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Tutorial 15: Quicksort

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Tutorial ID15
TitleQuicksort

What is Quicksort?

Quicksort is a sorting algorithm developed by Tony Hoare that, on average, makes O(nlog n) (big O notation) comparisons to sort n items. In the worst case, it makes O(n2) comparisons, though this behavior is rare. Quicksort is often faster in practice than other O(nlog n) algorithms. Additionally, quicksort's sequential and localized memory references work well with a cache. Quicksort can be implemented with an in-place partitioning algorithm, so the entire sort can be done with only O(log n) additional space. Quicksort (also known as "partition-exchange sort") is a comparison sort and, in space efficient implementations, is not a stable sort.

History

The quicksort algorithm was developed in 1960 by Tony Hoare while in the Soviet Union, as a visiting student at Moscow State University. At that time, Hoare worked in a project on machine translation for the National Physical Laboratory. He developed the algorithm in order to sort the words to be translated, to make them more easily matched to an already-sorted Russian-to-English dictionary that was stored on magnetic tape.

Algorithm

Quicksort is a divide and conquer algorithm. Quicksort first divides a large list into two smaller sub-lists: the low elements and the high elements. Quicksort can then recursively sort the sub-lists.
The steps are:
  1. Pick an element, called a pivot, from the list.
  2. Reorder the list so that all elements with values less than the pivot come before the pivot, while all elements with values greater than the pivot come after it (equal values can go either way). After this partitioning, the pivot is in its final position. This is called the partition operation.
  3. Recursively sort the sub-list of lesser elements and the sub-list of greater elements.
The base case of the recursion are lists of size zero or one, which never need to be sorted.
 
In simple pseudocode, the algorithm might be expressed as this:
  function quicksort('array')
      if length('array') ≤ 1
          return 'array'  // an array of zero or one elements is already sorted
      select and remove a pivot value 'pivot' from 'array'
      create empty lists 'less' and 'greater'
      for each 'x' in 'array'
          if 'x' ≤ 'pivot' then append 'x' to 'less'
          else append 'x' to 'greater'
      return concatenate(quicksort('less'), 'pivot', quicksort('greater')) // two recursive calls
 

Visualization

Visualization of the quicksort algorithm.
The horizontal lines are pivot values.

Comments

This is a good tutorial!   by Ho Wang on 2011-12-06 13:52:27

This tutorial is Good


Thankyou   by Larry on 2012-04-14 11:44:01
I found this tutorial very useful

ThankYou   by Larry on 2012-04-14 11:46:39
I found this tutorial very useful!

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