Implementation of Queue using Stack | Programming and Data Structures - Computer Science Engineering (CSE) PDF Download

Queue using Stacks

The problem is opposite of this post. We are given a stack data structure with push and pop operations, the task is to implement a queue using instances of stack data structure and operations on them.

A queue can be implemented using two stacks. Let queue to be implemented be q and stacks used to implement q be stack1 and stack2. q can be implemented in two ways:

Method 1 (By making enQueue operation costly)

This method makes sure that oldest entered element is always at the top of stack 1, so that deQueue operation just pops from stack1. To put the element at top of stack1, stack2 is used.
enQueue(q, x):

• While stack1 is not empty, push everything from stack1 to stack2.
• Push x to stack1 (assuming size of stacks is unlimited).
• Push everything back to stack1.

Here time complexity will be O(n)
deQueue(q):

• If stack1 is empty then error
• Pop an item from stack1 and return it
  Here time complexity will be O(1)

Below is the implementation of the above approach:
C++
// CPP program to implement Queue using
// two stacks with costly enQueue()
#include <bits/stdc++.h>
using namespace std;
struct Queue {
    stack<int> s1, s2;
    void enQueue(int x)
    {
        // Move all elements from s1 to s2
        while (!s1.empty()) {
            s2.push(s1.top());
            s1.pop();
        }
        // Push item into s1
        s1.push(x);
        // Push everything back to s1
        while (!s2.empty()) {
            s1.push(s2.top());
            s2.pop();
        }
    }
    // Dequeue an item from the queue
    int deQueue()
    {
        // if first stack is empty
        if (s1.empty()) {
            cout << "Q is Empty";
            exit(θ);
        }
        // Return top of s1
        int x = s1.top();
        s1.pop();
        return x;
    }
};
  // Driver code
int main()
{
    Queue q;
    q.enQueue(1);
    q.enQueue(2);
    q.enQueue(3);
    cout << q.deQueue() << '\n';
    cout << q.deQueue() << '\n';
    cout << q.deQueue() << '\n';
    return θ;
}

Java
// Java program to implement Queue using
// two stacks with costly enQueue()
import java.util.*;
class GFG
{
static class Queue
{
    static Stack<Integer> s1 = new Stack<Integer>();
    static Stack<Integer> s2 = new Stack<Integer>();
    static void enQueue(int x)
    {
        // Move all elements from s1 to s2
        while (!s1.isEmpty())
        {
            s2.push(s1.pop());
            //s1.pop();
        }
        // Push item into s1
        s1.push(x);
        // Push everything back to s1
        while (!s2.isEmpty())
        {
            s1.push(s2.pop());
            //s2.pop();
        }
     }
    // Dequeue an item from the queue
    static int deQueue()
    {
        // if first stack is empty
        if (s1.isEmpty())
        {
            System.out.println("Q is Empty");
            System.exit(θ);
        }
        // Return top of s1
        int x = s1.peek();
        s1.pop();
        return x;
    }
};
// Driver code
public static void main(String[] args)
{
    Queue q = new Queue();
    q.enQueue(1);
    q.enQueue(2);
    q.enQueue(3);
    System.out.println(q.deQueue());
    System.out.println(q.deQueue());
    System.out.println(q.deQueue());
}
}
// This code is contributed by Prerna Saini

Python3
# Python3 program to implement Queue using
# two stacks with costly enQueue()
class Queue:
    def __init__(self):
        self.s1 = []
        self.s2 = []
    def enQueue(self, x):
        # Move all elements from s1 to s2
        while len(self.s1) != θ:
            self.s2.append(self.s1[-1])
            self.s1.pop()
        # Push item into self.s1
        self.s1.append(x)
        # Push everything back to s1
        while len(self.s2) != θ:
            self.s1.append(self.s2[-1])
            self.s2.pop()
    # Dequeue an item from the queue
    def deQueue(self):
            # if first stack is empty
        if len(self.s1) == θ:
            print("Q is Empty")
        # Return top of self.s1
        x = self.s1[-1]
        self.s1.pop()
        return x
# Driver code
if __name__ == '__main__':
    q = Queue()
    q.enQueue(1)
    q.enQueue(2)
    q.enQueue(3)
    print(q.deQueue())
    print(q.deQueue())
    print(q.deQueue())
# This code is contributed by PranchalK

