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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 ]
If one instead groups the other way, say dividing the element list into 5 lists, computing the median of each, and then computing the median of these – i.e., grouping by a constant fraction, not a constant number – one does not as clearly reduce the problem, since it requires computing 5 medians, each in a list of elements, and then ...
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
Unlike quickselect, this algorithm is deterministic, not randomized. [2] [4] [5] It was the first linear-time deterministic selection algorithm known, [5] and is commonly taught in undergraduate algorithms classes as an example of a divide and conquer that does not divide into two equal subproblems.
Conversely, some sorting algorithms can be derived by repeated application of a selection algorithm; quicksort and quickselect can be seen as the same pivoting move, differing only in whether one recurses on both sides (quicksort, divide-and-conquer) or one side (quickselect, decrease-and-conquer).
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 whether they are less than or greater than the pivot. For this reason, it is sometimes called partition-exchange sort. [4] The sub-arrays are then sorted recursively.
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The Floyd-Rivest algorithm is a divide and conquer algorithm, sharing many similarities with quickselect. It uses sampling to help partition the list into three sets. It then recursively selects the kth smallest element from the appropriate set. The general steps are: Select a small random sample S from the list L.