Quick Sort

Quick Sort is a divide-and-conquer sorting algorithm. It selects a 'pivot' element and partitions the array such that elements smaller than the pivot go to the left, and larger ones go to the right, before recursively sorting the sub-arrays. Highly efficient in-place sorting utility.

Complexity Profile

Case	Complexity
Best Case	O(N log N)
Average Case	O(N log N)
Worst Case	O(N^2)
Space Complexity	O(log N)

Code Implementation

def quick_sort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[len(arr) // 2]
    left = [x for x in arr if x < pivot]
    middle = [x for x in arr if x == pivot]
    right = [x for x in arr if x > pivot]
    return quick_sort(left) + middle + quick_sort(right)

Real-World Applications

• In-place sorting library functions (e.g. C standard library qsort).
• Embedded microchips with highly restrictive RAM specifications.
• Real-time rendering systems where sorting speed is critical.