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What is Quicksort Algorithm?
1) The quicksort algorithm originated through C.A.R. Hoare. It's best average behaviour in terms of complexity
2) In a recursive manner until all the sublists are empty, at which point the list is sorted.
3) Partitioning can be effected concurrently, scanning the list left to right and right to left, interchanging elements in the wrong parts of the list.
4) The partitioning element is then placed between the resultant sublists.
|QUICKSORT (A, t, s)|
1:If t < s
2: q =partition (A, t, s)
3: Quicksort [A, t, (q - 1) ]
4: Quicksort [A, (q + 1), s]
PARTITION(A, t, s)
1: x = A[ s ]
2: i = (t - 1)
3:for j = t to (r - 1)
4:if a[ j ] <= x
5: i = (i + 1)
6: exchange A[ i ] with A[ j ]
7: exchange A[i + 1] with A[ s ]
8 return (i + 1)
Given a list of elements,
1) Take a partitioning element, and
2) Create a (sub) list,
- Such that all elements to the left of the partitioning element are less than it.
- And all elements to the right of it are greater than it.
3) Now repeat this partitioning effort on each of these two sublist.
Implementation of Quicksort:
|If anything to be partitioned|
choose a pivot
scan fromlefttoright until we find an element
-pivot: i point to it
Scan fromrighttoleft until we find an element
-pivot: loc points to it
IF I < loc
exchange pivotand loc-th element
UNTIL i > loc
exchange pivt and loc element
partition from 1st to loc-1st elements// i.e. quicksort 1st to loc
partition from loc-th to rth elements// i.e. quicksort loc-th to rt
Divide and conquer:
1) Quicksort is a divide and conquer algorithm
2) A divide and conquer algorithm is one which divides that problem into smallest problems where this works exactly the same procedure.