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Pairing Heap
A pairing heap is a type of heap data structure with relatively simple implementation and excellent practical amortized performance, introduced by Michael Fredman, Robert Sedgewick, Daniel Sleator, and Robert Tarjan in 1986. Pairing heaps are heap-ordered multiway tree structures, and can be considered simplified Fibonacci heaps. They are considered a "robust choice" for implementing such algorithms as Prim's MST algorithm, and support the following operations (assuming a min-heap): * ''find-min'': simply return the top element of the heap. * ''meld'': compare the two root elements, the smaller remains the root of the result, the larger element and its subtree is appended as a child of this root. * ''insert'': create a new heap for the inserted element and ''meld'' into the original heap. * ''decrease-key'' (optional): remove the subtree rooted at the key to be decreased, replace the key with a smaller key, then ''meld'' the result back into the heap. * ''delete-min'': remove ... [...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] |
Splay Tree
A splay tree is a binary search tree with the additional property that recently accessed elements are quick to access again. Like self-balancing binary search trees, a splay tree performs basic operations such as insertion, look-up and removal in big O notation, O(log ''n'') amortized analysis, amortized time. For random access patterns drawn from a non-uniform random distribution, their amortized time can be faster than logarithmic, proportional to the Entropy (information theory), entropy of the access pattern. For many patterns of non-random operations, also, splay trees can take better than logarithmic time, without requiring advance knowledge of the pattern. According to the unproven dynamic optimality conjecture, their performance on all access patterns is within a constant factor of the best possible performance that could be achieved by any other self-adjusting binary search tree, even one selected to fit that pattern. The splay tree was invented by Daniel Sleator and Rob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sartaj Sahni
Professor Sartaj Kumar Sahni (born July 22, 1949, in Pune, India) is a computer scientist based in the United States, and is one of the pioneers in the field of data structures. He is a distinguished professor in the Department of Computer and Information Science and Engineering at the University of Florida. Education Sahni received his BTech degree in electrical engineering from the Indian Institute of Technology Kanpur. Following this, he undertook his graduate studies at Cornell University in the USA, earning a PhD degree in 1973, under the supervision of Ellis Horowitz. Research and publications Sahni has published over 280 research papers and written 15 textbooks. His research publications are on the design and analysis of efficient algorithms, data structures, parallel computing, interconnection networks, design automation, and medical algorithms. With his advisor Ellis Horowitz, Sahni wrote two widely used textbooks, ''Fundamentals of Computer Algorithms'' and ''Fundamen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a General-purpose programming language, general-purpose, static typing, statically typed, purely functional programming, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research, and industrial applications, Haskell pioneered several programming language #Features, features such as type classes, which enable type safety, type-safe operator overloading, and Monad (functional programming), monadic input/output (IO). It is named after logician Haskell Curry. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). Haskell's Semantics (computer science), semantics are historically based on those of the Miranda (programming language), Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Left-child Right-sibling Binary Tree
Every multi-way or k-ary tree structure studied in computer science admits a representation as a binary tree, which goes by various names including child-sibling representation, left-child, right-sibling binary tree, doubly chained tree or filial-heir chain. In a binary tree that represents a multi-way tree , each node corresponds to a node in and has two pointers: one to the node's first child, and one to its next sibling in . The children of a node thus form a singly-linked list. To find a node 's 'th child, one needs to traverse this list: procedure kth-child(n, k): child ← n.child while k ≠ 0 and child ≠ nil: child ← child.next-sibling k ← k − 1 return child ''// may return nil'' The process of converting from a k-ary tree to an LC-RS binary tree is sometimes called the '' Knuth transform''. To form a binary tree from an arbitrary k-ary tree by this method, the root of the original tree is made the root of the binary tree. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubly-linked List
In computer science, a doubly linked list is a linked data structure that consists of a set of sequentially linked records called nodes. Each node contains three fields: two link fields (references to the previous and to the next node in the sequence of nodes) and one data field. The beginning and ending nodes' previous and next links, respectively, point to some kind of terminator, typically a sentinel node or null, to facilitate traversal of the list. If there is only one sentinel node, then the list is circularly linked via the sentinel node. It can be conceptualized as two singly linked lists formed from the same data items, but in opposite sequential orders. The two node links allow traversal of the list in either direction. While adding or removing a node in a doubly linked list requires changing more links than the same operations on a singly linked list, the operations are simpler and potentially more efficient (for nodes other than first nodes) because there is no nee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RAM Machine
