That's absolutely not the case. Many working pastry chefs (I just asked the two that I know) can do exactly what you're asking.

This strikes me as an analogy that does not work in your favor.

To know how to make a novel cake (not a recipe you've memorized), you need to have a good understanding of how the different ingredients interact. You probably even have a good sense of why they're there.

Those seem like exactly the qualities you'd want to look for in a cake maker. Sure, they'll probably be going from recipes in their day to day job. But they'll be able to tweak them intelligently too.

There are literally tv shows and contests where they do exactly this.

Yes, my understanding is that the parent comment is complaining that since it took people with phds years to derive an algorithm for the first time, that we should never expect anyone to implement one in an interview.

But, as with a concept like 0, making the cognitive leap to understanding that there should be a way to represent the lack of something is counterintuitive (indeed, consider Tony Hoare's billion dollar mistake. The "right" way to represent the absence of an object is a hard problem). However, once you've been exposed to it, it's not particularly challenging to rederive the necessary pieces.

So yes, complaining about BFS is, imo, akin to complaining about being asked what the result of the arithmetic operation `35 - 12 - 23` is.

Absolutely! I don't write the algorithm every day, but I interact graphs, trees, and other such structures on a daily basis in my job, and traversing them is something that I work on. Every time I run `rm -r` for example!

I'm not asked to implement BFS every day, but the concept of a tree traversal is incredibly common.

Even more explicitly, a lot of my recent work has been involving automated refactoring tooling, so there's lots of work with abstract syntax trees and control flow graphs, which are trees or graphs, and therefore need be traversed.

Neither BFS the concept, nor 0, the concept are particularly hard to understand. That's why I used the word "concept". If you disagree with that, I'd be interested in what you feel is exceedingly difficult about the breadth-first search algorithm to understand, or if you prefer, to explain why the time it takes to discover or first write down a concept is strongly correlated with its age.

Consider that BFS was first published in 1945, while the turing machine was published almost 10 years prior. Is BFS an implicitly more complex concept than a turing machine? That seems like a strange argument to make, but I'm certainly interested.