A more detailed explanation of the bound is here: http://people.csail.mit.edu/indyk/6.838-old/handouts/lec17.pdf
Using a higher bound does not impact correctness, but it does affect the complexity by a constant factor.
This tests if a number is prime. For example, with 13 and 15,
perl -e 'print "Prime" if ("a" x shift) !~ /^a?$|^(aa+?)\1+$/' 13
perl -e 'print "Prime" if ("a" x shift) !~ /^a?$|^(aa+?)\1+$/' 15
The explanation is correct, but this does not mention the fact that this is just one of the ways of partitioning possible: Hoare's. There are others such as Lomuto's, which is "simpler" while requiring more swaps. I am in favor of quicksort being explained/illustrated without a specific partition scheme chosen and without any in-place requirement, such as shown by code here: http://ideone.com/nW8fyr
It is easier to understand in-place partitioning schemes once you know what the algorithm itself is supposed to do.
The first int walks up to her and say: “Hey baby, my VM or yours?”. She slaps him and he walks back dejected.
The second int walks over. “Hey cute-stuff, can I cook you ‘Beans’ for breakfast?” After a quick slapping, he too walks back.
Then the Float ambles over casually: “Where those two primitive types bothering you?”, he remarks.
“Yes, I’m so glad you’re here”, she says. “They just had no Class!”
- Texas A&M UniversityComputer Science, 2014 - present
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