Divide and conquer
Algorithmic strategy: split the problem into smaller subproblems, solve them recursively, combine the results. "Divide and rule".
Classic examples: merge sort (split the array, sort halves, merge), quick sort (pick a pivot, partition, sort both sides), binary search, FFT, Karatsuba multiplication, Strassen's matrix multiplication. The Master Theorem gives the time complexity of the recurrence.
Naturally parallelisable — each recursion is independent. MapReduce and Hadoop are industrial divide-and-conquer over data. Trade-off: recursion overhead at the bottom; one often switches to insertion sort on small subarrays.