I recently found a book by Niklaus Wirth in a used book store; it’s a fascinating book and has been the source of a few recent exercises:

Niklaus Wirth, Eidgenössische Technische Hochschule, Zürich, Switzerland. Systematic Programming: An Introduction. 1973: Prentice-Hall, Inc. Englewood Cliffs, New Jersey. ISBN 0-13-880369-2.

Most of the book is concerned with teaching the syntax and semantics of Wirth’s language Pascal, but the final chapter is devoted to stepwise program development, where Wirth demonstrates by example four different problems which he solves by developing programs through a succession of stepwise refinements. The last section is a kind of “final exam” for readers; it’s the longest section of the book, by far, and gives a complete, detailed exposition of the solution to the following problem:

Generate a sequence of N characters, chosen from an alphabet of three elements (e.g., 1, 2, 3), such that no two immediately adjacent subsequences are equal.

For instance, the sequence of length N = 5 with the characters “12321″ is acceptable, but neither “12323″ nor “12123″ are.

Your task is to write a program that not only solves the stated problem but also gives all possible solutions, not just a single solution, for any given N. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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