Quicksort is one of the common sorting algorithms taught in computer science.

Here I shall attempt to give a brief and clear example in Python.

As a divide end conquer algorithm, three main steps are involved:

- Pick an element (pivot) in the list
- Partition the list so that all elements smaller than the pivot come before it and those bigger than the pivot come after it
- Recursively apply the previous steps to the smaller sublists before and after the pivot

This should leave you with a fully sorted list at the end.

Let's define a quicksort function

```
def quicksort(L, lo, hi):
"""Sorts elements between indices lo and hi inclusive
L - a list to sort
lo - index of the lower end in the range
hi - index of the higher end"""
# Base case: lo and hi are equal, i.e. only one element in sublist
# In this case, nothing is done on the list
if lo < hi:
# lo is less than hi, i.e. at least two elements in sublist
# the partitioning step, p is the final position of the
# pivot after partitioning
p = partition(L, lo, hi)
# Recursively sort the 'less than' partition
quicksort(L, lo, p - 1)
# Recursively sort the 'greater than' partition
quicksort(L, p + 1, hi)
# and that's it :-)
```

We then define the partition function that does the actual work. It picks an element in the list within the given range, and divides the list into segments less than or equal, and greater than the pivot.

```
def partition(L, lo, hi):
"""Partitions the list within the given range
L - a list to partition
lo - index of the lower end in list to start partitioning from
hi - index of higher end in list to end the partitioning"""
# There several schemes used to pick the pivot
# Here we shall use a one known as the 'Lomuto partition scheme'
# Where we simply pick the last item in the range as the pivot
pivot = L[hi]
# i is the next position in the list where we
# place an element less than or equal to the pivot
# We begin at the lower end
i = lo
# We iterate through the list from lo to hi - 1 (the pivot is at hi, remember?)
# separating elements less than or equal to the pivot
# from those greater than the pivot
j = lo
while j < hi:
# if element at j is less than or equal to the pivot
# swap it into location i
if L[j] <= pivot:
L[i], L[j] = L[j], L[i]
i += 1 # and increment i
# increment j
j += 1
# When the loop completes, we know that all elements before i are less than
# or equal to the pivot, and all elements from i onwards are greater than
# the pivot
# swap the pivot into it's correct position, separating these two parts
L[i], L[hi] = L[hi], L[i]
# Now the pivot is at position i, and all elements after i are greater than
# it
# return its position
return i
```

We can now test our quicksort function.

```
import random
# Create a list of 10 unsorted integers between 1 and 100 inclusive
list_to_sort = [random.randint(1, 100) for i in range(10)]
print("List before sorting: ", list_to_sort)
# Now let's sort the list
last_index = len(list_to_sort) - 1
quicksort(list_to_sort, 0, last_index)
print("List after sorting: ", list_to_sort)
```

You can read more on quicksort in its wikipedia page.

And here's an implementation in only 3 lines of python, if your into that sort of thing.

Here's the source code.

Also posted here

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