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Implementing Quicksort in Python

Elliot Forbes ⏰ 4 Minutes 📅 Nov 20, 2017

In this tutorial we are going to be looking at how you can implement the QuickSort algorithm using Python. This will include looking at how the underlying algorithm works, and the time/space complexity of the algorithm when implemented correctly.

Note - If you are applying for jobs at some of the top tech companies in the world then be aware that this algorithm may feature within their interview processes so it’s worthwhile memorizing some of the key information about it.

QuickSort Algorithm

Quicksort is one of the most popular sorting algorithms you will come across in computer science. This is because of it’s average case performance of O(n log n).

The Quicksorting algorithm uses a divide-and-conquer approach and recursively partitions the elements in an unsorted array around a randomly picked pivot element.

  • A Random Pivot element is chosen from our unsorted array.
  • We create 3 distinct partitions:
    • Equal - for all elements equal to our pivot element
    • Lower - for all elements lower than our pivot element
    • Higher - for all elements higher than our pivot element
  • We iterate through our array and sort those that are less than our pivot into the lower partition
  • We sort those that are higher than our pivot into the higher partition
  • We then recursively sort through these higher and lower partitions

Whilst this typically runs with a performance of O(n log n), it should be noted that the worst case performance for this algorithm is actually O(N^2) which occurs if you consistently choose the worst possible point in the array to pivot on.

Implementing this in Python

Now that we understand the logic behind the quicksorting algorithm, it’s time to implement this in Python. Below we’ll be defining a quicksort() function which will take in an array as it’s only parameter.

Note - I find this implementation of QuickSort to be the simplest and most straightforward implementation. However, it does not do in-place swaps and utilizes more memory than absolutely needed.

main.py
def quicksort(array):

    ## We define our 3 arrays
    less = []
    equal = []
    greater = []

    ## if the length of our array is greater than 1
    ## we perform a sort
    if len(array) > 1:
        ## Select our pivot. This doesn't have to be
        ## the first element of our array
        pivot = array[0]

        ## recursively go through every element
        ## of the array passed in and sort appropriately
        for x in array:
            if x < pivot:
                less.append(x)
            if x == pivot:
                equal.append(x)
            if x > pivot:
                greater.append(x)

        ## recursively call quicksort on gradually smaller and smaller
        ## arrays until we have a sorted list.
        return quicksort(less)+equal+quicksort(greater)

    else:
        return array

def main():
  print(quicksort([6,4,7,1,2,9,12,3]))

Testing it works

We can test this by doing the following:

python main.py
[1, 2, 3, 4, 6, 7, 9, 12]

Awesome, we can see from the output that this has successfully managed to sort our list of random integers and print it out!

In-Place Memory QuickSort Implementation

Now that we’ve looked at implementing the simplest version of QuickSort, let’s now take a look at a slightly more complex but memory-efficient implementation which does in-place sorts.

The most common way of implementing this version is to define a partition function which takes in 3 parameters:

  • The Array

  • The Start

  • The End

It’s in this partition function that the comparison and swaps take place:

def partition(arr, start, end):
  pivot = arr[begin]
  i = start + 1
  j = end - 1

  while True:
    while (i <= j and arr[i] <= pivot):
      i = i + 1
    while (i <= j and arr[j] >= pivot):
      j = j -1

    if i <= j:
      arr[i], arr[j], arr[j], arr[i]
    else:
      arr[start], arr[j] = arr[j], arr[start]
      return j

We can then modify our quicksort() function so that it leverages this new partition() function like so:

def quicksort(arr, start, end):
  if end - start > 1:
    p = partition(arr, start, end)
    quicksort(arr, start, p)
    quicksort(arr, p + 1, end)

Awesome, with these tweaks in place, we now have a QuickSort implementation that sorts arrays in-place and thus is far more efficient when it comes to memory utilization

Conclusion

If you found this tutorial useful or require further assistance or info then please let me know in the comments section below!

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