Bit Manipulation - Sum of Two Integers Without + Operator
What is the time complexity of the recursive bitwise sum algorithm for adding two integers a and b without using the + operator, assuming 32-bit integers?
What is the time complexity of the recursive bitwise sum algorithm for adding two integers a and b without using the + operator, assuming 32-bit integers?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Fixed integer size implies constant time
Since integers are 32-bit fixed size, the number of operations is bounded by a constant.Step 2: Recursion depth and bitwise operations are limited
Maximum recursion depth and bitwise operations are limited by fixed bit width, so complexity is O(1).Final Answer:
Option A -> Option AQuick Check:
Fixed 32-bit integers mean constant time complexity [OK]
Quick Trick: Fixed integer size means constant time complexity [OK]
Common Mistakes:
MISTAKES- Confusing input magnitude with bit length
- Assuming complexity depends on numeric value
- Thinking recursion depth varies with input size
Trap Explanation:
PITFALL- Though bit length affects complexity theoretically, fixed 32-bit integers mean constant time in practice.
Interviewer Note:
CONTEXT- Tests understanding of complexity with fixed-size integers versus variable input size.
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