Bubble Sort Essay Example

of O(n log n). Even other? (n2) sorting algorithms, like insertion sort, tend to perform better than bubble sort. Therefore, when n is large, bubble sort is not a practical sorting algorithm.

The primary advantage of bubble sort compared to other algorithms, including quicksort but excluding insertion sort, is its efficiency in detecting a sorted list. Bubble sort has a best-case performance of O(n) when sorting an already-sorted list. In contrast, most other algorithms, even ones with better average-case complexity, perform the entire sorting process and are therefore more complex. However, not only does insertion sort also have this detection mechanism, but it also performs better on a mostly sorted list with few inversions.

Rabbits and turtles are terms used to describe the behavior of elements in the bubble sort algorithm. The positions of these elements greatly impact the performance of the sort. While larger elements are easily swapped at the beginning of the list, smaller elements towards the end move very slowly to the front. To eliminate this issue, attempts have been made to improve the speed of the bubble sort by eliminating turtles. The cocktail sort is one such method that achieves this goal, but it still has a worst-case complexity of O(n2).

Comb sort is a sorting algorithm that compares elements separated by large gaps and gradually reduces the gap size to sort the list efficiently. Its average speed is similar to faster algorithms such as quicksort. Here is a step-by-step example of sorting the array "5 1 4 2 8" using the bubble sort algorithm. During each step, the elements being compared are shown in bold.

Three passes are required in total. In

the first pass, the algorithm compares and swaps elements to sort them. The second pass does the same thing. Finally, the algorithm needs one more pass without swapping to determine if the array is fully sorted.

The text describes the implementation of the bubble sort algorithm using pseudocode. The algorithm repeatedly compares and swaps adjacent elements until no more swaps are made or a certain condition is met. After each pass, the largest element is moved to its correct position. To optimize the algorithm, it is observed that on each pass, the n-th largest element is already in its final position. The provided code uses nested loops to compare and swap elements, with the outer loop tracking passes and the inner loop skipping sorted elements. Furthermore, it mentions that after each pass, all elements following the last swap are already sorted and do not need further checking. This optimization greatly reduces comparisons and adds minimal complexity.The presented approach demonstrates bubble sort using . The pseudocode for bubble sort is as follows:

procedure bubble sort( A: list of sortable items )
n = length(A)
repeat
swapped = false
for i = 1 to n-1 inclusive do:
if A[i-1] > A[i] then
swap(A[i-1], A[i])
swapped = true
end if
end for
n = n

- 1 until not swapped
end procedure

Additionally, a similar modification called cocktail shaker sort is mentioned. This variation continuously compares and swaps adjacent items to improve performance while maintaining the objective of bubble sort. The algorithm operates by traversing the list repeatedly and exchanging elements until they are sorted correctly. Notably, the largest element is given priority in sorting, which may cause smaller elements to take longer to reach their correct positions.

Although bubble sort is a simple sorting algorithm that is easy to understand and implement, its efficiency decreases significantly for larger lists due to its O(n2) complexity. In comparison to other O(n2) algorithms, such as insertion sort, bubble sort is usually less efficient. Nevertheless, because of its simplicity, bubble sort is often used as an introduction to algorithms and sorting algorithms for computer science students. However, some researchers like Owen Astrachan have actively criticized bubble sort and its continued use in computer science education, even recommending that it be eliminated from the curriculum.

The Jargon File describes Bogo sort as "the archetypical perversely awful algorithm" and labels bubble sort as "the generic bad algorithm". In his book, The Art of Computer Programming, Donald Knuth concludes that the bubble sort has no real advantages, aside from its catchy name and the fact that it presents interesting theoretical problems, which he discusses. Although bubble sort and insertion sort have equivalent worst-case running times, they differ greatly in the number of required swaps. Experimental findings, such as those from Astrachan, demonstrate that insertion sort performs considerably better even on random lists. Therefore, many modern algorithm textbooks prefer insertion sort over bubble sort. Additionally, bubble sort does not

interact well with modern CPU hardware.

Bubble sort requires twice as many writes, twice as many cache misses, and more branch mispredictions compared to insertion sort. Experiments in sorting strings in Java have shown that bubble sort is approximately 5 times slower than insertion sort and 40% slower than selection sort. In computer graphics, bubble sort is popular due to its ability to detect and fix small errors in almost-sorted arrays with linear complexity (2n). An example of its usage is in a polygon filling algorithm, where bounding lines are sorted based on their x coordinate at a specific scan line. The order of the lines changes (swapped) only at intersections of two lines, resulting in efficient sorting.