A.5.4: Queues

Learning Objectives

By the end of this lesson, you should:
  • be familiar with queue functionality time and space complexity
  • understand the difference between LIFO and FIFO
  • understand the python queue class example


Queues are similar to stacks except instead of removing elements from the end of a list, we can only remove elements from the front of a list. Instead of push and pop operations, queues have "enqueue" and "dequeue" operations respectively. Enqueue adds an element to the back of a queue, and dequeue removes an element from the front of a queue. Queues are FIFO- First In First Out.

Big-O of Queues

If we think of a list or, even worse, a stack, operations that affect the beginning of the data would run in at least O(n). Remember that in an array, removing something from the front is O(n). We can think of a queue as a doubly linked list so that taking things off the front or the back is always O(1).

Helpful Resources

  1. 1.
    ​This video is a concise introduction for the motivation and usage of queues.
  2. 2.
    ​This video is a more detailed introduction to queues and how to use them in Python.
  3. 3.
    Read pages 109-110 in the Cracking the Coding Interview PDF.

Queue Class

Notice we Python's built-in deque data structure because it supports more efficient popping (dequeuing) of the left-most element than Python Lists.
# We use the built-in Python deque data structure for queues.
# Deque is implemented using linked lists and more efficient
# than Python lists for popping the left-most element.
from collections import deque
class Queue:
Define a Queue class that supports the methods
1) .enqueue(element): Add element to back of queue
2) .dequeue(): Return element from front of queue
3) .size(): Return number of elements in queue
# self is a reference to the instance that was just created
def __init__(self): = deque()
# Return optional representation of class in string format
def __repr__(self):
return str(
def enqueue(self, element):
print(f"{element} joins the queue")
def dequeue(self):
element =
print(f"{element} leaves the queue")
return element
def size(self):
print(f"Queue contains {len(} elements")
return len(

Linked List Queue Class

From here.
class Node:
def __init__(self, data): = data = None
# A class to represent a queue
# The queue, front stores the front node
# of LL and rear stores the last node of LL
class Queue:
def __init__(self):
self.front = self.rear = None
def isEmpty(self):
return self.front == None
# Method to add an item to the queue
def EnQueue(self, item):
temp = Node(item)
if self.rear == None:
self.front = self.rear = temp
return = temp
self.rear = temp
# Method to remove an item from queue
def DeQueue(self):
if self.isEmpty():
temp = self.front
self.front =
if(self.front == None):
self.rear = None
# Driver Code
if __name__== '__main__':
q = Queue()
print("Queue Front " + str(
print("Queue Rear " + str(


Please use Python's deque data structure to represent queues.
Please fork starter code Repls and attempt solutions there. Feel free to compare with reference solutions after attempting each problem. Have fun!



  1. 1.
    1. 1.
      Hint: This may be solved more efficiently without queues, but see how we can implement it with queues first.