No, because appending with push_back() which strings must also support is required to have O(1) amortized time.

See my comment here for details: https://news.ycombinator.com/item?id=38032949

Depends what you mean by reasonable I suppose. If you just implement it naively, either by growing by 1 or a constant amount each time, it'll be O(n) amortized.

I'd call those potentially reasonable, in that it works and it doesn't break the standard. I probably wouldn't be mad if a student did that impl, but I'd mention it.

I would be surprised if a well-supported, non-toy implementation without strange constraints (eg not for embedded and not trying to optimize solely for size or simplicity or something) did something other than amortized O(1).

No, but there was an unreasonable one. Microsoft Foundation Classes, which preceded the STL. Originally, Their CString class extended the capacity in such a way that appending one character at a time had quadratic cost.

It was just using the naive approach (grow by the exact size), the same idea as Google is now proposing. https://news.ycombinator.com/item?id=38033206