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What is the space complexity of generating an n-bit Gray code sequence using the recursive reflected Gray code construction?

medium🪤 Complexity Trap Q6 of Q15
Bit Manipulation - Gray Code
What is the space complexity of generating an n-bit Gray code sequence using the recursive reflected Gray code construction?
AO(2ⁿ)
BO(n) recursion stack + O(2ⁿ) output list
CO(n x 2ⁿ)
DO(n)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze recursion stack space

    Recursion depth is n, so O(n) stack space.

  2. Step 2: Analyze output list space

    The output list stores 2ⁿ numbers, so O(2ⁿ) space.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Both recursion stack and output list contribute to space [OK]
Quick Trick: Recursive depth n plus output size 2ⁿ [OK]
Common Mistakes:
MISTAKES
  • Ignoring recursion stack space
  • Assuming output list is O(n)
Trap Explanation:
PITFALL
  • Candidates often forget recursion stack space or underestimate output size.
Interviewer Note:
CONTEXT
  • Tests understanding of auxiliary space in recursive algorithms.
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