Subsets & Combinations - Count Number of Max Bitwise-OR Subsets
Given the final count of max bitwise-OR subsets is 3 and the max OR value is 7, which of the following input arrays could produce this result?
Given the final count of max bitwise-OR subsets is 3 and the max OR value is 7, which of the following input arrays could produce this result?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify max OR = 7
Max OR 7 means subsets must combine to 7.Step 2: Check which input yields count=3 subsets with OR=7
[1,3,7] subsets with OR=7: {7}, {3,7}, {1,3,7} -> 3 subsets.Step 3: Verify other options
[1,2,4] max OR=7 but subsets with OR=7 are 1 (all elements). [7,7,7] max OR=7 but subsets with OR=7 are 7 (all non-empty). [0,7] max OR=7 but subsets with OR=7 are 1 ({7}).Final Answer:
Option A -> Option AQuick Check:
Only [1,3,7] matches count=3 subsets with OR=7 [OK]
Quick Trick: Count subsets with OR=7 for each input to match 3 [OK]
Common Mistakes:
MISTAKES- Assuming all max OR inputs have same count
- Ignoring duplicates
- Miscounting subsets
Trap Explanation:
PITFALL- Candidates often confuse max OR with subset count or ignore duplicates affecting counts.
Interviewer Note:
CONTEXT- Tests reverse reasoning from output to input understanding.
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