Lowest Worst-Case Complexity Sorting Algorithm: Merge Sort

Introduction:
In computer science, sorting algorithms are used to arrange a list of elements in a specific order. The efficiency of a sorting algorithm is measured by its time complexity, specifically the worst-case complexity. The worst-case complexity represents the maximum number of operations needed to sort the elements in the worst-case scenario.

Comparing the Sorting Algorithms:
To determine the sorting algorithm with the lowest worst-case complexity among the options provided, let's analyze each algorithm:

1. Bubble Sort:
- Worst-case complexity: O(n^2)
- Inefficient for large datasets
- Involves repeatedly swapping adjacent elements if they are in the wrong order

2. Quick Sort:
- Worst-case complexity: O(n^2)
- Efficient for average case, but can become inefficient for certain inputs, such as already sorted or nearly sorted data
- Divides the list into sublists based on a chosen pivot element and recursively sorts them

3. Selection Sort:
- Worst-case complexity: O(n^2)
- Inefficient for large datasets
- Involves finding the minimum element from the unsorted part of the array and swapping it with the first element

4. Merge Sort:
- Worst-case complexity: O(n log n)
- Efficient for large datasets
- Divides the list into smaller sublists, recursively sorts them, and then merges them back together

Explanation and Conclusion:
Based on the analysis above, Merge Sort has the lowest worst-case complexity among the provided options. It has a time complexity of O(n log n), which means its performance remains efficient even for large datasets. Merge Sort divides the list into smaller sublists, sorts them individually, and then merges them back together. This approach ensures that the number of operations required to sort the list grows at a slower rate compared to the other sorting algorithms.

Therefore, if the goal is to minimize the worst-case complexity when sorting a list of elements, Merge Sort is the most suitable choice among the given options.

Mergesort best, worst and average case is O(nlogn) only.