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Adaptive Heap Sort
In computer science, adaptive heap sort is a comparison-based sorting algorithm of the adaptive sort family. It is a variant of heap sort that performs better when the data contains existing order. Published by Christos Levcopoulos and Ola Petersson in 1992, the algorithm utilizes a new measure of presortedness, ''Osc,'' as the number of oscillations. Instead of putting all the data into the heap as the traditional heap sort did, adaptive heap sort only take part of the data into the heap so that the run time will reduce significantly when the presortedness of the data is high. Heapsort Heap sort is a sorting algorithm that utilizes binary heap data structure. The method treats an array as a complete binary tree and builds up a Max-Heap/Min-Heap to achieve sorting. It usually involves the following four steps. # Build a Max-Heap(Min-Heap): put all the data into the heap so that all nodes are either greater than or equal (less than or equal to for ''Min-Heap'') to each of i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Sort
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. The only requirement is that the operator forms a total preorder over the data, with: # if ''a'' ≤ ''b'' and ''b'' ≤ ''c'' then ''a'' ≤ ''c'' (transitivity) # for all ''a'' and ''b'', ''a'' ≤ ''b'' or ''b'' ≤ ''a'' ( connexity). It is possible that both ''a'' ≤ ''b'' and ''b'' ≤ ''a''; in this case either may come first in the sorted list. In a stable sort, the input order determines the sorted order in this case. A metaphor for thinking about comparison sorts is that someone has a set of unlabelled weights and a balance scale. Their goal is to line up the weights in order by their weight without any information except that obtained by placing two weights on the scale and seeing which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting Algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. For optimum efficiency, the input data should be stored in a data structure which allows random access rather than one that allows only sequential access. History and concepts From the beginning of compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adaptive Sort
A sorting algorithm falls into the adaptive sort family if it takes advantage of existing order in its input. It benefits from the presortedness in the input sequence – or a limited amount of disorder for various definitions of measures of disorder – and sorts faster. Adaptive sorting is usually performed by modifying existing sorting algorithms. Motivation Comparison-based sorting algorithms have traditionally dealt with achieving an optimal bound of '' O''(''n'' log ''n'') when dealing with time complexity. Adaptive sort takes advantage of the existing order of the input to try to achieve better times, so that the time taken by the algorithm to sort is a smoothly growing function of the size of the sequence ''and'' the disorder in the sequence. In other words, the more presorted the input is, the faster it should be sorted. This is an attractive feature for a sorting algorithm because nearly sorted sequences are common in practice. Thus, the performance of existing sor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heapsort
In computer science, heapsort is a comparison-based sorting algorithm. Heapsort can be thought of as an improved selection sort: like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region. Unlike selection sort, heapsort does not waste time with a linear-time scan of the unsorted region; rather, heap sort maintains the unsorted region in a heap data structure to more quickly find the largest element in each step. Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantage of a more favorable worst-case runtime (and as such is used by Introsort as a fallback should it detect that quicksort is becoming degenerate). Heapsort is an in-place algorithm, but it is not a stable sort. Heapsort was invented by J. W. J. Williams in 1964. This was also the birth of the heap, presented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christos Levcopoulos
Christos may refer to: * Jesus of Nazareth * Christ (title), a title for the Jewish Messiah in Christianity * Christos (surname) * Christos (given name) *, a Greek owned, Liberian flagged cargo ship in service 1962-71 See also * Christ (other) * Christo (other) * Christa (other) * Christus (other) {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ola Petersson
Ola may refer to: Places Panama *Olá, a subdistrict in Coclé Province *Olá District Russia *Ola, Russia, an urban settlement in Magadan Oblast *Ola District, an administrative division in Magadan Oblast *Ola (river), a river in Magadan Oblast United States *Ola, Arkansas, a city *Ola, Georgia, an unincorporated community *Ola, Idaho, an unincorporated community * Ola, South Dakota, a census-designated place * Ola, Kaufman County, Texas, an unincorporated community * Casa Linda Estates, Dallas, formerly known as Ola People * Ola (given name), a list of men and women with the name * Ola (surname), a list of men and women with the surname * Ola Svensson (born 1986), also known by the mononym Ola, Swedish singer-songwriter * Ola Nordmann, a national personification of Norwegians * Ola people, another name for the ''Wurla'', an indigenous people of Western Australia Other uses *Ola High School (other), the name of several high schools *Ola Cabs, an Indian online cab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Heap
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort. A binary heap is defined as a binary tree with two additional constraints: *Shape property: a binary heap is a ''complete binary tree''; that is, all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right. *Heap property: the key stored in each node is either greater than or equal to (≥) or less than or equal to (≤) the keys in the node's children, according to some total order. Heaps where the parent key is greater than or equal to (≥) the child keys are called ''max-heaps''; those where it is less than or equal to (≤) are called ''min-heaps''. Efficient (logarithmic time) algorithms are known for the two op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (''L'', ''S'', ''R''), where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is rooted, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measure Of Presortedness
Measure may refer to: * Measurement, the assignment of a number to a characteristic of an object or event Law * Ballot measure, proposed legislation in the United States * Church of England Measure, legislation of the Church of England * Measure of the National Assembly for Wales, primary legislation in Wales * Assembly Measure of the Northern Ireland Assembly (1973) Science and mathematics * Measure (data warehouse), a property on which calculations can be made * Measure (mathematics), a systematic way to assign a number to each suitable subset of that set * Measure (physics), a way to integrate over all possible histories of a system in quantum field theory * Measure (termination), in computer program termination analysis * Measuring coalgebra, a coalgebra constructed from two algebras * Measure (Apple), an iOS augmented reality app Other uses * ''Measure'' (album), by Matt Pond PA, 2000, and its title track * Measure (bartending) or jigger, a bartending tool ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Big O Notation
Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for '' Ordnung'', meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; a famous example of such a difference is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates. Big O notation characterizes functions according to their growth rate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Tree
In computer science, a Cartesian tree is a binary tree derived from a sequence of numbers; it can be uniquely defined from the properties that it is heap-ordered and that a symmetric (in-order) traversal of the tree returns the original sequence. Introduced by in the context of geometric range searching data structures, Cartesian trees have also been used in the definition of the treap and randomized binary search tree data structures for binary search problems. The Cartesian tree for a sequence may be constructed in linear time using a stack-based algorithm for finding all nearest smaller values in a sequence. Definition The Cartesian tree for a sequence of distinct numbers can be uniquely defined by the following properties: #The Cartesian tree for a sequence has one node for each number in the sequence. Each node is associated with a single sequence value. #A symmetric (in-order) traversal of the tree results in the original sequence. That is, the left subtree consists of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting Algorithms
In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. For optimum efficiency, the input data should be stored in a data structure which allows random access rather than one that allows only sequential access. History and concepts From the beginning of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
