II. Notes on Data Structuring * - Cornell University

NOTES ON DATA STRUCTURING 121
The choice between representations of multidimensional arrays is made
on quite different grounds. The standard representation is more economical
of storage, and gives good efficiency on sequencing through elements of the
array by rows, columns, or both. Furthermore, it is more convenient when
the arrays must be transferred as a whole between main and backing store.
However, on a machine with slow multiplication, it will be faster to use the
tree representation, and accept the extra storage required to hold the array
of addresses, which is small provided that the rows are not too short. If
each row contains only two words, there would be a fifty per cent overhead
on data storage.
There are several other possible reasons for choosing the tree represen-
tation:
(1) In some computing environments, where dynamic storage allocation
is standard, it may be difficult to obtain large consecutive areas, in which
case a large two-dimensional array can be split up into a number of smaller
rows which can be accommodated without trouble.
(2) It is possible to set up a scheme whereby some rows of the array are
held on backing store while other rows are being processed, and then the
backing store address of a row replaces the main store address in the base
array when that row is absent from store. Thus it is hoped to be able to process
arrays which are too large to be wholly accommodated in main store together
with the program that processes them. However, the economics of this
operation need to be carefully examined to ensure that the number of
backing store transfers involved is acceptable.
(3) In some applications, it is known that several matrices share the same
rows. In the tree representation it is possible to set up a single copy of such a
shared row, and merely take copies of its address rather than its full value.
But in such a case, the shared row must not be selectively updated.
(4) The tree representation is recommended even in the case of single-
dimensional arrays if the size of the individual elements is highly variable;
and on multidimensional arrays, if the length of the rows is highly variable.
Exercise
The character set of an input device includes only thirty characters, defined
by enumeration; they include the characters space, newline, newpage.
Characters may be read in one at a time from an input device to a buffer,
using a procedure call
read next character.
They should be assembled line by line into an array
page'display page,