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Insertion sort is widely used for small data sets, while for large data sets an asymptotically efficient sort is used, primarily heapsort, merge sort, or quicksort. Efficient implementations generally use a hybrid algorithm , combining an asymptotically efficient algorithm for the overall sort with insertion sort for small lists at the bottom ...
enabling processing of data in a defined order. The opposite of sorting, rearranging a sequence of items in a random or meaningless order, is called shuffling . For sorting, either a weak order, "should not come after", can be specified, or a strict weak order , "should come before" (specifying one defines also the other, the two are the ...
It combines the speed of insertion sort on small data sets with the speed of merge sort on large data sets. [8] To avoid having to make a series of swaps for each insertion, the input could be stored in a linked list, which allows elements to be spliced into or out of the list in constant time when the position in the list is known. However ...
The data conform to Zipf's law with exponent s to the extent that the plot approximates a linear (more precisely, affine) function with slope −s. For exponent s = 1 , one can also plot the reciprocal of the frequency (mean interword interval) against rank, or the reciprocal of rank against frequency, and compare the result with the line ...
It is still a commonly used algorithm for sorting. Overall, it is slightly faster than merge sort and heapsort for randomized data, particularly on larger distributions. [3] Quicksort is a divide-and-conquer algorithm. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays, according to ...
In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. . According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite direc
A polyphase merge sort is a variation of a bottom-up merge sort that sorts a list using an initial uneven distribution of sub-lists (runs), primarily used for external sorting, and is more efficient than an ordinary merge sort when there are fewer than eight external working files (such as a tape drive or a file on a hard drive).
The ! indicates cells that are header cells. In order for a table to be sortable, the first row(s) of a table need to be entirely made up out of these header cells. You can learn more about the basic table syntax by taking the Introduction to tables for source editing.