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In mathematics and computer science, an algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes and deduce valid inferences.
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.
Donald Ervin Knuth 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".
In computer science, linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list until a match is found or the whole list has been searched.
In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with either discrete or continuous values.
TeX, stylized within the system as TeX, is a typesetting program which was designed and written by computer scientist and Stanford University professor Donald Knuth and first released in 1978. The term now refers to the system of extensions – which includes software programs called TeX engines, sets of TeX macros, and packages which provide extra typesetting functionality – built around the original TeX language. TeX is a popular means of typesetting complex mathematical formulae; it has been noted as one of the most sophisticated digital typographical systems.
The Art of Computer Programming (TAOCP) is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. Volumes 1–5 are intended to represent the central core of computer programming for sequential machines.
Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Extra memory, usually a queue, is needed to keep track of the child nodes that were encountered but not yet explored.
In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Unlike other compressed representations, operations are performed directly on the compressed representation, i.e. without decompression.
Adaptive Huffman coding is an adaptive coding technique based on Huffman coding. It permits building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to changing conditions in data.
The TPK algorithm is a simple program introduced by Donald Knuth and Luis Trabb Pardo to illustrate the evolution of computer programming languages. In their 1977 work "The Early Development of Programming Languages", Trabb Pardo and Knuth introduced a small program that involved arrays, indexing, mathematical functions, subroutines, I/O, conditionals and iteration. They then wrote implementations of the algorithm in several early programming languages to show how such concepts were expressed.
Vaughan Pratt 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.
Line breaking, also known as word wrapping, is breaking a section of text into lines so that it will fit into the available width of a page, window or other display area. In text display, line wrap is continuing on a new line when a line is full, so that each line fits into the viewable window, allowing text to be read from top to bottom without any horizontal scrolling. Word wrap is the additional feature of most text editors, word processors, and web browsers, of breaking lines between words rather than within words, where possible. Word wrap makes it unnecessary to hard-code newline delimiters within paragraphs, and allows the display of text to adapt flexibly and dynamically to displays of varying sizes.
In computer science, dancing links (DLX) is a technique for adding and deleting a node from a circular doubly linked list. It is particularly useful for efficiently implementing backtracking algorithms, such as Knuth's Algorithm X for the exact cover problem. Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that finds all solutions to the exact cover problem. Some of the better-known exact cover problems include tiling, the n queens problem, and Sudoku.
Algorithm X is an algorithm for solving the exact cover problem. It is a straightforward recursive, nondeterministic, depth-first, backtracking algorithm used by Donald Knuth to demonstrate an efficient implementation called DLX, which uses the dancing links technique.
Uniform binary search is an optimization of the classic binary search algorithm invented by Donald Knuth and given in Knuth's The Art of Computer Programming. It uses a lookup table to update a single array index, rather than taking the midpoint of an upper and a lower bound on each iteration; therefore, it is optimized for architectures on which
A zero-suppressed decision diagram is a particular kind of binary decision diagram (BDD) with fixed variable ordering. This data structure provides a canonically compact representation of sets, particularly suitable for certain combinatorial problems. Recall the Ordered Binary Decision Diagram (OBDD) reduction strategy, i.e. a node is replaced with one of its children if both out-edges point to the same node. In contrast, a node in a ZDD is replaced with its negative child if its positive edge points to the terminal node 0. This provides an alternative strong normal form, with improved compression of sparse sets. It is based on a reduction rule devised by Shin-ichi Minato in 1993.
"The Complexity of Songs" is a scholarly article by computer scientist Donald Knuth published in 1977 as an in-joke about computational complexity theory. The article capitalizes on what it argues is the tendency of popular songs to devolve from long and content-rich ballads to highly repetitive texts with little or no meaningful content. The article states that a song of length N words may be produced remembering, e.g., only O(log N) words or even less.
Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in linear time, matching the time bound for alternative methods including Kosaraju's algorithm and the path-based strong component algorithm. The algorithm is named for its inventor, Robert Tarjan.
In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, is a binary search tree which provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities). Optimal BSTs are generally divided into two types: static and dynamic.
References
- ↑ Knuth, Donald (2011). The Art of Computer Programming, Volume 4A. Addison-Wesley Professional: Boston, MA, USA. p. 254,275.
- ↑ Yoshinaka, Ryo; Saitoh, Toshiki; Kawahara, Jun; Tsuruma, Koji; Iwashita, Hiroaki; Minato, Shin-Ichi (2012). "Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs". Algorithms. 5 (2): 176–213. doi: 10.3390/a5020176 .
