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By Clifford A. Shaffer

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For an excellent and highly readable (but more advanced) teaching introduction to algorithms, their design, and their analysis, see Introduction to Algorithms: A Creative Approach by Udi Manber [Man89]. For an advanced, encyclopedic approach, see Introduction to Algorithms by Cormen, Leiserson, and Rivest [CLRS01]. Steven S. Skiena’s The Algorithm Design Manual [Ski98] provides pointers to many implementations for data structures and algorithms that are available on the Web. For a gentle introduction to ADTs and program specification, see Abstract Data Types: Their Specification, Representation, and Use by Thomas, Robinson, and Emms [TRE88].

If the sequence contains n distinct members, then there are n! different permutations for the sequence. This is because there are n choices for the first member in the permutation; for each choice of first member there are n − 1 choices for the second member, and so on. Sometimes one would like to obtain a random permutation for a sequence, that is, one of the n! possible permutations is selected in such a way that each permutation has equal probability of being selected. A simple Java function for generating a random permutation is as follows.

4 17 Problems, Algorithms, and Programs Programmers commonly deal with problems, algorithms, and computer programs. These are three distinct concepts. Problems: As your intuition would suggest, a problem is a task to be performed. It is best thought of in terms of inputs and matching outputs. A problem definition should not include any constraints on how the problem is to be solved. The solution method should be developed only after the problem is precisely defined and thoroughly understood. However, a problem definition should include constraints on the resources that may be consumed by any acceptable solution.

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