To make the best-case count of key comparisons in a sorting algorithm equal to just n - 1, you can use a simple optimization called "early termination" or "stop early" when the algorithm detects that the list is already sorted. Here's how this can be implemented and whether it would be a worthwhile addition:

1. Early Termination Approach:
   • During the sorting process, the algorithm checks if, at any point, it hasn't made any swaps or comparisons for a full pass through the list. If there have been no swaps or comparisons, it means the list is already sorted (at least partially).
   • If no swaps or comparisons are made in a full pass, the algorithm can stop early, assuming the list is sorted, thus saving additional key comparisons.

For example, consider a simple sorting algorithm like Bubble Sort:

def bubble_sort(arr):
    n = len(arr)
    for i in range(n):
        swapped = False
        for j in range(0, n-i-1):
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]
                swapped = True
        # If no swaps were made, the list is sorted, and we can break out early.
        if not swapped:
            break

This early termination approach ensures that in the best-case scenario (when the input list is already sorted), the algorithm will only perform n - 1 key comparisons because it will terminate early after confirming the list's sorted order.

Is it worthwhile?:

• Adding early termination to a sorting algorithm can be worthwhile if you expect to encounter sorted or partially sorted lists frequently in your application. In such cases, it can significantly reduce the number of unnecessary comparisons and improve the algorithm's efficiency.
• However, not all sorting algorithms benefit equally from early termination. Bubble Sort, for instance, can benefit more from early termination than algorithms like Merge Sort or Quick Sort, which have different sorting strategies. In these cases, the impact on performance may be less significant.
• The effectiveness of early termination also depends on the distribution of input data. It's most beneficial when you expect to encounter already sorted or nearly sorted data.

In summary, adding early termination to a sorting algorithm can be a valuable optimization in some situations, but its impact on performance varies depending on the algorithm and the nature of the input data. It's one of many considerations when choosing a sorting algorithm for a specific task.