Question

I’m reading some texts about algorithmic complexity (and I’m planning to take an algorithms course later), but I don’t understand the following.

Say I’ve to search for an item in an unordered list, the number of steps it takes to find it would be proportional to the number of items on that list. Finding it in a list of 10 items could take 10 steps, doing the same for a list of 100000 items could take 100000 steps. So the algorithmic complexity would be linear, denoted by ‘O(n)’.

Now, this text[1] tells me if I were to sort the list by some property, say a social security number, the algorithmic complexity of finding an item would be reduced to O(log n), which is a lot faster, off course.
Now I can see this happening in case of a b-tree, but how does this apply to a list? Do I misunderstand the text, since English isn’t my native language?

[1]http://msdn.microsoft.com/en-us/library/ms379571.aspx

Answer 1

This works for any container that is randomly accessible. In the case of a list you would go to the middle element first. Assuming that’s not the target, the ordering tells you if the target will be in the upper sublist or the lower sublist. This essentially turns into a binary search, no different than searching through a b-tree.