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Beginning Algorithms by James Ross, Simon Harris

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Chapter 2. Iteration and Recursion

Iteration and recursion are two fundamental concepts without which it would be impossible to do much, if anything, useful in computing. Sorting names, calculating credit-card transaction totals, and printing order line items all require that each record, each data point, be processed to achieve the desired result.

Iteration is simply the repetition of processing steps. How many repetitions are required can be determined by many different factors. For example, to calculate the total of your stock portfolio, you would iterate over your stock holdings, keeping a running total until each holding has been processed. In this case, the number of repetitions is determined by how many holdings you happen to have. Recursion is another technique for solving problems. Recursion can often, though not always, be a more natural way of expressing an algorithm than iteration. If you've done any programming at all, you probably already know what recursion is — you just didn't know you knew.

A recursive algorithm involves a method or function calling itself. It does this by breaking a problem into smaller and smaller parts, each looking very similar to the larger part yet finer grained. This can be a difficult concept to grasp at first.

You will find that algorithms tend to fall naturally into one category or the other; they are most easily expressed either iteratively or recursively. Having said this, it is fair to say that recursive algorithms are fewer and farther ...

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