How are queues and stacks implemented in functional programming?

In functional programming, queues and stacks are implemented using recursive data structures like lists.

Functional programming languages, such as Haskell and Lisp, use immutable data structures. This means that once a data structure is created, it cannot be changed. Instead, any operation that would traditionally change the data structure creates a new one instead. This is a fundamental aspect of functional programming and it has significant implications for how data structures like queues and stacks are implemented.

A stack is a Last-In-First-Out (LIFO) data structure. In functional programming, a stack can be implemented as a singly linked list. The head of the list represents the top of the stack. Pushing an element onto the stack is done by prepending it to the list, which creates a new list. Popping an element off the stack is done by returning the tail of the list, which also creates a new list. This approach is efficient because both operations are constant time.

A queue is a First-In-First-Out (FIFO) data structure. Implementing a queue in a functional programming language is more challenging than implementing a stack because the element to be removed is at the end of the list, not the beginning. One common solution is to use a pair of lists. The front list contains the elements of the queue in the correct order, and the rear list contains new elements to be added to the queue in reverse order. When an element is added to the queue, it is prepended to the rear list. When an element is removed from the queue, it is taken from the front list. If the front list is empty, the rear list is reversed and becomes the new front list. This approach ensures that all operations are amortised constant time.

In conclusion, functional programming languages use recursive data structures and immutability to implement queues and stacks. This requires a different approach than in imperative programming languages, but it results in efficient and elegant solutions.