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A bidirectional variant of selection sort (called double selection sort or sometimes cocktail sort due to its similarity to cocktail shaker sort) finds both the minimum and maximum values in the list in every pass. This requires three comparisons per two items (a pair of elements is compared, then the greater is compared to the maximum and the ...
The earliest description of the bubble sort algorithm was in a 1956 paper by mathematician and actuary Edward Harry Friend, [4] Sorting on electronic computer systems, [5] published in the third issue of the third volume of the Journal of the Association for Computing Machinery (ACM), as a "Sorting exchange algorithm".
As another example, many sorting algorithms rearrange arrays into sorted order in-place, including: bubble sort, comb sort, selection sort, insertion sort, heapsort, and Shell sort. These algorithms require only a few pointers, so their space complexity is O(log n). [1] Quicksort operates in-place on the data to be sorted.
General method: insertion, exchange, selection, merging, etc. Exchange sorts include bubble sort and quicksort. Selection sorts include cycle sort and heapsort. Whether the algorithm is serial or parallel. The remainder of this discussion almost exclusively concentrates on serial algorithms and assumes serial operation.
The next pass, 3-sorting, performs insertion sort on the three subarrays (a 1, a 4, a 7, a 10), (a 2, a 5, a 8, a 11), (a 3, a 6, a 9, a 12). The last pass, 1-sorting, is an ordinary insertion sort of the entire array (a 1,..., a 12). As the example illustrates, the subarrays that Shellsort operates on are initially short; later they are longer ...
A further relaxation requiring only a list of the k smallest elements, but without requiring that these be ordered, makes the problem equivalent to partition-based selection; the original partial sorting problem can be solved by such a selection algorithm to obtain an array where the first k elements are the k smallest, and sorting these, at a total cost of O(n + k log k) operations.
We can easily construct a network of any size recursively using the principles of insertion and selection. Assuming we have a sorting network of size n, we can construct a network of size n + 1 by "inserting" an additional number into the already sorted subnet (using the principle underlying insertion sort).
For example, bubble sort may be faster than merge sort when only a few items are to be sorted; however either implementation is likely to meet performance requirements for a small list. Typically, programmers are interested in algorithms that scale efficiently to large input sizes, and merge sort is preferred over bubble sort for lists of ...