Quicksort with 3-way partition

Question

What is QuickSort with a 3-way partition?

Answer 1

Picture an array:

3, 5, 2, 7, 6, 4, 2, 8, 8, 9, 0

A two partition Quick Sort would pick a value, say 4, and put every element greater than 4 on one side of the array and every element less than 4 on the other side. Like so:

3, 2, 0, 2, 4, | 8, 7, 8, 9, 6, 5

A three partition Quick Sort would pick two values to partition on and split the array up that way. Lets choose 4 and 7:

3, 2, 0, 2, | 4, 6, 5, 7, | 8, 8, 9

It is just a slight variation on the regular quick sort.

You continue partitioning each partition until the array is sorted. The runtime is technically nlog₃(n) which varies ever so slightly from regular quicksort's nlog₂(n).