Quicksort, as its name, is one of the fastest sorting algorithms invented by Tony Hoare in 1959.

After this tutorial, I ensure you can achieve 2 things:

- Understand how the Quicksort algorithm works.
- Implement the Quicksort algorithm in Python.

Let's begin!

## 1. How Quicksort Works

### Divide-and-Conquer

Before going to the quicksort algorithm, you need to understand the divide-and-conquer paradigm.

Divide-and-conquer is used to find the optimal solution by breaking down the problem into smaller sub-problems. Then, we solve each sub-problem and combine the results to get the final solution.

The divide-and-conquer paradigm consists of 3 steps:

**Divide**: Break the problem into smaller sub-problems.**Conquer**: Solve each sub-problem recursively.**Combine**: Combine the results of each sub-problem to get the final solution.

### Quicksort Algorithm

The quicksort algorithm is based on the divide-and-conquer paradigm.

The quicksort algorithm consists of 2 steps:

**Divide**: Choose a pivot element* and partition the array into 2 sub-arrays: the left sub-array contains elements smaller than the pivot, and the right sub-array contains elements greater than the pivot.**Conquer**: Recursively sort the left and right sub-arrays.

*The pivot element is chosen randomly or deterministically. In this tutorial, we choose the middle element as the pivot.

## 2. QuickSort Implementation in Python

Here is the implementation of the quicksort algorithm in Python:

`def quicksort(arr, low, high): if low < high: pivot_index = partition(arr, low, high) quicksort(arr, low, pivot_index) quicksort(arr, pivot_index + 1, high) def partition(arr, low, high): pivot = arr[low] left = low + 1 right = high done = False while not done: while left <= right and arr[left] <= pivot: left = left + 1 while arr[right] >= pivot and right >= left: right = right - 1 if right < left: done = True else: arr[left], arr[right] = arr[right], arr[left] arr[low], arr[right] = arr[right], arr[low] return right # Example usage: arr = [3, 6, 8, 10, 1, 2, 1] quicksort(arr, 0, len(arr) - 1) print(arr)`