Implement Stack Using Queue in DSA C

Mental Model

A stack works like a pile where the last item added is the first removed. A queue works like a line where the first item added is the first removed. We can use a queue to mimic a stack by rearranging the order after each addition.

Analogy: Imagine a line of people (queue) but you want to always serve the last person who joined first (stack). After each new person joins, you make them go to the front of the line by moving everyone else behind them.

Queue: front -> [1] -> [2] -> [3] -> rear
Stack: top -> [3] -> [2] -> [1] -> bottom

Dry Run Walkthrough

Input: Push 1, Push 2, Push 3, Pop

Goal: Use a queue to behave like a stack and pop the last pushed element

Step 1: Push 1 into queue

front -> [1] -> rear

Why: Add first element normally

Step 2: Push 2 into queue, then rotate queue to move 2 to front

front -> [2] -> [1] -> rear

Why: Rotate so last pushed is at front to simulate stack top

Step 3: Push 3 into queue, then rotate queue to move 3 to front

front -> [3] -> [2] -> [1] -> rear

Why: Rotate again to keep last pushed element at front

Step 4: Pop from queue (remove front)

front -> [2] -> [1] -> rear

Why: Pop removes the last pushed element, simulating stack pop

Result:

front -> [2] -> [1] -> rear
Pop returned 3

Annotated Code

DSA C

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

#define MAX 100

typedef struct {
    int data[MAX];
    int front;
    int rear;
    int size;
} Queue;

void initQueue(Queue* q) {
    q->front = 0;
    q->rear = -1;
    q->size = 0;
}

int isEmpty(Queue* q) {
    return q->size == 0;
}

int isFull(Queue* q) {
    return q->size == MAX;
}

void enqueue(Queue* q, int val) {
    if (isFull(q)) return;
    q->rear = (q->rear + 1) % MAX;
    q->data[q->rear] = val;
    q->size++;
}

int dequeue(Queue* q) {
    if (isEmpty(q)) return -1;
    int val = q->data[q->front];
    q->front = (q->front + 1) % MAX;
    q->size--;
    return val;
}

int queueSize(Queue* q) {
    return q->size;
}

// Stack implemented using one queue
typedef struct {
    Queue q;
} StackUsingQueue;

void initStack(StackUsingQueue* s) {
    initQueue(&s->q);
}

void push(StackUsingQueue* s, int val) {
    enqueue(&s->q, val); // add new element
    int sz = queueSize(&s->q);
    // rotate queue to move new element to front
    for (int i = 0; i < sz - 1; i++) {
        int temp = dequeue(&s->q); // remove front
        enqueue(&s->q, temp);      // add it to rear
    }
}

int pop(StackUsingQueue* s) {
    if (isEmpty(&s->q)) return -1;
    return dequeue(&s->q); // front is top of stack
}

int main() {
    StackUsingQueue s;
    initStack(&s);

    push(&s, 1);
    push(&s, 2);
    push(&s, 3);

    int val = pop(&s);
    printf("Popped: %d\n", val);

    // Print remaining stack elements
    printf("Stack after pop: ");
    while (!isEmpty(&s.q)) {
        printf("%d ", dequeue(&s.q));
    }
    printf("\n");

    return 0;
}

enqueue(&s->q, val); // add new element

Add new element to queue rear

for (int i = 0; i < sz - 1; i++) { int temp = dequeue(&s->q); enqueue(&s->q, temp); }

Rotate queue to move last pushed element to front

return dequeue(&s->q); // front is top of stack

Pop removes front element which is stack top

Output

Popped: 3

Stack after pop: 2 1 

Complexity Analysis

Time: O(n) for push because we rotate all elements to keep last pushed at front; O(1) for pop as it just dequeues front

Space: O(n) for storing n elements in the queue

vs Alternative: Naive approach using two queues can have O(1) push but O(n) pop; this approach optimizes pop to O(1) at cost of O(n) push

Edge Cases

Pop from empty stack

Returns -1 indicating stack is empty

DSA C

if (isEmpty(&s->q)) return -1;

Push into full queue

Push is ignored as queue is full, no overflow handling

DSA C

if (isFull(q)) return;

When to Use This Pattern

When you need stack behavior but only have a queue, use this pattern to reorder elements after each push so pop is efficient.

Common Mistakes

Mistake: Not rotating the queue after push, so pop returns oldest element instead of last pushed
Fix: Rotate the queue by dequeuing and enqueuing all elements except the last pushed after each push

Mistake: Trying to pop from empty queue without checking, causing errors
Fix: Check if queue is empty before dequeueing in pop

Summary

Implements a stack using a single queue by rotating elements after each push.

Use when only queue data structure is available but stack operations are needed.

The key is to rotate the queue after each push so the last pushed element is always at the front.