ELISHEVA,
Thank you for taking the time to code this up. I agree, and pointed out, that there were optimizations to be made from my approach as I did it hastily. I am not at all convinced that it produces optimal results for all data sets. I think it is a good heuristic approach given the requirements (runtime of less than 3 seconds with small margin of error).

In order to disprove that it doesn't always produce optimal results, I don't need the rigor of a formal proof - I just need to come up with an example. If you are interested in such an example, it shouldn't be too difficult. A small enough data set should allow all possible partitions and combinations which can then be compared against the results of the heuristic algorithm. If you want, I can code that up?

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