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"Mostly-sorted" is a very vague definition.

Usually what people mean by mostly sorted in CS is that there is some small K such that each element in the input is no more than K places from the position it would be in if the input was sorted.

According to this definition, the "random tail" test data is not "mostly sorted".

Well you could extend the definition to allow a small number of items which are entirely out of place. The point is that the right sort algorithm depends a lot on tthe distribution of input data and how much you care about worst-case vs average case trade offs.

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