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Building on It

The purpose of The Practice of Programming was to teach good programming. At the time the book was written, Rob and I were still at Bell Labs, so we did not have firsthand experience of how the book would be best used in a classroom. It has been gratifying to discover that some of the material does work well in classes. I have used this code since 2000 as a vehicle for teaching important points about programming.

First, it shows how recursion is useful and leads to clean code in a novel setting; it's not yet another version of Quicksort (or factorial!), nor is it some kind of tree walk.

It's also a good example for performance experiments. Its performance is not very different from the system versions of grep, which shows that the recursive technique is not too costly and that it's not worth trying to tune the code.

On the other hand, it is also a fine illustration of the importance of a good algorithm. If a pattern includes several .* sequences, the straightforward implementation requires a lot of backtracking, and, in some cases, will run very slowly indeed.

The standard Unix grep has the same backtracking properties. For example, the command:

	grep 'a.*a.*a.*a.a'

takes about 20 seconds to process a 4 MB text file on a typical machine.

An implementation based on converting a nondeterministic finite automaton to a deterministic automaton, as in egrep, will have much better performance on hard cases; it can process the same pattern and the same input in less than one-tenth of a second, and running time in general is independent of the pattern.

Extensions to the regular expression class can form the basis of a variety of assignments. For example:

  1. Add other metacharacters, such as + for one or more occurrences of the previous character, or ? for zero or one matches. Add some way to quote metacharacters, such as \$ to stand for a literal occurrence of $.

  2. Separate regular expression processing into a compilation phase and an execution phase. Compilation converts the regular expression into an internal form that makes the matching code simpler or allows the subsequent matching to run faster. This separation is not necessary for the simple class of regular expressions in the original design, but it makes sense in grep-like applications where the class is richer and the same regular expression is used for a large number of input lines.

  3. Add character classes such as [abc] and [0-9], which in conventional grep notation match a or b or c and a digit, respectively. This can be done in several ways, the most natural of which seems to be replacing the char* variables of the original code with a structure:

    	typedef struct RE {
    	        int     type;   /* CHAR, STAR, etc. */ 
    	        int     ch;     /* the character itself */ 
    	        char    *ccl;   /* for [...] instead */
    	        int     nccl;   /* true if class is negated [^...] */
    	} RE;

    and modifying the basic code to handle an array of these instead of an array of characters. It's not strictly necessary to separate compilation from execution for this situation, but it turns out to be a lot easier. Students who follow the advice to pre-compile into such a structure invariably do better than those who try to interpret some complicated pattern data structure on the fly.

    Writing clear and unambiguous specifications for character classes is tough, and implementing them perfectly is worse, requiring a lot of tedious and uninstructive coding. I have simplified this assignment over time, and today most often ask for Perl-like shorthands such as \d for digit and \D for nondigit instead of the original bracketed ranges.

  4. Use an opaque type to hide the RE structure and all the implementation details. This is a good way to show object-oriented programming in C, which doesn't support much beyond this. In effect, this creates a regular expression class that uses function names like RE_new() and RE_match() for the methods instead of the syntactic sugar of an object-oriented language.

  5. Modify the class of regular expressions to be like the wildcards in various shells: matches are implicitly anchored at both ends, * matches any number of characters, and ? matches any single character. One can modify the algorithm or map the input into the existing algorithm.

  6. Convert the code to Java. The original code uses C pointers very well, and it's good practice to figure out the alternatives in a different language. Java versions use either String.charAt (indexing instead of pointers) or String.substring (closer to the pointer version). Neither seems as clear as the C code, and neither is as compact. Although performance isn't really part of this exercise, it is interesting to see that the Java implementation runs roughly six or seven times slower than the C versions.

  7. Write a wrapper class that converts from this class's regular expressions to Java's Pattern and Matcher classes, which separate the compilation and matching in a quite different way. This is a good example of the Adapter or Facade pattern, which puts a different face on an existing class or set of functions.

I've also used this code extensively to explore testing techniques. Regular expressions are rich enough that testing is far from trivial, but small enough that one can quickly write down a substantial collection of tests to be performed mechanically. For extensions like those just listed, I ask students to write a large number of tests in a compact language (yet another example of "notation") and use those tests on their own code; naturally, I use their tests on other students' code as well.

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