Implement Stack Using Queue in DSA Rust - Time & Space Complexity

Time Complexity: Implement Stack Using Queue

O(n)

Understanding Time Complexity

We want to understand how long it takes to do stack operations when using a queue to build it.

How does the time needed change as we add more items?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

use std::collections::VecDeque;

struct MyStack {
    queue: VecDeque<i32>,
}

impl MyStack {
    fn new() -> Self {
        MyStack { queue: VecDeque::new() }
    }

    fn push(&mut self, x: i32) {
        self.queue.push_back(x);
        for _ in 0..self.queue.len() - 1 {
            if let Some(front) = self.queue.pop_front() {
                self.queue.push_back(front);
            }
        }
    }
}
    

This code uses one queue to simulate a stack. The push operation moves elements to keep the newest on front.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop inside the push method that moves elements from front to back.
• How many times: It runs once for each element already in the queue, so n-1 times if there are n elements.

How Execution Grows With Input

Each push moves all existing elements to the back to keep the newest element at front.

Input Size (n)	Approx. Operations
10	About 9 moves inside the loop
100	About 99 moves inside the loop
1000	About 999 moves inside the loop

Pattern observation: The number of moves grows roughly the same as the number of elements already in the queue.

Final Time Complexity

Time Complexity: O(n)

This means pushing an item takes time proportional to how many items are already in the stack.

Common Mistake

[X] Wrong: "Push operation is always O(1) because it just adds one item."

[OK] Correct: Here, push moves all existing items to keep order, so it takes longer as the stack grows.

Interview Connect

Understanding how to build one data structure using another and analyzing its cost is a great skill for interviews and real coding.

Self-Check

"What if we used two queues instead of one? How would the time complexity of push and pop change?"

Practice

1. What is the main idea behind implementing a stack using a queue?

easy

A. Use one or two queues to simulate stack operations like push and pop

B. Use a queue to sort elements in ascending order

C. Use a stack to implement queue operations

D. Use two stacks to implement a queue

Solution

1. Step 1: Understand stack and queue operations

   A stack follows Last-In-First-Out (LIFO), while a queue follows First-In-First-Out (FIFO).

2. Step 2: Simulate stack using queue(s)

   By using one or two queues and carefully managing element order, we can mimic stack push and pop operations.

3. Final Answer:

   Use one or two queues to simulate stack operations like push and pop -> Option A

4. Quick Check:

   Stack via queue = simulate push/pop with queues [OK]

Hint: Remember stack is LIFO, queue is FIFO; simulate LIFO with queue(s) [OK]

Common Mistakes:

• Confusing stack and queue order
• Trying to sort elements instead of simulating stack
• Using stack to implement queue instead

2. Which Rust code snippet correctly declares a queue using VecDeque for implementing a stack?

easy

A. let mut queue = Vec::with_capacity(10);

B. let queue = Vec<i32>::new();

C. let mut queue: VecDeque<i32> = VecDeque::new();

D. let queue: VecDeque = Vec::new();

Solution

1. Step 1: Identify correct queue type in Rust

   VecDeque is the standard double-ended queue in Rust, suitable for queue operations.

2. Step 2: Check correct syntax for mutable queue declaration

   "let mut queue: VecDeque<i32> = VecDeque::new();" correctly declares a mutable queue of i32.

3. Final Answer:

   let mut queue: VecDeque<i32> = VecDeque::new(); -> Option C

4. Quick Check:

   VecDeque mutable queue declaration = let mut queue: VecDeque<i32> = VecDeque::new(); [OK]

Hint: Use VecDeque with mut keyword for queue in Rust [OK]

Common Mistakes:

• Using Vec instead of VecDeque for queue
• Missing mut keyword for mutable queue
• Wrong type annotations

3. Given this Rust code implementing push for stack using one queue, what is the queue state after pushing 1, then 2?

use std::collections::VecDeque;

struct Stack {
    queue: VecDeque<i32>,
}

impl Stack {
    fn new() -> Self {
        Stack { queue: VecDeque::new() }
    }

    fn push(&mut self, x: i32) {
        self.queue.push_back(x);
        let size = self.queue.len();
        for _ in 0..size - 1 {
            if let Some(val) = self.queue.pop_front() {
                self.queue.push_back(val);
            }
        }
    }
}

fn main() {
    let mut stack = Stack::new();
    stack.push(1);
    stack.push(2);
    println!("{:?}", stack.queue);
}

medium

A. [2, 1]

B. [1, 2]

C. [1]

D. [2]

Solution

1. Step 1: Trace push(1) operation

   Push 1: queue = [1]. No rotation since size=1.

2. Step 2: Trace push(2) operation

   Push 2: queue = [1, 2]. Rotate size-1=1 times: pop_front 1, push_back 1 -> queue = [2, 1].

3. Final Answer:

   [2, 1] -> Option A

4. Quick Check:

   After push 1,2 queue = [2,1] [OK]

Hint: After push, rotate queue to front to simulate stack top [OK]

Common Mistakes:

• Not rotating queue after push
• Confusing push_back and pop_front order
• Assuming queue keeps insertion order

4. Identify the bug in this pop method for stack implemented using one queue:

fn pop(&mut self) -> Option<i32> {
    self.queue.pop_back()
}

medium

A. pop_back() is invalid for VecDeque

B. pop_back() removes from the wrong end; should use pop_front()

C. pop_back() is correct; no bug

D. pop_back() requires mutable borrow error

Solution

1. Step 1: Understand queue ends in VecDeque

   VecDeque supports pop_front() and pop_back(), but our stack top is at front after push rotation.

2. Step 2: Check which end holds stack top

   After push rotation, stack top is at front, so pop_front() removes top, not pop_back().

3. Final Answer:

   pop_back() removes from the wrong end; should use pop_front() -> Option B

4. Quick Check:

   Stack top at front, pop_front() needed [OK]

Hint: Pop from front after rotation to get stack top [OK]

Common Mistakes:

• Using pop_back() instead of pop_front()
• Not rotating queue after push
• Confusing queue ends

5. How would you implement the top method for a stack using a single queue in Rust, assuming push rotates the queue so the top is at the front?

hard

A. Return the last element using queue.back().cloned()

B. Remove and return the last element using queue.pop_back()

C. Remove and return the first element using queue.pop_front()

D. Return the element at the front of the queue without removing it using queue.front().cloned()

Solution

1. Step 1: Recall queue rotation after push

   After push, queue is rotated so top element is at front.

2. Step 2: Access top without removing

   Use queue.front().cloned() to get top element without popping.

3. Final Answer:

   Return the element at the front of the queue without removing it using queue.front().cloned() -> Option D

4. Quick Check:

   Top element at front, use front().cloned() [OK]

Hint: Top is front element after rotation; use front().cloned() [OK]

Common Mistakes:

• Using pop_front() which removes element
• Using back() which is bottom of stack
• Removing element instead of just viewing