What is the time complexity of the optimal backtracking solution for Combination Sum II with n candidates and target sum W?

medium🪤 Complexity Trap Q5 of Q15

Subsets & Combinations - Combination Sum II (No Reuse, Duplicates)

AO(2^n * n)

BO(n * W)

CO(n^2 * W)

DO(n!)

Step-by-Step Solution

Solution:

Step 1: Analyze recursion tree size
Backtracking explores subsets, which can be up to 2^n subsets, each subset takes O(n) to copy.
Step 2: Confirm pruning does not reduce worst case
Pruning and duplicate skipping reduce average cases but worst case remains O(2^n * n).
Final Answer:
Option A -> Option A
Quick Check:
Exponential subsets times linear copy cost [OK]

Quick Trick: Backtracking subsets -> exponential time [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Candidates often mistake this for DP and pick O(n*W), forgetting exponential subset enumeration.

Interviewer Note:

CONTEXT

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