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Shellsort
Shellsort, also known as Shell sort or Shell's method, is an in-place algorithm, in-place comparison sort. It can be understood 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 the position faster than a simple nearest-neighbor exchange. 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. The algorithm was first published by Donald Shell in 1959, and has nothing to do with shells. 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 elem ... [...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] |
Donald Shell
Donald L. Shell (March 1, 1924 – November 2, 2015) was an American computer scientist who designed the Shellsort sorting algorithm. He acquired his Ph.D. in mathematics from the University of Cincinnati in 1959, and published the Shellsort algorithm in the ''Communications of the ACM'' in July that same year. Career Donald Shell acquired a B.S. in Civil Engineering from the Michigan College of Mining and Technology which is now Michigan Technological University. This was a four-year degree which he acquired in three years with the highest GPA given in the college's history. A record which persisted for more than 30 years. After acquiring his degree he went into the Army Corps of Engineers, and from there to the Philippines to help repair damages during World War II. When he returned after the war, he married Alice McCullough and returned to Michigan Technological University, where he taught mathematics. In 1949 they moved to Cincinnati, Ohio, for Don to work for General Electr ... [...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 collaborati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coin Problem
In mathematics, the coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Georg Frobenius, Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified Denomination (currency), 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 is Coprime integers#Coprimality in sets, setwise coprime. There is an explicit formula for the Frobenius number when there are only two different coin denominations, x and y , where the greatest common divisor of these two numbers is 1: 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 deno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Insertion Sort
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages: * Simple implementation: Jon Bentley shows a version that is three lines in C-like pseudo-code, and five lines when optimized. * Efficient for (quite) small data sets, much like other quadratic (i.e., O(''n''2)) sorting algorithms * More efficient in practice than most other simple quadratic algorithms such as selection sort or bubble sort * Adaptive, i.e., efficient for data sets that are already substantially sorted: the time complexity is O(''kn'') when each element in the input is no more than places away from its sorted position * Stable; i.e., does not change the relative order of elements with equal keys * In-place; i.e., only requires a constant amount O(1) of additional me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Sedgewick (computer Scientist)
Robert Sedgewick (born December 20, 1946) is an American computer scientist. He is the founding chair and the William O. Baker Professor in Computer Science at Princeton University and was a member of the board of directors of Adobe Systems (1990–2016). He previously served on the faculty at Brown University and has held visiting research positions at Xerox PARC, Institute for Defense Analyses, and INRIA. His research expertise is in algorithm science, data structures, and analytic combinatorics. He is also active in developing college curriculums in computer science. Early life Sedgewick was born on December 20, 1946, in Willimantic, Connecticut. During his childhood he lived in Storrs, Connecticut, where his parents Charles Hill Wallace Sedgewick and Rose Whelan Sedgewick were professors at the University of Connecticut. In 1958, he moved with his parents to Wheaton, Maryland, a suburb of Washington, D.C., where he attended Wheaton High School, graduating in 1964. Ed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adaptive Sort
A sorting algorithm falls into the adaptive sort family if it takes advantage of existing order in its input. It benefits from the presortedness in the input sequence – or a limited amount of disorder for various definitions of measures of disorder – and sorts faster. Adaptive sorting is usually performed by modifying existing sorting algorithms. Motivation Comparison-based sorting algorithms have traditionally dealt with achieving an optimal bound of '' O''(''n'' log ''n'') when dealing with time complexity. Adaptive sort takes advantage of the existing order of the input to try to achieve better times, so that the time taken by the algorithm to sort is a smoothly growing function of the size of the sequence ''and'' the disorder in the sequence. In other words, the more presorted the input is, the faster it should be sorted. This is an attractive feature for a sorting algorithm because sequences that nearly sorted are common in practice. Thus, the performance of exist ... [...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. It is a comparison-based sort since elements ''a'' and ''b'' are only swapped in ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Sort
A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list. The only requirement is that the operator forms a total preorder over the data, with: # if ''a'' ≤ ''b'' and ''b'' ≤ ''c'' then ''a'' ≤ ''c'' (transitivity) # for all ''a'' and ''b'', ''a'' ≤ ''b'' or ''b'' ≤ ''a'' ( connexity). It is possible that both ''a'' ≤ ''b'' and ''b'' ≤ ''a''; in this case either may come first in the sorted list. In a stable sort, the input order determines the sorted order in this case. Comparison sorts studied in the literature are "comparison-based". Elements ''a'' and ''b'' can be swapped or otherwise re-arranged by the algorithm only when the order between these elements has been established based on the outcomes of prior comparisons. This is the case when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shell Sorting Algorithm Color Bars
Shell may refer to: Architecture and design * Shell (structure), a thin structure ** Concrete shell, a thin shell of concrete, usually with no interior columns or exterior buttresses Science Biology * Seashell, a hard outer layer of a marine animal, found on beaches * Eggshell * Nutshell * Exoskeleton, an external covering of some animals ** Mollusc shell *** Bivalve shell *** Gastropod shell ** Shell, of a brachiopod * Turtle shell * Armadillo shell Physics and chemistry * Electron shell or a principal energy level of electrons outside an atom's nucleus * Nuclear shell model, a principal energy level of nucleons within an atom's nucleus * On shell and off shell, quantum field theory concepts depending on whether classical equations of motion are obeyed Mathematics * Spherical shell Organisations * Shell plc formerly Royal Dutch Shell plc, a British multinational oil and gas company ** Shell Oil Company or Shell USA ** Shell Australia ** Shell Canada ** Shell Nigeria * Shell co ... [...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] |
