EWD249 - 82

algorithm) can deduce that after that for the first time the trial sequence will have length = 101 and this is now the criterion to stop, but this is a rather indirect and tortuous way to establish the stopping criterion. (How tortuous it is was clearly demonstrated by those students who did not see that an unnecessary trial sequence was generated and declared for the trial sequence an array of 100 elements instead of 101.) The second objection is that the operation "increase trial sequence" never increases its length: after rejection of a trial sequence a superfluous test on the length is performed. (When I used this example for student examination examinations I had not stressed very explicitly in my lectures any problem solving principles, so my disappointment was not too severe. In a sense I am glad to have observed these examinations, for it was for me an incentive to stress problem solving principles as far as I could find, formulate and teach them.)

The program to which the above objections do not apply treats the empty sequence as a virtual solution, not to be printed. It has -to the same level of detail- the following structure:

"set trial sequence empty;
repeat extend trial sequence with zero;
       while no good do increase trial sequence;
       print trial sequence
until length = 100"

Here length is the length of the solution printed (if any), thus avoiding the tortuous reasoning for the stopping criterion. Also no superfluous last trial sequence (never to be investigated) will be generated, thanks to the fact that we have two loops inside each other, superfluous length testing no longer occurs. Those for whom efficiency is the main criterion will probably be most convinced by the last observation. I myself, who attach considerable importance to understandability, am attracted to the latter program because I can interpret it as a further refinement of the program structure

"set sequence empty;
repeat transform sequence to next solution;
       print sequence
until length = 100"

This (more abstract) program is only concerned with sequences that are solutions: