About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 100. Chapters: Adaptive algorithm, Adaptive coordinate descent, Algorism, Algorithm characterizations, Algorithm design, Algorithm examples, Backfitting algorithm, Biologically inspired algorithms, British Museum algorithm, Code Bisection, Differential Dynamic Programming, Divide and conquer algorithm, Division algorithm, Domain Generation Algorithm, Fourier division, Generalized distributive law, HAKMEM, Hindley-Milner, Holographic algorithm, Hyphenation algorithm, In-place algorithm, Kinodynamic planning, Kronecker substitution, List of algorithms, List of algorithm general topics, Manhattan address algorithm, Matching engine, Maze generation algorithm, Maze solving algorithm, Medical algorithm, Method of conditional probabilities, One-pass algorithm, Out-of-core algorithm, Ping-pong scheme, PR-CPA advantage, Predictor-corrector method, Principle of deferred decision, Randomization function, Randomized rounding, Reservoir sampling, RNA22, Run-time algorithm specialisation, Sardinas-Patterson algorithm, Sequential algorithm, Sieve of Eratosthenes, Simulation algorithms for atomic DEVS, Simulation algorithms for coupled DEVS, Spreading activation, Streaming algorithm, Super-recursive algorithm, The Art of Computer Programming, Timeline of algorithms, Tomasulo algorithm, XOR swap algorithm. Excerpt: In mathematics and computer science, an algorithm ( -g -ri-dh m) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. An algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input. Though al-Khw rizm 's algorism referred to the rules of performing arithmetic using Hindu-Arabic numerals and the systematic solution of linear and quadratic equations, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Godel-Herbrand-Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936-7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem. While there is no generally accepted formal definition of "algorithm," an informal definition could be "a set of rules that precisely defines a sequence of operations." For some people, a program is only an algorithm if it stops eventually; for others, a program is only an algorithm if it stops before a given number of calculation steps. A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers; an example (ther
