How does the comb sort algorithm work?

Comb sort is a comparison-based sorting algorithm that improves on bubble sort by using a larger gap between compared elements.

The comb sort algorithm works by repeatedly sorting pairs of elements that are a certain gap apart, rather than only sorting adjacent pairs like bubble sort. This gap starts as the length of the list and is gradually reduced until it is one, at which point the algorithm behaves like bubble sort. The gap is typically reduced by a shrink factor at each step, often chosen as 1.3.

The algorithm begins by setting the gap to the length of the list. It then compares each pair of elements that are this gap apart, swapping them if they are in the wrong order. Once it has compared all such pairs, it reduces the gap by the shrink factor and repeats the process. This continues until the gap is one, at which point it continues to compare and swap adjacent elements until the list is sorted.

The advantage of this approach is that it can move elements to their correct positions more quickly than bubble sort, as they can "jump" over many positions in a single step. This makes it particularly effective for lists with a lot of disorder. However, like bubble sort, it is still relatively inefficient for large lists compared to more advanced algorithms like quicksort or mergesort.

In terms of complexity, comb sort's average and worst-case time complexity is O(n^2), but with a smaller coefficient than bubble sort. This makes it faster in practice for many inputs. Its best-case time complexity is O(n log n), which occurs for nearly sorted lists. It is an in-place sort, meaning it doesn't require any extra space, and it is not stable, meaning equal elements may not retain their original order.

In summary, comb sort is a simple and intuitive sorting algorithm that improves on bubble sort by comparing and swapping elements that are a certain gap apart, rather than only adjacent elements. This allows it to move elements to their correct positions more quickly, making it more efficient for many inputs.