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Skew Binomial Heap
In computer science, a skew binomial heap (or skew binomial queue) is a data structure for priority queue operations. It is a variant of the binomial heap that supports constant-time insertion operations in the worst case, rather than amortized time. Motivation Just as binomial heaps are based on the binary number system, skew binary heaps are based on the skew binary number system. Ordinary binomial heaps suffer from worst case logarithmic complexity for insertion, because a carry operation may cascade, analogous to binary addition. Skew binomial heaps are based on the skew binary number system, where the kth digit (zero-indexed) represents 2^-1, instead of 2^k. Digits are either 0 or 1, except the lowest non-zero digit, which may be 2. An advantage of this system is that at most one carry operation is needed. For example, 60 is represented as 11200 in skew binary (31 + 15 + 7 + 7), and adding 1 produces 12000 (31 + 15 + 15). Since the next higher digit is guaranteed not to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heap (data Structure)
In computer science, a heap is a Tree (data structure), tree-based data structure that satisfies the heap property: In a ''max heap'', for any given Node (computer science), node C, if P is the parent node of C, then the ''key'' (the ''value'') of P is greater than or equal to the key of C. In a ''min heap'', the key of P is less than or equal to the key of C. The node at the "top" of the heap (with no parents) is called the ''root'' node. The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root. However, a heap is not a sorted structure; it can be regarded as being partially ordered. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority, or when insertions need to be interspersed wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Binomial Heap
In computer science, a skew binomial heap (or skew binomial queue) is a data structure for priority queue operations. It is a variant of the binomial heap that supports constant-time insertion operations in the worst case, rather than amortized time. Motivation Just as binomial heaps are based on the binary number system, skew binary heaps are based on the skew binary number system. Ordinary binomial heaps suffer from worst case logarithmic complexity for insertion, because a carry operation may cascade, analogous to binary addition. Skew binomial heaps are based on the skew binary number system, where the kth digit (zero-indexed) represents 2^-1, instead of 2^k. Digits are either 0 or 1, except the lowest non-zero digit, which may be 2. An advantage of this system is that at most one carry operation is needed. For example, 60 is represented as 11200 in skew binary (31 + 15 + 7 + 7), and adding 1 produces 12000 (31 + 15 + 15). Since the next higher digit is guaranteed not to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Option Type
Option or Options may refer to: Computing * Option key, a key on Apple computer keyboards * Option type, a polymorphic data type in programming languages * Command-line option, an optional parameter to a command *OPTIONS, an HTTP request method Literature * ''Options'' (novel), a novel by Robert Sheckley * ''Option'' (car magazine), a Japanese car magazine * ''Option'' (music magazine), a defunct American music magazine *"Options", a 1979 story by John Varley Legal rights *Option (aircraft purchasing) * South Tyrol Option Agreement, a forced resettling contract between fascist Italy and Nazi Germany regarding the German-speaking inhabitants of South Tyrol * Option (filmmaking), a contractual agreement between a film producer and a writer, in which the producer obtains the right to buy a screenplay from the writer before a certain date. *Option (finance), an instrument that conveys the right, but not the obligation, to engage in a future transaction (for example, on some u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Tarjan
Robert Endre Tarjan (born April 30, 1948) is an American computer scientist and mathematician. He is the discoverer of several graph theory algorithms, including his strongly connected components algorithm, and co-inventor of both splay trees and Fibonacci heaps. Tarjan is currently the James S. McDonnell Distinguished University Professor of Computer Science at Princeton University. Personal life and education He was born in Pomona, California. His father, George Tarjan (1912–1991), raised in Hungary, was a child psychiatrist, specializing in mental retardation, and ran a state hospital. Robert Tarjan's younger brother James became a chess grandmaster. As a child, Robert Tarjan read a lot of science fiction, and wanted to be an astronomer. He became interested in mathematics after reading Martin Gardner's mathematical games column in Scientific American. He became seriously interested in math in the eighth grade, thanks to a "very stimulating" teacher. While he was in hig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amortized Analysis
