How does the comb sort algorithm sort elements?

The Comb Sort algorithm sorts elements by repeatedly comparing and swapping elements at a certain "gap" apart.

The Comb Sort algorithm is an improvement on the Bubble Sort algorithm. It works by comparing elements that are a certain "gap" apart, rather than just comparing adjacent elements. This gap is initially a large value, typically the total length of the list being sorted, and is reduced in each iteration of the algorithm until it is 1, at which point the algorithm behaves like a Bubble Sort.

The algorithm begins by setting the gap to the length of the list. It then enters a loop, where it compares each element in the list with the element that is 'gap' places ahead of it. If the elements are in the wrong order, it swaps them. This process is repeated from the start of the list until a pass through the list is made without any swaps being necessary.

The gap is then reduced, typically by dividing it by a factor of 1.3 (this value has been found to provide good performance in practical applications). The process is then repeated with the new gap. This continues until the gap is 1, at which point the algorithm continues to compare and swap adjacent elements until the list is sorted.

The advantage of the Comb Sort algorithm over the Bubble Sort algorithm is that it can deal with "turtles", which are small values at the end of the list that move towards the start of the list very slowly in a Bubble Sort. By using a large gap, the Comb Sort can move these small values towards the start of the list much more quickly.

In terms of complexity, the Comb Sort algorithm performs well on average, with a time complexity of O(n^2/2^p) for a list of n elements and a gap reduction factor of 2^p. However, in the worst case, its time complexity is O(n^2), which is the same as Bubble Sort. Despite this, it typically performs significantly better than Bubble Sort in practical applications due to its ability to deal with "turtles".