II. Notes on Data Structuring * - Cornell University

procedure gensupersets;
NOTES ON DATA STRUCTURING
begin e: exam; save 1, save 2: powerset exam;
record; save 1 : = untried;
if size (trial) < k then
while untried ~ { ) do
begin e from untried;
end;
end gensupersets.
save 2: = untried /x incompat (e);
untried: - save 2;
trial: v {e);
if sessioncount (trial) < hallsize then
untried: v save 2;
trial: - {e)
untried: -- save 1
gensupersets;
The validity of this program depends on the fact that trial invariantly
satisfies all conditions (4) (5) and (6) for sessions of the timetable, as well as
always being a subset of remaining.
The reasoning is as follows"
for (4): gensupersets never generates a superset except when the size of the
trial is strictly less than k.
for (5): gensupersets is never entered when the sessioncount of trial is
greater than the hall size (we assume that no examcount is greater than
hallsize).
for (6): removal of incompatible sets from untried ensures that at all
times all exams remaining in untried are compatible with all exams of trial.
Therefore, transfer of an arbitrary exam from untried to trial can never
cause (6) to be violated.
Finally, at the initial call of gensupersets, untried ~ remaining. Untried is
an essentially non-increasing quantity: every addition of members to it has
always been preceded by removal of those very same members. Untried is
therefore always a subset of remaining; and trial, which is constructed only
from members of untried, must also always be a subset of remaining.
This completes our first version of an abstract program to construct
examination timetables. Collecting all the material together, it looks like this"
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