Dequeue

Dequeue - A Double Ended Queue

Front Back

<- uncons --------- unsnoc -> cons -> --------- <- snoc

Based on the Bankers Double Ended Queue as described by C. Okasaki in "Purely Functional Data Structures"

A queue that allows items to be put onto either the front (cons) or the back (snoc) of the queue in constant time, and constant time access to the element at the very front or the very back of the queue. Dequeuing an element from either end is constant time when amortized over a number of dequeues.

This queue maintains an invariant that whenever there are at least two elements in the queue, neither the front list nor back list are empty. In order to maintain this invariant, a dequeue from either side which would leave that side empty constructs the resulting queue by taking elements from the opposite side