Enqueue Operation in DSA Python - Time & Space Complexity

Time Complexity: Enqueue Operation

O(1)

Understanding Time Complexity

We want to understand how the time needed to add an item to a queue changes as the queue grows.

How does the enqueue operation's speed change when the queue gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

    def enqueue(self, item):
        self.items.append(item)

This code adds an item to the end of a queue represented by a list.

Identify Repeating Operations

• Primary operation: Adding an item to the end of the list using append.
• How many times: Once per enqueue call, no loops involved.

How Execution Grows With Input

Adding one item takes about the same time no matter how many items are already in the queue.

Input Size (n)	Approx. Operations
10	1 append operation
100	1 append operation
1000	1 append operation

Pattern observation: The time to add an item stays about the same even as the queue grows.

Final Time Complexity

Time Complexity: O(1)

This means adding an item takes a constant amount of time regardless of queue size.

Common Mistake

[X] Wrong: "Adding an item takes longer as the queue gets bigger because the list grows."

[OK] Correct: The append operation is designed to add at the end quickly, so it usually takes the same time no matter the size.

Interview Connect

Knowing that enqueue is fast helps you design efficient queues and shows you understand how data structures work behind the scenes.

Self-Check

"What if we used a linked list instead of a list for the queue? How would the time complexity of enqueue change?"

Practice

1. What does the enqueue operation do in a queue data structure?

easy

A. Returns the size of the queue

B. Removes an element from the front of the queue

C. Checks if the queue is empty

D. Adds an element to the end of the queue

Solution

1. Step 1: Understand the queue structure

   A queue works like a line where new elements join at the back.

2. Step 2: Define enqueue operation

   Enqueue means adding an element to the end of this line.

3. Final Answer:

   Adds an element to the end of the queue -> Option D

4. Quick Check:

   Enqueue = Add to end [OK]

Hint: Enqueue means add at the back of the queue [OK]

Common Mistakes:

• Confusing enqueue with dequeue
• Thinking enqueue removes elements
• Mixing enqueue with checking size

2. Which of the following is the correct syntax to enqueue an element 5 into a queue named q implemented as a Python list?

easy

A. q.enqueue(5)

B. q.push(5)

C. q.append(5)

D. q.insert(0, 5)

Solution

1. Step 1: Identify Python list method for adding at end

   Python lists use append() to add elements at the end.

2. Step 2: Match enqueue operation to list method

   Enqueue adds to the back, so q.append(5) is correct.

3. Final Answer:

   q.append(5) -> Option C

4. Quick Check:

   Enqueue in list = append() [OK]

Hint: Use append() to add at the end of a Python list [OK]

Common Mistakes:

• Using push() which is not a Python list method
• Using insert(0, 5) which adds at front
• Assuming enqueue is a built-in list method

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

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

medium

A. [30, 20, 10]

B. [10, 20, 30]

C. [10, 30, 20]

D. Error

Solution

1. Step 1: Trace each enqueue operation

   Appending 10, then 20, then 30 adds elements in order at the end.

2. Step 2: Check final queue state

   The list will be [10, 20, 30] after all appends.

3. Final Answer:

   [10, 20, 30] -> Option B

4. Quick Check:

   Appending in order = [10, 20, 30] [OK]

Hint: Appending adds elements in order at the end [OK]

Common Mistakes:

• Reversing the order of elements
• Thinking append adds at front
• Expecting an error due to empty list

4. Identify the error in the following enqueue implementation for a queue using a Python list:

def enqueue(queue, item):
    queue.insert(item)

q = [1, 2, 3]
enqueue(q, 4)
print(q)

medium

A. insert() requires two arguments: index and item

B. insert() cannot be used on lists

C. enqueue should use append() instead of insert()

D. queue is not defined

Solution

1. Step 1: Check insert() method usage

   Python list's insert() needs two arguments: position index and the item.

2. Step 2: Identify missing argument

   The code calls insert(item) with only one argument, causing an error.

3. Final Answer:

   insert() requires two arguments: index and item -> Option A

4. Quick Check:

   insert() needs index and item [OK]

Hint: insert() needs index and item arguments [OK]

Common Mistakes:

• Using insert() with one argument
• Confusing insert() with append()
• Ignoring Python method argument requirements

5. You have a queue implemented as a Python list. You want to enqueue multiple elements [7, 8, 9] at once while preserving order. Which code snippet correctly enqueues all elements in order?

hard

A. queue.extend([7, 8, 9])

B. for x in [7, 8, 9]:
queue.insert(0, x)

C. queue.append([7, 8, 9])

D. queue = [7, 8, 9] + queue

Solution

1. Step 1: Understand enqueue multiple elements

   Enqueue adds elements at the end preserving order.

2. Step 2: Analyze each option

   for x in [7, 8, 9]: queue.insert(0, x) inserts at front reversing order; queue.append([7, 8, 9]) appends list as single element; queue = [7, 8, 9] + queue prepends elements; queue.extend([7, 8, 9]) extends list adding elements in order at end.

3. Final Answer:

   queue.extend([7, 8, 9]) -> Option A

4. Quick Check:

   extend() adds multiple elements at end [OK]

Hint: Use extend() to add multiple elements at queue end [OK]

Common Mistakes:

• Using append() which nests list inside queue
• Using insert(0, x) which reverses order
• Prepending elements instead of appending