Bit Manipulation - Subsets Using Bitmask
What is the time complexity of the backtracking approach to generate all subsets of an input array of size n, assuming the array is sorted beforehand?
What is the time complexity of the backtracking approach to generate all subsets of an input array of size n, assuming the array is sorted beforehand?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify number of subsets generated
There are 2^n subsets in total.Step 2: Calculate work done per subset
Each subset can take up to O(n) time to copy or build, so total time is O(n * 2^n).Final Answer:
Option A -> Option AQuick Check:
Exponential subsets times linear work per subset [OK]
Quick Trick: Each subset generation costs O(n), total subsets 2^n [OK]
Common Mistakes:
MISTAKES- Confusing O(2^n) as total time ignoring subset size
- Mistaking factorial or polynomial complexities
Trap Explanation:
PITFALL- O(2^n) looks plausible but ignores copying subsets; O(n^2) is too small for exponential subsets.
Interviewer Note:
CONTEXT- Tests understanding of exponential subset enumeration and per-subset cost.
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