Question

Let \(S1\) and \(S2\) be two stacks. \(S1\) has a capacity of 4 elements, and \(S2\) has a capacity of 2 elements. \(S1\) already has 4 elements: 100, 200, 300, and 400, whereas \(S2\) is empty, as shown below. \begin{center} \includegraphics[width=8cm]{48.png} \end{center} Only the following three operations are available:
\texttt{PushToS2:} Pop the top element from \(S1\) and push it on \(S2\).
\texttt{PushToS1:} Pop the top element from \(S2\) and push it on \(S1\).
\texttt{GenerateOutput:} Pop the top element from \(S1\) and output it to the user. Note: - The pop operation is not allowed on an empty stack.
- The push operation is not allowed on a full stack. Which of the following output sequences can be generated by using the above operations?

• A. 100, 200, 400, 300
• B. 200, 300, 400, 100
• C. 400, 200, 100, 300
• D. 300, 200, 400, 100

Hint:

When solving stack-based problems, simulate the operations step by step to verify the feasibility of each sequence.

Answer 1

The Correct Option is B

The available operations allow for flexible reordering of elements in \(S1\) and \(S2\). By analyzing the given sequences:
1. Sequence (A): The sequence \(100, 200, 400, 300\) cannot be generated because \(400\) is above \(300\) in \(S1\), and moving \(400\) before \(300\) without outputting \(300\) is not possible. Hence, (A) is not feasible.
2. Sequence (B): The sequence \(200, 300, 400, 100\) can be generated as follows:
- Use \texttt{GenerateOutput} to output \(200\) and \(300\).
- Push \(400\) to \(S2\) and output \(100\).
- Retrieve \(400\) from \(S2\) and output it. Hence, (B) is feasible.
3. Sequence (C): The sequence \(400, 200, 100, 300\) can be generated by:
- Use \texttt{GenerateOutput} to output \(400\).
- Push \(300\) and \(200\) to \(S2\).
- Output \(100\) from \(S1\).
- Retrieve \(300\) from \(S2\) and output it. Hence, (C) is feasible.
4. Sequence (D): The sequence \(300, 200, 400, 100\) can be generated by:
- Push \(400\) to \(S2\).
- Use \texttt{GenerateOutput} to output \(300\) and \(200\).
- Retrieve \(400\) from \(S2\) and output it.
- Finally, output \(100\). Hence, (D) is feasible. Final Answer: \[ \boxed{\text{(B), (C), (D)}} \]