In computer science, amortized analysis is a method for analyzing a given algorithm's complexity, or how much of a resource, especially time or memory, it takes to execute. The motivation for amortized analysis is that looking at the worst-case run time can be too pessimistic. Instead, amortized analysis averages the running times of operations in a sequence over that sequence. As a conclusion: "Amortized analysis is a useful tool that complements other techniques such as worst-case and average-case analysis." For a given operation of an algorithm, certain situations (e.g., input parametrizations or data structure contents) may imply a significant cost in resources, whereas other situations may not be as costly. The amortized analysis considers both the costly and less costly operations together over the whole sequence of operations. This may include accounting for different types of input, length of the input, and other factors that affect its performance. History Amortize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the ''left child'' and the ''right child''. That is, it is a ''k''-ary tree with . A recursive definition using set theory is that a binary tree is a triple , where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton (a single–element set) containing the root. From a graph theory perspective, binary trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence, a term which appears in some early programming books before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than 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, but as defined above, a binary tree is always rooted. In ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OCaml
OCaml ( , formerly Objective Caml) is a General-purpose programming language, general-purpose, High-level programming language, high-level, Comparison of multi-paradigm programming languages, multi-paradigm programming language which extends the Caml dialect of ML (programming language), ML with Object-oriented programming, object-oriented features. OCaml was created in 1996 by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez, and others. The OCaml toolchain includes an interactive top-level Interpreter (computing), interpreter, a bytecode compiler, an optimizing native code compiler, a reversible debugger, and a package managerOPAM together with a composable build system for OCamlDune. OCaml was initially developed in the context of automated theorem proving, and is used in static program analysis, static analysis and formal methods software. Beyond these areas, it has found use in systems programming, web development, and specific financial utili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree (data Structure)
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. Whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forest (graph Theory)
In graph theory, a tree is an undirected graph in which any two vertices are connected by path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A directed tree, oriented tree,See .See . polytree,See . or singly connected networkSee . is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees. A rooted tree may be directed, called a directed rooted tree, either making all its edges point away from the root—in which case it is called an arborescence or out-tree—or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Binomial Heap Links
Skew may refer to: In mathematics * Skew lines, neither parallel nor intersecting. * Skew normal distribution, a probability distribution * Skew field or division ring * Skew-Hermitian matrix * Skew lattice * Skew polygon, whose vertices do not lie on a plane * Infinite skew polyhedron * Skew-symmetric graph * Skew-symmetric matrix * Skew tableau, a generalization of Young tableaux * Skewness, a measure of the asymmetry of a probability distribution * Shear mapping In science and technology *Skew, also synclinal or gauche in alkane stereochemistry *Skew ray (optics), an optical path not in a plane of symmetry * Skew arch, not at a right angle In computing * Clock skew * Transitive data skew, an issue of data synchronization In telecommunications * Skew (fax), unstraightness * Skew (antenna) a method to improve the horizontal radiation pattern Other uses * Volatility skew, in finance, a downward-sloping volatility smile * SKEW, the ticker symbol for the CBOE Skew Index See a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carry (arithmetic)
In elementary arithmetic, a carry is a Numerical digit, digit that is transferred from one column of digits to another column of more significant digits. It is part of the standard algorithm to addition, add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written to the same column and the "1" is carried to the left. When used in subtraction the operation is called a borrow. Carrying is emphasized in traditional mathematics, while curricula based on reform mathematics do not emphasize any specific method to find a correct answer. Carrying makes a few appearances in higher mathematics as well. In computing, carrying is an important function of adder (electronics), adder circuits. Manual arithmetic A typical example of carry is in the following pencil-and-paper addition: 1 27 + 59 ---- 86 7 + 9 = 16, and the digit 1 (number), 1 is the carry. The opposite is a borrow, as in − ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerth Stølting Brodal
In computer science, the Brodal queue is a heap/priority queue structure with very low worst case time bounds: O(1) for insertion, find-minimum, meld (merge two queues) and decrease-key and O(\mathrm(n)) for delete-minimum and general deletion. They are the first heap variant to achieve these bounds without resorting to amortization of operational costs. Brodal queues are named after their inventor Gerth Stølting Brodal.Gerth Stølting Brodal (1996). Worst-case efficient priority queues. Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pp. 52–58 While having better asymptotic bounds than other priority queue structures, they are, in the words of Brodal himself, "quite complicated" and " otapplicable in practice." Brodal and Okasaki describe a persistent ( purely functional) version of Brodal queues.Gerth Stølting Brodal and Chris Okasaki (1996)Optimal purely functional priority queues Journal of Functional Programming. Summary of running times Gerth Stølting Brodal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
