Bit Manipulation - Counting Bits (0 to N)
Consider two approaches to count bits from 0 to n: (1) Dynamic Programming using right shift, and (2) Brian Kernighan's bit counting trick. When is the DP approach preferable over Brian Kernighan's?
Consider two approaches to count bits from 0 to n: (1) Dynamic Programming using right shift, and (2) Brian Kernighan's bit counting trick. When is the DP approach preferable over Brian Kernighan's?
hard⚖️ Approach Comparison Q8 of Q15
Step-by-Step Solution
Solution:
Step 1: DP approach runs in O(n) time regardless of bit distribution
Brian Kernighan's depends on total set bits, which can be costly if many bits set.Step 2: For large n and dense bits, DP is preferable
DP avoids overhead of clearing bits repeatedly.Step 3: For small n, Brian Kernighan's may be faster due to low overhead
But question asks when DP is preferable, so large n with many set bits is the answer.Final Answer:
Option B -> Option BQuick Check:
DP is O(n), Brian Kernighan's depends on set bits count [OK]
Quick Trick: DP is O(n), Brian Kernighan's depends on set bits count [OK]
Common Mistakes:
MISTAKES- Assuming DP always better
- Ignoring overhead for small inputs
- Confusing space trade-offs
Trap Explanation:
PITFALL- Candidates often think DP is always better, ignoring constant overhead for small inputs.
Interviewer Note:
CONTEXT- Tests tradeoff reasoning between two common bit counting approaches
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