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By Gerard J Holzmann; American Telephone and Telegraph Company

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5. Eliminating Recursion with for Expressions Problem You want to derive an output sequence from an input sequence where each item in the output is an arbitrarily complex functio input and the sizes of each sequence are not necessarily the same. 0. Use a recursive XSLT template. 0's for expression. Here we show four cases demonstrating how the for expression can map sequences of differ and output sizes. Aggregation (: Sum of squares. :) sum(for $x in $numbers return $x * $x) (: Average of squares.

In this particular case, it improved matters but did not do as well as the solution. An important goal in all recursive implementations is to try to structure the algorithm so that each recursive call sets up a subproblem that is at least half as large as the current problem. This setup causes the recursion to "bottom out" more quickly. Following this advice results in the solution to reverse, shown in Example 2-3. Example 2-3. An efficient (but not ideal) implementation 55 56 This solution is the first one I came up with, and it works well even on large strings (1,000 characters or more).

53 54 1. reverse("abcdef") (input) 2. reverse(def)+reverse("abc") 3. reverse("ef") + "d" + reverse("bc") + "a" 4. "f" + "e" + "d" + "c" + "b" + "a" 5. fedcba (result) Considering more obvious XSLT implementations of reverse is instructive because they provide lessons in how and how not to implement recursive solutions in other contexts. One of the worst algorithms is probably the one that many would think of on their first try. The idea is to swap the first and last character of the string, continue to the second and next to last, and so on until you reach the middle, at which point you are done.

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