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What is the auxiliary space complexity (excluding output) of the recursive backtracking approach generating all subsets of size n?

medium🪤 Complexity Trap Q6 of Q15
Subsets & Combinations - Subsets
What is the auxiliary space complexity (excluding output) of the recursive backtracking approach generating all subsets of size n?
AO(2^n * n)
BO(n) recursion stack space
CO(n)
DO(n * 2^n)
Step-by-Step Solution
Solution:

  1. Step 1: Identify auxiliary space excluding output

    Output space is O(2^n * n), but auxiliary space is recursion stack depth.

  2. Step 2: Recursion stack depth equals maximum recursion depth n

    Each recursive call adds one element, so max depth is O(n).

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Auxiliary space is recursion stack O(n) [OK]
Quick Trick: Recursion stack depth equals input size n [OK]
Common Mistakes:
MISTAKES
  • Confusing output space with auxiliary space
  • Forgetting recursion stack space
Trap Explanation:
PITFALL
  • Candidates often confuse output space with auxiliary recursion stack space, picking larger complexities.
Interviewer Note:
CONTEXT
  • Tests understanding of space complexity in recursion
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