Hello there! Today, we will explore Linked Lists, a core data structure crucial for organized data management and establishing relationships between data using PHP.

We will mark some essential milestones: an introduction to Linked Lists, their real-world applications, their implementation in PHP, and the different operations you can perform on them.

By the end of this lesson, you will be well-equipped to implement and operate Linked Lists in PHP. Let's get started!

A Linked List is a linear data structure similar to arrays. But, unlike arrays, they are not stored in contiguous memory locations. Each element in a Linked List is part of a node. A node comprises data and a reference (or link) to the next node in the sequence. This structure facilitates efficient insertions and deletions.

The head is also an essential concept in Linked Lists. It is the first node in the list and a reference to the entire list. The head is a null reference if the Linked List is empty.

Singly linked lists come up quite often in coding interviews. Interviewers from tech giants, start-ups, and just about every company testing your coding abilities will pose challenges based on this concept.

Here's another interesting point: While singly linked lists might not be extensively used in real-world applications, they form the foundational knowledge for understanding doubly linked lists, which are indeed quite common.

To begin implementing Linked Lists, we first need to understand the structure of a node, the building block of a Linked List. In PHP, we create a class to represent this node.

A Node class will consist of data (the data you want to store) and next (the reference to the next node). In our case, we'll create a Node class to store integer data.

php
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1class Node {
2    public $data;
3    public $next;
4
5    public function __construct($data) {
6        $this->data = $data;
7        $this->next = null;
8    }
9}

Fantastic! You now know how to set up a node in a Linked List in PHP.

In this section, we'll learn how to add a new node at the end of our Linked List. We'll implement an append function in our LinkedList class for this.

php
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1class Node {
2    public $data;
3    public $next;
4
5    public function __construct($data) {
6        $this->data = $data;
7        $this->next = null;
8    }
9}
10
11class LinkedList {
12    private $head;
13
14    public function __construct() {
15        $this->head = null;
16    }
17
18    public function append($data) {
19        $node = new Node($data);
20
21        if ($this->head === null) {
22            $this->head = $node;
23        } else {
24            $last = $this->head;
25            while ($last->next !== null) {
26                $last = $last->next;
27            }
28            $last->next = $node;
29        }
30    }
31}

The code checks if head is null, which would be the case for an empty list. If that's true, head is set to the new node, meaning this new node is the first and only node in the list. If the linked list is not empty (head is not null), the code enters a loop to navigate to the end of the list. The new node is then appended after the last node in the list.

Now, what if we want to add a new node at the beginning of our list? We'll write a function addFirst to achieve this operation in PHP.

php
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1class LinkedList {
2    private $head;
3
4    public function __construct() {
5        $this->head = null;
6    }
7
8    public function addFirst($data) {
9        $node = new Node($data);
10        
11        if ($this->head !== null) {
12            $node->next = $this->head;
13        }
14
15        $this->head = $node;
16    }
17}

It simply reassures the head is reset to this new node, effectively placing it at the start of the list.

Removing a node from a Linked List is also an essential functionality. We will add a delete function to our LinkedList class to remove a node with a particular data value in PHP.

php
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1class LinkedList {
2    private $head;
3
4    public function __construct() {
5        $this->head = null;
6    }
7
8    public function delete($data) {
9        if ($this->head === null) return;
10
11        if ($this->head->data === $data) {
12            $this->head = $this->head->next;
13            return;
14        }
15
16        $current = $this->head;
17        while ($current->next !== null) {
18            if ($current->next->data === $data) {
19                $current->next = $current->next->next;
20                return;
21            }
22            $current = $current->next;
23        }
24    }
25}

We traverse the list as in the append operation, searching for a node with specific data. If found, it is removed from the list by retargeting the previous node to the node after the target.

While understanding the implementation of Linked Lists is great, it's equally crucial to comprehend the performance of our operations. This understanding generally comes through complexity analysis, examining the time (number of operations) and space (memory used) needed for an operation.

Here's a summary of the performance of particular operations in Linked Lists:

• Accessing an element: It has O(n) time complexity because, in the worst-case scenario, we'd have to traverse through the entire list.
• Inserting or deleting a node: It's O(1) if we're adding or removing from the front of the list. However, if it's at the end or in the middle, it would be O(n) because we'd have to traverse the list to find the position.

Great job sticking with it throughout this intriguing journey, from understanding the concept of Linked Lists to implementing them in PHP, exploring critical operations, and understanding their performance!

Up ahead, we have lined up some practice sessions. These sessions will provide you with real-time experience implementing and manipulating Linked Lists in PHP.