In computer science, random-access machine (RAM or RA-machine) is a model of computation that describes an abstract machine in the general class of register machines. The RA-machine is very similar to the counter machine but with the added capability of 'indirect addressing' of its registers. The 'registers' are intuitively equivalent to Random-access memory, main memory of a common computer, except for the additional ability of registers to store natural numbers of any size. Like the counter machine, the RA-machine contains the execution instructions in the finite-state portion of the machine (the so-called Harvard architecture). The RA-machine's equivalent of the universal Turing machinewith its Computer program, program in the registers as well as its datais called the random-access stored-program machine or RASP-machine. It is an example of the so-called von Neumann architecture and is closest to the common notion of a computer. Together with the Turing machine and counter-m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D-ary Heap
The -ary heap or -heap is a priority queue data structure, a generalization of the binary heap in which the nodes have children instead of 2. Thus, a binary heap is a 2-heap, and a ternary heap is a 3-heap. According to Tarjan and Jensen et al., -ary heaps were invented by Donald B. Johnson in 1975.. This data structure allows decrease priority operations to be performed more quickly than binary heaps, at the expense of slower delete minimum operations. This tradeoff leads to better running times for algorithms such as Dijkstra's algorithm in which decrease priority operations are more common than delete min operations. Additionally, -ary heaps have better memory cache behavior than binary heaps, allowing them to run more quickly in practice despite having a theoretically larger worst-case running time. Like binary heaps, -ary heaps are an in-place data structure that use no additional storage beyond that needed to store the array of items in the heap.. Data structure The -ary h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symposium On Discrete Algorithms
The Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) is an academic conference in the fields of algorithm design and discrete mathematics. It is considered to be one of the top conferences for research in algorithms. SODA has been organized annually since 1990, typically in January. SODA is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT) and the SIAM Activity Group on Discrete Mathematics, and in format is more similar to a theoretical computer science Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Associati ... conference than to a mathematics conference.. Distributed by Howard Karloff with thcall for papers for SODA 1998 History The first Symposium on Discrete Algorithms was held in 1990 at San Francisco, organized by David Johnson. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prim's Algorithm
In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a Weighted graph, weighted undirected graph. This means it finds a subset of the edge (graph theory), edges that forms a Tree (graph theory), tree that includes every Vertex (graph theory), vertex, where the total weight of all the graph theory, edges in the tree is minimized. The algorithm operates by building this tree one vertex at a time, from an arbitrary starting vertex, at each step adding the cheapest possible connection from the tree to another vertex. The algorithm was developed in 1930 by Czech people, Czech mathematician Vojtěch Jarník and later rediscovered and republished by computer scientists Robert C. Prim in 1957 and Edsger W. Dijkstra in 1959. Therefore, it is also sometimes called the Jarník's algorithm, Prim–Jarník algorithm, Prim–Dijkstra algorithm. or the DJP algorithm.. Other well-known algorithms for this problem include Kruskal's algorithm and Borů ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization and storage format that is usually chosen for Efficiency, efficient Data access, access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the Function (computer programming), functions or Operator (computer programming), operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, Relational database, relational databases commonly use B-tree indexes for data retrieval, while compiler Implementation, implementations usually use hash tables to look up Identifier (computer languages), identifiers. Data s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Heap
In computer science, a Fibonacci heap is a data structure for priority queue operations, consisting of a collection of heap-ordered trees. It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap. Michael L. Fredman and Robert E. Tarjan developed Fibonacci heaps in 1984 and published them in a scientific journal in 1987. Fibonacci heaps are named after the Fibonacci numbers, which are used in their running time analysis. The amortized times of all operations on Fibonacci heaps is constant, except ''delete-min''. Deleting an element (most often used in the special case of deleting the minimum element) works in O(\log n) amortized time, where n is the size of the heap. This means that starting from an empty data structure, any sequence of ''a'' insert and ''decrease-key'' operations and ''b'' ''delete-min'' operations would take O(a + b\log n) worst case time, where n is the maximum heap size. In a binary o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
