Subsets & Combinations - Count Number of Max Bitwise-OR Subsets
What is the time complexity of the bitmask enumeration approach for counting the number of max bitwise-OR subsets in an array of length n?
What is the time complexity of the bitmask enumeration approach for counting the number of max bitwise-OR subsets in an array of length n?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify outer loop over all subsets
There are 2^n subsets, so outer loop runs 2^n times.Step 2: Identify inner loop over elements for each subset
For each subset, we check up to n elements to compute OR, so inner loop is O(n).Final Answer:
Option D -> Option DQuick Check:
2^n subsets x n elements per subset -> O(n * 2^n) [OK]
Quick Trick: Each subset requires checking n elements -> O(n * 2^n) [OK]
Common Mistakes:
MISTAKES- Confusing 2^n subsets with O(2^n) ignoring inner loop
- Assuming quadratic or factorial complexity
Trap Explanation:
PITFALL- Ignoring the inner loop over n elements leads to underestimating complexity as O(2^n).
Interviewer Note:
CONTEXT- Tests understanding of nested loops and exponential subset enumeration complexity.
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