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The Quicksort sorting algorithm

Citation

(http://en.wikipedia.org/wiki/Quicksort, 21 April 2013)

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.

Illustration

See the visualization of Quicksort on Wikipedia:

http://en.wikipedia.org/wiki/Quicksort

See various illustrations of Quicksort as available on YouTube, e.g.:

Quick-sort with Hungarian (Küküllőmenti legényes) folk dance

Quicksort in Haskell

-- Polymorphic sorting
sort :: Ord a => [a] -> [a]
sort [] = []
sort (pivot:rest) =
             (sort lesser)
          ++ [pivot]
          ++ (sort greater)
  where
    lesser  = filter (< pivot) rest
    greater = filter (>= pivot) rest

The first equation models that an empty list is sorted vacuously. The second equation picks the head of the list as the 'pivot' element, which is used to partition the input. Indeed, all elements 'lesser' than 'pivot' are collected in one helper list and all elements 'greater' (or equal) than 'pivot' are collected in another helper list. Quicksort is then invoked recursively on 'lesser' and 'greater' and the intermediate results are appended with the 'pivot' element in between.

The implementation is exercised as follows: 

main = do
  let input = [2,4,3,1,4]
  print $ sort input -- [1,2,3,4,4]

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