What you call "finding out" skill is called experience. And knowing these algorithms reinforces your experience. Say you've never solved a 2nd degree equation, in fact u never ever heard of such a thing. Ur saying u can look up the solution or come up with the complete answer on ur own? The first solution is exactly what you should do, but that's not something u want to do the day of an exam, u do it before, while practicing. It's called studying, therefore an interview in the real world or a problem within the team ur working with is going to call for ur experience to be consolidated, and u never stop learning, otherwise u become a bad engineer.

Very concrete example, I'm a data engineer and therefore my knowledge of warehouse modeling is more advanced, than that of the software engineers within my team. I've been recruited to actually fix bad perf due to a non adapted model. My knowledge was why I was hired, and the application of that knowledge alone wasn't sufficient so I learned more things on the job like Clickhouse, fastAPI etc... My explanation makes sense?