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I know the standard specifies that it is for vectors, but what about strings?
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So time complexity of push_back() is O(1).
std::string::push_back() in C++The push_back() member function is provided to append characters. Appends character c to the end of the string, increasing its length by one. Syntax : void string:: push_back (char c) Parameters: Character which to be appended.
The amortized time of vector::push_back is constant.
Append is a special function in the string library of C++ which is used to append string of characters to another string and returns * this operator. This is similar to push_back or += operator, but it allows multiple characters to append at the same time.
Yes, it is amortized constant time. See table 101 on page 716 of this document:
Table 101 lists operations that are provided for some types of sequence containers but not others. An implementation shall provide these operations for all container types shown in the “container” column, and shall implement them so as to take amortized constant time.
Operation | Description | Container
---------------+----------------------+----------------------------------
a.push_back(t) | Appends a copy of t. | basic_string, deque, list, vector
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