Comb sort is a comparison-based sorting algorithm that was devised by Włodzimierz Dobosiewicz in 1980. It is an improvement over bubble sort and is known for its simplicity and relatively efficient performance.
The basic idea behind comb sort is to eliminate small turtles (small elements near the end of the list) by comparing elements that are far apart. The algorithm works by repeatedly swapping adjacent elements with a fixed gap called the "comb" until the list is sorted. The gap is initially set to the size of the input list and is reduced in each iteration by a shrink factor typically greater than 1.
The pseudocode for the comb sort algorithm is as follows -
function combSort(array):
gap := length(array)
shrinkFactor := 1.3
swapped := true
while gap > 1 or swapped:
gap := floor(gap / shrinkFactor)
swapped := false
for i := 0 to length(array) - gap:
if array[i] > array[i + gap]:
swap(array[i], array[i + gap])
swapped := true
In each iteration of the outer loop, the gap is reduced by the shrink factor until it reaches 1. The inner loop compares adjacent elements with a distance of the current gap and swaps them if they are out of order. If any swaps occur in an iteration, the swapped flag is set to true, indicating that the list may not be fully sorted yet.
The shrink factor of 1.3 is commonly used as it has been empirically determined to be an efficient choice for the algorithm. However, other shrink factors can also be used.
Comb sort has an average-case time complexity of O(n^2/2^p), where n is the number of elements in the input list and p is the number of increments used. In the worst-case scenario, when the input list is reverse sorted, the time complexity is O(n^2). However, in practice, comb sort often performs better than bubble sort due to the elimination of small turtles.
It's worth noting that comb sort is not as widely used as some other sorting algorithms such as quicksort or merge sort. These other algorithms generally have better average and worst-case time complexities.
The name "comb sort" comes from the idea that the algorithm works by combing through the list and moving smaller elements towards the beginning, similar to combing through tangled hair.
Comb sort is an in-place sorting algorithm, which means it does not require additional memory to perform the sorting. The elements are rearranged within the original array itself.
The shrink factor, which determines the gap reduction in each iteration, affects the efficiency of the algorithm. A larger shrink factor reduces the number of iterations but increases the number of comparisons and swaps in each iteration. Conversely, a smaller shrink factor reduces the number of comparisons and swaps but requires more iterations. The choice of the shrink factor is a trade-off between these factors.
Comb sort is not stable, meaning that the relative order of elements with equal values may not be preserved after sorting.
The best-case time complexity of comb sort is O(n log n), which occurs when the input list is already sorted. However, the average-case time complexity is still worse than other efficient sorting algorithms like quicksort or merge sort.
Comb sort has some advantages over bubble sort. It eliminates small turtles more quickly, which are small elements that are far from their correct positions. By using larger gaps and gradually reducing them, comb sort moves these small elements closer to their correct positions faster than bubble sort, reducing the number of passes required to sort the list.
The worst-case time complexity of comb sort, O(n^2), can be improved by using a technique called "shaker sort" or "cocktail sort." In this variation, after each pass, the algorithm performs a pass in the opposite direction to move the largest elements towards the end of the list. This additional step improves the performance in certain cases but does not change the average-case time complexity.
While comb sort is not as commonly used as some other sorting algorithms due to its higher time complexity compared to efficient alternatives, it can still be useful for educational purposes or as an alternative sorting option in specific scenarios.