Quicksort: Difference between revisions

Revision as of 17:41, 23 August 2024

Revision as of 22:41, 12 November 2024

Line 35:

# Otherwise pick a value, called a ''pivot'', that occurs in the range (the precise manner of choosing depends on the partition routine, and can involve randomness).

# ''Partition'' the range: reorder its elements, while determining a point of division, so that all elements with values less than the pivot come before the division, while all elements with values greater than the pivot come after it; elements that are equal to the pivot can go either way. Since at least one instance of the pivot is present, most partition routines ensure that the value that ends up at the point of division is equal to the pivot, and is now in its final position (but termination of quicksort does not depend on this, as long as sub-ranges strictly smaller than the original are produced).

# [[Recursion (computer science)|Recursively]] apply the quicksort to the sub-range up to the point of division and to the sub-range after it, possibly excluding from both ranges the element equal to the pivot at the point of division. (If the partition produces a possibly larger sub-range near the boundary where all elements are known to be equal to the pivot, these can be excluded as well.)

The choice of partition routine (including the pivot selection) and other details not entirely specified above can affect the algorithm's performance, possibly to a great extent for specific input arrays. In discussing the efficiency of quicksort, it is therefore necessary to specify these choices first. Here we mention two specific partition methods.