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What is the space complexity of the backtracking with bitmask and memoization solution for the Matchsticks to Square problem with n matchsticks?

medium🪤 Complexity Trap Q6 of Q15
Subsets & Combinations - Matchsticks to Square
What is the space complexity of the backtracking with bitmask and memoization solution for the Matchsticks to Square problem with n matchsticks?
AO(n)
BO(2^n)
CO(n + 2^n)
DO(n * 2^n)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze memoization storage

    Memo stores results for up to 2^n states, so O(2^n) space.

  2. Step 2: Consider recursion stack

    Recursion depth up to n, so O(n) auxiliary stack space.

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    Memo + recursion stack -> O(n + 2^n) [OK]
Quick Trick: Memo table + recursion stack -> O(n + 2^n) [OK]
Common Mistakes:
MISTAKES
  • Ignoring recursion stack space
  • Assuming only memo space matters
Trap Explanation:
PITFALL
  • Candidates often forget recursion stack space adds to total space complexity.
Interviewer Note:
CONTEXT
  • Tests understanding of space usage in recursive memoized solutions.
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