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Thinking Recursively

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Thinking Recursively, 9780471816522 (0471816523), John Wiley & Sons, 1986
At its essence, computer science is the study of problems and their solutions. More specifically, computer science is concerned with finding systematic procedures that guarantee a correct solution to a given problem. Such procedures are called algorithms.

This book is about a particular class of algorithms, called recursive algorithms, which turn out to be quite important in computer science. For many problems, the use of recursion makes it possible to solve complex problems using programs that are surprisingly concise, easily understood, and algorithmically efficient. For the student seeing this material for the first time, however, recursion appears to be obscure, difficult, and mystical. Unlike other problemsolving techniques which have closely related counterparts in everyday life, recursion is an unfamiliar idea and often requires thinking about problems in a new and different way. This book is designed to provide the conceptual tools necessary to approach problems from this recursive point of view.

Informally, recursion is the process of solving a large problem by reducing it to one or more subproblems which are (1) identical in structure to the original problem and (2) somewhat simpler to solve. Once that original subdivision has been made, the same decompositional technique is used to divide each of these subproblems into new ones which are even less complex. Eventually, the subproblems become so simple that they can be then solved without further subdivision, and the complete solution is obtained by reassembling the solved components.
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