Which modification to the optimal algorithm is necessary?
hard🎤 Interviewer Follow-up Q15 of Q15
Bit Manipulation - Bitwise AND of Numbers Range
Suppose the problem is extended to find the bitwise AND of all numbers in the range [left, right], but now left and right can be negative integers. Which modification to the optimal algorithm is necessary?
AConvert negative numbers to their 2's complement positive equivalents and then apply the algorithm.
BUse a mask to limit the bit-length and shift both numbers until equal, considering sign bits.
CNo modification needed; the existing bit-clearing approach works for negative numbers.
DIterate through the entire range because bitwise AND with negatives is undefined.
Step-by-Step Solution
Solution:
Step 1: Understand negative number representation
Negative integers use 2's complement, so sign bits affect bitwise AND results.
Step 2: Modify approach
Masking to limit bit-length and shifting both numbers until equal handles sign bits correctly and finds common prefix.
Step 3: Reject naive iteration
Iterating entire range is inefficient and unnecessary; direct bitwise manipulation with sign awareness is needed.
Final Answer:
Option B -> Option B
Quick Check:
Handling sign bits requires masking and shifting, not naive bit-clearing [OK]
Quick Trick:Handle sign bits with masking and shifting for negatives [OK]
Common Mistakes:
MISTAKES
Assuming algorithm works unchanged for negatives
Trying to convert negatives to positives incorrectly
Iterating entire range for negatives
Trap Explanation:
PITFALL
Ignoring sign bits leads to incorrect results; naive bit-clearing fails on negative inputs.
Interviewer Note:
CONTEXT
Tests candidate's depth in bitwise operations and handling edge cases beyond positives.
Master "Bitwise AND of Numbers Range" in Bit Manipulation
3 interactive learning modes - each teaches the same concept differently
