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What is the space complexity of the recursive backtracking approach to generate all subsets of an array of size n?

medium🪤 Complexity Trap Q6 of Q15
Bit Manipulation - Subsets Using Bitmask
What is the space complexity of the recursive backtracking approach to generate all subsets of an array of size n?
AO(n * 2^n)
BO(2^n)
CO(n + 2^n)
DO(n)
Step-by-Step Solution
Solution:

  1. Step 1: Account for recursion stack

    Maximum recursion depth is O(n) due to path length.

  2. Step 2: Account for result storage

    All subsets stored require O(n * 2^n) space, which dominates recursion stack space.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Space is dominated by output storage of all subsets [OK]
Quick Trick: Output storage O(n*2^n) dominates stack O(n) [OK]
Common Mistakes:
MISTAKES
  • Ignoring recursion stack space
  • Assuming output space only
Trap Explanation:
PITFALL
  • Candidates often underestimate total space complexity by ignoring output size.
Interviewer Note:
CONTEXT
  • Tests understanding of auxiliary space beyond output storage.
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