Commit 6abd2965 authored by Tom Almeida's avatar Tom Almeida

updated README

parent a4bf7bd6
# Quicksort
## Complexity of O(`nlog(n)`)
The best pivot creates partitions of equal length (or lengths differing by 1).
The worst pivot creates an empty partition (for example, if the pivot is the first or last element of a sorted array).
The run-time of Quicksort ranges from O(n log n) with the best pivots, to O(n^2) with the worst pivots, where ` n` is the number of elements in the array.
A simple version of Quicksort is as follows:
```
function quicksort(array)
less, equal, greater := three empty arrays
if length(array) > 1
pivot := select any element of array
for each x in array
if x < pivot then add x to less
if x = pivot then add x to equal
if x > pivot then add x to greater
quicksort(less)
quicksort(greater)
array := concatenate(less, equal, greater)
```
A better quicksort algorithm works in place, by swapping elements within the array, to avoid the memory allocation of more arrays.
```
function quicksort(array)
if length(array) > 1
pivot := select any element of array
left := first index of array
right := last index of array
while left ≤ right
while array[left] < pivot
left := left + 1
while array[right] > pivot
right := right - 1
if left ≤ right
swap array[left] with array[right]
left := left + 1
right := right - 1
quicksort(array from first index to right)
quicksort(array from left to last index)
```
Quicksort is often compared to Mergesort as they both have an average time complexity of O(nlogn). According to the perldoc:
> On average, mergesort does fewer comparisons than quicksort, so it may be better when complicated comparison routines are used. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort() to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times.
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