TITLE: How many operation are required to sort a array of numbers.
QUESTION [6 upvotes]: On StackOverflow, a simple question inspired me to create an equation for a answer. But it turn out that, it is kind of complicated (IMHO) mathematical problem, namely: 

Given an array of n elements, is it possible in O(n) time, to figure
  out how many operations* will be required, if we were to sort that
  array of elements using bubble sort algorithm ?


*total number of swaps.

REPLY [3 votes]: I don't believe so. This is equivalent to computing the Kendall tau coefficient. There are a couple algorithms for doing this (one of which involves using a Merge sort to compute how many steps Bubble sort would take) but they are $O(n\cdot log\ n)$.