What happens if I use vector::begin() instead of std::back_inserter(vector) for output of set_intersection?

Question

I have been using the highly concise and intuitive C++ syntax for finding the intersection of two sorted vectors and putting the result in a third vector<

Answer 1

The important requirement for an output iterator is that it be valid and write-able for the range
[out, out+size of output).

Passing c.begin() will lead to the values being overwritten which only works if the container c holds enough elements to overwrite. Imagine that c.begin() returns a pointer to an array of size 0 - then you'll see the problem when writing *out++ = 7;.

back_inserter adds every assigned value to a vector (via push_back) and provides a concise way of making the STL-algorithms extend a range - it overloads the operators that are used for iterators appropriately.

Thus

 std::set_intersection(a.begin(),a.end(),b.begin(),b.end(),
                       c.begin());

invokes undefined behavior once set_intersection writes something to its output iterator, that is, when the set intersection of a and b isn't empty.

Can a conforming implementation silently extend the vector in this case, so that begin() is in fact an appending OutputIterator like back_inserter is?

Of course. It's undefined behavior. (This is a humorous approach of telling you that you shouldn't even consider using this, no matter the effects on any implementation.)