Another useful data structure that is similar to the stack is called a queue. Data are stored in and retrieved from a queue on a first-infirst-out (FIFO) basis. Thus, if we assume that the queue grows in the direction of increasing addresses in the memory, which is a common practice, new data are added at the back (high-address end) and retrieved from the front (low-address end) of the queue. There are two important differences between how a stack and a queue are implemented. One end of the stack is fixed (the bottom), while the other end rises and falls as data are pushed and popped. A single pointer is needed to point to the top of the stack at any given time. On the other hand, both ends of a queue move to higher addresses as data are added at the back and removed from the front. So two pointers are needed to keep track of the two ends of the queue. A FIFO queue of bytes is to be implemented in the memory, occupying a fixed region of k bytes. The necessary pointers are an IN pointer and an OUT pointer. The IN pointer keeps track of the location where the next byte is to be appended to the back of the queue, and the OUT pointer keeps track of the location containing the next byte to be removed from the front of the queue.

(a) As data items are added to the queue, they are added at successively higher addresses until the end of the memory region is reached. What happens next, when a new item is to be added to the queue?

(b) Choose a suitable definition for the IN and OUT pointers, indicating what they point to in the data structure. Use a simple diagram to illustrate your answer.

(c) Show that if the state of the queue is described only by the two pointers, the situations when the queue is completely full and completely empty are indistinguishable.

(d) What condition would you add to solve the problem in part (c)?

(e) Propose a procedure for manipulating the two pointers IN and OUT to append and remove items from the queue.