Suppose implementation supports an instruction REVERSE, which reverses the order of elements on the stack, in addition to the PUSH and POP instructions. Which one of the following statements is TRUE with respect to this modified stack?a)A queue cannot be implemented using this stack.b)A queue can be implemented where ENQUEUE takes a single instruction and DEQUEUE takes a sequence of two instructions.c)A queue can be implemented where ENQUEUE takes a sequence of three instructions and DEQUEUE takes a single instruction.d)A queue can be implemented where both ENQUEUE and DEQUEUE take a single instruction each.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Implementation with REVERSE instruction and its impact on stack operations

The given implementation supports three instructions - PUSH, POP, and REVERSE. The REVERSE instruction reverses the order of elements on the stack. Let us try to understand the impact of this instruction on stack operations.

Impact of REVERSE instruction on stack operations

When the REVERSE instruction is executed, the elements on the stack are reversed, i.e., the top element becomes the bottom element, and the bottom element becomes the top element. This means that the order of elements on the stack is changed.

For example, if the stack contains elements A, B, and C (where A is the top element and C is the bottom element), and the REVERSE instruction is executed, then the stack will contain elements C, B, and A (where C is the top element and A is the bottom element).

This has the following implications:

- When a POP operation is performed after a REVERSE operation, the bottom element (which was originally the top element before the REVERSE operation) is removed from the stack.
- When a PUSH operation is performed after a REVERSE operation, the element is added to the bottom of the stack (which was originally the top of the stack before the REVERSE operation).

Implementing a queue using the modified stack

Now, let us consider the options given in the question and try to determine if a queue can be implemented using the modified stack.

Option A: A queue cannot be implemented using this stack.

This option is incorrect. A queue can be implemented using a stack, and the REVERSE instruction does not prevent this.

Option B: A queue can be implemented where ENQUEUE takes a single instruction and DEQUEUE takes a sequence of two instructions.

This option is also incorrect. In a queue, the ENQUEUE operation adds an element to the back of the queue, and the DEQUEUE operation removes an element from the front of the queue. Since the modified stack can only add elements to the bottom of the stack (which was originally the top of the stack before the REVERSE operation), we cannot implement ENQUEUE with a single instruction. Similarly, we cannot implement DEQUEUE with a sequence of two instructions.

Option C: A queue can be implemented where ENQUEUE takes a sequence of three instructions and DEQUEUE takes a single instruction.

This option is correct. We can implement ENQUEUE using the following sequence of instructions:

- Perform a REVERSE operation.
- Push the element onto the top of the stack.
- Perform another REVERSE operation to restore the original order of elements on the stack.

This will add the element to the bottom of the stack (which was originally the top of the stack before the REVERSE operation), effectively adding it to the back of the queue.

We can implement DEQUEUE using a single POP instruction, which will remove the front element of the queue (which is the top element of the stack).

Option D: A queue can be implemented where both ENQUEUE and DEQUEUE take a single instruction each.

This option is incorrect. As explained earlier, we cannot implement ENQUEUE and DEQUEUE with a single instruction each.

Conclusion

In conclusion, the correct statement with respect to the modified stack is option C. We can implement a queue where ENQUEUE takes a sequence of three instructions and DEQUEUE takes a single instruction.

Similar Computer Science Engineering (CSE) Doubts

Suppose a stack implementation supports an instruction REVERSE, which reverses the order of elements on the stack, in addition to the PUSH and POP instructions. Which one of the following statements is TRUE with respect to this modified stack? .

Suppose a stack implementation supports an instruction REVERSE, which reverses the order of elements on the stack, in addition to the PUSH and POP instructions. Which one of the following statements is TRUE (with respect to this modified stack)?

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