Merge Sort

Merge sort is an efficient, stable, and comparison-based sorting algorithm that divides the unsorted list into smaller sublists, sorts those sublists, and then merges them to obtain a sorted list. It has a worst-case complexity of O(n log n).

Bubble Sort

Bubble sort is a simple and inefficient sorting algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. It has a worst-case complexity of O(n^2).

Quick Sort

Quick sort is an efficient, comparison-based sorting algorithm that uses a divide-and-conquer strategy. It selects a pivot element and partitions the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. It then recursively sorts the sub-arrays. Quick sort has a worst-case complexity of O(n^2), but on average it has a complexity of O(n log n).

Selection Sort

Selection sort is a simple and inefficient sorting algorithm that repeatedly finds the minimum element from the unsorted part of the list and puts it at the beginning. It has a worst-case complexity of O(n^2).

Comparison of Worst-Case Complexities:

- Merge sort: O(n log n)
- Bubble sort: O(n^2)
- Quick sort: O(n^2)
- Selection sort: O(n^2)

Conclusion:

Among the given sorting algorithms, Merge sort has the lowest worst-case complexity of O(n log n). This means that it performs better than the other algorithms when dealing with larger input sizes. Merge sort's divide-and-conquer approach ensures that it consistently achieves this efficiency, regardless of the initial order of the elements. On the other hand, bubble sort, quick sort, and selection sort all have worst-case complexities of O(n^2), making them less efficient for large-scale sorting tasks.