<s>[INST] Write a python code to implement quick sort [/INST] Sure, here's an example implementation of quick sort in Python:

``` 
def quick_sort(arr):
    if len(arr) <= 1:
        return arr
    else:
        pivot = arr[0]
        left = []
        right = []
        for i in range(1, len(arr)):
            if arr[i] < pivot:
                left.append(arr[i])
            else:
                right.append(arr[i])
        return quick_sort(left) + [pivot] + quick_sort(right)
``` 
This implementation uses the first element of the array as the pivot, and then partitions the array into two sub-arrays based on whether their elements are less than or greater than the pivot. It then recursively applies the same process to each sub-array and concatenates the results.

To use this implementation, you can simply call the quick_sort() function and pass in the array you want to sort as an argument, like this:
``` 
arr = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]
sorted_arr = quick_sort(arr)
print(sorted_arr)  # Output: [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9]
``` 
I hope this helps!</s>\ <s>[INST] Thanks! Can you now add comments to the function so it's easier to understand? Also please add tests to ensure that the function is working correctly. [/INST] # Improving the function
Here's the same function from before but now with comments:

```python
def quick_sort(arr: list):
    # if empty or a single element list, nothing to sort
    if len(arr) <= 1:
        return arr

    # select element at index 0 as pivot and initialize
    # lists to store left and right partitions wrt to it
    pivot = arr[0]
    left = []
    right = []
    
    # loop over the rest of the elements (from index 1 onwards)
    # and put them into the left partition if smaller than the pivot
    # and into the right partition otherwise
    for i in range(1, len(arr)):
        if arr[i] < pivot:
            left.append(arr[i])
        else:
            right.append(arr[i])

    # sort the left and right partitions and return merged lists
    return quick_sort(left) + [pivot] + quick_sort(right)
```

I've slightly improved it for readability by making the first check into a guard condition (essentially I removed the `else` part).

## Further possible technical improvements
Note that there still many potential areas for improvement for this piece of code. In particular, we can:
- make the partitioning be done in-place (save memory)
- do a much more clever way of selecting the pivot via:
    - Choosing a pivot at random (stochastically try to avoid $O(N^2)$ wort-case performance)
    - Choose the median (via the Median-of-medians algorithms, etc.)
    - Choose mean, mode etc.

# Tests

Here are some tests against Python's built-in [`sorted`](https://docs.python.org/3/library/functions.html#sorted) function:

```python
import random


def test_sorting_function_against_sorted(sorting_fn, size, max_int=10_000):
    # seed for reproducibility as we're using randomness in our tests!
    random.seed(42)  # seed the random number generator

    for size in range(size):
        # generate a random list of integers
        lst = [random.randint(-abs(max_int), abs(max_int)) for _ in range(size)]
        # sort the list using given sorting_fn
        actual = sorting_fn(lst)
        # sort the list using Python's built-in sorted function
        expected = sorted(lst)
        # assert that the two sorted lists are equal
        assert actual == expected, "Oh no! The sorting function doesn't work!"


# test empty list
test_sorting_function_against_sorted(quick_sort, size=0)

# test single list
test_sorting_function_against_sorted(quick_sort, size=1)

# test lists with lots of numbers
test_sorting_function_against_sorted(quick_sort, size=10_000)
```

If you have any further questions or requests, please do not hesitate! 😊</s>