Quick Sort is a highly efficient and widely used sorting algorithm that also follows the divide-and-conquer approach. It selects a 'pivot' element from the array, partitions the other elements into two subarrays (elements less than the pivot and elements greater than the pivot), and recursively sorts the subarrays. Quick Sort is known for its average time complexity of O(n log n), although in the worst case, it can degrade to O(n²).

How Quick Sort Works

Step-by-step Explanation

1. Choose a pivot: Pick an element from the array to act as the pivot. This can be any element, but common strategies include choosing the first element, the last element, or a random element.
2. Partition the array: Rearrange the array so that elements smaller than the pivot come before it, and elements greater than the pivot come after it.
3. Recursively sort the subarrays: Apply the same process to the two subarrays (left of the pivot and right of the pivot) until the entire array is sorted.

Quick Sort Algorithm

Quick Sort involves two main operations:

1. Partitioning the array around a pivot element.
2. Recursively sorting the subarrays formed by partitioning.

Quick Sort Code Implementation in JavaScript

Let's implement Quick Sort using a recursive approach with a pivot selection.

Code Explanation

• quickSort(arr): This function sorts the array by first selecting the last element as the pivot. It then divides the array into two subarrays: left (containing elements less than the pivot) and right (containing elements greater than the pivot). It recursively sorts the subarrays and merges them back together.

Time and Space Complexity

• Time Complexity: Quick Sort has a best and average time complexity of O(n log n). However, in the worst case (when the pivot is poorly chosen), the time complexity can degrade to O(n²).
• Space Complexity: The space complexity of Quick Sort is O(log n) for the recursive calls in the best case, but it could go up to O(n) in the worst case.

Conclusion

Quick Sort is a highly efficient sorting algorithm that performs well in practice due to its average time complexity of O(n log n). Its worst-case performance can be avoided with a good pivot selection strategy. Quick Sort is widely used in scenarios where performance is crucial, and its recursive nature makes it a simple yet powerful algorithm for sorting arrays.