II. Notes on Data Structuring * - Cornell University

NOTES ON DATA STRUCTURING 131
little problem for representation and manipulation on modern digital com-
puters. Furthermore, they provide the essential basis on which all other more
advanced structures are built.
The most important distinction between elementary structured types and
types of advanced structure is that in the former case the cardinality of the
type is strictly finite, provided that the cardinality of the constituent types is.
The distinction between a finite and an infinite set is one of profound mathe-
matical significance, and it has many consequences relating to methods of
representation and manipulation.
(1) Since the number of potential values of the type may be infinite, the
amount of storage allocated to hold a value of an advanced structure is not
determinable from the declaration itself. It is normally only determined
when the program is actually running, and in many cases, varies during the
execution of the program. In the case of an elementary structure, the number
of different potential values is finite, and the maximum amount of storage
required to hold any value is fixed and determinable from the form of the
declaration.
(2) When the size of a structured value is fairly large, it is more efficient
to update individual components of the structure separately, rather than to
assign a fresh value to the entire structure. Even for elementary types, it
has been found sometimes more efficient to perform selective updating,
particularly for unpacked representations of Cartesian products and for
arrays. The increased efficiency of selective updating is usually even more
pronounced in the case of advanced data structures.
(3) Advanced data structures, whose size varies dynamically, require some
scheme of dynamic storage allocation and relinquishment. The units of
storage which are required are usually linked together by pointers, sometimes
known as references or addresses; and their release is accomplished either by
explicitly programmed operations, or by some form of general garbage
collection. The use of dynamic storage allocation and pointers leads to a
significant complexity of processing, and the problems can be particularly
severe when the data has to be transferred between the main and backing
store of a computer. No problems of this kind need arise in the case of
elementary data structures.
(4) The choice of a suitable representation for an advanced data structure
is often far more difficult than for an elementary structure; the efficiency of
the various primitive operations depends critically on the choice of repre-
sentation, and therefore a sensible choice of representation requires a
knowledge of the relative frequency with which these operations will be
invoked. This knowledge is especially important when a part or all of the
structure is held on a backing store; and in this case, the choice of repre-
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