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Selection algorithms include quickselect, and the median of medians algorithm. When applied to a collection of n {\displaystyle n} values, these algorithms take linear time , O ( n ) {\displaystyle O(n)} as expressed using big O notation .
In computer science, selection sort is an in-place comparison sorting algorithm.It has a O(n 2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort.
In computer science, quickselect is a selection algorithm to find the kth smallest element in an unordered list, also known as the kth order statistic.Like the related quicksort sorting algorithm, it was developed by Tony Hoare, and thus is also known as Hoare's selection algorithm. [1]
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. Median of medians finds an approximate median in linear time.
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.
More abstractly, given an O(n) selection algorithm, one can use it to find the ideal pivot (the median) at every step of quicksort and thus produce a sorting algorithm with O(n log n) running time. Practical implementations of this variant are considerably slower on average, but they are of theoretical interest because they show an optimal ...
For typical serial sorting algorithms, good behavior is O(n log n), with parallel sort in O(log 2 n), and bad behavior is O(n 2). Ideal behavior for a serial sort is O(n), but this is not possible in the average case. Optimal parallel sorting is O(log n). Swaps for "in-place" algorithms. Memory usage (and use of other computer resources).
The resulting algorithm is called partial quicksort and requires an expected time of only O(n + k log k), and is quite efficient in practice, especially if a selection sort is used as a base case when k becomes small relative to n. However, the worst-case time complexity is still very bad, in the case of a bad pivot selection.