The Art of Computer Programming, Volume 2: The Seminumerical by Donald E. Knuth

By Donald E. Knuth

The bible of all basic algorithms and the paintings that taught a lot of today's software program builders so much of what they find out about laptop programming. —Byte, September 1995 I can't start to let you know what number satisfying hours of analysis and game they've got afforded me! i've got pored over them in vehicles, eating places, at paintings, at home... or even at a bit League online game while my son wasn't within the line-up

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Extra resources for The Art of Computer Programming, Volume 2: The Seminumerical Algorithms

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In the salary example, the problem may be specified in the form of a request for a number that represents the sum of the salaries of a list of employees of an organization. This list may vary in length but must be organized in a particular fashion. 4). An algorithmic problem has been solved when an appropriate algorithm has been found. The black box has then actually been provided with contents; it “works” according to that algorithm. In other words, the black box can produce the appropriate output from any legal input by executing the process that is prescribed and governed by that algorithm.

A characterization of a legal, possibly infinite, collection of potential input sets, and 2. a specification of the desired outputs as a function of the inputs. It is assumed that either a description of the allowed basic actions or a hardware configuration together with its built-in basic actions are also provided in advance. A solution to an algorithmic problem consists of an algorithm, composed of elementary instructions prescribing actions from the agreed-on set. This algorithm, when executed for any legal input set, solves the problem, producing the output as required.

Combination. When the end of a sentence is found, the algorithm adds 1 to a counter (that is, a “noted number,” as in the salary summation algorithm), which was initialized to 0 at the start. It then resumes its search for “money” from the beginning of the next sentence; that is, from the letter following the combination. Of course, the algorithm must keep looking out for the end of the text, so that it can output the value of the counter when it is reached. The algorithm takes the form of an external loop whose duty it is to count the relevant sentences.

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