How do you implement a priority queue using a linked list?

A priority queue can be implemented using a linked list by inserting elements in order based on their priority.

In a priority queue, elements are assigned a priority when they are added to the queue. The element with the highest priority is always at the front of the queue. When two elements have the same priority, they are served according to their order in the queue.

To implement a priority queue using a linked list, you would start by creating a node class. This class would have two properties: the data (or value) of the node, and the priority of the node. The priority is used to determine the order of the nodes in the queue.

Next, you would create the priority queue class. This class would have a head property, which points to the first node in the linked list, and a size property, which keeps track of the number of nodes in the list.

The priority queue class would also have two methods: enqueue and dequeue. The enqueue method is used to add a new node to the queue. When a new node is added, the method would start at the head of the list and traverse the list until it finds a node with a lower priority, at which point it would insert the new node before the lower priority node. If no such node is found, the new node is added at the end of the list.

The dequeue method is used to remove the node with the highest priority from the queue. Since the list is sorted by priority, this would always be the node at the head of the list. The method would simply update the head property to point to the next node in the list, effectively removing the first node from the queue.

In this way, a priority queue can be implemented using a linked list. It's important to note that this implementation has a time complexity of O(n) for enqueue operations, as it may need to traverse the entire list to find the correct insertion point. However, dequeue operations are O(1), as they simply involve removing the head node.