Shortest possible depth of a leaf in decision tree (comparison sorting algorithm)

Question

What is the shortest possible depth of a leaf in decision tree refering to comparison sorting algorithm ?

Does it change depending on the alogrithm?

Answer 1

The absolute best case happens when we just check every element and see that the data's already sorted.

This will result in n-1 comparisons and thus the leaf will have a depth of n-1.

Practically, this happens for insertion sort (which isn't all that good otherwise though).

Does it change depending on the algorithm?

Absolutely. The best case of an algorithm is a good indicator - the shortest depth for one with O(n log n) best case would be longer than the shortest depth for one with O(n) best case.