Quick Sort is one of the most efficient sorting algorithms, using a divide-and-conquer strategy. It works by selecting a pivot element, partitioning the array so smaller elements go left and larger elements go right, then recursively sorting the subarrays. This approach makes Quick Sort very fast for most datasets.
Pivot selection is crucial for Quick Sort performance. The first element method is simple but performs poorly on already sorted data. Last element selection has similar issues. Middle element selection provides better average performance by reducing worst-case scenarios. Random pivot selection offers the best average-case guarantee and helps avoid adversarial inputs that could degrade performance.
The partitioning process is the core of Quick Sort. We start by choosing a pivot, then use two pointers moving from opposite ends. The left pointer moves right until it finds an element greater than or equal to the pivot. The right pointer moves left until it finds an element less than or equal to the pivot. When both pointers find such elements, we swap them. This continues until the pointers cross, ensuring all elements smaller than the pivot are on the left, and larger elements are on the right.
This complete walkthrough shows how Quick Sort recursively divides the problem. Starting with the original array, we partition around a pivot, creating two subarrays. Each subarray is then sorted independently using the same process. The recursion continues until we reach base cases of single elements or empty arrays. Different colors represent different recursion levels, showing how the call stack builds up and then unwinds to produce the final sorted result.
Quick Sort's time complexity varies based on pivot selection. In the best and average cases, it achieves O(n log n) performance when pivots divide the array roughly evenly, creating log n recursion levels with n work per level. However, the worst case is O(n squared) when pivots consistently create unbalanced partitions. The space complexity is O(log n) due to recursion stack depth. Compared to other algorithms, Quick Sort typically outperforms Bubble Sort and matches Merge Sort's average performance while offering better cache locality.