Queues
November 1, 2013
One of the basic data structures in computer science is the queue, in which items are inserted into the data structure and retrieved in the order in which they were inserted; the standard operations on a queue are enqueue, dequeue, and isEmpty.
Your task is to write functions to implement a queue. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
Implemented in Go.
Implementation in SML.
signature QUEUE = sig type 'a queue exception EmptyQ val empty: 'a queue val enqueue: 'a queue -> 'a -> 'a queue val dequeue: 'a queue -> 'a * 'a queue val isEmpty: 'a queue -> bool end structure ListQueue :> QUEUE = struct type 'a queue = 'a list * 'a list exception EmptyQ val empty = ([], []) fun enqueue (xs, ys) x = (x::xs, ys) fun dequeue ([], []) = raise EmptyQ | dequeue (xs, []) = dequeue ([], rev f) | dequeue (xs, y::ys) = (y, (xs, ys)) fun isEmpty ([], []) = true | isEmpty _ = false endvar Queue = function (items) { this.elements = items || []; }; Queue.prototype.enqueue = function (item) { this.elements.push(item); return this; }; Queue.prototype.dequeue = function () { return this.elements.shift(); }; Queue.prototype.isEmpty = function () { return this.elements.length === 0; }; window.tasksQueue = new Queue(["Wake Up", "Shower"]); tasksQueue.enqueue("Dress") .enqueue("Have Breakfast") .enqueue("Go to work"); while(!tasksQueue.isEmpty()) { console.log(tasksQueue.dequeue()); }Okasaki “banker’s queues” in Haskell:
import Prelude hiding (head,tail) import qualified Prelude as P data Queue a = Q [a] {-# UNPACK #-} !Int [a] {-#UNPACK#-} !Int -- toList is faster than just removing items one at a time because it avoids all the queue rotations. toList :: Queue a -> [a] toList (Q fs _ rs _) = fs ++ reverse rs -- fromList is faster than just snocing items on one at a time because it -- avoids all the queue rotations. It also produces a queue in the optimal state, with everything in the front list. fromList :: [a] -> Queue a fromList l = Q l (length l) [] 0 size (Q _ flen _ rlen) = flen+rlen emptyq = Q [] 0 [] 0 head :: Queue a -> a head (Q [] _ _ _) = error "Cannot get the head of an empty queue." head (Q (h:_) _ _ _) = h tail :: Queue a -> Queue a tail (Q [] _ _ _) = error "Cannot get the tail of an empty queue." tail (Q (f:fs) flen rs rlen) = queue fs (flen-1) rs rlen snoc :: Queue a -> a -> Queue a snoc (Q fs flen rs rlen) x = queue fs flen (x:rs) (rlen+1) queue :: [a] -> Int -> [a] -> Int -> Queue a queue f flen r rlen | flen >= rlen = Q f flen r rlen | otherwise = Q (f++reverse r) (flen+rlen) [] 0I forgot to mention above that if the size operation is not needed, it’s possible to save a bit of space by storing only the difference between the front and rear lengths, rather than the lengths themselves.