II. Notes on Data Structuring * - Cornell University

NOTES ON DATA STRUCTURING 165
An alternative and much simpler representation is simply to record for
each exam which session it occurs in. This requires only
array exam of 1.. 60
This representation is made possible only by the fact that the sessions of the
timetable are mutually exclusive.
(4) examcount : array exam of integer
A standard representation is the obvious choice.
(5) remaining, untried, save 1, save 2
These variables start rather full, and get emptier as the program progresses.
Their average density is therefore about fifty percent, and there is no point
in adopting a sparse representation. Furthermore, the frequency of standard
set operations applied to them indicate a standard bitpattern representation.
(6) incompat
The most frequent use of elements of incompat is to subtract them from
untried. They should therefore also use the bitpattern representation. This
will require 500 x 500 bits, of the order of 10000 words. This is by far the
largest data structure required, but its total size is probably fully justified
by the extra speed which it imparts to the program, and since it is acceptable
on most computers on which this program will run, it does not seem worth
while to seek a more compact representation.
(7) load
The load of each student is the primary input data for the problem; it may
also be extremely voluminous. It is therefore doubly fortunate that the
program only needs to make a single scan of the data; for not only will this
enable the data to be presented as an external sequence; it also means that
the representation can be designed to be suitable for human reading, writing,
and punching.
We therefore allocate one card for each student, and use ten columns of
six characters each to hold the examination numbers. To save unnecessary
punching, the first blank column will signify the end of the examination set.
For identification purposes, each card should also contain the student
number; fortunately this can be wholly ignored by the program, though it
should probably be checked to avoid duplications or omissions.
Exercise
Code the abstract program described above using the recommended data
representations.