Implement a queue using a linked list

We will store a reference to the front and back of the queue in order to make enqueuing and dequeuing run in O(1) constant time. Every time we want to insert into the queue, we add the new element to the end of the linked list and update the back pointer. When we want to dequeue we return the first node in the linked list and update the front pointer.

// queue is initially empty
var Queue = {front: null, back: null};

// we will use a node to keep track of the elements
// in the queue which is represented by a linked list
function Node(data, next) {
  this.data = data;
  this.next = next;
} 

// add elements to queue in O(1) time
function Enqueue(element) {
  var N = new Node(element, null);
  if (Queue.back === null) {
    Queue.front = N;
    Queue.back = N; 
  } else { 
    Queue.back.next = N; 
    Queue.back = Queue.back.next;
  } 
}

// remove first element from queue in O(1) time
function Dequeue() {
  if (Queue.front !== null) { 
    var first = Queue.front;
    Queue.front = Queue.front.next; 
    return first.data;
  } else {
    if (Queue.back !== null) { Queue.back = null; }
    return 'Cannot dequeue because queue is empty';
  }
}

Enqueue('a'); 
Enqueue('b'); 
Enqueue('c'); 
Dequeue();