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Shell Sort
Shellsort, also known as Shell sort or Shell's method, is an in-place comparison sort. It can be seen as either a generalization of sorting by exchange ( bubble sort) or sorting by insertion (insertion sort). The method starts by sorting pairs of elements far apart from each other, then progressively reducing the gap between elements to be compared. By starting with far apart elements, it can move some out-of-place elements into position faster than a simple nearest neighbor exchange. Donald Shell published the first version of this sort in 1959. The running time of Shellsort is heavily dependent on the gap sequence it uses. For many practical variants, determining their time complexity remains an open problem. Description Shellsort is an optimization of insertion sort that allows the exchange of items that are far apart. The idea is to arrange the list of elements so that, starting anywhere, taking every ''h''th element produces a sorted list. Such a list is said to be ''h' ... [...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 into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for 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. For optimum efficiency, the input data should be stored in a data structure which allows random access rather than one that allows only sequential access. History and concepts From the beginning of compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vaughan Ronald Pratt
Vaughan Pratt (born April 12, 1944) is a Professor Emeritus at Stanford University, who was an early pioneer in the field of computer science. Since 1969, Pratt has made several contributions to foundational areas such as search algorithms, sorting algorithms, and primality testing. More recently, his research has focused on formal modeling of concurrent systems and Chu spaces. Career Raised in Australia and educated at Knox Grammar School, where he was dux in 1961, Pratt attended Sydney University, where he completed his masters thesis in 1970, related to what is now known as natural language processing. He then went to the United States, where he completed a Ph.D. thesis at Stanford University in only 20 months under the supervision of advisor Donald Knuth. His thesis focused on analysis of the Shellsort sorting algorithm and sorting networks. Pratt was an assistant professor at MIT (1972 to 1976) and then associate professor (1976 to 1982). In 1974, working in collaboratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Yao
Andrew Chi-Chih Yao (; born December 24, 1946) is a Chinese computer scientist and computational theorist. He is currently a professor and the dean of Institute for Interdisciplinary Information Sciences (IIIS) at Tsinghua University. Yao used the minimax theorem to prove what is now known as Yao's Principle. Yao was a naturalized U.S. citizen, and worked for many years in the U.S. In 2015, together with Yang Chen-Ning, he renounced his U.S. citizenship and became an academician of the Chinese Academy of Sciences. Early life Yao was born in Shanghai, China. He completed his undergraduate education in physics at the National Taiwan University, before completing a Doctor of Philosophy in physics at Harvard University in 1972, and then a second PhD in computer science from the University of Illinois at Urbana–Champaign in 1975. Academic career Yao was an assistant professor at Massachusetts Institute of Technology (1975–1976), assistant professor at Stanford University ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coin Problem
The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations, for example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number of the set. The Frobenius number exists as long as the set of coin denominations has no common divisor greater than 1. There is an explicit formula for the Frobenius number when there are only two different coin denominations, ''x'' and ''y'': the Frobenius number is then ''xy'' − ''x'' − ''y''. If the number of coin denominations is three or more, no explicit formula is known. However, for any fixed number of coin denominations, there is an algorithm computing the Frobenius number in polynomial time (in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stack Overflow
In software, a stack overflow occurs if the call stack pointer exceeds the stack bound. The call stack may consist of a limited amount of address space, often determined at the start of the program. The size of the call stack depends on many factors, including the programming language, machine architecture, multi-threading, and amount of available memory. When a program attempts to use more space than is available on the call stack (that is, when it attempts to access memory beyond the call stack's bounds, which is essentially a buffer overflow), the stack is said to ''overflow'', typically resulting in a program crash. Causes Infinite recursion The most-common cause of stack overflow is excessively deep or infinite recursion, in which a function calls itself so many times that the space needed to store the variables and information associated with each call is more than can fit on the stack. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Merge Sort
