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I don't know what happened, but I got to level 21 somehow. :)

This is cool and handy for lecturers explaining sorting/searching.

In practice: merge, insertion and dual pivot [1] /single pivot quick(er)sort [2] are the usual tools in the toolbox, that like everything, depend on the specific use. Oh, and radix sort for rainbow tables.

On DPQS, there's apparently a method for 1.8n ln n + O(n) [3]

References:

  1. http://www.iaroslavski.narod.ru/quicksort/DualPivotQuicksort.pdf

  2. The FlashSort Algorithm
     http://www.neubert.net/FSOIntro.html

  3. Optimal Partitioning for Dual Pivot Quicksort
     http://arxiv.org/abs/1303.5217

  4. Algorithm 271: quickersort (1965) 
     http://citeseerx.ist.psu.edu/showciting?cid=846385
  
  5. (and, of course) https://www.amazon.com/Art-Computer-Programming-Volume-Searching/dp/0201896850
 
     (same shrtnd) http://amzn.to/134daLz
This is great context. Thank you.