Bit Manipulation - Bitwise AND of Numbers Range
You need to find the bitwise AND of all integers between two given numbers inclusive. Which approach guarantees the most efficient solution without iterating through the entire range?
You need to find the bitwise AND of all integers between two given numbers inclusive. Which approach guarantees the most efficient solution without iterating through the entire range?
easy🔍 Pattern Recognition Q11 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the problem
We want the bitwise AND of all numbers in a range, which is equivalent to finding the common prefix of their binary representations.Step 2: Identify the approach
Shifting both numbers right until they are equal effectively finds the common prefix bits. Shifting back restores the prefix to its original position, giving the AND result.Final Answer:
Option A -> Option AQuick Check:
Shifting until equal finds common prefix efficiently [OK]
Quick Trick: Find common prefix by shifting both numbers [OK]
Common Mistakes:
MISTAKES- Trying brute force iteration for large ranges
- Using DP which is unnecessary
- Sorting numbers to find AND
Trap Explanation:
PITFALL- Brute force looks straightforward but is inefficient; DP seems plausible but overcomplicates; sorting is unrelated to AND operation.
Interviewer Note:
CONTEXT- Tests if candidate recognizes bitwise prefix pattern instead of naive iteration.
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