {
return;
}
if (len1 < temp.length) {
System.arraycopy(data, from, temp, 0, len1);
System.arraycopy(data, second, data, from, len2);
System.arraycopy(temp, 0, data, from + len2, len1);
return;
} else if (len2 < temp.length) {
System.arraycopy(data, second, temp, 0, len2);
System.arraycopy(data, from, data, from + len2, len1);
System.arraycopy(temp, 0, data, from, len2);
return;
}
reverseBlock(from, second - 1);
reverseBlock(second, to);
reverseBlock(from, to);
}
/**
* Reverse all elements in a block.
*
* @param from the index of the first element
* @param to the index of the last element
*/
private void reverseBlock(int from, int to) {
while (from < to) {
T old = data[from];
data[from++] = data[to];
data[to--] = old;
}
}
/**
* Select a pivot. To ensure a good pivot is select, the median element of a
* sample of the data is calculated.
*
* @param from the index of the first element
* @param to the index of the last element
* @return the pivot
*/
private T selectPivot(int from, int to) {
int count = (int) (6 * Math.log10(to - from));
count = Math.min(count, temp.length);
int step = (to - from) / count;
for (int i = from, j = 0; i < to; i += step, j++) {
temp[j] = data[i];
}
T pivot = select(temp, 0, count - 1, count / 2);
return pivot;
}
/**
* Select the specified element.
*
* @param d the array
* @param from the index of the first element
* @param to the index of the last element
* @param k which element to return (1 means the lowest)
* @return the specified element
*/
private T select(T[] d, int from, int to, int k) {
while (true) {
int pivotIndex = (to + from) >>> 1;
int pivotNewIndex = selectPartition(d, from, to, pivotIndex);
int pivotDist = pivotNewIndex - from + 1;
if (pivotDist == k) {
return d[pivotNewIndex];
} else if (k < pivotDist) {
to = pivotNewIndex - 1;
} else {
k = k - pivotDist;
from = pivotNewIndex + 1;
}
}
}
/**
* Partition the elements to select an element.
*
* @param d the array
* @param from the index of the first element
* @param to the index of the last element
* @param pivotIndex the index of the pivot
* @return the new index
*/
private int selectPartition(T[] d, int from, int to, int pivotIndex) {
T pivotValue = d[pivotIndex];
swap(d, pivotIndex, to);
int storeIndex = from;
for (int i = from; i <= to; i++) {
if (comp.compare(d[i], pivotValue) < 0) {
swap(d, storeIndex, i);
storeIndex++;
}
}
swap(d, to, storeIndex);
return storeIndex;
}
/**
* Swap two elements in the array.
*
* @param d the array
* @param a the index of the first element
* @param b the index of the second element
*/
private void swap(T[] d, int a, int b) {
T t = d[a];
d[a] = d[b];
d[b] = t;
}
}
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