What is a double-ended queue and how is it used?

A double-ended queue, or deque, is a data structure that allows insertion and removal of elements from both ends.

A double-ended queue, often abbreviated to deque (pronounced 'deck'), is a generalised version of a queue. In a standard queue, elements are added at the rear and removed from the front, following the principle of First In, First Out (FIFO). However, a deque allows for more flexibility, as elements can be added or removed from both the front and the rear.

This flexibility makes deques useful in a variety of scenarios. For example, they can be used to implement a breadth-first search in graph algorithms, where elements are typically added at the rear and removed from the front. However, if the algorithm needs to explore a different branch of the graph, it can add elements to the front of the deque, effectively prioritising them over the elements added earlier.

Deques can also be used in scenarios where data needs to be processed in a Last In, First Out (LIFO) manner, effectively acting as a stack. This can be useful in scenarios such as parsing expressions or navigating web pages, where the most recent element needs to be accessed first.

In terms of implementation, deques can be implemented using a doubly-linked list, where each node has a reference to both the next node and the previous node. This allows for efficient addition and removal of elements at both ends. Alternatively, they can be implemented using a circular buffer, where the front and rear of the deque are mapped to indices of an array.

In summary, a double-ended queue is a versatile data structure that can be used in a variety of scenarios where elements need to be added or removed from both ends. Its flexibility makes it a useful tool in the arsenal of any computer scientist.