S1 has capacity 4, already has elements 100 (bottom), 200, 300, 400 (top). S2 has capacity 2 and is

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Question

S1 has capacity 4, already has elements 100 (bottom), 200, 300, 400 (top). S2 has capacity 2 and is empty. Three operations are available: PushToS2 (pop from S1, push to S2), PushToS1 (pop from S2, push to S1), GenerateOutput (pop from S1 and output). Pop on empty stack and push on full stack are not allowed. Which of the following output sequences can be generated?

Accepted Answer

Correct Answer: (B), (C), and (D)Concept -- Stack Operations and Reachable Permutations:Initial S1 (top to bottom): 400, 300, 200, 100. S2 is empty.Option B (200, 300, 400, 100): PushToS2 (move 400 to S2), PushToS2 (move 300 to S2, S2 full: top=300, bottom=400). GenerateOutput (output 200). GenerateOutput (output 100? No, S1 top is 200). Wait: after moving 400 and 300 to S2, S1 has: top=200, bottom=100. GenerateOutput outputs 200. Then PushToS1 (move 300 from S2 to S1). GenerateOutput outputs 300. PushToS1 (move 400 from S2 to S1). GenerateOutput outputs 400. GenerateOutput outputs 100. Sequence: 200, 300, 400, 100. Valid.Option C (400, 200, 100, 300): GenerateOutput outputs 400. PushToS2 (move 300). GenerateOutput outputs 200. GenerateOutput outputs 100. PushToS1 (move 300). GenerateOutput outputs 300. Sequence: 400, 200, 100, 300. Valid.Option D (300, 200, 400, 100): PushToS2 (move 400 to S2). GenerateOutput outputs 300. GenerateOutput outputs 200. PushToS1 (move 400 back). GenerateOutput outputs 400. GenerateOutput outputs 100. Sequence: 300, 200, 400, 100. Valid.Option A (100, 200, 400, 300): To output 100 first, we need to empty S1 down to 100. But moving 400, 300, 200 to S2 requires 3 pushes to S2, but S2 has capacity only 2. Not possible to get 100 first without violating capacity. Invalid.

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