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A sorting algorithm is stable if whenever there are two records R and S with the same key, and R appears before S in the original list, then R will always appear before S in the sorted list. When equal elements are indistinguishable, such as with integers, or more generally, any data where the entire element is the key, stability is not an issue.
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 patience sorting algorithm can be applied to process control. Within a series of measurements, the existence of a long increasing subsequence can be used as a trend marker. A 2002 article in SQL Server magazine includes a SQL implementation, in this context, of the patience sorting algorithm for the length of the longest increasing subsequence.
The time for this method is dominated by the sorting step, which requires () time using a comparison sort. [2] [3] Even when integer sorting algorithms may be used, these are generally slower than the linear time that may be achieved using specialized selection algorithms. Nevertheless, the simplicity of this approach makes it attractive ...
Bitonic mergesort is a parallel algorithm for sorting. It is also used as a construction method for building a sorting network.The algorithm was devised by Ken Batcher.The resulting sorting networks consist of ( ()) comparators and have a delay of ( ()), where is the number of items to be sorted. [1]
Although not of practical significance, it remains of theoretical interest in connection with the problem of sorting with a minimum number of comparisons. [3] The same algorithm may have also been independently discovered by Stanisław Trybuła and Czen Ping. [4] An animation of the merge-algorithm sorting an array of randomized values.
Problems of sufficient simplicity are solved directly. For example, to sort a given list of n natural numbers, split it into two lists of about n/2 numbers each, sort each of them in turn, and interleave both results appropriately to obtain the sorted version of the given list (see the picture). This approach is known as the merge sort algorithm.
Introselect works by optimistically starting out with quickselect and only switching to a worst-case linear-time selection algorithm (the Blum-Floyd-Pratt-Rivest-Tarjan median of medians algorithm) if it recurses too many times without making sufficient progress. The switching strategy is the main technical content of the algorithm.