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Radix Heap
A radix heap is a data structure for realizing the operations of a monotone priority queue. A set of elements to which a key is assigned can then be managed. The run time of the operations depends on the difference between the largest and smallest key or constant. The data structure consists mainly of a series of buckets, the size of which increases exponentially. Prerequisites # all keys are natural numbers; # max. key - min. key \le C for constant C; # the ''extract-min'' operation is monotonic; that is, the values returned by successive ''extract-min'' calls are monotonically increasing. Description of data structure The three most important fields Fields may refer to: Music *Fields (band), an indie rock band formed in 2006 *Fields (progressive rock band), a progressive rock band formed in 1971 * ''Fields'' (album), an LP by Swedish-based indie rock band Junip (2010) * "Fields", a song by ... are: # b of size B := \lfloor log(C+1)\rfloor + 1, with 0 as the lowest index, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or 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 databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotone Priority Queue
In computer science, a monotone priority queue is a variant of the priority queue abstract data type in which the priorities of extracted items are required to form a monotonic sequence. That is, for a priority queue in which each successively extracted item is the one with the minimum priority (a min-heap), the minimum priority should be monotonically increasing. Conversely for a max-heap the maximum priority should be monotonically decreasing. The assumption of monotonicity arises naturally in several applications of priority queues, and can be used as a simplifying assumption to speed up certain types of priority queues. A necessary and sufficient condition on a monotone priority queue is that one never attempts to add an element with lower priority than the most recently extracted one. Applications Monotone priority queues arise naturally when arranging events in order of time, such as network timeouts or discrete event simulation. An event can cause some action to be schedule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression. The formula for exponential growth of a variable at the growth rate , as time goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is x_t = x_0(1+r)^t where is the value of at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Numbers
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal numbers'', and numbers used for ordering are called ''ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by success ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heap (data Structure)
In computer science, a heap is a specialized tree-based data structure which is essentially an almost complete tree that satisfies the heap property: in a ''max heap'', for any given node C, if P is a 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 inters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonically Increasing
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field (computer Science)
In computer science, data that has several parts, known as a '' record,'' can be divided into fields (data fields). Relational databases arrange data as sets of database records, so called rows. Each record consists of several ''fields''; the fields of all records form the columns. Examples of fields: name, gender, hair colour. In object-oriented programming, a ''field'' (also called ''data member'' or ''member variable'') is a particular piece of data encapsulated within a class or object. In the case of a regular field (also called ''instance variable''), for each instance of the object there is an instance variable: for example, an Employee class has a Name field and there is one distinct name per employee. A static field (also called ''class variable'') is one variable, which is shared by all instances. Fields are abstracted by properties, which allow them to be read and written as if they were fields, but these can be translated to getter and setter method calls. Fixed l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
