Complexity analysis of queue operations involves evaluating the time and space complexities associated with various operations that can be performed on queues. Queues are linear data structures that follow the First In, First Out (FIFO) principle, where elements are inserted at one end (rear) and removed from the other end (front). The primary operations on queues include enqueue (insertion), dequeue (removal), peek (accessing the front element without removing it), and checking if the queue is empty or full. Here's a detailed analysis of these operations:
Enqueue Operation
The enqueue operation involves adding an element to the rear of the queue.
Time Complexity: The time complexity of the enqueue operation is $$O(1)$$ because it involves a constant amount of work to insert an element at the rear end of the queue[1][2][5]. This is true for both array-based and linked list implementations of queues.
Space Complexity: The space complexity for enqueue operation is also $$O(1)$$ as it only requires space for storing one additional element[1][2].
Dequeue Operation
The dequeue operation involves removing an element from the front of the queue.
Time Complexity: The time complexity of the dequeue operation is $$O(1)$$ because it involves a constant amount of work to remove an element from the front of the queue[1][2]. This is consistent across both array-based and linked list implementations.
Space Complexity: The space complexity for dequeue operation is $$O(1)$$ as no additional space is required for performing the operation[1][2].
Peek Operation
The peek operation involves accessing the element at the front of the queue without removing it.
Time Complexity: The time complexity of the peek operation can vary. In the case of array-based implementation, it is $$O(1)$$ as it directly accesses the element at the front index[1]. However, if a linked...
