Visualising cksort

As part of the development of my first draft for the sorting algorithm, I spent a lot of time visualising existing sorting algorithms at the excellent website http://www.sorting-algorithms.com/ . Looking at the different algorithms allowed me to think about how I might develop my own sort to try and improve performance in some of the common cases listed there and do well in areas most do badly. Until now I was unable to generate pretty graphs like those ones, but with Serge Belyshev's help I manage to get some rudimentary versions (without the nice arrows and different shading that the website above has) to see how swaps occur.

The following graphs visualise only the writes to the main array, and an update occurs only whenever a value is changed in the main array. This tends to correlate quite well with the overall number of comparisons as well so the time taken to complete in these examples should give you an idea of where cksort performs.

I would have liked to have visualised completely sorted data, but since no moves of data occur in cksort, there is nothing to show.

These graphs correspond to 50 entries of values 0-50, so the equivalent of clicking the 50 button on sorting algorithms above. Putting them in the same order as the site above here they are (note I do NOT have the same data so you cannot compare them directly, though the ballpark performance scales should be comparable):

EDIT: NOTE These graphs link samples from the latest version of  cksort which performs better than this original post described.

Random data

Nearly sorted

Reversed

Few Unique

Part of the reason I wanted to visualise these sorts was to demonstrate how cksort worked visually, but another reason was for me to examine it and see where its weakness is and how I might improve it. Interestingly, in my testing, the worst data for cksort was a sawtooth pattern as I mentioned in my last post. Furthermore, if I "heapify" the unsorted data on every pass, it gets much slower. Looking at the random data example above, it seems that with multiple passes, it intrinsically tends to heapify the data anyway, which is counterproductive. So assuming I can improve on it, this is the area I need to concentrate on. Perhaps after a few passes if the number of clustered "highs" drops to minimal, it may be better to switch to a heap sort for the remaining data. At least it's clear in the above examples where cksort does perform well!