We're talking about several orders of magnitude here.
Is a web page that loads in fifty seconds 'correct' or is it wrong? Is a video format that can only decode 2 frames per second correct, or wrong?
Often, timeliness is an unstated part of the requirements, in which case an academically pleasing solution that isn't practical doesn't fulfill the requirements.
I think you're missing the point.
A quadtree is a compact way to store a partition of two-dimensional space, much like you'd store a binary heap in an array.
The implementation of a recursive data structure or algorithm can usually take advantage of tail recursion or trampolining. The practical implementation of a theoretical algorithm may look extremely different, much like you wouldn't literally translate abstract pseudocode to the language of your choice.
> Is a web page that loads in fifty seconds 'correct' or is it wrong?
Neither: it's probably using JavaScript to perform an AJAX request to get some data in a bespoke markup format, then using JavaScript to parse that markup format and build DOM entries, all because the developer thinks HTML is 'so 90s, dude!'
> Is a web page that loads in fifty seconds 'correct' or is it wrong?
Of course it is correct - this is how the internet was/is with a 14k or 56k dialup modem, I don't blame you for not remembering/not experiencing it. I remember watching JPEGs render progressively from a blurry mess one at a time, or sometimes not at all. It took way more than 50 seconds to load and render all elements on a typical website.
Depends on the business constraints. Wrong is not just "returns invalid results".
There's also the notion of wrong or right solution for a particular problem (which the phrase above already assumes). E.g. for a game where things have to run in 60hz, a slow algorithm would be the wrong solution to use.
The reverse is also true: a solution can return wrong results in the absolute sense (e.g. false positives) and still be correct for our business case. This is the case with things like Bloom filters for example.
