The algorithmic problems I deal with are things like:
- Why the hell is this API call running O(n*m) SQL queries? Can I tweak my logic and use of the ORM get it down to O(1)? The ORM doesn't let you forget about the underlying algorithms, it just makes it easy for you to shoot yourself in the foot if you don't understand them.
- Why is my single SQL query so slow? DB optimization is very much a "classic algorithmic problem", in that you need to understand the operations the DB performs and optimization is reducing its search space / # of operations.
- We're using too many jQuery pseudoselectors like ":hidden" and they're causing framerate drop on a particular page; can we use some dynamic programming / memoization techniques to dramatically reduce use of pseudoselectors?
- We need to figure out what font size will allow a piece of text to fit within a container on a PDF, but the bounds of the font (space consumed) don't scale perfectly linearly with the font's point-size. Finding the best fit is a search problem!
- And that's not even getting into infrastructure scaling issues! Do you know why Vertica might be a better fit for your data set and end user needs than Hadoop? If you understand the difference between an ETL approach and a MapReduce approach to data analysis, you're thinking about algorithms!
I spend a meaningful amount of time on "classical algorithmic problems" while doing frontend and backend web development, even if I've never had to re-implement mergesort.
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?
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.
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.
Oh you could just know the basics and classical algorithms and able to do a smell test of algorithmic performance.