A linked list is a data structure composed of a group of nodes, each node linking to the next node in the sequence. Each node consist of two elements, .data which stores the contents of the node, and .next which is a reference to the next node.

Linked lists are one of the simplest data structures. They allow for efficient insertion or removal of elements from any position in the sequence.

To add a new node with data to the start of a linked list:

• Create a new node containing data
• Point the .next of the new node to the current first node
• Point the start of the list first to the new node

This runs in $O(1)$ time.

# Removing nodes

To remove data from a linked list:

• If the first node .data is equal to data:
• Point the start of the list to the node after the first node
• Otherwise:
• Find a node prev just before a node with .data equal to data
• Point prev.next to prev.next.next, skipping the node being removed

Finding the node to remove runs in $O(n)$ time. Removing the node runs in $O(1)$ time. If the previous node to the node to be removed is already available, for example during iteration, then removing the node always runs in $O(1)$ time.

This visualisation allows the adding or removal of nodes to a linked list. Use the buttons on the right of the code to trigger running the commands on the list.