Quick sort algorithm

Definition of quicksort

Quicksort is a type of Divide and Conquer algorithm like merge sort, it works by choosing an element as a pivot from the giving array, and appending the greater elements to the selected pivot, and shifting the smaller elements before it.

Time and Space complexity

The space complexity of quicksort is O(log n)

best-case	average case	worst-case
O(n log n)	O(n log n)	O(n^2) when the list is already sorted, or the pivot is min or max value of the giving list

Implementation of quick sort using python

def QuickSortAlgorithm(arr: list) -> list:
    """
        [ name ] => Quick Sort
        [ type ] => Sorting algorithms
        [ time complexity ] => (
            1. best case:  O(n log n)
            2. average case: O(n log n)
            3. worst case: O(n^2) { when the pivot is the (min or max) value of the giving list, or the list is already sorted }
        )
        [ space complexity ] => O(log n)
        [params] => (
            arr {list} list to sort
        )
        [return] => {list} sorted list 
    """
    # size of array
    n = len(arr)
    if n <= 1:
        return arr
    # pivote = arr[mid] 
    pivot = arr[n // 2]
    smallerThanPivot = []
    greaterThanPivot = []
    for i in range(len(arr)):
        # do not append pivot to (greaterThanPivot) => continue
        if arr[i] == pivot:
            continue
        # if the element is greater than or equal pivot
        if arr[i] >= pivot:
            # append the element that is greater than pivot to greaterThanPivot array
            greaterThanPivot.append(arr[i])
        else:
            # if the element is smaller than pivot append it to smallerThanPivot
            smallerThanPivot.append(arr[i])

    return QuickSortAlgorithm(smallerThanPivot) + [pivot] + QuickSortAlgorithm(greaterThanPivot)

References and useful resources

• https://www.youtube.com/watch?v=8hly31xKli0&t=16878s
• https://www.geeksforgeeks.org/when-does-the-worst-case-of-quicksort-occur/
• https://en.wikipedia.org/wiki/Quicksort
• https://www.youtube.com/watch?v=PgBzjlCcFvc
• https://www.youtube.com/watch?v=7h1s2SojIRw
• https://www.youtube.com/watch?v=0SkOjNaO1XY

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