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Binomial Heap
In computer science, a binomial heap is a data structure that acts as a priority queue but also allows pairs of heaps to be merged. It is important as an implementation of the mergeable heap abstract data type (also called meldable heap), which is a priority queue supporting merge operation. It is implemented as a heap similar to a binary heap but using a special tree structure that is different from the complete binary trees used by binary heaps. Binomial heaps were invented in 1978 by Jean Vuillemin. Binomial heap A binomial heap is implemented as a set of binomial trees (compare with a binary heap, which has a shape of a single binary tree), which are defined recursively as follows: * A binomial tree of order 0 is a single node * A binomial tree of order k has a root node whose children are roots of binomial trees of orders k-1, k-2, ..., 2, 1, 0 (in this order). A binomial tree of order k has 2^k nodes, and height k. The name comes from the shape: a binomial tree o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. 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 repositories o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Logarithm
In mathematics, the binary logarithm () is the power to which the number must be raised to obtain the value . That is, for any real number , :x=\log_2 n \quad\Longleftrightarrow\quad 2^x=n. For example, the binary logarithm of is , the binary logarithm of is , the binary logarithm of is , and the binary logarithm of is . The binary logarithm is the logarithm to the base and is the inverse function of the power of two function. As well as , an alternative notation for the binary logarithm is (the notation preferred by ISO 31-11 and ISO 80000-2). Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in information theory. In comput ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Priority Queue
In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure in which each element additionally has a ''priority'' associated with it. In a priority queue, an element with high priority is served before an element with low priority. In some implementations, if two elements have the same priority, they are served according to the order in which they were enqueued; in other implementations ordering of elements with the same priority remains undefined. While coders often implement priority queues with heaps, they are conceptually distinct from heaps. A priority queue is a concept like a list or a map; just as a list can be implemented with a linked list or with an array, a priority queue can be implemented with a heap or with a variety of other methods such as an unordered array. Operations A priority queue must at least support the following operations: * ''is_empty'': check whether the queue has no elements. * ''inser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Event Simulation
A discrete-event simulation (DES) models the operation of a system as a ( discrete) sequence of events in time. Each event occurs at a particular instant in time and marks a change of state in the system. Between consecutive events, no change in the system is assumed to occur; thus the simulation time can directly jump to the occurrence time of the next event, which is called next-event time progression. In addition to next-event time progression, there is also an alternative approach, called incremental time progression, where time is broken up into small time slices and the system state is updated according to the set of events/activities happening in the time slice. Because not every time slice has to be simulated, a next-event time simulation can typically run faster than a corresponding incremental time simulation. Both forms of DES contrast with continuous simulation in which the system state is changed continuously over time on the basis of a set of differential equations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Binary Number System
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 tableau * 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 flip turnover Skew may refer to: In mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Binomial Heap
In computer science, a skew binomial heap (or skew binomial queue) is a variant of the binomial heap that supports constant-time insertion operations in the worst case, rather than the logarithmic worst case and constant amortized time of the original binomial heap. Just as binomial heap In computer science, a binomial heap is a data structure that acts as a priority queue but also allows pairs of heaps to be merged. It is important as an implementation of the mergeable heap abstract data type (also called meldable heap), wh ...s are based on the binary number system, skew binary heaps are based on the skew binary number system. References Priority queues Heaps (data structures) {{algorithm-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amortized Time
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 Amortized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Merge Algorithm
Merge algorithms are a family of algorithms that take multiple sorted lists as input and produce a single list as output, containing all the elements of the inputs lists in sorted order. These algorithms are used as subroutines in various sorting algorithms, most famously merge sort. Application The merge algorithm plays a critical role in the merge sort algorithm, a comparison-based sorting algorithm. Conceptually, the merge sort algorithm consists of two steps: # Recursively divide the list into sublists of (roughly) equal length, until each sublist contains only one element, or in the case of iterative (bottom up) merge sort, consider a list of ''n'' elements as ''n'' sub-lists of size 1. A list containing a single element is, by definition, sorted. # Repeatedly merge sublists to create a new sorted sublist until the single list contains all elements. The single list is the sorted list. The merge algorithm is used repeatedly in the merge sort algorithm. An example merge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Heap Merge2
Binomial may refer to: In mathematics *Binomial (polynomial), a polynomial with two terms * Binomial coefficient, numbers appearing in the expansions of powers of binomials *Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition *Binomial theorem, a theorem about powers of binomials *Binomial type, a property of sequences of polynomials In probability and statistics * Binomial distribution, a type of probability distribution *Binomial process *Binomial test, a test of significance In computing science *Binomial heap, a data structure In linguistics *Binomial pair, a sequence of two or more words or phrases in the same grammatical category, having some semantic relationship and joined by some syntactic device In biology * Binomial nomenclature, a Latin two-term name for a species, such as ''Sequoia sempervirens'' In finance *Binomial options pricing model, a numerical method for the valuation of options In politics * Binomial voting system, a voting system use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Heap Merge1
Binomial may refer to: In mathematics *Binomial (polynomial), a polynomial with two terms *Binomial coefficient, numbers appearing in the expansions of powers of binomials *Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition *Binomial theorem, a theorem about powers of binomials *Binomial type, a property of sequences of polynomials In probability and statistics *Binomial distribution, a type of probability distribution *Binomial process *Binomial test, a test of significance In computing science *Binomial heap, a data structure In linguistics *Binomial pair, a sequence of two or more words or phrases in the same grammatical category, having some semantic relationship and joined by some syntactic device In biology * Binomial nomenclature, a Latin two-term name for a species, such as ''Sequoia sempervirens'' In finance *Binomial options pricing model, a numerical method for the valuation of options In politics *Binomial voting system Binomial may refer to: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linked List
In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes which together represent a sequence. In its most basic form, each node contains: data, and a reference (in other words, a ''link'') to the next node in the sequence. This structure allows for efficient insertion or removal of elements from any position in the sequence during iteration. More complex variants add additional links, allowing more efficient insertion or removal of nodes at arbitrary positions. A drawback of linked lists is that access time is linear (and difficult to pipeline). Faster access, such as random access, is not feasible. Arrays have better cache locality compared to linked lists. Linked lists are among the simplest and most common data structures. They can be used to implement several other common abstract data types, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
