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Sorted Array
A sorted array is an array data structure in which each element is sorted in numerical, alphabetical, or some other order, and placed at equally spaced addresses in computer memory. It is typically used in computer science to implement static lookup tables to hold multiple values which have the same data type. Sorting an array is useful in organising data in ordered form and recovering them rapidly. Overview Sorted arrays are the most space-efficient data structure with the best locality of reference for sequentially stored data. Elements within a sorted array are found using a binary search, in O(log ''n''); thus sorted arrays are suited for cases when one needs to be able to look up elements quickly, e.g. as a set or multiset data structure. This complexity for lookups is the same as for self-balancing binary search trees. In some data structures, an array of structures is used. In such cases, the same sorting methods can be used to sort the structures according to some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann
John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, integrating Basic research, pure and Applied science#Applied research, applied sciences and making major contributions to many fields, including mathematics, physics, economics, computing, and statistics. He was a pioneer in building the mathematical framework of quantum physics, in the development of functional analysis, and in game theory, introducing or codifying concepts including Cellular automaton, cellular automata, the Von Neumann universal constructor, universal constructor and the Computer, digital computer. His analysis of the structure of self-replication preceded the discovery of the structure of DNA. During World War II, von Neumann worked on the Manhattan Project. He developed the mathematical models behind the explosive lense ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Array
In computer science, a dynamic array, growable array, resizable array, dynamic table, mutable array, or array list is a random access, variable-size list data structure that allows elements to be added or removed. It is supplied with standard libraries in many modern mainstream programming languages. Dynamic arrays overcome a limit of static arrays, which have a fixed capacity that needs to be specified at allocation. A dynamic array is not the same thing as a dynamically allocated array or variable-length array, either of which is an array whose size is fixed when the array is allocated, although a dynamic array may use such a fixed-size array as a back end.See, for example, thsource code of java.util.ArrayList class from OpenJDK 6 Bounded-size dynamic arrays and capacity A simple dynamic array can be constructed by allocating an array of fixed-size, typically larger than the number of elements immediately required. The elements of the dynamic array are stored contiguous ... [...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 Search Algorithm
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Binary search runs in logarithmic time in the worst case, making O(\log n) comparisons, where n is the number of elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting Algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a List (computing), list into an Total order, order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the Algorithmic efficiency, efficiency of other algorithms (such as search algorithm, search and merge algorithm, merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for Canonicalization, canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. Although some algorithms are designed for sequential access, the highest-performing algorithms assum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Art Of Computer Programming
''The Art of Computer Programming'' (''TAOCP'') is a comprehensive multi-volume monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. it consists of published volumes 1, 2, 3, 4A, and 4B, with more expected to be released in the future. The Volumes 1–5 are intended to represent the central core of computer programming for sequential machines; the subjects of Volumes 6 and 7 are important but more specialized. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001. The first published installment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". Knuth is the author of the multi-volume work '' The Art of Computer Programming''. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB computer programming systems des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EDVAC
EDVAC (Electronic Discrete Variable Automatic Computer) was one of the earliest electronic computers. It was built by Moore School of Electrical Engineering at the University of Pennsylvania. Along with ORDVAC, it was a successor to the ENIAC. Unlike ENIAC, it was binary rather than decimal, and was designed to be a stored-program computer. ENIAC inventors, John Mauchly and J. Presper Eckert, proposed the EDVAC's construction in August 1945. A contract to build the new computer was signed in April 1946 with an initial budget of US$100,000. EDVAC was delivered to the Ballistic Research Laboratory in 1949. The Ballistic Research Laboratory became a part of the US Army Research Laboratory in 1952. Functionally, EDVAC was a binary serial computer with automatic addition, subtraction, multiplication, programmed division and automatic checking with an ultrasonic serial memory having a capacity of 1,024 44-bit words. EDVAC's average addition time was 864 microseconds and it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Merge Sort
In computer science, merge sort (also commonly spelled as mergesort and as ) is an efficient, general-purpose, and comparison sort, comparison-based sorting algorithm. Most implementations of merge sort are Sorting algorithm#Stability, stable, which means that the relative order of equal elements is the same between the input and output. Merge sort is a divide-and-conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Herman Goldstine, Goldstine and von Neumann as early as 1948. Algorithm Conceptually, a merge sort works as follows: #Divide the unsorted list into ''n'' sub-lists, each containing one element (a list of one element is considered sorted). #Repeatedly Merge algorithm, merge sublists to produce new sorted sublists until there is only one sublist remaining. This will be the sorted list. Top-down implementation Example C-like code using indices for top-down merge sort algorit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Access
Random access (also called direct access) is the ability to access an arbitrary element of a sequence in equal time or any datum from a population of addressable elements roughly as easily and efficiently as any other, no matter how many elements may be in the set. In computer science it is typically contrasted to sequential access which requires data to be retrieved in the order it was stored. For example, data might be stored notionally in a single sequence like a row, in two dimensions like rows and columns on a surface, or in multiple dimensions. However, given all the coordinates, a program can access each record about as quickly and easily as any other. In this sense, the choice of datum is arbitrary in the sense that no matter which item is sought, all that is needed to find it is its address, i.e. the coordinates at which it is located, such as its row and column (or its track and record number on a magnetic drum). At first, the term "random access" was used because th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amortized Analysis
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 Amortize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-balancing Binary Search Tree
In computer science, a self-balancing binary search tree (BST) is any node-based binary search tree that automatically keeps its height (maximal number of levels below the root) small in the face of arbitrary item insertions and deletions.Donald Knuth. '' The Art of Computer Programming'', Volume 3: ''Sorting and Searching'', Second Edition. Addison-Wesley, 1998. . Section 6.2.3: Balanced Trees, pp.458–481. These operations when designed for a self-balancing binary search tree, contain precautionary measures against boundlessly increasing tree height, so that these abstract data structures receive the attribute "self-balancing". For height-balanced binary trees, the height is defined to be logarithmic O(\log n) in the number n of items. This is the case for many binary search trees, such as AVL trees and red–black trees. Splay trees and treaps are self-balancing but not height-balanced, as their height is not guaranteed to be logarithmic in the number of items. Self-bal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
