If we talk about arrays and linked lists we know the pros and cons about both of them. No matter which programming language we use arrays benefit from direct access to its items, while linked lists are more memory efficient for particular tasks.

The items of a linked list keep a reference to their successor, so we can easily walk through the entire list. However we don’t have direct access to its elements. Thus we can’t go directly to its middle element! Even more – in particular implementations of a linked list we don’t know its length. But in some cases linked lists are far more effective than arrays. For instance reversing an array of non-numeric values require constant additional memory, but also requires n/2 exchanges. The same taks using linked lists is not only performed in linear time, but doesn’t require any additional memory. The only thing we need to do is to reverse the links – no movement of values and the items remain at the same place in the memory.

Merging of two arrays often require more space (proportional of the space of the two arrays) or many exchanges in case we try to do it in place. The same task on linked lists is far more effective with only changing pointers and without moving the values.

Arrays or Linked Lists are More Memory Efficient

Many developers consider linked lists as something used only in college, but actually they can be very useful in practice as well. However how practically useful they are? Let’s see the following PHP experiment.

Here we have one class called “Item”, which is designed to keep only one integer value as its key and to point to its successor. Practically this class is designed to be used by a singly linked list, but let say we put some of these objects into an array and the same amount of the “Item” objects into a linked lists so what are the results?

First let’s see the code!

class Item
{
    protected $_key = '';
    protected $_next = null;
    
    public function __construct($key)
    {
        $this->_key = $key;
    }
    
    public function setNext(&$next) { $this->_next = $next; }
    public function &getNext() { return $this->_next; }
    
    public function setKey($key) { $this->_key = $key; }
    public function getKey() { return $this->_key; }
    
    public function __toString()
    {
        return $this->_key . "\n";
    }
}

This is the “Item” class and here we have the Linked_List class. As you can see this is the very basic implementation of a linked list with only one “insert” method and the magic __toString() in order to print the entire list. The insert method pushes an item at the end of the list thus the insertion is O(1).

class Linked_List 
{
    protected $_head = null;
    protected $_tail = null;
    
    public function insert($item)
    {
        if ($this->_head == null) {
            $this->_head = $item;
            $this->_tail = $item;
            return;
        }
        
        $this->_tail->setNext($item);
        $this->_tail = $item;
    }
    
    public function __toString()
    {
        $current = $this->_head;
        $output = '';
        
        while ($current) {
            $output .= $current->getKey() . "\n";
            $current = $current->getNext();
        }
        
        return $output;
    }
}

Now let’s see the creation of an array with N objects of class “Item”.

$n = 10000;
$a = array();
for ($i = 0; $i < $n; $i++) {
    $a[$i] = new Item($i);
}

The same thing but using the Linked_List class follows on the lines below.

$n = 10000;
$a = new Linked_List();
for ($i = 0; $i < $n; $i++) {
    $a->insert(new Item($i));
}

And the Winner is ...

More memory efficient is ... the linked list! On the next chart we can see the results. It's clear that for 10K objects the array uses nearly 1MB more memory than the linked list!

So what do you think now? Will you use linked list in your code or not?

Final Words

Although the linked list seems to be more memory efficient we don't have direct acess to it's items. In the same time often we don't need direct access, we just need to walk through the array, which doesn't benefit from the direct access. In PHP this is usally done with some loop construction as "foreach". So why we have such results in the experiment above. First our linked list is really very basic. It doesn't have any functionality, which in fact shouldn't affect memory usage much more. The array in the other hand keeps indexes for each of its items so this results in additional space. This explains a bit the victory of the linked list in the memory efficiency test.

In the other hand PHP can't have the full benefit of using linked lists, trees and other data structures since it keeps them in memory only for the request. In this case C, C++, Java loads a data structure in memory till the software runs so unfortunately coding complex data structures in PHP doesn't look as a great option. Indeed here we have an entire "Item" class only to keep an integer. Instead we can use an array of integers!

The linked list is a data structure in which the items are ordered in a linear way. Although modern programming languages support very flexible and rich libraries that works with arrays, which use arrays to represent lists, the principles of building a linked list remain very important. The way linked lists are implemented is a ground level in order to build more complex data structures such as trees.

It’s true that almost every operation we can perform on a linked list can be done with an array. It’s also true that some operations can be faster on arrays compared to linked lists.

However understanding how to implement the basic operations of a linked list such as INSERT, DELETE, INSERT_AFTER, PRINT and so on is crucial in order to implement data structures as rooted trees, B-trees, red-black trees, etc.

