A data structure, or abstract data type (ADT), is a model that is defined by a collection of operations that can be performed on itself and is limited by the constraints on the effects of those operations. It creates a wall between what can be done to the underlying data and how it is to be done.

Most of us are familiar with stacks and queues in normal everyday usage, but what do supermarket queues and vending machines have to do with data structures? Let’s find out. In this article I’ll introduce you to two basic abstract data types – stack and queue – which have their origins in everyday usage.

Stacks

In common usage, a stack is a pile of objects which are typically arranged in layers – for example, a stack of books on your desk, or a stack of trays in the school cafeteria. In computer science parlance, a stack is a sequential collection with a particular property, in that, the last object placed on the stack, will be the first object removed. This property is commonly referred to as last in first out, or LIFO. Candy, chip, and cigarette vending machines operate on the same principle; the last item loaded in the rack is dispensed first.

In abstract terms, a stack is a linear list of items in which all additions to (a “push”) and deletions from (a “pop”) the list are restricted to one end – defined as the “top” (of the stack). The basic operations which define a stack are:

init – create the stack.

– create the stack. push – add an item to the top of the stack.

– add an item to the top of the stack. pop – remove the last item added to the top of the stack.

– remove the last item added to the top of the stack. top – look at the item on the top of the stack without removing it.

– look at the item on the top of the stack without removing it. isEmpty – return whether the stack contains no more items.

A stack can also be implemented to have a maximum capacity. If the stack is full and does not contain enough slots to accept new entities, it is said to be an overflow – hence the phrase “stack overflow”. Likewise, if a pop operation is attempted on an empty stack then a “stack underflow” occurs.

Knowing that our stack is defined by the LIFO property and a number of basic operations, notably push and pop, we can easily implement a stack using arrays since arrays already provide push and pop operations.

Here’s what our simple stack looks like:

<?php class ReadingList { protected $stack ; protected $limit ; public function __construct ( $limit = 10 ) { $this - > stack = array ( ) ; $this - > limit = $limit ; } public function push ( $item ) { if ( count ( $this - > stack ) < $this - > limit ) { array_unshift ( $this - > stack , $item ) ; } else { throw new RunTimeException ( 'Stack is full!' ) ; } } public function pop ( ) { if ( $this - > isEmpty ( ) ) { throw new RunTimeException ( 'Stack is empty!' ) ; } else { return array_shift ( $this - > stack ) ; } } public function top ( ) { return current ( $this - > stack ) ; } public function isEmpty ( ) { return empty ( $this - > stack ) ; } }

In this example, I’ve used array_unshift() and array_shift() , rather than array_push() and array_pop() , so that the first element of the stack is always the top. You could use array_push() and array_pop() to maintain semantic consistency, in which case, the Nth element of the stack becomes the top. It makes no difference either way since the whole purpose of an abstract data type is to abstract the manipulation of the data from its actual implementation.

Let’s add some items to the stack:

<?php $myBooks = new ReadingList ( ) ; $myBooks - > push ( 'A Dream of Spring' ) ; $myBooks - > push ( 'The Winds of Winter' ) ; $myBooks - > push ( 'A Dance with Dragons' ) ; $myBooks - > push ( 'A Feast for Crows' ) ; $myBooks - > push ( 'A Storm of Swords' ) ; $myBooks - > push ( 'A Clash of Kings' ) ; $myBooks - > push ( 'A Game of Thrones' ) ;

To remove some items from the stack:

<?php echo $myBooks - > pop ( ) ; echo $myBooks - > pop ( ) ; echo $myBooks - > pop ( ) ;

Let’s see what’s at the top of the stack:

<?php echo $myBooks - > top ( ) ;

What if we remove it?

<?php echo $myBooks - > pop ( ) ;

And if we add a new item?

<?php $myBooks - > push ( 'The Armageddon Rag' ) ; echo $myBooks - > pop ( ) ;

You can see the stack operates on a last in first out basis. Whatever is last added to the stack is the first to be removed. If you continue to pop items until the stack is empty, you’ll get a stack underflow runtime exception.

PHP Fatal error: Uncaught exception 'RuntimeException' with message 'Stack is empty!' in /home/ignatius/Data Structures/code/array_stack.php:33 Stack trace: #0 /home/ignatius/Data Structures/code/example.php(31): ReadingList->pop() #1 /home/ignatius/Data Structures/code/array_stack.php(54): include('/home/ignatius/...') #2 {main} thrown in /home/ignatius/Data Structures/code/array_stack.php on line 33

Oh, hello… PHP has kindly provided a stack trace showing the program execution call stack prior and up to the exception!

The SPLStack

The SPL extension provides a set of standard data structures, including the SplStack class (PHP5 >= 5.3.0). We can implement the same object, although much more tersely, using an SplStack as follows:

<?php class ReadingList extends SplStack { }

The SplStack class implements a few more methods than we’ve originally defined. This is because SplStack is implemented as a doubly-linked list, which provides the capacity to implement a traversable stack.

A linked list, which is another abstract data type itself, is a linear collection of objects (nodes) used to represent a particular sequence, where each node in the collection maintains a pointer to the next node in collection. In its simplest form, a linked list looks something like this:

In a doubly-linked list, each node has two pointers, each pointing to the next and previous nodes in the collection. This type of data structure allows for traversal in both directions.

Nodes marked with a cross (X) denotes a null or sentinel node – which designates the end of the traversal path (i.e. the path terminator).

Since ReadingList is implemented as an SplStack , we can traverse the stack forward (top-down) and backward (bottom-up). The default traversal mode for SplStack is LIFO:

<?php foreach ( $myBooks as $book ) { echo $book . "n" ; }

To traverse the stack in reverse order, we simply set the iterator mode to FIFO (first in, first out):

<?php $myBooks - > setIteratorMode ( SplDoublyLinkedList :: IT_MODE_FIFO | SplDoublyLinkedList :: IT_MODE_KEEP ) ; foreach ( $myBooks as $book ) { echo $book . "n" ; }

Queues

If you’ve ever been in a line at the supermarket checkout, then you’ll know that the first person in line gets served first. In computer terminology, a queue is another abstract data type, which operates on a first in first out basis, or FIFO. Inventory is also managed on a FIFO basis, particularly if such items are of a perishable nature.

The basic operations which define a queue are:

init – create the queue.

– create the queue. enqueue – add an item to the “end” (tail) of the queue.

– add an item to the “end” (tail) of the queue. dequeue – remove an item from the “front” (head) of the queue.

– remove an item from the “front” (head) of the queue. isEmpty – return whether the queue contains no more items.

Since SplQueue is also implemented using a doubly-linked list, the semantic meaning of top and pop are reversed in this context. Let’s redefine our ReadingList class as a queue:

<?php class ReadingList extends SplQueue { } $myBooks = new ReadingList ( ) ; $myBooks - > enqueue ( 'A Game of Thrones' ) ; $myBooks - > enqueue ( 'A Clash of Kings' ) ; $myBooks - > enqueue ( 'A Storm of Swords' ) ;

SplDoublyLinkedList also implements the ArrayAccess interface so you can also add items to both SplQueue and SplStack as array elements:

<?php $myBooks [ ] = 'A Feast of Crows' ; $myBooks [ ] = 'A Dance with Dragons' ;

To remove items from the front of the queue:

<?php echo $myBooks - > dequeue ( ) . "n" ; echo $myBooks - > dequeue ( ) . "n" ;

enqueue() is an alias for push() , but note that dequeue() is not an alias for pop() ; pop() has a different meaning and function in the context of a queue. If we had used pop() here, it would remove the item from the end (tail) of the queue which violates the FIFO rule.

Similarly, to see what’s at the front (head) of the queue, we have to use bottom() instead of top() :

<?php echo $myBooks - > bottom ( ) . "n" ;

Summary

In this article, you’ve seen how the stack and queue abstract data types are used in programming. These data structures are abstract, in that they are defined by the operations that can be performed on itself, thereby creating a wall between its implementation and the underlying data.

These structures are also constrained by the effect of such operations: You can only add or remove items from the top of the stack, and you can only remove items from the front of the queue, or add items to the rear of the queue.