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What is the time complexity of the optimal backtracking solution for Combination Sum II with n candidates, considering sorting and pruning?

medium🪤 Complexity Trap Q13 of Q15
Subsets & Combinations - Combination Sum II (No Reuse, Duplicates)
What is the time complexity of the optimal backtracking solution for Combination Sum II with n candidates, considering sorting and pruning?
AO(n^2) due to nested loops and pruning
BO(2^n * n) because each subset can be generated and copying path costs O(n)
CO(n * target) similar to classic DP subset sum
DO(n!) due to permutations of candidates
Step-by-Step Solution

  1. Step 1: Identify recursion tree size

    Backtracking explores subsets, up to 2^n subsets in worst case.

  2. Step 2: Account for path copying cost

    Each valid combination copied costs O(n), so total time is O(2^n * n).

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Exponential subsets with path copying dominates [OK]
Quick Trick: Backtracking subsets generate 2^n possibilities, each copied O(n) time [OK]
Common Mistakes:
MISTAKES
  • Confusing with DP O(n*target)
  • Assuming pruning reduces to polynomial
  • Thinking permutations cause factorial time
Trap Explanation:
PITFALL
  • O(n^2) looks plausible due to loops but pruning and recursion dominate; DP complexity is different problem.
Interviewer Note:
CONTEXT
  • Tests if candidate understands exponential backtracking complexity and copying cost.
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