Question

I’ve wrote an algorithm that looks for duplicates in unsorted lists. It does n – m operations on each iteration where m is iteration number and n is size of input list. What is its big O?

Answer 1

O(n^2). The work here is n+(n-1)+(n-2)+...+1 = n(n+1)/2.

A more intuitive way to look at it is that you do at least n/2 work for at least n/2 iterations, so you do at least n^2/4 work.