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"""
A pure Python implementation of the quick sort algorithm

For doctests run following command:
python3 -m doctest -v quick_sort.py

For manual testing run:
python3 quick_sort.py
"""
from typing import List


def quick_sort(collection: list) -> list:
    """A pure Python implementation of quick sort algorithm

    :param collection: a mutable collection of comparable items
    :return: the same collection ordered by ascending

    Examples:
    >>> quick_sort([0, 5, 3, 2, 2])
    [0, 2, 2, 3, 5]
    >>> quick_sort([])
    []
    >>> quick_sort([-2, 5, 0, -45])
    [-45, -2, 0, 5]
    """
    if len(collection) < 2:
        return collection
    pivot = collection.pop()  # Use the last element as the first pivot
    greater: List[int] = []  # All elements greater than pivot
    lesser: List[int] = []  # All elements less than or equal to pivot
    for element in collection:
        (greater if element > pivot else lesser).append(element)
    return quick_sort(lesser) + [pivot] + quick_sort(greater)


if __name__ == "__main__":
    user_input = input("Enter numbers separated by a comma:\n").strip()
    unsorted = [int(item) for item in user_input.split(",")]
    print(quick_sort(unsorted))

Quick Sort

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Problem Statement

Given an unsorted array of n elements, write a function to sort the array

Approach

  • Make the right-most index value pivot
  • partition the array using pivot value
  • quicksort left partition recursively
  • quicksort right partition recursively

Time Complexity

  • O(n^2) Worst case performance
  • O(n log n) Best-case performance
  • O(n log n) Average performance

Space Complexity

O(log n) Worst case

Founder's Name

Tony Hoare in 1959

Example

arr[] = {10, 80, 30, 90, 40, 50, 70}
Indexes:  0   1   2   3   4   5   6

low = 0, high =  6, pivot = arr[h] = 70
Initialize index of smaller element, i = -1

Traverse elements from j = low to high-1
j = 0 : Since arr[j] <= pivot, do i++ and swap(arr[i], arr[j])
i = 0
arr[] = {10, 80, 30, 90, 40, 50, 70} // No change as i and j
                                     // are same

j = 1 : Since arr[j] > pivot, do nothing
// No change in i and arr[]

j = 2 : Since arr[j] <= pivot, do i++ and swap(arr[i], arr[j])
i = 1
arr[] = {10, 30, 80, 90, 40, 50, 70} // We swap 80 and 30

j = 3 : Since arr[j] > pivot, do nothing
// No change in i and arr[]

j = 4 : Since arr[j] <= pivot, do i++ and swap(arr[i], arr[j])
i = 2
arr[] = {10, 30, 40, 90, 80, 50, 70} // 80 and 40 Swapped
j = 5 : Since arr[j] <= pivot, do i++ and swap arr[i] with arr[j]
i = 3
arr[] = {10, 30, 40, 50, 80, 90, 70} // 90 and 50 Swapped

We come out of loop because j is now equal to high-1.
Finally we place pivot at correct position by swapping
arr[i+1] and arr[high] (or pivot)
arr[] = {10, 30, 40, 50, 70, 90, 80} // 80 and 70 Swapped

Now 70 is at its correct place. All elements smaller than
70 are before it and all elements greater than 70 are after
it.

Code Implementation Links

Video Explanation

A video explaining the Quick Sort Algorithm