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As a baseline algorithm, selection of the th smallest value in a collection of values can be performed by the following two steps: . Sort the collection; If the output of the sorting algorithm is an array, retrieve its th element; otherwise, scan the sorted sequence to find the th element.
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 ...
Related problems include approximate sorting (sorting a sequence to within a certain amount of the correct order), partial sorting (sorting only the k smallest elements of a list, or finding the k smallest elements, but unordered) and selection (computing the kth smallest element). These can be solved inefficiently by a total sort, but more ...
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
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.
Sorting a set of unlabelled weights by weight using only a balance scale requires a comparison sort algorithm. A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list.
Such a component or property is called a sort key. For example, the items are books, the sort key is the title, subject or author, and the order is alphabetical. A new sort key can be created from two or more sort keys by lexicographical order. The first is then called the primary sort key, the second the secondary sort key, etc.
In computer science, the median of medians is an approximate median selection algorithm, frequently used to supply a good pivot for an exact selection algorithm, most commonly quickselect, that selects the kth smallest element of an initially unsorted array.