GATE CSE 2001 | Question: 2.16

Question

What is the minimum number of stacks of size $n$ required to implement a queue of size $n$?

• A. One
• B. Two
• C. Three
• D. Four

Comments

$$\begin{aligned} &\textbf{Enqueue}(Q, x):\\ &\quad \text{Push } x \text{ into } S_1 \end{aligned}$$

 

$$\begin{aligned} &\textbf{Dequeue}(Q):\\ &\quad \textbf{if } S_2 \text{ is empty then}\\ &\quad\quad \Big|~ \text{Move all elements of } S_1 \text{ to } S_2\\ &\quad \textbf{end if}\\ &\quad \text{Pop and return top element from } S_2 \end{aligned}$$

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note : reverse() operation is not mentioned for the stack in the question . so don't assume reverse operation as a basic operation to solve the question . otherwise the ans will be 1 instead of 2 . correct ans is 2.

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$\underline{why \ even \ bother\  about \ reverse }$

say i push 1,2,3,4 into stack now i wanna deque, i.e pop 1 but 1 is at the botton so can't be poped so i definitely need 2 stacks

Answer 1

A queue can be implemented using two stacks.

Let queue be represented as " $q$ "
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 newly entered element is always at the bottom of stack 1, so that deQueue operation just pops from stack1. To put the element at top of stack1, stack2 is used.

$enQueue(q, x)$

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

$dnQueue(q)$

1. If stack1 is empty then error
2. Pop an item from stack1 and return it

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).

$deQueue(q)$

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.

Correct Answer: $B$

Comments

in method 1), newly entered element is being entered at bottom of stack1, not on top. on top there is most old element which being popped first.

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Corrected. Thanks :)

Answer 2

ans b)

Comments

is it a theory or any explanation is present?

Answer 3

Two stacks we need to implement one queue

Answer 4

Two stacks of size n required to implement a queue of size n

Answer 5

Two. One stack is used for enqueue operations, and the other stack is used for dequeue operations. The enqueue stack is used to push elements onto the queue, and the dequeue stack is used to pop elements off of the queue. To implement a queue using stacks, the elements are first pushed onto the enqueue stack. When a dequeue operation is performed, the elements are popped from the enqueue stack and pushed onto the dequeue stack. The top element of the dequeue stack is then returned as the dequeued element. This process ensures that the first element pushed onto the queue is also the first element to be popped off of the queue, which is the behavior of a queue.

Answer 6

Option (B)  

As Firstly enter all element into stack 1 then from stack 1 to stack 2 then follow pop operation...