Quicksort with 3-way partition

Question

What is QuickSort with a 3-way partition?

Answer 1

if you really grind out the math using Akra-Bazzi formula leaving the number of partitions as a parameter, and then optimize over that parameter, you'll find that e ( =2.718...) partitions gives the fastest performance. in practice, however, our language constructs, cpus, etc are all optimized for binary operations so the standard partitioning to two sets will be fastest.