In computer science, merge sort (also commonly spelled as mergesort) is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the order of equal elements is the same in 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 Goldstine and von Neumann as early as 1948. Algorithm Conceptually, a merge sort works as follows: #Divide the unsorted list into ''n'' sublists, each containing one element (a list of one element is considered sorted). #Repeatedly 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 algorithm that recursively splits the list (called ''runs'' in this example) into sublists until sublist size ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quicksort
Quicksort is an efficient, general-purpose sorting algorithm. Quicksort was developed by British computer scientist Tony Hoare in 1959 and published in 1961, it is still a commonly used algorithm for sorting. Overall, it is slightly faster than merge sort and heapsort for randomized data, particularly on larger distributions. Quicksort is a divide-and-conquer algorithm. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. For this reason, it is sometimes called partition-exchange sort. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory to perform the sorting. Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. Most implementations of quicksort are not stable, meaning that the relative order of equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coprime
In mathematics, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. One says also '' is prime to '' or '' is coprime with ''. The numbers 8 and 9 are coprime, despite the fact that neither considered individually is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition. Notation and testing Standard notations for relatively prime integers and are: and . In their 1989 textbook '' Concrete Mathematics'', Ronald Graham, Donald Knuth, and Oren Patashnik proposed that the notation a\perp b be used to indicate that and are relatively prime and that the term "prime" be used instead of coprime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greatest Common Divisor
In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers ''x'', ''y'', the greatest common divisor of ''x'' and ''y'' is denoted \gcd (x,y). For example, the GCD of 8 and 12 is 4, that is, \gcd (8, 12) = 4. In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), etc. Historically, other names for the same concept have included greatest common measure. This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see below). Overview Definition The ''greatest common divisor'' (GCD) of two nonzero integers and is the greatest positive integer such that is a divisor of both and ; that is, there are integers and such that and , and is the larges ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bitonic Sorter
Bitonic mergesort is a parallel algorithm for sorting. It is also used as a construction method for building a sorting network. The algorithm was devised by Ken Batcher. The resulting sorting networks consist of O(n\log^2(n)) comparators and have a delay of O(\log^2(n)), where n is the number of items to be sorted. A sorted sequence is a monotonically non-decreasing (or non-increasing) sequence. A ''bitonic'' sequence is a sequence with x_0 \leq \cdots \leq x_k \geq \cdots \geq x_ for some k, 0 \leq k arr OR (bitwiseAND (i, k) != 0) AND (arr < arr ) swap the elements arr and arr See also *[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting Network
In computer science, comparator networks are abstract devices built up of a fixed number of "wires", carrying values, and comparator modules that connect pairs of wires, swapping the values on the wires if they are not in a desired order. Such networks are typically designed to perform sorting on fixed numbers of values, in which case they are called sorting networks. Sorting networks differ from general comparison sorts in that they are not capable of handling arbitrarily large inputs, and in that their sequence of comparisons is set in advance, regardless of the outcome of previous comparisons. In order to sort larger amounts of inputs, new sorting networks must be constructed. This independence of comparison sequences is useful for parallel execution and for implementation in hardware. Despite the simplicity of sorting nets, their theory is surprisingly deep and complex. Sorting networks were first studied circa 1954 by Armstrong, Nelson and O'Connor, who subsequently patented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ricardo Baeza-Yates
Ricardo A. Baeza-Yates (born March 21, 1961) is a Chilean- Catalan computer scientist that currently is a Research Professor at the Institute for Experiential AI of Northeastern University in the Silicon Valley campus. He is also part-time professor at Universitat Pompeu Fabra in Barcelona and Universidad de Chile in Santiago. He is an expert member of the Global Partnership on Artificial Intelligence, a member of Spain's Advisory Council on AI, and a member of the Association for Computing Machinery's US Technology Policy Subcommittee on AI and Algorithms. From June 2016 until June 2020 he was CTO of NTENT, a semantic search technology company. Before, until February 2016, he was VP of Research for Yahoo! Labs, leading teams in United States, Europe and Latin America. He obtained a Ph.D. from the University of Waterloo with ''Efficient Text Searching'', supervised by Gaston Gonnet and granted in 1989. His research interests include: * Algorithms and data structures. His co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
