Queue Data Structure

5 min read
A narrow stree with a queue of people in the rainPhoto by Ethan Hu

The queue data structure is a collection of items that follow the first-in, first out principle. The first added element will be the first element to be removed from the queue. So, elements are added in the back and removed from the front.

An analogy would be a simple line of people waiting for the next train. In the software engineering context, an example is a web server receiving and responding requests.

The main API methods are enqueue (add) and dequeue (remove). But we can also add other methods as part of the API implementation: size, front, back, and is_empty.

We can create a Queue class as a wrapper and use the Python list to store the queue data. This class will have the implementation of the enqueue, dequeue, size, front, back, and is_empty methods.

The first step is to create a class definition and how we are gone store our items.

class Queue:
    def __init__(self):
        self.items = []

This is basically what we need for now. Just a class and its constructor. When the instance is created, it will have the items list to store the queue items.

For the enqueue method, we just need to use the list append method to add new items. The new items will be placed in the last index of this items list. So the front item from the queue will always be the first item.

def enqueue(self, item):

It receives the new item and appends it to the list.

The size method only counts the number of the queue items by using the len function.

def size(self):
    return len(self.items)

The idea of the is_empty method is to verify if the list has or not items in it. If it has, returns False. Otherwise, True. To count the number of items in the queue, we can simply use the size method already implemented.

def is_empty(self):
    return self.size() == 0

The pop method from the list data structure can also be used to dequeue the item from the queue. It dequeues the first element as it is expected for the queue. The first added item.

def dequeue(self):
    return self.items.pop(0)

But we need to handle the queue emptiness. For an empty list, the pop method raises an exception IndexError: poop from empty list. So we can create an exception class to handle this issue.

class Emptiness(Exception):

And uses it when the list is empty:

def dequeue(self):
    if self.is_empty():
        raise Emptiness('The Queue is empty')

    return self.items.dequeue()

If it is empty, we raise this exception. Otherwise, we can dequeue the front item from the queue.

We use this same emptiness strategy for the front method:

def front(self):
    if self.is_empty():
        raise Emptiness('The Queue is empty')

    return self.items[0]

If it has at least one item, we get the front, the first added item in the queue.

Also the same emptiness strategy for the back method:

def back(self):
    if self.is_empty():
        raise Emptiness('The Queue is empty')

    return self.items[-1]

If it has at least one item, we get the back item, the last added item in the queue.

Queue usage

I created some helper functions to help test the queue usage.

def test_enqueue(queue, item):

def test_dequeue(queue):

def test_emptiness(queue):
    is_empty = queue.is_empty()

def test_size(queue):
    size = queue.size()

def test_front(queue):
    front = queue.front()

def test_back(queue):
    back = queue.back()

They basically call a queue method and print the expected result from the method call.

The usage will be something like:

queue = Queue()

test_emptiness(queue)  # True
test_size(queue)  # 0

test_enqueue(queue, 1)  # [1]
test_enqueue(queue, 2)  # [1, 2]
test_enqueue(queue, 3)  # [1, 2, 3]
test_enqueue(queue, 4)  # [1, 2, 3, 4]
test_enqueue(queue, 5)  # [1, 2, 3, 4, 5]

test_emptiness(queue)  # False
test_size(queue)  # 5
test_front(queue)  # 1
test_back(queue)  # 5

test_dequeue(queue)  # [2, 3, 4, 5]
test_dequeue(queue)  # [3, 4, 5]
test_dequeue(queue)  # [4, 5]
test_dequeue(queue)  # [5]

test_emptiness(queue)  # False
test_size(queue)  # 1
test_front(queue)  # 5
test_back(queue)  # 5

test_dequeue(queue)  # []

test_emptiness(queue)  # True
test_size(queue)  # 0

We first instantiate a new queue from the Queue class.

  • So now we can verify its emptiness: yes, it is!
  • Verify size: 0.
  • Enqueue 5 new items to the queue: [1, 2, 3, 4, 5].
  • Verify emptiness again: not anymore!
  • Verify size: 5.
  • Get the front element: 1 because it was the first added item.
  • Get the back element: 5 because it was the last added item.
  • Dequeue 4 items: 1, 2, 3, and 4.
  • Verify emptiness: it is not empty yet!
  • The size is 1 and the back and front are the same number: 5
  • Dequeue the remaining item.
  • Verify emptiness: it is empty now!
  • Size is back to 0.

Another way of testing it

Enqueue 5 new items:

queue = Queue()

Loop through the items and print each one.

for item in queue.items:

Test front and back.

test_front(queue) # 1
test_back(queue) # 5

Dequeue all.

while not queue.is_empty():

Test size.

test_size(queue) # 0

Runtime and Space complexities

Now about space and runtime complexities for each method implemented.

The space is pretty simple. It's a list, so it's O(n) where n is the current number of items in the stack.

The runtime for each method is O(1), constant time.


Twitter Github