Quicksort Versions

Here are the three versions of quicksort:

1.) Basic Quicksort.

2.) Random Pivot Point. The partition algorithm randomly pick an index value of the the array it is looking at. The array element at the location is the partition value.

3.) Median-of-three Partitioning.

Analyze performance of each version using lemma and proof, known theorems, etc... Describe each version of quicksort as extensively as possible. Also talk about Big O notation for all of them.