You called a general function std::upper_bound. The way this function works is: if it is called on random access iterator, such as std::vector<int>::iterator, a binary search is performed, achieving $$$O(\log n)$$$ (since it is possible to access any position in constant time). Otherwise, if the iterator is not random access (such as std::set<int>::iterator), std::upper_bould can't do any better than to just advance the iterator linearly to find the answer.

On the other hand, std::set<int>::upper_boupd has access to the inner workings of set, which is a binary search tree, so it can go up and down the tree in a smart way to get the answer in $$$O(\log n)$$$.

please get your facts straight. The problem was clearly upper_bound