<s>[INST] So I've been trying to understand the concept of algorithmic complexity, specifically the difference between O(n) and O(n log n).
I've been using various analogies and thought experiments to help myself grasp it.

Here's my thought experiment so far:

Imagine I have a huge library with n books on a shelf. To find a specific book, I have to look at each book one by one, which would be O(n). But to make it more efficient, I could organize the books in alphabetical order and use a binary search, which would be O(log n).

Wait, no... that can't be right.

Can you help me explain why my thought experiment is wrong and what a correct analogy would be?[/INST]