Enqueue Operation in DSA Rust - Time & Space Complexity

Time Complexity: Enqueue Operation

O(1)

Understanding Time Complexity

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

How does the enqueue operation scale when the queue gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

struct Queue {
    items: Vec<i32>,
}

impl Queue {
    fn enqueue(&mut self, value: i32) {
        self.items.push(value);
    }
}
    

This code adds a new value to the end of a queue implemented with a dynamic array.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding an element to the end of the vector (push).
• How many times: Once per enqueue call.

How Execution Grows With Input

Each enqueue adds one element. Most of the time, adding is quick and takes the same effort no matter the size.

Input Size (n)	Approx. Operations
10	1 (simple add)
100	1 (simple add)
1000	1 (simple add)

Pattern observation: The time to add stays mostly the same as the queue grows.

Final Time Complexity

Time Complexity: O(1)

This means adding an item takes about the same time no matter how many items are already in the queue.

Common Mistake

[X] Wrong: "Enqueue takes longer as the queue grows because it has to move all items."

[OK] Correct: The vector adds at the end without moving existing items. Occasionally it resizes, but this cost is spread out and does not happen every time.

Interview Connect

Knowing that enqueue is usually quick helps you explain efficient queue operations and compare with other data structures.

Self-Check

"What if we used a linked list instead of a vector? 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 number of elements in 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 queue behavior

   A queue works like a line where new people join at the end.

2. Step 2: Define enqueue operation

   Enqueue means adding a new element at the back of the queue.

3. Final Answer:

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

4. Quick Check:

   Enqueue = Add at end [OK]

Hint: Enqueue always adds at the back of the queue [OK]

Common Mistakes:

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

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

easy

A. queue.push_front(5);

B. queue.enqueue(5);

C. queue.push_back(5);

D. queue.insert(5);

Solution

1. Step 1: Identify VecDeque enqueue method

   In Rust, VecDeque uses push_back to add elements at the end.

2. Step 2: Check options for correct method

   Only queue.push_back(5); correctly adds 5 at the back.

3. Final Answer:

   queue.push_back(5); -> Option C

4. Quick Check:

   VecDeque enqueue = push_back [OK]

Hint: Use push_back to enqueue in VecDeque [OK]

Common Mistakes:

• Using push_front instead of push_back
• Using non-existent enqueue method
• Using insert without index

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

use std::collections::VecDeque;

fn main() {
    let mut queue = VecDeque::new();
    queue.push_back(10);
    queue.push_back(20);
    queue.push_back(30);
    queue.push_back(40);
    println!("{:?}", queue);
}

medium

A. [10, 20, 30, 40]

B. [40, 30, 20, 10]

C. [10, 20, 30]

D. Compilation error

Solution

1. Step 1: Trace enqueue operations

   Elements 10, 20, 30, 40 are added in order at the back of the queue.

2. Step 2: Understand VecDeque print format

   Printing the queue shows elements in insertion order inside square brackets.

3. Final Answer:

   [10, 20, 30, 40] -> Option A

4. Quick Check:

   Enqueue order preserved in VecDeque [OK]

Hint: VecDeque prints elements in insertion order [OK]

Common Mistakes:

• Assuming push_back adds at front
• Confusing output order
• Expecting compilation error

4. Identify the error in the following Rust code that tries to enqueue an element into a queue:

use std::collections::VecDeque;

fn main() {
    let mut queue = VecDeque::new();
    queue.enqueue(15);
    println!("{:?}", queue);
}

medium

A. VecDeque cannot store integers directly

B. VecDeque has no method named 'enqueue'

C. println! macro syntax is incorrect

D. Missing 'mut' keyword for queue variable

Solution

1. Step 1: Check VecDeque methods

   VecDeque does not have an 'enqueue' method; it uses 'push_back' to add elements.

2. Step 2: Verify other code parts

   The queue is mutable and println! syntax is correct; VecDeque supports integers.

3. Final Answer:

   VecDeque has no method named 'enqueue' -> Option B

4. Quick Check:

   Use push_back, not enqueue [OK]

Hint: VecDeque uses push_back, not enqueue [OK]

Common Mistakes:

• Using enqueue method on VecDeque
• Forgetting mut keyword (not error here)
• Misreading println! syntax

5. You want to implement a queue using a Rust Vec where enqueue adds elements at the end and dequeue removes from the front. Which of the following code snippets correctly enqueues the element 7?

hard

A. queue.push(7);

B. queue.insert(0, 7);

C. queue.remove(0); queue.push(7);

D. queue.pop(); queue.push(7);

Solution

1. Step 1: Understand enqueue in Vec-based queue

   Enqueue means adding at the end, so push adds element at the back.

2. Step 2: Analyze options

   queue.push(7); uses push(7) which correctly adds 7 at the end. Others either insert at front or remove elements.

3. Final Answer:

   queue.push(7); -> Option A

4. Quick Check:

   Vec enqueue = push at end [OK]

Hint: Use push to enqueue in Vec-based queue [OK]

Common Mistakes:

• Using insert(0, val) which adds at front
• Removing elements before enqueue
• Using pop which removes last element