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In-place
In computer science, an in-place algorithm is an algorithm that operates directly on the input data structure without requiring extra space proportional to the input size. In other words, it modifies the input in place, without creating a separate copy of the data structure. An algorithm which is not in-place is sometimes called not-in-place or out-of-place. In-place can have slightly different meanings. In its strictest form, the algorithm can only have a Space complexity, constant amount of extra space, counting everything including Subroutine, function calls and Pointer (computer programming), pointers. However, this form is very limited as simply having an index to a length array requires bits. More broadly, in-place means that the algorithm does not use extra space for manipulating the input but may require a small though nonconstant extra space for its operation. Usually, this space is , though sometimes anything in is allowed. Note that space complexity also has varied ... [...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] |
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] |
Heapsort
In computer science, heapsort is an efficient, comparison-based sorting algorithm that reorganizes an input array into a heap (a data structure where each node is greater than its children) and then repeatedly removes the largest node from that heap, placing it at the end of the array in a similar manner to Selection sort. Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantages of very simple implementation and a more favorable worst-case runtime. Most real-world quicksort variants include an implementation of heapsort as a fallback should they detect that quicksort is becoming degenerate. Heapsort is an in-place algorithm, but it is not a stable sort. Heapsort was invented by J. W. J. Williams in 1964. The paper also introduced the binary heap as a useful data structure in its own right. In the same year, Robert W. Floyd published an improved version that could sort an array in-place, continuing his earlier research ... [...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] |
Selection Algorithm
In computer science, a selection algorithm is an algorithm for finding the kth smallest value in a collection of ordered values, such as numbers. The value that it finds is called the order statistic. Selection includes as special cases the problems of finding the minimum, median, and maximum element in the collection. Selection algorithms include quickselect, and the median of medians algorithm. When applied to a collection of n values, these algorithms take linear time, O(n) as expressed using big O notation. For data that is already structured, faster algorithms may be possible; as an extreme case, selection in an already-sorted array takes Problem statement An algorithm for the selection problem takes as input a collection of values, and a It outputs the smallest of these values, or, in some versions of the problem, a collection of the k smallest values. For this to be well-defined, it should be possible to sort the values into an order from smallest to largest; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trim (programming)
In computer programming, trimming (trim) or stripping (strip) is a string manipulation in which leading and trailing whitespace is removed from a string. For example, the string (enclosed by apostrophes) ' this is a test ' would be changed, after trimming, to 'this is a test' Variants Left or right trimming The most popular variants of the trim function strip only the beginning or end of the string. Typically named ltrim and rtrim respectively, or in the case of Python: lstrip and rstrip. C# uses TrimStart and TrimEnd, and Common Lisp string-left-trim and string-right-trim. Pascal and Java do not have these variants built-in, although Object Pascal (Delphi) has TrimLeft and TrimRight functions. Whitespace character list parameterization Many trim functions have an optional parameter to specify a list of characters to trim, instead of the default whitespace characters. For example, PHP and Python allow this optional parameter, while Pascal and Java do not. With Common Lisp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selection Sort
In computer science, selection sort is an in-place comparison sorting algorithm. It has a O(''n''2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity and has performance advantages over more complicated algorithms in certain situations, particularly where auxiliary memory is limited. The algorithm divides the input list into two parts: a sorted sublist of items which is built up from left to right at the front (left) of the list and a sublist of the remaining unsorted items that occupy the rest of the list. Initially, the sorted sublist is empty and the unsorted sublist is the entire input list. The algorithm proceeds by finding the smallest (or largest, depending on sorting order) element in the unsorted sublist, exchanging (swapping) it with the leftmost unsorted element (putting it in sorted order), and moving the sublist boundaries one element to the right. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shell Sort
Shellsort, also known as Shell sort or Shell's method, is an 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 element produces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undirected Graph
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called '' vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing money is not necessarily reciprocated. Gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The ACM
The ''Journal of the ACM'' (''JACM'') is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' (''CACM'') is the monthly journal of the Association for Computing Machinery (ACM). History It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are i ...'' References External links * {{DEFAULTSORT:Journal Of The Acm Academic journals established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Depth-first Search
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. Extra memory, usually a stack, is needed to keep track of the nodes discovered so far along a specified branch which helps in backtracking of the graph. A version of depth-first search was investigated in the 19th century by French mathematician Charles Pierre Trémaux as a strategy for solving mazes. Properties The time and space analysis of DFS differs according to its application area. In theoretical computer science, DFS is typically used to traverse an entire graph, and takes time where , V, is the number of vertices and , E, the number of edges. This is linear in the size of the graph. In these applications it also uses space O(, V, ) in the worst case to store the stack of vertices on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are Regular expression#Patterns for non-regular languages, augmented with features that allow the recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by regular grammar, Type-3 grammars. Formal definition The collection of regular languages over an Alphabet (formal languages), alphabet Σ is defined recursively as follows: * The empty language ∅ is a regular language. * For each ''a'' ∈ Σ (''a'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
