What is a deque and how does it integrate stack and queue properties?

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

In more detail, a deque is a type of queue in which elements can be added or removed from both the front and the rear. This is in contrast to a traditional queue, where elements can only be added at the rear and removed from the front, and a stack, where elements can only be added and removed from the top. The term 'deque' is a contraction of 'double-ended queue', which aptly describes its functionality.

The integration of stack and queue properties in a deque is achieved through its double-ended nature. Like a stack, a deque allows for the addition and removal of elements at the same end (the 'top' of the stack corresponds to one end of the deque). Like a queue, a deque also allows for the addition of elements at one end and the removal of elements at the other end. This makes deques a versatile data structure that can be used in a variety of applications where both stack-like and queue-like operations are needed.

In terms of implementation, a deque can be implemented using a doubly-linked list, where each node has a link to both its next node and its previous node. This allows for efficient addition and removal of elements at both ends of the deque. Alternatively, a deque can also be implemented using a dynamic array, where the array is resized as elements are added or removed.

In terms of usage, deques are particularly useful in certain algorithms and data manipulation tasks. For example, they can be used in a breadth-first search algorithm, where elements are added at the rear of the deque and removed from the front, effectively implementing a queue. They can also be used in a depth-first search algorithm, where elements are added and removed at the same end of the deque, effectively implementing a stack.