When can we say that a queue is full using double linked lists?

Answer 1

If you use a doubly-linked list to implement a queue then the queue is full whenever it is not empty. However, given that a list dynamically shrinks and expands to accommodate all the elements within it, we can never really say it is full per se because its true capacity is ultimately determined by the amount of available memory and that can vary from one moment to the next.

Note that you do not need to use a doubly-linked list to implement a queue since there is no need to physically traverse a queue. We only need constant-time access to the head (for extractions) and the tail (for insertions). We still need to maintain links between the nodes, however just one link per node would suffice for this. As such, an adapted singly-linked list (also known as a forward list) would consume less memory than a doubly-linked list would. The only change we need to make is to add one pointer to keep track of the tail node.

Note also that a singly-linked list generally does not maintain a count of its elements which helps improve efficiency even further. It's usually sufficient to know if the list is empty or not empty and we can easily determine that in constant-time simply by examining the head node state; if it points to null, then the list is empty otherwise it is not empty (or "full" if you prefer). The same applies to a queue; we're usually only interested in knowing if a queue actually exists before we extract the front element, and that can only be the case if there's at least one element in the queue (i.e., the queue is not empty). The actual number of elements is rarely of any importance, but we can easily adapt a singly-linked list to accommodate a count if we really needed one.