II. Notes on Data Structuring * - Cornell University

136 c.A.R. HOARE
(3) If the only operations are writing and reading back (push down and
pop up), the sequence is known as a stack; the initial value of a stack is
always empty, and the final value is not usually preserved.
(4) If the only operations are writing to the end and reading from the
beginning, the sequence is known as a queue; again, the initial value is always
empty, and the final value is not usually preserved.
(5) If" reading and writing at both ends of a sequence are permitted, the
sequence is sometimes known as a deque (double-ended queue). However,
to make all four operations equally efficient requires some complexity of
representation, so it is fortunate that most programs can get by without
using deques.
8.2. REPRESENTATION
8.2.1. Contiguous representation
The simplest method of representing a sequence is to allocate to it a fixed
contiguous area of storage, adequate to hold all items actually required.
This method is suitable if the value (or at least the length) of the sequence is
constant throughout the execution of the program--for example, a string of
characters intended to be used as an output message or title.
In some cases, the length of the sequence is unknown at the time the
program is written, but is known on entry to the block in which the sequence
is declared, and this length remains constant throughout the existence of the
sequence. In such cases, it is possible to allocate a contiguous area of storage
in the local workspace of the block, using the standard stack method of store
allocation and deallocation.
Even if the length of the sequence is subject to variation, it is sometimes
possible to place an acceptably small upper bound on its length, and allocate
permanently this maximum area. If the limit is exceeded during a run of the
program, the programmer must be willing to accept its immediate termina-
tion. In addition to the fixed area, a pointer or count is required to indicate
the current beginning and end of the sequence. In the case of a stack, the first
item is always at the beginning, and only one pointer to the top of the stack
is required. In the case of a queue, the sequence will at times overlap the
end of the store area, and be continued again at the beginning. Such a
representation is known as a cyclic buffer, and may be used in a parallel
programming situation to communicate information between processes
running in parallel. In this case, when a writing process finds the buffer full,
it has to wait until a reading process reduces the size of the sequence again.
Similarly, the reading process must wait when the buffer is empty.
Another case where the contiguous representation is the best is when the
program requires only a single sequence, which may therefore occupy the