Consider the following statements : S1 : A queue can be implemented using two…

Answer: Both statements are correct.

• Implementing a queue using two stacks (amortized O(1) per operation):

  1. Maintain two stacks: stack_in and stack_out.

  2. Enqueue(x): push x onto stack_in.

  3. Dequeue(): if stack_out is empty, pop all elements from stack_in and push them onto stack_out; then pop from stack_out.

  Complexity: Amortized O(1) per enqueue/dequeue because each element is moved at most once between stacks.

• Implementing a stack using two queues (example: push-costly method):

  1. Maintain two queues: q1 (holds current stack order) and q2 (temporary).

  2. Push(x): enqueue x into q2, then dequeue all elements from q1 and enqueue them into q2; swap q1 and q2. Now q1 has the new element at the front (top of stack).

  3. Pop(): dequeue from q1 (this returns the last pushed element).

  Complexity: Push is O(n) and pop is O(1) in this method. There is an alternative (pop-costly) method where push is O(1) and pop is O(n).