II. Notes on Data Structuring * - Cornell University

140 c. A, R. HOARE
mark-collect garbage collection. Although it appears to relieve the pro-
grammer of the responsibility of explicit control of main store allocation and
deallocation, this can be dangerous in non-trivial computer applications
where the responsibility is one that cannot so lightly be evaded.
In the case of a deque, when reading is required in both directions, a single-
linked chain is no longer adequate; and the usual solution is to adjoin two
pointers to each item in the chain, one pointing to the previous item and one
pointing to the following item. In fact these two pointers can be compressed
into a single word containing only the difference between them. Since in
the first and last items one of the pointers is a standard null value, the value
of the other pointer from these items can always be obtained by subtraction.
On reading or writing, the value of the link location for the new first or last
item can be readily adjusted, since at this stage the address of the previous
first or last item is still known. The detailed working out of this scheme is
left as an exercise.
An alternative method of linking the items of a chain is to collect all links
together in a single contiguous table, preferably of fixed length. This giwes a
form of tree representation for the sequence, and permits ready scanning
in both directions. But it places an upper bound on the number of items in
the sequence; and it means that the locations used for links must be per-
manently allocated, even at times when the sequence is relatively short.
This problem can be mitigated by the use of blocking.
8.2.3 Blocked Representation
One disadvantage of chaining is the amount of extra storage required to hold
the links, and the time taken to administer the free store chain on each
operation. These problems are particularly severe when the size of the
individual items of the sequence are small and the sequence is long. The
method of solving this problem is to use blocking; that is, a combination of
the contiguous and chained techniques.
In this technique, a fixed-length block of storage is allocated, sufficient to
hold perhaps between ten and a hundred items. When this block is filled, a
new block is chained to it, using any of the methods described in the previous
section. On input, a block is not released to free store until all the items it
contains have been scanned. Thus the amount of store used on links can be
reduced to negligible proportions. This can be of particular benefit in the
tree representation of the chain.
As mentioned above, the use of blocking can also avoid the
problems arising from variable-length dynamic storage allocation, since the
size of the block may be held constant for all sequences, independent of the
size of their items. Furthermore, in cases where part or all of the sequence
is to be held on backing store, the use of blocking is almost universally