Sorting Algorithm Tutorials - Herong's Tutorial Examples - Version 6.01, by Dr. Herong Yang
Quicksort - Implementation Improvements
This section provides a tutorial on how to improve the performance of the Quicksort implementation in different areas.
There are ways to improve my first implementation of the Quicksort algorithm.
First, we can improve the division process by replacing the one-way loop with a two-way loop to reduce the number of swapping operations.
Another area that can be improved is when sections are being divided smaller enough, like number of elements less than 3, or 4. Instead of dividing them further, we can sort them directly.
Here is my improved version of Quicksort:
/** * HyArrays.java * This class contains sorting methods similar to java.util.Arrays. * All sorting methods should have a signature of * %Sort(Object[] a, int fromIndex, int toIndex) * where "fromIndex" is inclusive, and "toIndex" is exclusive. * Copyright (c) 2011 by Dr. Herong Yang, herongyang.com */ public class HyArrays { public static void quickSortImproved(Object[] a, int fromIndex, int toIndex) { Object d; if (toIndex-fromIndex<=1) { return; } else if (toIndex-fromIndex==2) { if (((Comparable)a[fromIndex]).compareTo(a[toIndex-1])>0) { d = a[toIndex-1]; a[toIndex-1] = a[fromIndex]; a[fromIndex] = d; } } else { int iLeft = fromIndex + 1; int iRight = toIndex - 1; Comparable p = (Comparable) a[fromIndex]; while (iLeft<iRight) { while (iLeft<toIndex-1 && p.compareTo(a[iLeft])>=0) { iLeft++; } while (iRight>fromIndex+1 && p.compareTo(a[iRight])<=0) { iRight--; } if (iLeft>=iRight) break; d = a[iRight]; a[iRight] = a[iLeft]; a[iLeft] = d; } if (iLeft>fromIndex+1) { d = a[iRight]; a[iRight] = a[fromIndex]; a[fromIndex] = d; } if (iLeft==iRight && iRight==toIndex) { quickSortImproved(a, fromIndex, iRight); } else if (iLeft==iRight && iRight==fromIndex) { quickSortImproved(a, iLeft, toIndex); } else { quickSortImproved(a, fromIndex, iRight); quickSortImproved(a, iLeft, toIndex); } } } }
Here is the result of this version:
Array size: 10000 Average sorting time: 16 milliseconds Number of tests: 1000 Performance: 1.6 O(N) nanoseconds Performance: 0.12041199826559247 O(N*Log2(N)) nanoseconds Performance: 1.6E-4 O(N*N) nanoseconds Array size: 20000 Average sorting time: 40 milliseconds Number of tests: 1000 Performance: 2.0 O(N) nanoseconds Performance: 0.13998042141880435 O(N*Log2(N)) nanoseconds Performance: 1.0E-4 O(N*N) nanoseconds Array size: 30000 Average sorting time: 70 milliseconds Number of tests: 1000 Performance: 2.3333333333333335 O(N) nanoseconds Performance: 0.15688726823636978 O(N*Log2(N)) nanoseconds Performance: 7.777777777777778E-5 O(N*N) nanoseconds
The results is interesting. The improvement is significant. The performance is much better than my initial version. It actually performs better than the JDK implementation when N = 10000 and 20000.
Last update: 2011.
Table of Contents
Introduction of Sorting Algorithms
Java API for Sorting Algorithms
Insertion Sort Algorithm and Implementation
Selection Sort Algorithm and Implementation
Bubble Sort Algorithm and Implementation
►Quicksort Algorithm and Implementation
Quicksort - Algorithm Introduction
Quicksort - Java Implementation
►Quicksort - Implementation Improvements
Merge Sort Algorithm and Implementation
Heap Sort Algorithm and Implementation
Shell Sort Algorithm and Implementation