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Cocktail sort algorithm functions by sorting the list in both directions, first forward then backward, in a repeating cycle.

Cocktail sort, also known as bidirectional bubble sort, cocktail shaker sort, shaker sort, ripple sort, shuffle sort, or shuttle sort, is a variation of the bubble sort algorithm. It differs from the bubble sort by not only sorting the list in one direction each pass through the list, but also in the opposite direction. This means that after the first pass, the largest number is at the end of the list, and the smallest number is at the start of the list.

The algorithm begins by comparing each pair of adjacent items and swapping them if they are in the wrong order. This process continues from the beginning of the list to the end, moving the highest value to the end of the list. This is similar to the bubble sort, where the largest number 'bubbles' up to the end of the list.

However, unlike the bubble sort, the cocktail sort does not start the next pass at the beginning of the list. Instead, it goes in the opposite direction, from the end of the list to the beginning. It again compares each pair of adjacent items and swaps them if they are in the wrong order. This moves the smallest number to the beginning of the list.

The algorithm continues this process, going back and forth through the list until no more swaps are needed. This means that the list is now sorted.

One of the advantages of the cocktail sort over the bubble sort is that it can handle 'turtles', which are small numbers at the end of the list, much more efficiently. These numbers move to the beginning of the list very slowly in a bubble sort, but much faster in a cocktail sort.

However, like the bubble sort, the cocktail sort is not suitable for large lists, as its average and worst-case computational complexity is O(n^2), where n is the number of items. This means that the time it takes to sort the list increases quadratically with the number of items, making it inefficient for large lists.

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