The average speed of Comb sort is comparable to quicksort

The distance and direction that elements must move during the sort determine bubble sort's performance because elements move in different directions at different speeds. An element that must move toward the end of the list can move quickly because it can take part in successive swaps. For example, the largest element in the list will win every swap, so it moves to its sorted position on the first pass even if it starts near the beginning. On the other hand, an element that must move toward the beginning of the list cannot move faster than one step per pass, so elements move toward the beginning very slowly. If the smallest element is at the end of the list, it will take n-1 passes to move it to the beginning. This has led to these types of elements being named rabbits and turtles, respectively, after the characters in Aesop's fable of The Tortoise and the Hare.

Various efforts have been made to eliminate turtles to improve upon the speed of bubble sort. Comb sort compares elements separated by large gaps, and can move turtles extremely quickly before proceeding to smaller and smaller gaps to smooth out the list. Its average speed is comparable to faster algorithms like quicksort.

Comb sort is a relatively simple sorting algorithm originally designed by Włodzimierz Dobosiewicz and Artur Borowy in 1980, later rediscovered (and given the name "Combsort") by Stephen Lacey and Richard Box in 1991. Comb sort improves on bubble sort in the same way that Shellsort improves on insertion sort.

def combsort(data):
    gap_float = length = len(data)
    is_sorted = False
    while not is_sorted:
        gap_float /= 1.3
        gap = int(gap_float)
        if gap <= 1:
            is_sorted = True
            gap = 1
        for i in range(length - gap):
            sm = gap + i
            if data[i] > data[sm]:
                data[i], data[sm] = data[sm], data[i]
                is_sorted = False

x = [6, 5, 3, 1, 8, 7, 2, 4]
combsort(x)
print(x)

Cocktail sort is a bi-directional bubble sort that goes from beginning to end, and then reverses itself, going end to beginning. It can move turtles fairly well, but it retains O(n²) worst-case complexity.

Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order. The pass through the list is repeated until the list is sorted. The algorithm, which is a comparison sort, is named for the way smaller or larger elements "bubble" to the top of the list.

Starting from the beginning of the list, compare every adjacent pair, swap their position if they are not in the right order (the latter one is smaller than the former one). After each iteration, one less element (the last one) is needed to be compared until there are no more elements left to be compared.

This simple algorithm performs poorly in real world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as C, C++, and Python.

The only significant advantage that bubble sort has over most other algorithms, even quicksort, but not insertion sort, is that the ability to detect that the list is sorted efficiently is built into the algorithm. When the list is already sorted (best-case), the complexity of bubble sort is only O(n). By contrast, most other algorithms, even those with better average-case complexity, perform their entire sorting process on the set and thus are more complex.

However, not only does insertion sort share this advantage, but it also performs better on a list that is substantially sorted (having a small number of inversions). Additionally, if this behavior is desired, it can be trivially added to any other algorithm by checking the list before the algorithm runs.

Bubble sort should be avoided in the case of large collections. It will not be efficient in the case of a reverse-ordered collection.

Bubble sort also interacts poorly with modern CPU hardware. It produces at least twice as many writes as insertion sort, twice as many cache misses, and asymptotically more branch mispredictions. Experiments by Astrachan sorting strings in Java show bubble sort to be roughly one-fifth as fast as an insertion sort and 70% as fast as a selection sort.

Donald Knuth, in The Art of Computer Programming, concluded that "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", some of which he then discusses.

六级/考研单词: bubble, swap, turtle, respective, fable, eliminate, comb, insert, cocktail, reverse, adjacent, latter, merge, detect, thereby, invert, desire, trivial, interact, hardware, compute