Question

How can 5 distinct integers be sorted using at most 7 comparisons?

Answer 1

Sorting five distinct integers can be done with at most seven comparisons using an insertion sort algorithm, by iteratively inserting each additional integer into the already sorted list, taking up to two comparisons for the third, and up to three each for the fourth and fifth integers.

Step-by-step explanation:

The question relates to the concept of sorting algorithms in computer science or discrete mathematics and asks how to sort five distinct integers using at most seven comparisons. A common sorting method that can achieve this is called insertion sort. The steps would follow something like:

1. Compare the first two integers, sort them.
2. Insert the third integer into the sorted order by comparing it with the first two. This can take up to two comparisons.
3. Insert the fourth integer into the sorted list, which could take up to three comparisons.
4. Insert the fifth integer into the sorted list, which can also take up to three comparisons.

Extreme optimization might bring down the number of comparisons by making use of decision trees or other strategies. Note that the worst-case scenario is mentioned here; often, fewer comparisons would be enough if data is partially sorted or if lucky choices are made early on.