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Apart from maybe the last one, none of them are classical algo problems.

They're basic math problems.

Query takes N milliseconds which is too long, mainly consisting of z & c when I run my profiler. It does x * y = z of these things and a * b = c of these things.

As z is the biggest number, can I reduce x or y?

Basic maths.

And even the last one you're better off actually trying out the technologies to trying to armchair theorize which tech is a better fit as without reading all their code you can't really see what they're really doing compared to what they say they do. Heroku being a pertinent case in point.

What's "classical" in your book?

Search trees, dynamic programming, and reducing an algorithm's worst-case runtime are about as "classical" as you get; that's why they're in every beginning algorithms textbook.

Unless you know "classical algorithms" and their typical performance characteristics, you are bound to waste time tweaking and may even rediscover a few complexity theorems, reductions and even complexity classes all on your own.

Oh you could just know the basics and classical algorithms and able to do a smell test of algorithmic performance.

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