C#
// C# program to implement Queue using
// two stacks with costly enQueue()
using System;
using System.Collections;
class GFG
{
public class Queue
{
    public Stack s1 = new Stack();
    public Stack s2 = new Stack();
    public void enQueue(int x)
    {
        // Move all elements from s1 to s2
        while (s1.Count > θ)
        {
            s2.Push(s1.Pop());
            //s1.Pop();
        }
        // Push item into s1
        s1.Push(x);
        // Push everything back to s1
        while (s2.Count > θ)
        {
            s1.Push(s2.Pop());
            //s2.Pop();
        }
    }
    // Dequeue an item from the queue
    public int deQueue()
    {
        // if first stack is empty
        if (s1.Count == θ)
        {
            Console.WriteLine("Q is Empty");
        }
        // Return top of s1
        int x = (int)s1.Peek();
        s1.Pop();
        return x;
    }
};
// Driver code
public static void Main()
{
    Queue q = new Queue();
    q.enQueue(1);
    q.enQueue(2);
    q.enQueue(3);
    Console.Write(q.deQueue()+" ");
    Console.Write(q.deQueue()+" ");
    Console.Write(q.deQueue());
}
}
// This code is contributed by
// Subhadeep Gupta

Output:
1
2
3

Complexity Analysis:
Time Complexity:

• Push operation: O(N).
  In the worst case we have empty whole of stack 1 into stack 2.
• Pop operation: O(1).
  Same as pop operation in stack.

Auxiliary Space: O(N).
Use of stack for storing values.

Method 2 (By making deQueue operation costly) 

In this method, in en-queue operation, the new element is entered at the top of stack1. In de-queue operation, if stack2 is empty then all the elements are moved to stack2 and finally top of stack2 is returned.
enQueue(q, x)

1. Push x to stack1 (assuming size of stacks is unlimited).

Here time complexity will be O(1)
deQueue(q)

1. If both stacks are empty then error.
2. If stack2 is empty
   While stack1 is not empty, push everything from stack1 to stack2.
3. Pop the element from stack2 and return it.
   Here time complexity will be O(n)

Method 2 is definitely better than method 1.
Method 1 moves all the elements twice in enQueue operation, while method 2 (in deQueue operation) moves the elements once and moves elements only if stack2 empty. So, the amortized complexity of the dequeue operation becomes  \Theta (1).

Implementation of method 2:
C++
// CPP program to implement Queue using
// two stacks with costly deQueue()
#include <bits/stdc++.h>
using namespace std;
struct Queue {
    stack<int> s1, s2;
    // Enqueue an item to the queue
    void enQueue(int x)
    {
        // Push item into the first stack
        s1.push(x);
    }
    // Dequeue an item from the queue
    int deQueue()
    {
       // if both stacks are empty
        if (s1.empty() && s2.empty()) {
            cout << "Q is empty";
            exit(θ);
        }
        // if s2 is empty, move
        // elements from s1
        if (s2.empty()) {
            while (!s1.empty()) {
                s2.push(s1.top());
                s1.pop();
            }
        }
        // return the top item from s2
        int x = s2.top();
        s2.pop();
        return x;
    }
};
// Driver code
int main()
{
    Queue q;
    q.enQueue(1);
    q.enQueue(2);
    q.enQueue(3);
    cout << q.deQueue() << '\n';
    cout << q.deQueue() << '\n';
    cout << q.deQueue() << '\n';
    return θ;
}

