I did not study computer science in any substantial way, and I hardly consider myself a computer scientist, but I do have a nose for algorithms despite not really thinking about it in a structured way. I think lot of people get wrapped up in the notation without realizing they can approach the problem in a completely different way. Case in point, a professor at a University in the US created a parts-of-speech tagger and released the source in the early 2000's. I wanted to leverage this tagger to create a topic oriented search engine, but it was WAY too slow. It took about 10 seconds to tag a document (back in 2003 on decent hardware), and since I needed to tag hundreds of millions of documents, and despite having about 15 servers at my disposal, this was not going to work. So I dug into that algorithm and realized it was trying to test all of it's conditions all of the time to figure out which rule would apply. I redesigned it to index the rules and only apply them if it was possible for that rule to have some effect. Or something like that, the details are now fuzzy. The speedup was roughly 1000x, and made the tagger usable at scale.
Plot twist: I took a computer science class (as a Mech E major) taught by that same professor years earlier and failed it. That class was Data Structures.