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Algorithms and Programming: Problems and Solutions (Springer Undergraduate Texts in Mathematics and Technology)

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Somebody once said that one may prove the correctness of an algorithm, but not of a program. One of the main goals of this book is to convince the reader that things are not so bad.

A well-known programmer, C.A.R. Hoare, said that the beauty of a program is not an additional benefit but a criterion that separates success from failure. If, while solving problems in this book, you come to appreciate the beauty of a well-written program with each part in its correct place, the author’s goal will have been reached.

Theoretically this book can be used to study programming without a computer: one could write (correct) programs with pencil and paper. But in practice the ability to run the programs is a challenge and a reward that makes programming a fun.

We have utilized the problem-solution format. Some chapters are collections of problems having a common topic, while others are devoted to one specific algorithm (e.g., chapter 16 covers LR(1)-parsing). The chapters are more or less independent, but the concluding chapters are more difficult. Chapters 1–7 cover material usually included in undergraduate courses while chapters 15–16 are more appropriate for a graduate compiler course. In each chapter we have tried to give problems at different levels starting with easy exercises.

Problems are usually provided with solutions, answers or hints. However, we strongly recommend to read the solution only after the reader makes a good faith attempt to solve it independently.

The book is restricted to “micro-programming” leaving aside another very important topic: how to split the program into a manageable parts with nice interfaces between them. (Probably this can be learned only by reading and modifying rather large programs.)

Pascal is used as a programming language; though being outdated, it is reasonably clear, so the readers familiar with any other procedural language (C, Modula, Oberon, etc.) will encounter no difficulties. For the reader’s convenience, a short appendix is added that lists basic differences between Pascal and C. It is intended to help the reader who knows C to understand the program notation in the book (but cannot replace textbooks on C).
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