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GATE CSE 2024 Session 2 Q48: Output sequences possible with two bounded stacks

Question

Let S1 and S2 be two stacks. S1 has capacity of 4 elements. S2 has capacity of 2 elements. S1 already has 4 elements: 100, 200, 300, and 400, whereas S2 is empty, as shown below.

Stack S1
400 (Top)
300
200
100
Stack S2

Only the following three operations are available:

PushToS2: Pop the top element from S1 and push it on S2.

PushToS1: Pop the top element from S2 and push it on S1.

GenerateOutput: Pop the top element from S1 and output it to the user.

Note that the pop operation is not allowed on an empty stack and the push operation is not allowed on a full stack.

Which of the following output sequences can be generated by using the above operations?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
Show answer and explanation

Answer: B, C, D (official GATE 2024 final answer key)

Concept used: Simulating stack permutations with a limited-capacity auxiliary stack.

First step: To output an element, everything above it in S1 must go to S2, which holds at most 2; check whether (A) needs to park 3 elements.

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Source: official GATE 2024 Session 2 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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