Is this a divide-and-conquer algorithm?
"Divide &amp; Conquer" is not a very fixed notion. It usually goes along the lines of


  D&amp;C algorithms divide the problem and solve recursively.


That's not very strong, for the following reasons.


What I would call inductive algorithms do this, but are usually not considered divide &amp; conquer algorithms. Given a problem of size $n$, inductive algorithms solve subproblems (typically one) of size $n-c$ for some constant $c$ and derive a solution for the original problem. See here for an example.
Dynamic programming does exactly that, but it's not usually considered d&amp;c. The difference is that in DP, subproblems overlap, which they don't in d&amp;c. Also, we often don't know which subproblem is the "right" one, so we try out all possible partitionings (which causes overlapping).


Now, one might say that inductive and d&amp;c algorithms are orthogonal special cases of dynamic programming, but that's for another discussion.

In order to "define" divide &amp; conquer against those other types of algorithms, consider this:


  D&amp;C algorithms divide the problem of size $n$ into non-overlapping¹ subproblems of size $\frac{n}{c}$, solves (some of²) them recursively and combines the solutions to a solution of the original problem.


By this "definition", your algorithm is not divide &amp; conquer.

As for runtimes, d&amp;q algorithms can typically be analysed (roughly) using the 
master theorem. As you can see from the three cases, all kinds of runtimes of the form $n^a\log^bn$ can result, depending on the quality of the division and the runtime of the combining step.




As I write the part about runtimes, it occurs to me that this may be too strong. Overlaps by a constant (sized part) are fine.
Binary search can be considered the ultimate divide &amp; conquer: by dividing cleverly, combining is unnecessary.