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Disjoint-set Data Structure
In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of Disjoint sets, disjoint (non-overlapping) Set (mathematics), sets. Equivalently, it stores a partition of a set into disjoint subsets. It provides operations for adding new sets, merging sets (replacing them by their Union (set theory), union), and finding a representative member of a set. The last operation makes it possible to find out efficiently if any two elements are in the same or different sets. While there are several ways of implementing disjoint-set data structures, in practice they are often identified with a particular implementation called a disjoint-set forest. This is a specialized type of Forest (graph theory), forest which performs unions and finds in near-constant Amortized analysis, amortized time. To perform a sequence of addition, union, or find operations on a disjoint-set forest with node ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Bernard A
Bernard ('' Bernhard'') is a French and West Germanic masculine given name. It is also a surname. The name is attested from at least the 9th century. West Germanic ''Bernhard'' is composed from the two elements ''bern'' "bear" and ''hard'' "brave, hardy". Its native Old English reflex was ''Beornheard'', which was replaced by the French form ''Bernard'' that was brought to England after the Norman Conquest. The name ''Bernhard'' was notably popular among Old Frisian speakers. Its wider use was popularized due to Saint Bernhard of Clairvaux (canonized in 1174). Bernard is the second most common surname in France. Geographical distribution As of 2014, 42.2% of all known bearers of the surname ''Bernard'' were residents of France (frequency 1:392), 12.5% of the United States (1:7,203), 7.0% of Haiti (1:382), 6.6% of Tanzania (1:1,961), 4.8% of Canada (1:1,896), 3.6% of Nigeria (1:12,221), 2.7% of Burundi (1:894), 1.9% of Belgium (1:1,500), 1.6% of Rwanda (1:1,745), 1.2% of Germany ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Minimum Spanning Tree
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible. More generally, any edge-weighted undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of the minimum spanning trees for its connected components. There are many use cases for minimum spanning trees. One example is a telecommunications company trying to lay cable in a new neighborhood. If it is constrained to bury the cable only along certain paths (e.g. roads), then there would be a graph containing the points (e.g. houses) connected by those paths. Some of the paths might be more expensive, because they are longer, or require the cable to be buried deeper; these paths would be represented by edges with larger weights. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Dynamic Array
In computer science, a dynamic array, growable array, resizable array, dynamic table, mutable array, or array list is a random access, variable-size list data structure that allows elements to be added or removed. It is supplied with standard libraries in many modern mainstream programming languages. Dynamic arrays overcome a limit of static arrays, which have a fixed capacity that needs to be specified at allocation. A dynamic array is not the same thing as a dynamically allocated array or variable-length array, either of which is an array whose size is fixed when the array is allocated, although a dynamic array may use such a fixed-size array as a back end.See, for example, thsource code of java.util.ArrayList class from OpenJDK 6 Bounded-size dynamic arrays and capacity A simple dynamic array can be constructed by allocating an array of fixed-size, typically larger than the number of elements immediately required. The elements of the dynamic array are stored contiguously a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Parent Pointer Tree
In computer science, an in-tree or parent pointer tree is an -ary tree data structure in which each node has a pointer to its parent node, but no pointers to child nodes. When used to implement a set of stacks, the structure is called a spaghetti stack, cactus stack or sahuaro stack (after the sahuaro, a kind of cactus). Parent pointer trees are also used as disjoint-set data structures. The structure can be regarded as a set of singly linked lists that share part of their structure, in particular, their tails. From any node, one can traverse to ancestors of the node, but not to any other node. Use in compilers A compiler for a language such as C creates a spaghetti stack as it opens and closes symbol tables representing block scopes. When a new block scope is opened, a symbol table is pushed onto a stack. When the closing curly brace is encountered, the scope is closed and the symbol table is popped. But that symbol table is remembered, rather than destroyed. And of course it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Proof Assistant
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. System comparison * ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. * Coq – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification. * HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems the logical core is a library of their programming langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Persistent Data Structure
In computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjans' 1986 article. A data structure is partially persistent if all versions can be accessed but only the newest version can be modified. The data structure is fully persistent if every version can be both accessed and modified. If there is also a meld or merge operation that can create a new version from two previous versions, the data structure is called confluently persistent. Structures that are not persistent are called ''ephemeral''. These types of data structures are particularly common in logical and functional programming, as languages in those paradigms discourage (or fully forbi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Michael Saks (mathematician)
Michael Ezra Saks is an American mathematician. He is currently the Department Chair of the Mathematics Department at Rutgers University (2017–) and from 2006 until 2010 was director of the Mathematics Graduate Program at Rutgers University. Saks received his Ph.D. from the Massachusetts Institute of Technology in 1980 after completing his dissertation titled ''Duality Properties of Finite Set Systems'' under his advisor Daniel J. Kleitman. A list of his publications and collaborations may be found at DBLP. In 2016 he became a Fellow of the Association for Computing Machinery. Research Saks research in computational complexity theory, combinatorics, and graph theory has contributed to the study of lower bounds in order theory, randomized computation, and space–time tradeoff. In 1984, Saks and Jeff Kahn showed that there exist a tight information-theoretical lower bound for sorting under partially ordered information up to a multiplicative constant. Ithe first super-linear lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Michael Fredman
Michael Lawrence Fredman is an emeritus professor at the Computer Science Department at Rutgers University, United States. He earned his Ph.D. degree from Stanford University in 1972 under the supervision of Donald Knuth. He was a member of the mathematics department at the Massachusetts Institute of Technology from 1974 to 1976. and of the Computer Science and Engineering department at the University of California, San Diego until 1992. . Among his contributions to computer science are the development of the Fibonacci heap in a joint work with , the |
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Ackermann Function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive. After Ackermann's publication of his function (which had three non-negative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of numerous variants of the original function. One common version, the two-argument Ackermann–Péter function is defined as follows for nonnegative integers ''m'' and ''n'': : \begin \operatorname(0, n) & = & n + 1 \\ \operatorname(m+1, 0) & = & \operatorname(m, 1) \\ \operatorname(m+1, n+1) & = & \operatorname(m, \operatorname(m+1, n)) \end Its value grows rapidly, even for small inputs. For example, is an integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Robert Tarjan
Robert Endre Tarjan (born April 30, 1948) is an American computer scientist and mathematician. He is the discoverer of several graph algorithms, including Tarjan's off-line lowest common ancestors 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, and the Chief Scientist at Intertrust Technologies Corporation. Early life and education He was born in Pomona, California. His father, raised in Hungary, was a child psychiatrist, specializing in mental retardation, and ran a state hospital. As a child, 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 high school, Tarjan got a job, where he work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Jeffrey Ullman
Jeffrey David Ullman (born November 22, 1942) is an American computer scientist and the Stanford W. Ascherman Professor of Engineering, Emeritus, at Stanford University. His textbooks on compilers (various editions are popularly known as the dragon book), theory of computation (also known as the Cinderella book), data structures, and databases are regarded as standards in their fields. He and his long-time collaborator Alfred Aho are the recipients of the 2020 Turing Award, generally recognized as the highest distinction in computer science. Career Ullman received a Bachelor of Science degree in engineering mathematics from Columbia University in 1963 and his PhD in electrical engineering from Princeton University in 1966. He then worked for three years at Bell Labs. In 1969, he returned to Princeton as an associate professor, and was promoted to full professor in 1974. Ullman moved to Stanford University in 1979, and served as the department chair from 1990 to 1994. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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John Hopcroft
John Edward Hopcroft (born October 7, 1939) is an American theoretical computer scientist. His textbooks on theory of computation (also known as the Cinderella book) and data structures are regarded as standards in their fields. He is the IBM Professor of Engineering and Applied Mathematics in Computer Science at Cornell University, Co-Director of the Center on Frontiers of Computing Studies at Peking University, and the Director of the John Hopcroft Center for Computer Science at Shanghai Jiao Tong University. Education He received his bachelor's degree from Seattle University in 1961. He received his master's degree and Ph.D. from Stanford University in 1962 and 1964, respectively. He worked for three years at Princeton University and since then has been at Cornell University. Hopcroft is the grandson of Jacob Nist, founder of the Seattle-Tacoma Box Company. Career In addition to his research work, he is well known for his books on algorithms and formal languages coautho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |