edu.princeton.cs.algs4.QuickBentleyMcIlroy Maven / Gradle / Ivy
/******************************************************************************
* Compilation: javac QuickBentleyMcIlroy.java
* Execution: java QuickBentleyMcIlroy < input.txt
* Dependencies: StdOut.java StdIn.java
* Data files: https://algs4.cs.princeton.edu/23quicksort/tiny.txt
* https://algs4.cs.princeton.edu/23quicksort/words3.txt
*
* Uses the Bentley-McIlroy 3-way partitioning scheme,
* chooses the partitioning element using Tukey's ninther,
* and cuts off to insertion sort.
*
* Reference: Engineering a Sort Function by Jon L. Bentley
* and M. Douglas McIlroy. Softwae-Practice and Experience,
* Vol. 23 (11), 1249-1265 (November 1993).
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code QuickBentleyMcIlroy} class provides static methods for sorting
* an array using an optimized version of quicksort (using Bentley-McIlroy
* 3-way partitioning, Tukey's ninther, and cutoff to insertion sort).
*
* For additional documentation,
* see Section 2.3 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class QuickBentleyMcIlroy {
// cutoff to insertion sort, must be >= 1
private static final int INSERTION_SORT_CUTOFF = 8;
// cutoff to median-of-3 partitioning
private static final int MEDIAN_OF_3_CUTOFF = 40;
// This class should not be instantiated.
private QuickBentleyMcIlroy() { }
/**
* Rearranges the array in ascending order, using the natural order.
* @param a the array to be sorted
*/
public static void sort(Comparable[] a) {
sort(a, 0, a.length - 1);
}
private static void sort(Comparable[] a, int lo, int hi) {
int n = hi - lo + 1;
// cutoff to insertion sort
if (n <= INSERTION_SORT_CUTOFF) {
insertionSort(a, lo, hi);
return;
}
// use median-of-3 as partitioning element
else if (n <= MEDIAN_OF_3_CUTOFF) {
int m = median3(a, lo, lo + n/2, hi);
exch(a, m, lo);
}
// use Tukey ninther as partitioning element
else {
int eps = n/8;
int mid = lo + n/2;
int m1 = median3(a, lo, lo + eps, lo + eps + eps);
int m2 = median3(a, mid - eps, mid, mid + eps);
int m3 = median3(a, hi - eps - eps, hi - eps, hi);
int ninther = median3(a, m1, m2, m3);
exch(a, ninther, lo);
}
// Bentley-McIlroy 3-way partitioning
int i = lo, j = hi+1;
int p = lo, q = hi+1;
Comparable v = a[lo];
while (true) {
while (less(a[++i], v))
if (i == hi) break;
while (less(v, a[--j]))
if (j == lo) break;
// pointers cross
if (i == j && eq(a[i], v))
exch(a, ++p, i);
if (i >= j) break;
exch(a, i, j);
if (eq(a[i], v)) exch(a, ++p, i);
if (eq(a[j], v)) exch(a, --q, j);
}
i = j + 1;
for (int k = lo; k <= p; k++)
exch(a, k, j--);
for (int k = hi; k >= q; k--)
exch(a, k, i++);
sort(a, lo, j);
sort(a, i, hi);
}
// sort from a[lo] to a[hi] using insertion sort
private static void insertionSort(Comparable[] a, int lo, int hi) {
for (int i = lo; i <= hi; i++)
for (int j = i; j > lo && less(a[j], a[j-1]); j--)
exch(a, j, j-1);
}
// return the index of the median element among a[i], a[j], and a[k]
private static int median3(Comparable[] a, int i, int j, int k) {
return (less(a[i], a[j]) ?
(less(a[j], a[k]) ? j : less(a[i], a[k]) ? k : i) :
(less(a[k], a[j]) ? j : less(a[k], a[i]) ? k : i));
}
/***************************************************************************
* Helper sorting functions.
***************************************************************************/
// is v < w ?
private static boolean less(Comparable v, Comparable w) {
if (v == w) return false; // optimization when reference equal
return v.compareTo(w) < 0;
}
// does v == w ?
private static boolean eq(Comparable v, Comparable w) {
if (v == w) return true; // optimization when reference equal
return v.compareTo(w) == 0;
}
// exchange a[i] and a[j]
private static void exch(Object[] a, int i, int j) {
Object swap = a[i];
a[i] = a[j];
a[j] = swap;
}
/***************************************************************************
* Check if array is sorted - useful for debugging.
***************************************************************************/
private static boolean isSorted(Comparable[] a) {
for (int i = 1; i < a.length; i++)
if (less(a[i], a[i-1])) return false;
return true;
}
// print array to standard output
private static void show(Comparable[] a) {
for (int i = 0; i < a.length; i++) {
StdOut.println(a[i]);
}
}
/**
* Reads in a sequence of strings from standard input; quicksorts them
* (using an optimized version of quicksort);
* and prints them to standard output in ascending order.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
String[] a = StdIn.readAllStrings();
QuickBentleyMcIlroy.sort(a);
assert isSorted(a);
show(a);
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/