Name some Queue implementations and compare them by efficiency of operations

Queues are fundamental data structures in computer science, and there are several ways to implement them, each with its own efficiency characteristics. Here are some common queue implementations and a comparison of their efficiency:

1. Array-Based Queue

Implementation:

• Uses a fixed-size array to store elements.
• Two pointers, front and rear, track the start and end of the queue.

Efficiency:

• Enqueue (Insertion): $$O(1)$$ if the array is not full.
• Dequeue (Deletion): $$O(1)$$.
• Access Time: $$O(1)$$ for accessing any element.
• Space Complexity: $$O(n)$$, where $$n$$ is the size of the array.

Advantages:

• Constant time for insertion and deletion.
• Efficient memory usage for small queues.

Disadvantages:

• Fixed size, requiring resizing if the queue grows beyond the initial capacity, which can be expensive.

2. Linked List-Based Queue

Implementation:

• Uses a linked list where each node points to the next node.
• Two pointers, front and rear, track the start and end of the queue.

Efficiency:

• Enqueue (Insertion): $$O(1)$$.
• Dequeue (Deletion): $$O(1)$$.
• Access Time: $$O(n)$$ for accessing elements sequentially.
• Space Complexity: $$O(n)$$, where $$n$$ is the number of elements in the queue.

Advantages:

• Dynamic size, no need for resizing.
• Efficient for frequent insertions and deletions.

Disadvantages:

• Higher memory overhead due to storage of pointers.
• Slower access time compared to array-based queues.

3. Circular Queue

Implementation:

• Uses an array in a circular fashion to reuse memory space.
• Two pointers, front and rear, track the start and end of the queue.

Efficiency:

• Enqueue (Insertion): $$O(1)$$.
• Dequeue (Deletion): $$O(1)$$.
• Access Time: $$O(1)$$ for accessing any element.
• Space Complexity: $$O(n)$$, where $$n$$ is the size of the array.

Advantages:

• Efficient memory utilization by reusing space.
• Constant time for insertion and deletion.

Disadvantages:

• Fixed size, requiring resizing if the queue grows beyond the initial capacity.

4. Priority Queue

Implementation:

• Can be implemented using arrays, linked lists, or binary heaps.
• Elements are dequeued based on priority rather than order of insertion.

Efficiency:

• Enqueue (Insertion): $$O(\log n)$$ for binary heap implementation.
• Dequeue (Deletion): $$O(\log n)$$ for binary heap implementation.
• Access Time: $$O(1)$$ for accessing the highest priority element.
• Space Complexity: $$O(n)$$, where $$n$$ is the number of elements in the queue.

Advantages:

• Efficient for scenarios where elements need to be processed based on priority.
• Dynamic size.

Disadvantages:

• More complex to implement.
• Ov...