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Potential Method
In computational complexity theory, the potential method is a method used to analyze the amortized time and space complexity of a data structure, a measure of its performance over sequences of operations that smooths out the cost of infrequent but expensive operations.. Definition of amortized time In the potential method, a function Φ is chosen that maps states of the data structure to non-negative numbers. If ''S'' is a state of the data structure, Φ(''S'') represents work that has been accounted for ("paid for") in the amortized analysis but not yet performed. Thus, Φ(''S'') may be thought of as calculating the amount of potential energy stored in that state. The potential value prior to the operation of initializing a data structure is defined to be zero. Alternatively, Φ(''S'') may be thought of as representing the amount of disorder in state ''S'' or its distance from an ideal state. Let ''o'' be any individual operation within a sequence of operations on some data stru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of logic gate, gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC (programming language), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...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] |
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] |
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] |
Least Significant Bit
In computing, bit numbering is the convention used to identify the bit positions in a binary number. Bit significance and indexing In computing, the least significant bit (LSb) is the bit position in a binary integer representing the lowest-order place of the integer. Similarly, the most significant bit (MSb) represents the highest-order place of the binary integer. The LSb is sometimes referred to as the ''low-order bit''. Due to the convention in positional notation of writing less significant digits further to the right, the LSb also might be referred to as the ''right-most bit''. The MSb is similarly referred to as the ''high-order bit'' or ''left-most bit''. In both cases, the LSb and MSb correlate directly to the least significant digit and most significant digit of a decimal integer. Bit indexing correlates to the positional notation of the value in base 2. For this reason, bit index is not affected by how the value is stored on the device, such as the value's byte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Weight
The Hamming weight of a string (computer science), string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a given set of bits, this is the number of bits set to 1, or the digit sum of the Binary numeral system, binary representation of a given number and the Taxicab geometry, ''ℓ''₁ norm of a bit vector. In this binary case, it is also called the population count, popcount, sideways sum, or bit summation. History and usage The Hamming weight is named after the American mathematician Richard Hamming, although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James Whitbread Lee Glaisher, James W. L. Glaisher to give a formula for Gould's sequence, the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transdichotomous Machine Model
In computational complexity theory, and more specifically in the analysis of algorithms with integer data, the transdichotomous model is a variation of the random-access machine in which the machine word size is assumed to match the problem size. The model was proposed by Michael Fredman and Dan Willard, who chose its name "because the dichotomy between the machine model and the problem size is crossed in a reasonable manner." In a problem such as integer sorting in which there are integers to be sorted, the transdichotomous model assumes that each integer may be stored in a single word of computer memory, that operations on single words take constant time per operation, and that the number of bits that can be stored in a single word is at least . The goal of complexity analysis in this model is to find time bounds that depend only on and not on the actual size of the input values or the machine words.. In modeling integer computation, it is necessary to assume that machine words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Number
A binary number is a number expressed in the Radix, 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 computer, 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 Thoma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counter (digital)
In digital electronics, a counter is a sequential logic circuit that counts and stores the number of positive or negative transitions of a clock signal. A counter typically consists of flip-flop (electronics), flip-flops, which store a value representing the current count, and in many cases, additional logic to effect particular counting sequences, qualify clocks and perform other functions. Each relevant clock transition causes the value stored in the counter to increment or decrement (increase or decrease by one). A digital counter is a finite state machine, with a ''clock'' input signal and multiple output signals that collectively represent the state. The state indicates the current count, encoded directly as a binary number, binary or binary-coded decimal (BCD) number or using encodings such as one-hot or Gray code. Most counters have a ''reset'' input which is used to initialize the count. Depending on the design, a counter may have additional inputs to control functions suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stack (abstract Data Type)
In computer science, a stack is an abstract data type that serves as a collection (abstract data type), collection of elements with two main operations: * Push, which adds an element to the collection, and * Pop, which removes the most recently added element. Additionally, a peek (data type operation), peek operation can, without modifying the stack, return the value of the last element added. The name ''stack'' is an analogy to a set of physical items stacked one atop another, such as a stack of plates. The order in which an element added to or removed from a stack is described as last in, first out, referred to by the acronym LIFO. As with a stack of physical objects, this structure makes it easy to take an item off the top of the stack, but accessing a Data, datum deeper in the stack may require removing multiple other items first. Considered a sequential collection, a stack has one end which is the only position at which the push and pop operations may occur, the ''top'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if x is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), and For example, the absolute value of 3 and the absolute value of −3 is The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. Terminology and notation In 1806, Jean-Robert Argand introduced the term ''module'', meaning ''unit of measure'' in French, specifically for the ''complex'' absolute value,Oxford English Dictionary, Draft Revision, Ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
