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Quickselect
In computer science, quickselect is a selection algorithm to find the ''k''th smallest element in an unordered list, also known as the ''k''th order statistic. Like the related quicksort sorting algorithm, it was developed by Tony Hoare, and thus is also known as Hoare's selection algorithm. Like quicksort, it is efficient in practice and has good average-case performance, but has poor worst-case performance. Quickselect and its variants are the selection algorithms most often used in efficient real-world implementations. Quickselect uses the same overall approach as quicksort, choosing one element as a pivot and partitioning the data in two based on the pivot, accordingly as less than or greater than the pivot. However, instead of recursing into both sides, as in quicksort, quickselect only recurses into one side – the side with the element it is searching for. This reduces the average complexity from O(n\log n) to O(n), with a worst case of O(n^2). As with quicksort, quic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median Of Medians
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 ''k''th smallest element of an initially unsorted array. Median of medians finds an approximate median in linear time. Using this approximate median as an improved pivot, the worst-case complexity of quickselect reduces from quadratic to ''linear'', which is also the asymptotically optimal worst-case complexity of any selection algorithm. In other words, the median of medians is an approximate median-selection algorithm that helps building an asymptotically optimal, exact general selection algorithm (especially in the sense of worst-case complexity), by producing good pivot elements. Median of medians can also be used as a pivot strategy in quicksort, yielding an optimal algorithm, with worst-case complexity O(n\log n). Although this approach optimizes the asymptotic worst-cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selection Algorithm
In computer science, a selection algorithm is an algorithm for finding the kth smallest value in a collection of ordered values, such as numbers. The value that it finds is called the order statistic. Selection includes as special cases the problems of finding the minimum, median, and maximum element in the collection. Selection algorithms include quickselect, and the median of medians algorithm. When applied to a collection of n values, these algorithms take linear time, O(n) as expressed using big O notation. For data that is already structured, faster algorithms may be possible; as an extreme case, selection in an already-sorted array takes Problem statement An algorithm for the selection problem takes as input a collection of values, and a It outputs the smallest of these values, or, in some versions of the problem, a collection of the k smallest values. For this to be well-defined, it should be possible to sort the values into an order from smallest to largest; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Introselect
In computer science, introselect (short for "introspective selection") is a selection algorithm that is a hybrid of quickselect and median of medians which has fast average performance and optimal worst-case performance. Introselect is related to the introsort sorting algorithm: these are analogous refinements of the basic quickselect and quicksort algorithms, in that they both start with the quick algorithm, which has good average performance and low overhead, but fall back to an optimal worst-case algorithm (with higher overhead) if the quick algorithm does not progress rapidly enough. Both algorithms were introduced by David Musser in , with the purpose of providing generic algorithms for the C++ Standard Library that have both fast average performance and optimal worst-case performance, thus allowing the performance requirements to be tightened. However, in most C++ Standard Library implementations, a different "introselect" algorithm is used, which combines quickselect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quicksort
Quicksort is an efficient, general-purpose sorting algorithm. Quicksort was developed by British computer scientist Tony Hoare in 1959 and published in 1961. 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. 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. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory to perform the sorting. Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. It is a comparison-based sort since elements ''a'' and ''b'' are only swapped in ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floyd–Rivest Algorithm
In computer science, the Floyd-Rivest algorithm is a selection algorithm developed by Robert W. Floyd and Ronald L. Rivest that has an optimal expected number of comparisons within lower-order terms. It is functionally equivalent to quickselect, but runs faster in practice on average. It has an expected running time of and an expected number of comparisons of . The algorithm was originally presented in a Stanford University technical report containing two papers, where it was referred to as SELECT and paired with PICK, or median of medians. It was subsequently published in Communications of the ACM, Volume 18: Issue 3. Algorithm 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 ''k''th smallest element from the appropriate set. The general steps are: # Select a small random sample ''S'' from the list ''L''. # From ''S'', recur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quicksort
Quicksort is an efficient, general-purpose sorting algorithm. Quicksort was developed by British computer scientist Tony Hoare in 1959 and published in 1961. 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. 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. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory to perform the sorting. Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. It is a comparison-based sort since elements ''a'' and ''b'' are only swapped in ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Musser
David "Dave" Musser is a professor emeritus of computer science at the Rensselaer Polytechnic Institute in Troy, New York, United States. He is known for his work in generic programming, particularly as applied to C++, and his collaboration with Alexander Stepanov. Their work together includes coining the term "generic programming" in , and led to the creation of the C++ Standard Template Library (STL). In , he developed the sorting algorithm called introsort (also known as introspective sort), and the related selection algorithm called introselect In computer science, introselect (short for "introspective selection") is a selection algorithm that is a hybrid of quickselect and median of medians which has fast average performance and optimal worst-case performance. Introselect is related ..., to provide algorithms that are both efficient and have optimal worst-case performance, for use in the STL. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Eppstein
David Arthur Eppstein (born 1963) is an American computer scientist and mathematician. He is a distinguished professor of computer science at the University of California, Irvine. He is known for his work in computational geometry, graph algorithms, and recreational mathematics. In 2011, he was named an ACM Fellow. Biography Born in Windsor, England, in 1963, Eppstein received a B.S. in mathematics from Stanford University in 1984, and later an M.S. (1985) and Ph.D. (1989) in computer science from Columbia University, after which he took a postdoctoral position at Xerox's Palo Alto Research Center. He joined the UC Irvine faculty in 1990, and was co-chair of the Computer Science Department there from 2002 to 2005. In 2014, he was named a Chancellor's Professor. In October 2017, Eppstein was one of 396 members elected as fellows of the American Association for the Advancement of Science. Eppstein is an amateur digital photographer. He is also a Wikipedia editor and admi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
