## Queues

NB.
Do not confuse thepriority queue withthe ordinary queue (here). The priority queue is, for example, used in Heap sort. |

The *queue* is an abstract data type that obeys a
**F**irst **I**n
**F**irst **O**ut (FIFO)
rule.
It is used where elements are processed in the order in
which they arrive.
As such it finds many uses in computer operating systems -
for example the process queue, the print queue.

type queue = empty_queue | addq Element_Type × queue Operations: front :queue -> Element_Type addq :Element_Type × queue -> queue popq :queue -> queue empty :queue -> boolean Rules: front(addq(e, empty_queue)) = e front(addq(e, q)) = front(q), if q not empty front(empty_queue) = error popq(addq(e, empty_queue)) = empty_queue popq(addq(e, q)) = addq(e, popq(q)), if q not empty popq(empty_queue) = error empty(empty_queue) = true empty(addq(e, q)) = false

**The Queue Abstract Data Type.**

If queues do not share elements, procedures may be written to manipulate them as side-effects, much as for stacks. Frequently front and popq are combined in one procedure which returns the front elements and removes it from the queue.

### Example: Breadth-First Traversal of a Tree

A queue is used in the algorithm to traverse a tree in breadth-first order. This is given in the chapter on binary trees.

### Queue by Array

A queue can be implemented by an array of elements. Two integers point to the first and last elements respectively. Pointer arithmetic is done modulo the maximum size. For this reason it is more convenient if the array index runs from zero to the maximum size minus one.

L . A l l i s o n |

0 1 2 3 4 5 6=m-1 - - a b c - - ^ ^ | | | last first

**Queue.**

0 1 2 3 4 5 6=m-1 f g - - - d e ^ ^ | | last first

**Queue, some time later.**

This implementation places a limit on the number of elements
and is often called a *bounded queue*.

### Queue by Circular List

There are various ways of implementing a queue by a list. Since front and addq require fast access to opposite ends of the list, a pointer can be kept to each end of the list. A neat variation is to use a circular list where the queue variable points to the last element:

q----------->------------| | | v 1----->2----->3----->.....----->n-->--| ^ | | | | | | | |--------<-----------------------------

**nil**pointer.

[C/Queue/Queue.h] [C/Queue/Ops.c]

*breadth-first*[tree] traversal.

### Exercises

- In an Object oriented Language: Implement a class which exports the standard queue operations and which privately implements the queue by an array.
- Give an implementation of a queue using a linear list and pointers to the first and last elements.