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Introduction

Kurt Cagle posted an article about helping his daughter with sums. Since I should be doing marking today, it was clearly imperative to look at the problem and see how I would code it. I'm also working on my SQL tutor so there is some connection I could use to justify this diversion if questioned.

Kurt's code is specific to a sum structure (the range of digits, the size of numbers the number of numbers). This code generalises over these parameters, not merely because I think that makes a more interesting application, but because generalisation often leads to a cleaner design. As ever, it's hard to hit the Goldilocks spot, not too much, not too little. For me it always takes a bit of experimentation - surely I should be able to apply a design technique to hit the sweet spot?

Approach

• The problem specification is read from parameters
• A function generates a sequence of random digits (random-digits) used for each of each of the rows.
• A pair of functions convert between an integer and a sequence of digits (number-to-digits and digits-to-number).
• The sum is rendered in a table to get fixed spacing. The number of digits in the sum of the numbers determines the number of columns in the table
• A function converts an integer into a seqence of cells padded with blanks at the beginning (number-to-row) ,prefixing the last row with a + and underling.
• The interface is taken from Kurt's code, hide/showing the answer.

Version one

• XQuery source
• Kurt's problem set
• Harder problem - 5 rows with 6 columns including 0

Generalised interface

Adding an interface to change the problem specification could be achieved in several ways, including XForms. This version uses a very simple model definition which is used to generate a form or a parameterised URL and to extract values from the URL.

• Kurt's problem set
• Harder problem - 5 rows with 6 columns including 0
• XQuery source
• Module source

Generalized base

One magic number remains - the 10 of the base. Its tempting to use a global variable to set this property of the problem specification, but I'd rather parameterize the functions. Max base is 10. An obvious extention is to be be able to do hex sums but digits cant be integers then.

• Kurt's problem set
• Binary problem
• XQuery source

Sometimes it appears that the number of rows is less than the number specified. This is because sometimes 0 is generated as the number which is rendered as all spaces.

Re-factoring

The function to generate rows from numbers is ugly and over-specific. In fact the styling of the last row to create a line doesn't work when zeros are allowed, and the operator might be parameterised too, but the code to converted to padded cells would be the same.

Refactoring the number-to-row function and using an hr element to divide problem from answer yields a more statisfactory solution:

• Kurt's problem set
• Binary problem
• XQuery source

Lessons Learnt

• It is always easier to improve on someone else's ideas than think of your own problems.
• Generalisation can make code cleaner and more understandable (but you can go too far)
• Where possible, functions should be designed to be inverse pairs. This helps with testing.
• Iterative refactoring is a necessary programming process.
• XML namespaces are still a headache to me. I often resort to using a wildcard namespace as in the final script when namespaces are mixed.