Complexity
The complexity of cocktail sort in big O notation is for both the worst case and the average case, but it becomes closer to if the list is mostly ordered before applying the sorting algorithm, for example, if every element is at a position that differs at most k (k ≥ 1) from the position it is going to end up in, the complexity of cocktail sort becomes .
Cocktail sort is also briefly discussed in the book The Art of Computer Programming, along with similar refinements of bubble sort. In conclusion, Knuth states about bubble sort and its improvements (Knuth 1998, p. 110):
But none of these refinements leads to an algorithm better than straight insertion ; and we already know that straight insertion isn't suitable for large N. In short, the bubble sort seems to have nothing to recommend it, except a catchy name and the fact that it leads to some interesting theoretical problems. —D. E. KnuthRead more about this topic: Cocktail Sort
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