Bit Manipulation - Bitwise AND of Numbers Range
Given the intermediate state where left=3 (0b11), right=3 (0b11), and shift=2 after right-shifting both numbers until equal, what was the original input range?
Given the intermediate state where left=3 (0b11), right=3 (0b11), and shift=2 after right-shifting both numbers until equal, what was the original input range?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Recall that left and right are shifted right by 'shift' times to become equal
Here, left=3, right=3 after shifting 2 times means original numbers were left<<2 and right<<2 plus possible bits.Step 2: Calculate original left = 3 << 2 = 12, original right must be between 12 and 15 to become 3 after shifting
Only right=13 fits the condition (13 >> 2 = 3).Final Answer:
Option C -> Option CQuick Check:
Shifted values and shift count match original range [OK]
Quick Trick: Original = shifted value << shift count [OK]
Common Mistakes:
MISTAKES- Not applying shift count correctly
- Assuming right is max shifted value
Trap Explanation:
PITFALL- Candidates often forget to reverse the shift or consider range boundaries properly.
Interviewer Note:
CONTEXT- Tests ability to reverse engineer inputs from intermediate algorithm state.
Master "Bitwise AND of Numbers Range" in Bit Manipulation
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