Quick Sort in Data Structure

What is Quick Sort in Data Structure?

Quick Sort is a divide-and-conquer algorithm that selects an element as a pivot and partitions the given array around that pivot.

Selecting the Pivot Element in the Data Structure

There are numerous methods of selecting pivots:

• Always select the first element as the pivot.
• Always choose the last element as the pivot.
• Choose a random element as the pivot.
• Select the middle element as the pivot.

Working of Quick Sort

• Partitioning is the fundamental operation of quickSort.
• The purpose of partitioning is to place the pivot in the proper sorted location.
• Smaller elements move to the left, whereas larger ones move to the right of the pivot.
• Partitioning occurs recursively on both sides of the pivot.
• This method will finally sort the array.

Complexity Analysis of Quick Sort Algorithm

Time Complexity

Best Case Complexity

In Quicksort, the best case happens when the pivot element is in the middle or close to the middle. The best-case time complexity for quicksort is O(n*logn).

Average Case Complexity

This arises when the array elements are jumbled and do not appropriately climb or descend. The average case time complexity for quicksort is O(n*logn).

Worst Case Complexity

In quick sort, the worst case happens when the pivot element is either the largest or the smallest element. Assume that the pivot element is always the final element in the array; the worst-case scenario occurs when the array is already sorted in ascending or descending order. The worst-case time complexity for quicksort is O(n2).

Space Complexity

The worst-case space complexity is O(n), which occurs when n recursive calls are made. A quick sort algorithm has an average space complexity of O(long).

Applications of Quick Sort Algorithm

• Numerical Analysis: Quick sort works well with priority queues for accurate calculations.
• Call Optimization: Tail-recursion allows for call optimization.
• Database Management: Due to its quickness, Quicksort is great for effective searching.

Advantages of Quick Sort Algorithm

• Efficiency: Suitable for huge datasets.
• In-place Sorting: Sorts without requiring additional memory.
• Simple Implementation: The logic is basic and easy to implement.

Disadvantages of Quick Sort Algorithm

• Unstable Sorting: Doesn't ensure that equal elements are arranged in a relative order.
• Worst-case scenario: Extreme pivots result in unbalanced partitions and require O(n^2) complexity.
• Pivot Dependency: The choice of pivot has a significant impact on performance, particularly with sorted arrays.
• Recursive Overhead: When dealing with huge datasets, recursion might cause stack overflows.
• Not adaptive: does not optimize for pre-existing order; always partitions the full array.
• Inefficient for Small Data: Overhead and recursion may be inefficient for tiny arrays.