|
Binomial Heap
In computer science, a binomial heap is a data structure that acts as a priority queue. It is an example of a mergeable heap (also called meldable heap), as it supports merging two heaps in logarithmic time. It is implemented as a Heap (data structure), 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 tree data structure, 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 of order k has \tbinom k d nodes at depth d, a ... [...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] |
Binary Numeral System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" ( zero) and "1" ( one). A ''binary number'' may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two. The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harrio ... [...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 (abstract data type), queue or stack (abstract data type), stack abstract data type. In a priority queue, each element has an associated ''priority'', which determines its order of service. Priority queue serves highest priority items first. Priority values have to be instances of an ordered data type, and higher priority can be given either to the lesser or to the greater values with respect to the given order relation. For example, in Java (programming language), Java standard library, ''PriorityQueues the least elements with respect to the order have the highest priority. This implementation detail is without much practical significance, since passing to the converse relation, opposite order relation turns the least values into the greatest, and vice versa. While priority queues are often implemented using Heap (data structure) , heaps, they are conceptually distinct. A priority queue can ... [...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 d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Binary Number System
The skew binary number system is a non-standard positional numeral system in which the ''n''th digit contributes a value of 2^ - 1 times the digit (digits are indexed from 0) instead of 2^ times as they do in binary. Each digit has a value of 0, 1, or 2. A number can have many skew binary representations. For example, a decimal number 15 can be written as 1000, 201 and 122. Each number can be written uniquely in skew binary canonical form where there is only at most one instance of the digit 2, which must be the least significant nonzero digit. In this case 15 is written canonically as 1000. Examples Canonical skew binary representations of the numbers from 0 to 15 are shown in following table: Arithmetical operations The advantage of skew binary is that each increment operation can be done with at most one carry operation. This exploits the fact that 2 (2^ - 1) + 1 = 2^ - 1 . Incrementing a skew binary number is done by setting the only two to a zero and incrementing the ne ... [...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] |
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 Amortiz ... [...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 * Binomial series, a mathematical series 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 In taxonomy, binomial nomenclature ("two-term naming system"), also called binary nomenclature, is a formal system of naming species of living things by giving each a name ... [...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 data access time is linear in respect to the number of nodes in the list. Because nodes are serially linked, accessing any node requires that the prior node be accessed beforehand (which introduces difficulties in pipelining). Faster access, such as random access, is not feasible. Arrays have better cache ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
