Bit Manipulation - Bitwise AND of Numbers Range
Consider two approaches to compute bitwise AND of numbers range: (1) Brute force iteration over the range, and (2) shifting both numbers until equal. When is approach (2) clearly better than (1)?
Consider two approaches to compute bitwise AND of numbers range: (1) Brute force iteration over the range, and (2) shifting both numbers until equal. When is approach (2) clearly better than (1)?
hard⚖️ Approach Comparison Q8 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand brute force iterates over all numbers in range
Its time complexity is O(right - left), which is slow for large ranges.Step 2: Shifting approach runs in O(log right) and benefits when numbers share many prefix bits
Long common prefix means fewer shifts and faster computation.Final Answer:
Option A -> Option AQuick Check:
Large ranges with common prefix favor shifting approach [OK]
Quick Trick: Shifting approach exploits common prefix for speed [OK]
Common Mistakes:
MISTAKES- Assuming brute force is always better for small ranges
- Ignoring common prefix impact
Trap Explanation:
PITFALL- Candidates often overlook that shifting approach is better when common prefix is long, not just small ranges.
Interviewer Note:
CONTEXT- Tests tradeoff reasoning between brute force and bit manipulation.
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