Queue Implementation Using Array in DSA Python - Time & Space Complexity

Time Complexity: Queue Implementation Using Array

O(1)

Understanding Time Complexity

We want to understand how the time taken by queue operations changes as the number of items grows.

How does adding or removing items affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following queue operations using an array.

class Queue:
    def __init__(self, capacity):
        self.queue = [None] * capacity
        self.front = 0
        self.rear = 0
        self.size = 0

    def enqueue(self, item):
        if self.size == len(self.queue):
            raise Exception('Queue is full')
        self.queue[self.rear] = item
        self.rear = (self.rear + 1) % len(self.queue)
        self.size += 1

    def dequeue(self):
        if self.size == 0:
            raise Exception('Queue is empty')
        item = self.queue[self.front]
        self.front = (self.front + 1) % len(self.queue)
        self.size -= 1
        return item
    

This code adds items to the rear and removes from the front using a circular array.

Identify Repeating Operations

Look at what repeats when we add or remove items.

• Primary operation: Assigning or reading one element in the array.
• How many times: Exactly once per enqueue or dequeue call.

How Execution Grows With Input

Each enqueue or dequeue does a fixed amount of work, no matter how many items are in the queue.

Input Size (n)	Approx. Operations
10	1 operation per enqueue or dequeue
100	1 operation per enqueue or dequeue
1000	1 operation per enqueue or dequeue

Pattern observation: The work stays the same per operation, regardless of queue size.

Final Time Complexity

Time Complexity: O(1)

This means each add or remove action takes the same small amount of time, no matter how many items are in the queue.

Common Mistake

[X] Wrong: "Removing an item from the front takes longer as the queue grows because we have to shift elements."

[OK] Correct: This implementation uses a circular array, so no shifting happens. The front index just moves forward, keeping removal time constant.

Interview Connect

Understanding this helps you explain why queues can be efficient and how to implement them well, a skill often valued in coding discussions.

Self-Check

"What if we used a simple array without circular indexing and shifted elements on dequeue? How would the time complexity change?"

Practice

1. What is the main characteristic of a queue implemented using an array?

easy

A. It follows First-In-First-Out (FIFO) order

B. It follows Last-In-First-Out (LIFO) order

C. It allows random access to elements

D. It automatically sorts elements

Solution

1. Step 1: Understand queue behavior

   A queue adds elements at the rear and removes from the front, following FIFO.

2. Step 2: Compare options

   LIFO is for stacks, random access and sorting are not queue properties.

3. Final Answer:

   It follows First-In-First-Out (FIFO) order -> Option A

4. Quick Check:

   Queue = FIFO [OK]

Hint: Queue always removes the oldest element first [OK]

Common Mistakes:

• Confusing queue with stack (LIFO)
• Thinking queue allows random access
• Assuming queue sorts elements automatically

2. Which of the following is the correct way to initialize an empty queue using an array in Python?

easy

A. queue = ()

B. queue = {}

C. queue = set()

D. queue = []

Solution

1. Step 1: Identify array type in Python

   Python lists are used as arrays and initialized with [] for empty list.

2. Step 2: Check other options

   {} is dict, () is tuple, set() is a set, none are arrays.

3. Final Answer:

   queue = [] -> Option D

4. Quick Check:

   Empty array = [] [OK]

Hint: Use [] to create empty list (array) in Python [OK]

Common Mistakes:

• Using {} which creates a dictionary
• Using () which creates a tuple
• Using set() which is unordered

3. What will be the output of the following code?

queue = []
queue.append(10)
queue.append(20)
queue.append(30)
print(queue.pop(0))
print(queue)

medium

A. 30
[10, 20]

B. 10
[20, 30]

C. 10
[10, 20, 30]

D. 20
[10, 30]

Solution

1. Step 1: Trace queue operations

   Append adds 10, 20, 30 to queue: [10, 20, 30]. pop(0) removes first element 10.

2. Step 2: Check print outputs

   First print outputs 10, second print outputs remaining queue [20, 30].

3. Final Answer:

   10 [20, 30] -> Option B

4. Quick Check:

   pop(0) removes front = 10 [OK]

Hint: pop(0) removes front element in queue [OK]

Common Mistakes:

• Using pop() instead of pop(0) removes last element
• Confusing append order
• Expecting pop(0) to remove last element

4. Identify the error in this queue implementation using an array:

queue = []
queue.append(1)
queue.append(2)
queue.pop()
print(queue)

medium

A. pop() removes last element, not front

B. append() is used incorrectly

C. queue should be a dictionary

D. print statement syntax error

Solution

1. Step 1: Understand pop() behavior

   pop() without index removes last element, not front as queue requires.

2. Step 2: Check queue correctness

   Queue must remove front element, so pop(0) should be used instead of pop().

3. Final Answer:

   pop() removes last element, not front -> Option A

4. Quick Check:

   Queue removal = pop(0) front [OK]

Hint: Use pop(0) to dequeue from front [OK]

Common Mistakes:

• Using pop() removes last, not front
• Confusing append usage
• Thinking queue is a dictionary

5. Given a fixed-size array of length 3, what happens if you try to enqueue 4 elements in a queue implemented using this array without resizing or circular logic?

hard

A. The queue automatically resizes to fit 4 elements

B. The 4th element replaces the first element

C. The queue overflows and cannot add the 4th element

D. The queue removes the last element to add the 4th

Solution

1. Step 1: Understand fixed-size array limits

   An array of length 3 can hold only 3 elements; no extra space for 4th.

2. Step 2: Check enqueue behavior without resizing

   Without resizing or circular logic, adding 4th element causes overflow error or failure.

3. Final Answer:

   The queue overflows and cannot add the 4th element -> Option C

4. Quick Check:

   Fixed array size = no extra elements [OK]

Hint: Fixed array size limits enqueue capacity [OK]

Common Mistakes:

• Assuming automatic resizing happens
• Thinking 4th element replaces first
• Believing queue removes last element automatically