Quick Sort

Quick Sort is a divide-and-conquer sorting algorithm that works by selecting a pivot element, partitioning the array into two subarrays (elements less than the pivot and elements greater than the pivot), and recursively sorting those subarrays.

How Quick Sort Works

The Quick Sort algorithm follows these steps:

1. Choose a pivot: Select an element from the array to act as the pivot. This can be the first, last, middle, or a randomly chosen element.
2. Partition the array: Rearrange the elements in such a way that all elements less than the pivot are on the left, and all elements greater than the pivot are on the right.
3. Recursively sort the subarrays: Apply the same logic to the left and right subarrays created during partitioning.
4. Combine the sorted subarrays to get the sorted list.

Partitioning Logic

The partitioning step is the core of Quick Sort. The goal is to ensure the pivot is placed in its correct sorted position, with all smaller elements to its left and larger elements to its right.

Advantages of Quick Sort

1. Efficient on average: Very fast for most real-world datasets.
2. In-place sorting: Requires minimal extra memory.
3. Divide and Conquer: Divide problem into smaller subproblems.

Disadvantages of Quick Sort

1. Worst-case performance: O(n2)O(n^2)O(n2) in certain scenarios unless careful pivot selection is done.
2. Recursive implementation might lead to stack overflow for very large arrays.

Pivot Selection Strategies

To minimize the risk of hitting the worst-case performance, pivot selection is important. Common strategies include:

1. Last Element as Pivot - As shown in the example.
2. First Element as Pivot.
3. Median-of-three pivoting - Choose the median of the first, middle, and last elements to improve partitioning balance.
4. Randomized Pivot - Randomly select a pivot to avoid worst-case scenarios.