A simple expected running time analysis for randomized “divide and conquer” algorithms

There are many randomized “divide and conquer” algorithms, such as randomized Quicksort, whose operation involves partitioning a problem of size n uniformly at random into two subproblems of size k and image that are solved recursively. We present a simple combinatorial method for analyzing the expected running time of such algorithms, and prove that under very weak assumptions this expected running time will be asymptotically equivalent to the running time obtained when problems are always split evenly into two subproblems of size image.