<s>[INST] ### Quicksort Tutorials Point
Quicksort  is a popular sorting algorithm that uses the divide-and-conquer technique to sort an array. Here are some key steps to using quicksort in your code:

1.  **Choose the Pivot Element**: Choose an element from the array to serve as the pivot. The pivot can be any element from the array. In the standard "Lomuto" partition scheme, the pivot is chosen as the last element of the array.
2.  **Partition the Array**: Partition the array around the pivot element. This involves rearranging the array such that all elements less than the pivot are on the left of the pivot, and all elements greater than the pivot are on the right. The partition step is performed in such a way that the pivot element is placed in its final sorted position.
3.  **Recursively Sort the Subarrays**: Recursively apply the quicksort algorithm to the subarray of elements less than the pivot and the subarray of elements greater than the pivot.

Here is a Python code snippet that demonstrates the quicksort algorithm:

```python
def quicksort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[len(arr) - 1]  # Choose the last element as the pivot
    left = [x for x in arr[:-1] if x <= pivot]  # Elements less than or equal to the pivot
    middle = [pivot]  # The pivot element
    right = [x for x in arr[:-1] if x > pivot]  # Elements greater than the pivot
    return quicksort(left) + middle + quicksort(right)

# Example usage
arr = [64, 34, 25, 12, 22, 11, 90]
print("Original array:", arr)
print("Sorted array:", quicksort(arr))
```

### Output:

```
Original array: [64, 34, 25, 12, 22, 11, 90]
Sorted array: [11, 12, 22, 25, 34, 64, 90]
```

### Explanation:

The quicksort function takes an array as input and returns the sorted array. The base case for the recursion is when the array has one or zero elements, in which case it is already sorted. Otherwise, the function chooses the last element as the pivot, partitions the array around the pivot, and recursively sorts the subarrays.

The partition step is performed using list comprehensions, which creates three lists: `left`, `middle`, and `right`. The `left` list contains elements less than or equal to the pivot, the `middle` list contains the pivot element, and the `right` list contains elements greater than the pivot. The function then recursively calls itself on the `left` and `right` lists and combines the results with the `middle` list to produce the sorted array.

### Time Complexity:

The time complexity of the quicksort algorithm is O(n log n) on average, although it can be O(n^2) in the worst case if the pivot is chosen poorly. The space complexity is O(log n) due to the recursive call stack.

### Note:

The quicksort algorithm is not a stable sort, meaning that equal elements may not keep their original order in the sorted array.

In this explanation, can you identify the various parts of the explanation (name, definition, code snippet, explanation, examples, output, time complexity, note)?[/INST]