Understanding Linked Lists

• A Linked List is a type of abstract data structure (ADS) that stores elements in a sequential manner.
• Each element (or node) in a linked list consists of two items: the data and a reference/link to the next node.
• The start of the list is known as the head. If the list is empty, the head is a null reference.
• Unlike arrays, linked lists are not stored in continuous blocks of memory. Instead, each element points to the next, forming a chain-like structure.

Types of Linked Lists

• A Singly Linked List is a type of linked list where each node points to the next node in the sequence. It is called 'singly' because each node has a single link to another node.
• A Doubly Linked List has nodes with two references - one to the next node and another to the previous node. This allows traversal in both directions.
• A Circular Linked List is similar to a singly linked list, but the last node in the list points back to the first (head), forming a loop.

Operations on Linked Lists

• Insertion: Adding a new node to the list. This can be at the beginning (prepending), at the end (appending), or in between two nodes.
• Deletion: Removing a node from the list, linking any previous node to any next node directly if needed.
• Traversal: Moving through the list, usually starting at the head and following the references until reaching the end of the list (indicated by a null reference).
• Searching: Finding if an element exists within the list by traversing the nodes.

Advantages and Disadvantages of Linked Lists

• Advantages: Linked lists are dynamic and can easily grow or shrink in size as needed. Insertion and deletion operations are generally efficient.
• Disadvantages: They use more memory than arrays as they need to store the pointers as well as the data. Random access is not allowed - one must start at the head and traverse to reach a particular element.

Complexities of Linked List Operations

• The time complexity for adding or removing elements from a linked list is O(1), assuming we already know the node on which we are operating.
• However, search or access operations have a time complexity of O(n), because it may, in the worst case, have to traverse all elements of the list.
• The space complexity of a linked list is O(n), where n is the number of elements in the list.