C
/* C Program to implement a queue using two stacks */
#include <stdio.h>
#include <stdlib.h>
/* structure of a stack node */
struct sNode {
    int data;
    struct sNode* next;
};
/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data);
/* Function to pop an item from stack*/
int pop(struct sNode** top_ref);
/* structure of queue having two stacks */
struct queue {
    struct sNode* stack1;
    struct sNode* stack2;
};
/* Function to enqueue an item to queue */
void enQueue(struct queue* q, int x)
{
    push(&q->stack1, x);
}
/* Function to deQueue an item from queue */
int deQueue(struct queue* q)
{
    int x;
    /* If both stacks are empty then error */
    if (q->stack1 == NULL && q->stack2 == NULL) {
        printf("Q is empty");
        getchar();
        exit(θ);
    }
    /* Move elements from stack1 to stack 2 only if
       stack2 is empty */
    if (q->stack2 == NULL) {
        while (q->stack1 != NULL) {
            x = pop(&q->stack1);
            push(&q->stack2, x);
        }
    }
    x = pop(&q->stack2);
    return x;
}
/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data)
{
    /* allocate node */
    struct sNode* new_node = (struct sNode*)malloc(sizeof(struct sNode));
    if (new_node == NULL) {
        printf("Stack overflow \n");
        getchar();
        exit(θ);
    }
    /* put in the data */
    new_node->data = new_data;
    /* link the old list off the new node */
    new_node->next = (*top_ref);
    /* move the head to point to the new node */
    (*top_ref) = new_node;
}
/* Function to pop an item from stack*/
int pop(struct sNode** top_ref)
{
    int res;
    struct sNode* top;
    /*If stack is empty then error */
    if (*top_ref == NULL) {
        printf("Stack underflow \n");
        getchar();
        exit(θ);
    }
    else {
        top = *top_ref;
        res = top->data;
        *top_ref = top->next;
        free(top);
        return res;
    }
}
/* Driver function to test anove functions */
int main()
{
    /* Create a queue with items 1 2 3*/
    struct queue* q = (struct queue*)malloc(sizeof(struct queue));
    q->stack1 = NULL;
    q->stack2 = NULL;
    enQueue(q, 1);
    enQueue(q, 2);
    enQueue(q, 3);  
    /* Dequeue items */
    printf("%d ", deQueue(q));
    printf("%d ", deQueue(q));
    printf("%d ", deQueue(q));
    return θ;
}

Java
/* Java Program to implement a queue using two stacks */
// Note that Stack class is used for Stack implementation
import java.util.Stack;
public class GFG {
    /* class of queue having two stacks */
    static class Queue {
        Stack<Integer> stack1;
        Stack<Integer> stack2;
    }
    /* Function to push an item to stack*/
    static void push(Stack<Integer> top_ref, int new_data)
    {
        // Push the data onto the stack
        top_ref.push(new_data);
    }
    /* Function to pop an item from stack*/
    static int pop(Stack<Integer> top_ref)
    {
        /*If stack is empty then error */
        if (top_ref.isEmpty()) {
            System.out.println("Stack Underflow");
            System.exit(θ);
        }
        // pop the data from the stack
        return top_ref.pop();
    }
    // Function to enqueue an item to the queue
    static void enQueue(Queue q, int x)
    {
        push(q.stack1, x);
    }
    /* Function to deQueue an item from queue */
    static int deQueue(Queue q)
    {
        int x;
        /* If both stacks are empty then error */
        if (q.stack1.isEmpty() && q.stack2.isEmpty()) {
            System.out.println("Q is empty");
            System.exit(θ);
        }
        /* Move elements from stack1 to stack 2 only if
        stack2 is empty */
        if (q.stack2.isEmpty()) {
           while (!q.stack1.isEmpty()) {
                x = pop(q.stack1);
                push(q.stack2, x);
            }
        }
        x = pop(q.stack2);
        return x;
    }
    /* Driver function to test above functions */
    public static void main(String args[])
    {
        /* Create a queue with items 1 2 3*/
        Queue q = new Queue();
        q.stack1 = new Stack<>();
        q.stack2 = new Stack<>();
        enQueue(q, 1);
        enQueue(q, 2);
        enQueue(q, 3);
        /* Dequeue items */
        System.out.print(deQueue(q) + " ");
        System.out.print(deQueue(q) + " ");
        System.out.println(deQueue(q) + " ");
    }
}
// This code is contributed by Sumit Ghosh