Overview

Unlike arrays where we don’t have pointers to the next and the previous item, the linked list is designed to support such pointers. In some implementations there is only one pointer pointing to the successor of the item. This kind of data structures are called singly linked lists. In this case the the last element doesn’t have a successor, so the pointer to its next element usualy is NULL. However the most implemented version of a linked list supports two pointers. These are the so called doubly linked lists.

Let’s take a look at some examples. Here’s an array:

A[2, 'hello', 'world', 13, 31]

We know that A[0] contains the number 2, while A[1] contains the word (string) “hello”. This is the very basic array representation where the indices are consecutive and start from 0.

In that case we know that if we’re looking at the item with index i, its next element has an index i+1, while his predecessor’s index is i-1. Thus we can easily iterate over items. However if we have an array with only 5 elements A[5] doesn’t exists, and in most of the cases is NULL. In other words array items are defined by their indices, and can be accessed directly with their index.

In the other hand most of the programming languages support associative arrays also called hash maps.

An associative array in PHP can be something like this.

$a = array(
	'hello' => 'world',
	31	=> 12,
	'b7'	=> 144,
);

Now because the indices are not consecutive integers we don’t know the successor and the predecessor of the current item. Yes, there is some internal pointer that can give us the link to the previous and the next item, but explicitly we can’t refer them.

Of course some libraries may have functions that can point us to the next item, such a function is next() in PHP.

As we see arrays can replace the typical pointer-like representation of a linked list, but as I said already this data structure is crucial in order to understand more complex data structures.

Typically the linked list is implemented with two classes. The first one describing the item and the other one containing the main operations of the list such as search, insert, delete, etc.

The first class, typically called Item is a normal class containing various info about an item. In terms of persons, for instance, this class can contain the first and last names of the person, his address, phone etc. However it’s very important that this class contains pointers to its previous and its next objects.

In our terms each object of class Person will contain a pointer to a next object of the same class Person.

class Person
{
	public $next = null;
	public $prev = null;
	
	protected $_firstName = '';
	protected $_lastName = '';
	protected $_phone = '';
	
	
	public function __construct($firstName, $lastName, $phone)
	{
		$this->_firstName = $firstName;
		$this->_lastName = $lastName;
		$this->_phone = $phone;
	}
	
	public function __toString()
	{
		return 'First name: ' . $this->_firstName 
			 . ', Last name: ' . $this->_lastName 
			 . ', Phone: ' . $this->_phone;
	}
}

So we must first design the structure of an item.

The following thing to do is to define a linked list as an abstraction over a real world list, just like the stack and the queue. We can implement various operations for a linked list like insert, delete, insertBefore, insertAfter, sort, search, insertSorted etc. It’s up to the developer to decide which operations he wants to use. And of course this depends on the application.

Implementation

Operations

We can perform and define as much operations as we need. For instance we can code a linked list only with the basic insert, delete and print, but we can also go for insertBefore, insertAfter, deleteBefore, deleteAfter, insertSorted, which are described on the diagrams below.

Insert

Inserting in the front of a list seems much like inserting into a queue. In this case the new item becomes the head of the list and its successor is the previous head of the list.

class LList
{
	public $head;
	public $tail;
	
	public function insert($item) 
	{
		$item->next = $this->head;
		
		if ($this->head != null) {
			$this->head->prev = $item;
		}
		
		$this->head = $item;
	}

	public function __toString()
	{
		$cur = $this->head;
		
		$output = '';
		while ($cur) {
			$output .= $cur . ' ';
			
			$cur = $cur->next;
		}
		
		return $output . "\n";
	}
}

$ll = new LList();

$a = new Person('John', 'Smith', '555 9401');
$b = new Person('James', 'Johnes', '555 2454');

$ll->insert($a);
$ll->insert($b);

// James Johnes 555 2454
// John Smith 555 9401
echo $ll;

Delete

Delete the head of the list is much like deleting an item from a queue. However we can implement also deleting a custom element that’s inside the list.

class LList
{
	public $head;
	public $tail;
	
	public function insert($item) 
	{
		$item->next = $this->head;
		
		if ($this->head != null) {
			$this->head->prev = $item;
		}
		
		$this->head = $item;
	}
	
	public function delete($item) 
	{
		$cur = $this->head;
		
		while ($cur) {
			
			if ($cur == $item) {
				$prev = $cur->prev;
				$next = $cur->next;
				
				if ($prev != null) {
					$prev->next = $next;
				} else {
					// because head points to the first item
					$this->head = $next;
				}
				
				if ($next != null) {
					$next->prev = $prev;
				}
				
				return $cur;
			}
		
			$cur = $cur->next;
		}
	}

	public function __toString()
	{
		$cur = $this->head;
		
