The Universe of Discourse
           
Wed, 14 Feb 2007

Subtlety or sawed-off shotgun?

1
  1 1
2
  1 1 1
  2 1
3
  1 1 1 1
  1 2 3
  3 2
4
  1 1 1 1 1
  1 1 2 6
  2 2 3
  3 1 8
  4 6
5
  1 1 1 1 1 1
  2 1 1 1 10
  2 2 1 15
  3 1 1 20
  3 2 20
  4 1 30
  5 24
6
 1 1 1 1 1 1 1
  2 1 1 1 1 15
  2 2 1 1 45
  2 2 2 15
  3 1 1 1 40
  3 2 1 120
  3 3 40
  4 1 1 90
  4 2 90
  5 1 144
  6 120

There's a line in one of William Gibson's short stories about how some situations call for a subtle and high-tech approach, and others call for a sawed-off shotgun. I think my success as a programmer, insofar as I have any, comes from knowing when to deploy each kind of approach.

In a recent article I needed to produce the table that appears at left.

This was generated by a small computer program. I learned a long time ago that although it it tempting to hack up something like this by hand, you should usually write a computer program to do it instead. It takes a little extra time up front, and that time is almost always amply paid back when you inevitably decide that that table should have three columns instead of two, or the lines should alternate light and dark gray, or that you forgot to align the right-hand column on the decimal points, or whatever, and then all you have to do is change two lines of code and rerun the program, instead of hand-editing all 34 lines of the output and screwing up two of them and hand-editing them again. And again. And again.

When I was making up the seating chart for my wedding, I used this approach. I wrote a raw data file, and then a Perl program to read the data file and generate LaTeX output. The whole thing was driven by make. I felt like a bit of an ass as I wrote the program, wondering if I wasn't indulging in an excessive use of technology, and whether I was really going to run the program more than once or twice. How often does the seating chart need to change, anyway?

Gentle readers, that seating chart changed approximately one million and six times.

Order
Higher-Order Perl
Higher-Order Perl
with kickback
no kickback
The Nth main division of the table at left contains one line for every partition of the integer N. The right-hand entry in each line (say 144) is calculated by a function permcount, which takes the left-hand entry (say [5, 1]) as input. The permcount function in turn calls upon fact to calculate factorials and choose to calculate binomial coefficients.

But how is the left-hand column generated? In my book, I spent quite a lot of time discussing generation of partitions of an integer, as an example of iterator techniques. Some of these techniques are very clever and highly scalable. Which of these clever partition-generating techniques did I use to generate the left-hand column of the table?


Why, none of them, of course! The left-hand column is hard-wired into the program:

        while (<DATA>) {
          chomp;
          my @p = split //;
          ...
        }

        ...
        __DATA__
        1
        11
        2
        111
        12
        3
        ...
        51
        6
I guessed that it would take a lot longer to write code to generate partitions, or even to find it already written and use it, than it would just to generate the partitions out of my head and type them in. This guess was correct. The only thing wrong with my approach is that it doesn't scale. But it doesn't need to scale.


The sawed-off shotgun wins!


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