Suppose you need to find the bitwise AND of all numbers in the range [left, right], but now the numbers are 64-bit unsigned integers and the range can be extremely large (up to 2^64). Which approach would you choose and why?
ABrute force iteration over the range since 64-bit numbers are manageable
BUse the bit-clearing optimal approach since it depends on differing bits, which is efficient even for large ranges
CUse a segment tree to store AND values for subranges
DBetter approach shifting both numbers until equal, as it scales logarithmically with number size
Step-by-Step Solution
Solution:
Step 1: Consider the input size: 64-bit numbers with huge ranges
Brute force is impossible due to range size; segment tree is impractical for 2^64 range.
Step 2: Compare shifting approach and bit-clearing approach
Shifting approach is O(log right), but bit-clearing approach depends on differing bits, which is at most 64, making it efficient.
Step 3: Choose bit-clearing approach for guaranteed efficiency on large 64-bit ranges
It runs in O(k) where k ≤ 64, constant time for fixed bit width.
Final Answer:
Option B -> Option B
Quick Check:
Bit-clearing approach scales best for large 64-bit ranges [OK]
Quick Trick:Bit-clearing approach runs in O(number of differing bits) ≤ 64 [OK]
Common Mistakes:
MISTAKES
Choosing brute force or segment tree for huge ranges
Ignoring bit width limits
Trap Explanation:
PITFALL
Candidates may pick shifting approach without realizing bit-clearing is more efficient for fixed bit width.
Interviewer Note:
CONTEXT
Tests ability to select scalable approach for very large input sizes.
Master "Bitwise AND of Numbers Range" in Bit Manipulation
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