DAA - QuickSort Problem(BCA- IV Sem KSWU)

Quicksort 

    Quicksort is a sorting algorithm that utilizes the divide and conquer strategy. It works by dividing the input array into smaller subarrays, sorting them independently, and then combining them to achieve a fully sorted array. 

    Here's a brief explanation of how Quicksort uses the divide and conquer approach:

1. Select a pivot element from the array. This pivot element will help divide the array into two subarrays.
2. Rearrange the array so that all elements smaller than the pivot are placed before it, and all elements greater than the pivot are placed after it. This process is called partitioning.
3. Now, the pivot is in its final sorted position.
4. Recursively apply steps 1-3 to the subarray on the left of the pivot (elements smaller than the pivot) and the subarray on the right of the pivot (elements greater than the pivot).
5. Repeat the process until all subarrays have been sorted.
6. Finally, combine the sorted subarrays to obtain the fully sorted array.

advantages and disadvantages of QUICKSORT problem

Advantages:

• Efficiency: Quicksort is known for its efficient average-case time complexity of O(n log n). It performs well on average and is often faster than other sorting algorithms.
• In-Place Sorting: Quicksort can be implemented to sort the elements in-place, meaning it doesn't require additional memory proportional to the input size. This can be advantageous when memory usage is a concern.
• Simplicity: Quicksort has a relatively simple implementation compared to other sorting algorithms like Merge Sort or Heap Sort.

Disadvantages:

• Worst-Case Time Complexity: In the worst-case scenario, where the pivot selection consistently leads to highly imbalanced partitions, Quicksort's time complexity can be O(n^2). This can occur when the input is already sorted or nearly sorted. However, proper pivot selection strategies, like choosing a random pivot or using median-of-three pivot, can mitigate this issue.
• Non-Stable Sorting: Quicksort is not a stable sorting algorithm, meaning that the relative order of equal elements might not be preserved after sorting.
• Dependency on Pivot Selection: Quicksort's performance heavily relies on the selection of the pivot. Choosing a poorly selected pivot can result in degraded performance, particularly in terms of time complexity.