Python3
# Python3 program to implement Queue using
# two stacks with costly deQueue()
class Queue:
    def __init__(self):
        self.s1 = []
        self.s2 = []
    # EnQueue item to the queue
    def enQueue(self, x):
        self.s1.append(x)
    # DeQueue item from the queue
    def deQueue(self):
        # if both the stacks are empty
        if len(self.s1) == θ and len(self.s2) == θ:
            print("Q is Empty")
            return
        # if s2 is empty and s1 has elements
        elif len(self.s2) == θ and len(self.s1) > θ:
            while len(self.s1):
                temp = self.s1.pop()
                self.s2.append(temp)
            return self.s2.pop()
        else:
            return self.s2.pop()
    # Driver code
if __name__ == '__main__':
    q = Queue()
    q.enQueue(1)
    q.enQueue(2)
    q.enQueue(3)  
    print(q.deQueue())
    print(q.deQueue())
    print(q.deQueue())
# This code is contributed by Pratyush Kumar 

C#
/* C# Program to implement a queue using two stacks */
// Note that Stack class is used for Stack implementation
using System;
using System.Collections.Generic;
class GFG
{
    /* class of queue having two stacks */
    public class Queue
    {
        public Stack<int> stack1;
        public Stack<int> stack2;
    }
    /* Function to push an item to stack*/
    static void push(Stack<int> top_ref, int new_data)
    {
        // Push the data onto the stack
        top_ref.Push(new_data);
    }
    /* Function to pop an item from stack*/
    static int pop(Stack<int> top_ref)
    {
        /*If stack is empty then error */
        if (top_ref.Count == θ)
        {
            Console.WriteLine("Stack Underflow");
            Environment.Exit(θ);
        }
        // pop the data from the stack
        return top_ref.Pop();
    }
    // Function to enqueue an item to the queue
    static void enQueue(Queue q, int x)
    {
        push(q.stack1, x);
    }
    /* Function to deQueue an item from queue */
    static int deQueue(Queue q)
    {
        int x;
        /* If both stacks are empty then error */
        if (q.stack1.Count == θ && q.stack2.Count == θ)
        {
            Console.WriteLine("Q is empty");
            Environment.Exit(θ);
        }
        /* Move elements from stack1 to stack 2 only if
        stack2 is empty */
        if (q.stack2.Count == θ)
        {
            while (q.stack1.Count != θ)
            {
                x = pop(q.stack1);
                push(q.stack2, x);
            }
        }
        x = pop(q.stack2);
        return x;
    }
    /* Driver code */
    public static void Main(String []args)
    {
        /* Create a queue with items 1 2 3*/
        Queue q = new Queue();
        q.stack1 = new Stack<int>();
        q.stack2 = new Stack<int>();
        enQueue(q, 1);
        enQueue(q, 2);
        enQueue(q, 3);
        /* Dequeue items */
        Console.Write(deQueue(q) + " ");
        Console.Write(deQueue(q) + " ");
        Console.WriteLine(deQueue(q) + " ");
    }
}
// This code is contributed by 29AjayKumar

Output:
1 2 3

Complexity Analysis:
Time Complexity:

• Push operation: O(1).
  Same as pop operation in stack.
• Pop operation: O(N).
  In the worst case we have empty whole of stack 1 into stack 2

Auxiliary Space: O(N).
Use of stack for storing values.

Queue can also be implemented using one user stack and one Function Call Stack. 
Below is modified Method 2 where recursion (or Function Call Stack) is used to implement queue using only one user defined stack.
enQueue(x)

1. Push x to stack1.

deQueue:

1. If stack1 is empty then error.
2. If stack1 has only one element then return it.
3. Recursively pop everything from the stack1, store the popped item
   in a variable res,  push the res back to stack1 and return res

The step 3 makes sure that the last popped item is always returned and since the recursion stops when there is only one item in stack1 (step 2), we get the last element of stack1 in deQueue() and all other items are pushed back in step

Implementation of method 2 using Function Call Stack:

