Subsets & Combinations - Count Number of Max Bitwise-OR Subsets
Which of the following problems CANNOT be solved efficiently by enumerating subsets and counting those with maximum bitwise OR?
Which of the following problems CANNOT be solved efficiently by enumerating subsets and counting those with maximum bitwise OR?
easy🔍 Pattern Recognition Q2 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze problem suitability for max bitwise OR subset pattern
Counting subsets with max OR or AND can be done by subset enumeration and tracking OR/AND values.Step 2: Identify problem incompatible with max OR subset pattern
Bitwise XOR does not have monotonic properties like OR; max XOR subsets require different approaches (e.g., basis of vector space).Final Answer:
Option C -> Option CQuick Check:
Max XOR subset counting needs different algorithm than max OR subsets [OK]
Quick Trick: Max XOR subsets need linear algebra, not subset enumeration [OK]
Common Mistakes:
MISTAKES- Assuming XOR behaves like OR or AND
- Trying to use OR-based pruning for XOR
- Confusing sum with bitwise ops
Trap Explanation:
PITFALL- Candidates often think all bitwise max subset problems are solved similarly, but XOR is fundamentally different.
Interviewer Note:
CONTEXT- Checks candidate's understanding of problem patterns and their limits.
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