Divide-and-conquer is an algorithmic technique in which a problem is divided into smaller subproblems, whose solutions are combined to a solution of the original problem. Classical examples include mergesort, quicksort, and FFT.
Divide-and-conquer is an algorithm technique in which a problem is divided into smaller subproblems, which are solved recursively, and their solutions are then combined into a solution of the original problem. The running time of such algorithms can often be computed using the Master theorem or its generalization, the Akra–Bazzi theorem.
As an example, mergesort and quicksort each partition their input into two subarrays ("divide"), which are then sorted recursively and put together ("conquer"). In the case of mergesort, divide is trivial and conquer requires work. The opposite is true for quicksort. The running times of both algorithms satisfies the recurrence $T(n) = 2T(n/2) + \Theta(n)$, whose solution is $\Theta(n\log n)$.