I'm curious how this works in the case of reinvention. Some algorithms are so simple that there is basically one canonical way of writing it. I'm assuming copyright doesn't cover the independent implementation in such cases?

Reinvention is ok in term of copyright. Patent would prohibit it.

What would happen if I patented "left pad" in a bunch of languages?

Behold the three pillars of IP protection.

Copyright protects the What (tangible creative works, such as, printed publications, movies, sound recordings, source code, and so on)

Trademark protects the Who (who made this service or product)

Patent protects the How (how does this widget do what is does)

it would be an invalid patent (or at least should be), because 1. There is prior art 2. it is obvious to a domain expert But given the US patent office's track record, I wouldn't be too surprised if you were able to get a patent. Just don't expect it to hold up in court.

But then, if you're patent trolling - does it even need to hold up in court?

IF cost_of_settlement < cost_of_court_action THEN pay_up(); /* ? */

Yep. Until you threaten someone willing to stand up to it, even if it is expensive.

Code cannot be patented - copyright covers that.

Patents on software are not that simple - it needs to describe an entire physical system that gives value to a user, not just an abstract function that does computation.

Your patent would be rejected presumably

The patent would get thrown out on review

Not if you avoid the common names and invent a new name for it. Nowadays they are just doing some searches and patent granted.

Hypothetically, until we get to Google v. Oracle, and now really nobody has any idea what the hell is going on.