To implement a stack using queue(with only enqueue and dequeue operations), how many queues will you need?

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Question: To implement a stack using queue(with only enqueue and dequeue operations), how many queues will you need?
a) 1
b) 2
c) 3
d) 4
Answer: b

Explanation:

To implement a stack using queues, you need two queues. This is because the stack follows the Last In, First Out (LIFO) principle, while a queue follows the First In, First Out (FIFO) principle. To mimic the behavior of a stack using queues, you can use the following two approaches:

Approach 1: Push Operation is Costly

  • Idea: Make the push operation costly so that the pop operation becomes efficient.
  • Steps:
    1. Let the two queues be q1 and q2.
    2. When a new element is pushed, enqueue it into q2.
    3. Dequeue all elements from q1 and enqueue them into q2. This reverses the order of elements, maintaining the LIFO order in q2.
    4. Swap the names of q1 and q2. Now, q1 contains the stack elements in the correct order, and q2 is empty for future use.
    5. To pop an element, simply dequeue from q1.
  • Time Complexity:
    • Push: O(n)O(n)O(n) (due to the transfer of elements between q1 and q2).
    • Pop: O(1)O(1)O(1) (just a dequeue operation).

Approach 2: Pop Operation is Costly

  • Idea: Make the pop operation costly so that the push operation becomes efficient.
  • Steps:
    1. Let the two queues be q1 and q2.
    2. When a new element is pushed, enqueue it directly into q1.
    3. To pop an element:
      • Dequeue all elements from q1 except the last one and enqueue them into q2.
      • The last dequeued element from q1 is the one to be popped (LIFO order).
      • Swap the names of q1 and q2. Now, q1 again holds the stack elements in the correct order, and q2 is empty for future use.
  • Time Complexity:
    • Push: O(1)O(1)O(1) (simple enqueue operation).
    • Pop: O(n)O(n)O(n) (due to the transfer of elements to maintain the stack order).

Why Two Queues Are Needed

  • A single queue cannot reverse the order of elements efficiently while preserving the LIFO property.
  • Two queues allow you to transfer elements between them, enabling the reversal of the order or selective dequeuing to mimic stack behavior.

Explanation for Implementing a Queue Using Stacks

This part of your query is about implementing a queue using stacks.

To implement a queue using two stacks, the operations are adjusted as follows:

  • Push operation is efficient (O(1)O(1)O(1)).
  • Pop operation becomes costly (O(n)O(n)O(n)) because all elements need to be transferred between the stacks to preserve the FIFO order.

In summary, to implement:

  1. A stack using a queue → 2 queues are needed.
  2. A queue using stacks → 2 stacks are needed.
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