Interestingly, the C++ standard doesn't specify a cost for this, or an implementation. So there could be some C++ implementation out there somewhere that just copies the whole string on each append.
This is in contrast to std::vector, where the cost of adding one element to the end _is_ specified to be amortized O(1).
Table 76 (page 797-798 of the C++20 draft [0]; page numbers read 789-790) specifies the sequence operations on containers that shall take amortized constant time. Among these includes push_back() for basic_string.
[0] https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2020/n48...
This was also the case in the C++11 draft, and quite possibly before then as well. (I don't have a copy of the C++03 spec handy)
;-)
1. Both std::vector<T> and std::basic_string<T> support push_back(T) with amortized constant performance.
2. Additionally, std::basic_string<T> has an operator+=(T) that behaves semantically identical to push_back(T), but does not have a complexity requirement imposed by the standard.
You're technically correct that the standard theoretically allows push_back(T) and operator+=(T) to have different time complexities, so you could make operator+=(T) run in linear time if you're trolling (but in that case, why stop at O(N) and not make it O(2^N) or something?), but since push_back(T) and +=(T) need to be equivalent and the former needs to run in O(1) amortized time, there is no reason to make the latter perform worse than the former.
See my comment here for details: https://news.ycombinator.com/item?id=38032949