II. Notes on Data Structuring * - Cornell University

160 c.A.R. HOARE
already to be possible, but excluding any exams which have already been
tried. We therefore introduce a variable:
untried: powerset exam,
and a procedure
procedure gensupersets,
which generates and records all possible supersets of trial by adding one or
more exams from untried to it. This procedure will be called from within
"suitable".
function suitable" session;
begin trial, bestsofar" session; e'exam; untried'powerset exam ;
end;
e from remainder;
trial: = bestsofar: = {e};
untried'= remaining- trial- incompat (e);
gensupersets;
suitable: = bestsofar
Note that the first value of the trial is the unitset of some exam chosen from
the remainder according to some as yet undefined criterion. The justification
for this is that the chosen exam must eventually feature in some session of
the timetable, and it might as well be this one. If this prior choice were not
made, gensupersets would keep on generating the same supersets on every
cycle of the major loop of the timetabling program.
As another significant optimisation, we have removed from untried any
exams which are incompatible with the exams in the trial, since there is no
need to even consider the addition of any of these exams to the trial.
The generation of supersets of a given trial may proceed by selecting
each exam from untried, and adding it to trial. If the result is still valid, it
should be recorded, and the new value of trial is then a suitable session to
act as a basis for further superset generation. This suggests a recursive
program structure. Of course, the exam added to trials should also be sub-
tracted from untried, to avoid unnecessary repetitions; and it is very advan-
tageous to remove from untried any exams which are incompatible with the
exam just added to the trial, so that these do not have to be considered again
in future. Also, the values of trial and untried must be left unchanged
by each call, so any change made to them must be recorded and restored in
variables save 1 and save 2.