		$output = '';
		while ($cur) {
			$output .= $cur . ' ';
			
			$cur = $cur->next;
		}
		
		return $output . "\n";
	}
}

$ll = new LList();

$a = new Person('John', 'Smith', '555 9401');
$b = new Person('James', 'Johnes', '555 2454');
$c = new Person('Jeanne', 'Francois', '333 2323');

$ll->insert($a);
$ll->insert($b);
$ll->insert($c);

// prints objects $c, $b, $a:
// Jeanne Francois 333 2323
// James Johnes 555 2454
// John Smith 555 9401
echo $ll;

$ll->delete($b);

// prints objects $c, $a:
// Jeanne Francois 333 2323
// John Smith 555 9401
echo $ll;

Insert before & insert after

Inserting before and after needs a reference to an already existing list item. After that the new object is inserted into it right place, as shown on the images below.

class LList
{
	public $head;
	public $tail;
	
	public function insert($item) 
	{
		$item->next = $this->head;
		
		if ($this->head != null) {
			$this->head->prev = $item;
		}
		
		$this->head = $item;
	}
	
	public function insertAfter($newItem, $item) 
	{
		$cur = $this->head;
		while ($cur) {
			if ($cur == $item) {
				$next = $cur->next;
				
				$cur->next = $newItem;
				$newItem->prev = $cur;
				
				if ($next != null) {
					$newItem->next = $next;
					$next->prev = $newItem;
				}
				return;
			}
			$cur = $cur->next;
		}
		
		$this->head = $this->tail = $item;
	}

	public function __toString()
	{
		$cur = $this->head;
		
		$output = '';
		while ($cur) {
			$output .= $cur . ' ';
			
			$cur = $cur->next;
		}
		
		return $output . "\n";
	}
}

$ll = new LList();

$a = new Person('John', 'Smith', '555 9401');
$b = new Person('James', 'Johnes', '555 2454');
$c = new Person('Jeanne', 'Francois', '333 2323');

$ll->insert($a);
$ll->insert($c);

// inserts $b after $a
$ll->insertAfter($b, $c);

// Jeanne Francois 333 2323
// James Johnes 555 2454
// John Smith 555 9401
echo $ll;

Insert a new object before an item is the same as insert after, but instead of splitting the list after the given item, we split it before it.

Search

Searching into a list can be modified depending on the application needs. Here we just compare the searched object with a list item.

class LList
{
	public $head;
	public $tail;
	
	public function insert($item) 
	{
		$item->next = $this->head;
		
		if ($this->head != null) {
			$this->head->prev = $item;
		}
		
		$this->head = $item;
	}
	
	public function insertAfter($item, $key) 
	{
		$cur = $this->head;
		while ($cur) {
			if ($cur->data == $key) {
				$next = $cur->next;
				
				$cur->next = $item;
				$item->prev = $cur;
				
				if ($next != null) {
					$item->next = $next;
					$next->prev = $item;
				}
				return;
			}
			$cur = $cur->next;
		}
		
		$this->head = $this->tail = $item;
	}

	public function search($item)
	{
		$cur = $this->head;
		
		while ($cur) {
			if ($cur == $item) {
				return 1;
			}
			
			$cur = $cur->next;
		}
		
		return 0;
	}
	
	public function __toString()
	{
		$cur = $this->head;
		
		$output = '';
		while ($cur) {
			$output .= $cur . ' ';
			
			$cur = $cur->next;
		}
		
		return $output . "\n";
	}
}

$ll = new LList();

$a = new Person('John', 'Smith', '555 9401');
$b = new Person('James', 'Johnes', '555 2454');
$c = new Person('Jeanne', 'Francois', '333 2323');

$ll->insert($a);
$ll->insert($b);

// 1, because $b is in the list
echo $ll->search($b);

// 0, cause $c isn't in the list
echo $ll->search($c);

The operations here are only one sub-set of all possible operations you can implement on a linked list. It all depends on our needs. However the principles are important, so we can implement more complex data structures.

Application

It’s true that linked list are a very basic data structure. Someone may wonder why we should code and implement linked list since we can do the same (with almost every modern programming language/library) with arrays. The answer is that data structures as trees are difficult to implement with arrays, so it’s easy to code them using pointers. Thus linked lists is a ground level for understanding them. Indeed each linked list is a tree with only one branch as shown on the image below.