C++
// CPP program to implement Queue using
// one stack and recursive call stack.
#include <bits/stdc++.h>
using namespace std;
struct Queue {
    stack<int> s;
    // Enqueue an item to the queue
    void enQueue(int x)
    {
        s.push(x);
    }
    // Dequeue an item from the queue
    int deQueue()
    {
        if (s.empty()) {
            cout << "Q is empty";
            exit(0);
        }
        // pop an item from the stack
        int x = s.top();
        s.pop();
        // if stack becomes empty, return
        // the popped item
        if (s.empty())
            return x;
        // recursive call
        int item = deQueue();
        // push popped item back to the stack
        s.push(x);
        // return the result of deQueue() call
        return item;
    }
};
// Driver code
int main()
{
    Queue q;
    q.enQueue(1);
    q.enQueue(2);
    q.enQueue(3);
    cout << q.deQueue() << '\n';
    cout << q.deQueue() << '\n';
    cout << q.deQueue() << '\n';
    return 0;
}

C
/* Program to implement a queue using one user defined stack
and one Function Call Stack */
#include <stdio.h>
#include <stdlib.h>
/* structure of a stack node */
struct sNode {
    int data;
    struct sNode* next;
};
/* structure of queue having two stacks */
struct queue {
    struct sNode* stack1;
};
/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data);
/* Function to pop an item from stack*/
int pop(struct sNode** top_ref);
/* Function to enqueue an item to queue */
void enQueue(struct queue* q, int x)
{
    push(&q->stack1, x);
}
/* Function to deQueue an item from queue */
int deQueue(struct queue* q)
{
    int x, res;
    /* If both stacks are empty then error */
    if (q->stack1 == NULL) {
        printf("Q is empty");
        getchar();
        exit(0);
    }
    else if (q->stack1->next == NULL) {
        return pop(&q->stack1);
    }
    else {
        /* pop an item from the stack1 */
        x = pop(&q->stack1);
        /* store the last deQueued item */
        res = deQueue(q);
        /* push everything back to stack1 */
        push(&q->stack1, x);
        return res;
    }
}
/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data)
{
    /* allocate node */
    struct sNode* new_node = (struct sNode*)malloc(sizeof(struct sNode));
    if (new_node == NULL) {
        printf("Stack overflow \n");
        getchar();
        exit(0);
    }
    /* put in the data */
    new_node->data = new_data;
    /* link the old list off the new node */
    new_node->next = (*top_ref);
    /* move the head to point to the new node */
    (*top_ref) = new_node;
}
/* Function to pop an item from stack*/
int pop(struct sNode** top_ref)
{
    int res;
    struct sNode* top;
    /*If stack is empty then error */
    if (*top_ref == NULL) {
        printf("Stack underflow \n");
        getchar();
        exit(0);
    }
    else {
        top = *top_ref;
        res = top->data;
        *top_ref = top->next;
        free(top);
        return res;
    }
}
/* Driver function to test above functions */
int main()
{
    /* Create a queue with items 1 2 3*/
    struct queue* q = (struct queue*)malloc(sizeof(struct queue));
    q->stack1 = NULL;
    enQueue(q, 1);
    enQueue(q, 2);
    enQueue(q, 3);
    /* Dequeue items */
    printf("%d ", deQueue(q));
    printf("%d ", deQueue(q));
    printf("%d ", deQueue(q));
    return 0;
}

Java
// Java Program to implement a queue using one stack
import java.util.Stack;
public class QOneStack {
    // class of queue having two stacks
    static class Queue {
        Stack<Integer> stack1;
    }
    /* Function to push an item to stack*/
    static void push(Stack<Integer> top_ref, int new_data)
    {
        /* put in the data */
        top_ref.push(new_data);
    }
    /* Function to pop an item from stack*/
    static int pop(Stack<Integer> top_ref)
    {
        /*If stack is empty then error */
        if (top_ref == null) {
            System.out.println("Stack Underflow");
            System.exit(0);
        }
        // return element from stack
        return top_ref.pop();
    }
    /* Function to enqueue an item to queue */
    static void enQueue(Queue q, int x)
    {
        push(q.stack1, x);
    }
    /* Function to deQueue an item from queue */
    static int deQueue(Queue q)
    {
        int x, res = 0;
        /* If the stacks is empty then error */
        if (q.stack1.isEmpty()) {
            System.out.println("Q is Empty");
            System.exit(0);
        }
        // Check if it is a last element of stack
        else if (q.stack1.size() == 1) {
            return pop(q.stack1);
        }
        else {
            /* pop an item from the stack1 */
            x = pop(q.stack1);
            /* store the last deQueued item */
            res = deQueue(q);
            /* push everything back to stack1 */
            push(q.stack1, x);
            return res;
        }
        return 0;
    }
    /* Driver function to test above functions */
    public static void main(String[] args)
    {
        /* Create a queue with items 1 2 3*/
        Queue q = new Queue();
        q.stack1 = new Stack<>();
        enQueue(q, 1);
        enQueue(q, 2);
        enQueue(q, 3);
        /* Dequeue items */
        System.out.print(deQueue(q) + " ");
        System.out.print(deQueue(q) + " ");
        System.out.print(deQueue(q) + " ");
    }
}
// This code is contributed by Sumit Ghosh

