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Quicksort is a type of divide-and-conquer algorithm for sorting an array, based on a partitioning routine; the details of this partitioning can vary somewhat, so that quicksort is really a family of closely related algorithms. Applied to a range of at least two elements, partitioning produces a division into two consecutive non empty sub-ranges ...
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.
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]
The solution to this problem is of interest for designing sorting algorithms; in particular, variants of the quicksort algorithm that must be robust to repeated elements may use a three-way partitioning function that groups items less than a given key (red), equal to the key (white) and greater than the key (blue). Several solutions exist that ...
Identifying the in-place algorithms with L has some interesting implications; for example, it means that there is a (rather complex) in-place algorithm to determine whether a path exists between two nodes in an undirected graph, [3] a problem that requires O(n) extra space using typical algorithms such as depth-first search (a visited bit for ...
Multi-key quicksort, also known as three-way radix quicksort, [1] is an algorithm for sorting strings.This hybrid of quicksort and radix sort was originally suggested by P. Shackleton, as reported in one of C.A.R. Hoare's seminal papers on quicksort; [2]: 14 its modern incarnation was developed by Jon Bentley and Robert Sedgewick in the mid-1990s. [3]
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.
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.