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

Time Complexity: Implement Stack Using Queue

O(n)

Understanding Time Complexity

We want to understand how the time taken changes when we use a queue to build a stack.

Specifically, how the operations like push and pop grow as we add more items.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

#include <stdio.h>
#include <stdlib.h>

#define MAX 100

int queue[MAX];
int front = 0, rear = 0;

void enqueue(int x) {
    queue[rear++] = x;
}

int dequeue() {
    return queue[front++];
}

void push(int x) {
    int size = rear - front;
    enqueue(x);
    for (int i = 0; i < size; i++) {
        enqueue(dequeue());
    }
}

int pop() {
    if (front == rear) return -1; // empty
    return dequeue();
}

int main() {
    push(1);
    push(2);
    push(3);
    printf("%d ", pop());
    printf("%d ", pop());
    return 0;
}
    

This code uses one queue to simulate a stack by rearranging elements on each push.

Identify Repeating Operations

• Primary operation: The for-loop inside the push function that moves existing elements.
• How many times: It runs once for each element already in the queue before adding the new one.

How Execution Grows With Input

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

Input Size (n)	Approx. Operations in push
10	About 10 moves
100	About 100 moves
1000	About 1000 moves

Pattern observation: The number of moves grows linearly with the number of elements.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Push operation is always O(1) because we just add one element."

[OK] Correct: Here, push rearranges all existing elements, so it takes longer as the stack grows.

Interview Connect

Understanding how to build one data structure using another shows your problem-solving skills and helps you think about efficiency.

Self-Check

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

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 differences

   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 cleverly, we can reorder elements to behave like a stack for 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 of the following is the correct syntax to declare a queue in C using the standard library?

easy

A. queue<int> q;

B. struct queue q;

C. #include \nqueue q;

D. No standard queue in C; must implement manually

Solution

1. Step 1: Check C standard library support

   C language does not have a built-in queue data structure in its standard library.

2. Step 2: Understand queue implementation in C

   Queues must be implemented manually using arrays or linked lists in C.

3. Final Answer:

   No standard queue in C; must implement manually -> Option D

4. Quick Check:

   C lacks built-in queue; manual implementation needed [OK]

Hint: C has no built-in queue; implement yourself [OK]

Common Mistakes:

• Assuming C has STL-like queue
• Using C++ syntax in C code
• Including non-existent headers

3. Consider the following code snippet implementing push operation of a stack using one queue in C-like pseudocode:

void push(int x) {
    q.push(x);
    int size = q.size();
    for (int i = 0; i < size - 1; i++) {
        int val = q.front();
        q.pop();
        q.push(val);
    }
}

What will be the order of elements in the queue after pushing 1, then 2, then 3?

medium

A. 3 -> 2 -> 1 -> null

B. 1 -> 2 -> 3 -> null

C. 2 -> 3 -> 1 -> null

D. 3 -> 1 -> 2 -> null

Solution

1. Step 1: Push 1

   Queue after push: [1]

2. Step 2: Push 2

   Push 2: queue becomes [1,2], then rotate first element: pop 1, push 1 -> queue is [2,1]

3. Step 3: Push 3

   Push 3: queue is [2,1,3], rotate first two elements: pop 2 push 2, pop 1 push 1 -> queue is [3,2,1]

4. Final Answer:

   3 -> 2 -> 1 -> null -> Option A

5. Quick Check:

   Newest element at front after push = 3 -> 2 -> 1 [OK]

Hint: After push, rotate queue to put new element front [OK]

Common Mistakes:

• Not rotating queue after push
• Assuming queue order is same as push order
• Confusing front and back of queue

4. The following code attempts to implement pop operation for a stack using two queues. Identify the error:

int pop() {
    if (q1.empty()) return -1;
    while (q1.size() > 1) {
        q2.push(q1.front());
        q1.pop();
    }
    int top = q1.front();
    q1.pop();
    swap(q1, q2);
    return top;
}

medium

A. The queues q1 and q2 are not initialized properly

B. The pop operation does not handle empty stack correctly

C. No error; the code correctly implements pop

D. The swap(q1, q2) should be before popping the last element

Solution

1. Step 1: Analyze pop logic

   Elements except last are moved from q1 to q2, last element is popped from q1.

2. Step 2: Swap queues

   Swapping q1 and q2 makes q1 the queue with remaining elements for next operations.

3. Final Answer:

   No error; the code correctly implements pop -> Option C

4. Quick Check:

   Pop moves all but last, returns last, swaps queues [OK]

Hint: Pop moves all but last to second queue, then swap [OK]

Common Mistakes:

• Swapping queues too early
• Not checking empty queue before pop
• Forgetting to swap queues after pop

5. You want to implement a stack using two queues. Which approach ensures that the pop() operation is O(1) time complexity, and push() is O(n)?

hard

A. Make pop costly by moving all but last from q1 to q2, then popping last from q1

B. Make push costly by pushing element to empty q2, then moving all from q1 to q2, swap q1 and q2

C. Use a single queue and rotate elements after each push

D. Use two stacks instead of queues

Solution

1. Step 1: Understand push costly approach

   Push inserts element into empty q2, moves all q1 elements to q2, then swaps q1 and q2. This makes newest element front in q1.

2. Step 2: Pop becomes O(1)

   Pop just dequeues from q1 front, which is the top of stack, so pop is O(1).

3. Final Answer:

   Make push costly by pushing element to empty q2, then moving all from q1 to q2, swap q1 and q2 -> Option B

4. Quick Check:

   Push costly + pop O(1) = push rearranges queues [OK]

Hint: Push costly rearranges queues; pop just dequeues front [OK]

Common Mistakes:

• Confusing which operation is costly
• Using single queue for O(1) pop incorrectly
• Choosing two stacks instead of queues