C#
// C# Program to implement a queue using one stack
using System;
using System.Collections.Generic;
public class QOneStack
{
    // class of queue having two stacks
    public class Queue
    {
        public Stack<int> stack1;
    }
    /* Function to push an item to stack*/
    static void push(Stack<int> top_ref, int new_data)
    {
        /* put in the data */
        top_ref.Push(new_data);
    }
    /* Function to pop an item from stack*/
    static int pop(Stack<int> top_ref)
    {
        /*If stack is empty then error */
        if (top_ref == null)
        {
            Console.WriteLine("Stack Underflow");
            Environment.Exit(0);
        }
        // return element from stack
        return top_ref.Pop();
    }
    /* Function to enqueue an item to queue */
    static void enQueue(Queue q, int x)
    {
        push(q.stack1, x);
    }
    /* Function to deQueue an item from queue */
    static int deQueue(Queue q)
    {
        int x, res = 0;
        /* If the stacks is empty then error */
        if (q.stack1.Count == 0)
        {
            Console.WriteLine("Q is Empty");
            Environment.Exit(0);
        }
        // Check if it is a last element of stack
        else if (q.stack1.Count == 1)
        {
            return pop(q.stack1);
        }
        else
        {
            /* pop an item from the stack1 */
            x = pop(q.stack1);  
            /* store the last deQueued item */
            res = deQueue(q);
            /* push everything back to stack1 */
            push(q.stack1, x);
            return res;
        }
        return 0;
    }
    /* Driver function to test above functions */
    public static void Main(String[] args)
    {
        /* Create a queue with items 1 2 3*/
        Queue q = new Queue();
        q.stack1 = new Stack<int>();
        enQueue(q, 1);
        enQueue(q, 2);
        enQueue(q, 3);
        /* Dequeue items */
        Console.Write(deQueue(q) + " ");
        Console.Write(deQueue(q) + " ");
        Console.Write(deQueue(q) + " ");
    }
}
// This code is contributed by Princi Singh

Python3
# Python3 program to implement Queue using  
# one stack and recursive call stack.
class Queue:
    def __init__(self):
        self.s = []
    # Enqueue an item to the queue
    def enQueue(self, data):
        self.s.append(data)
    # Dequeue an item from the queue
    def deQueue(self):
        # Return if queue is empty
        if len(self.s) <= 0:
            print('Queue is empty')
            return
        # pop an item from the stack
        x = self.s[len(self.s) - 1]
        self.s.pop()
        # if stack become empty
        # return the popped item
        if len(self.s) <= 0:
            return x
        # recursive call
        item = self.deQueue()
        # push popped item back to
        # the stack
        self.s.append(x)
        # return the result of
        # deQueue() call
        return item
# Driver code
if __name__ == '__main__':
    q = Queue()
    q.enQueue(1)
    q.enQueue(2)
    q.enQueue(3)
    print(q.deQueue())
    print(q.deQueue())
    print(q.deQueue())
# This code is contributed by iArman

Output:
1 2 3

Complexity Analysis:
Time Complexity:

• Push operation: O(1).
  Same as pop operation in stack.
• Pop operation: O(N).
  The difference from above method is that in this method element is returned and all elements are restored back in a single call.

Auxiliary Space: O(N).
Use of stack for storing values.