Machine Theory

Algorithmics : the spirit of computing by David Harel, Yishai Feldman

By David Harel, Yishai Feldman

The top promoting 'Algorithmics' offers an important, strategies, tools and effects which are basic to the technology of computing.  It starts off by means of introducing the elemental rules of algorithms, together with their buildings and strategies of knowledge manipulation.  It then is going directly to show the best way to layout actual and effective algorithms, and discusses their inherent limitations.  because the writer himself says within the preface to the book; 'This publication makes an attempt to give a readable account of a few of crucial and simple issues of laptop technology, stressing the basic and powerful nature of the technology in a kind that's nearly self sufficient of the main points of particular desktops, languages and formalisms'.

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This algorithmic segment is called a subroutine or a procedure and it is activated (or invoked, or called) twice in the main algorithm, once with “money” as its parameter, and once with the “. ” combination. The text of the subroutine is provided separately, and it refers to the varying parameter by a name, say X . cls March 18, 2004 13:47 2. Algorithms and Data 27 (2) if the end of the text is reached, output the counter’s value and stop; (3) otherwise return to the main algorithm. The main part of the algorithm will utilize the search subroutine twice, by instructions of the form “call search-for ‘money’ ” and “call search-for ‘.

2), will be used freely in the sequel. You are encouraged to seek the reason for using N − 1 and adding the final salary separately, rather than simply using N and then producing the output and halting. Notice that the algorithm fails if the list is empty (that is, if N is 0), since the second part of clause (1) makes no sense. cls March 18, 2004 13:47 2. Algorithms and Data 21 sense when it has reached the end of the list. The resulting algorithm would look very much like the version given, but would use the form “repeat the following until end of list reached” in clause (2).

This is the problem we should really be trying to solve, since once an algorithm is available, every instance of the puzzle, be it the three-, four-, or 3078-ring version, can be solved simply by running the algorithm with the desired number of rings as input. Well, how is it done? The answer is simple: by the magic of recursion. ■ A Solution to the Towers of Hanoi The algorithm presented here accomplishes the task of moving N rings from A to B via C in the following way. It first checks to see whether N is 1, in which case it simply moves the one ring it was asked to deal with to its destination (or, more precisely, it outputs a description of the one move that will do the job), and then returns immediately.

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