Subsets & Combinations - Subsets II (With Duplicates)
What is the time complexity of the backtracking approach with sorting and skipping duplicates for generating all unique subsets from an array of length n?
What is the time complexity of the backtracking approach with sorting and skipping duplicates for generating all unique subsets from an array of length n?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze number of subsets
There are up to 2^n subsets for n elements.Step 2: Consider sorting and copying subsets
Sorting is O(n log n), but dominant cost is generating subsets and copying each subset of average length O(n), so total O(2^n * n).Final Answer:
Option A -> Option AQuick Check:
Exponential subsets times linear copy cost [OK]
Quick Trick: Generating subsets is exponential, copying subsets adds linear factor [OK]
Common Mistakes:
MISTAKES- Confusing with polynomial time
- Ignoring cost of copying subsets
Trap Explanation:
PITFALL- Candidates often underestimate copying cost or confuse with factorial or polynomial complexities.
Interviewer Note:
CONTEXT- Tests candidate's understanding of exponential subset generation and copying overhead.
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