Bit Manipulation - Sum of Two Integers Without + Operator
What is the worst-case time complexity of the iterative bitwise sum algorithm that adds two 32-bit integers without using the '+' operator?
What is the worst-case time complexity of the iterative bitwise sum algorithm that adds two 32-bit integers without using the '+' operator?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the algorithm
The iterative bitwise sum uses XOR and AND operations repeatedly until carry becomes zero.Step 2: Analyze carry propagation
Each iteration shifts the carry left by one bit, effectively moving the carry bit towards the most significant bit.Step 3: Number of iterations
In the worst case, carry propagates through all bits, so the number of iterations is proportional to the number of bits, i.e., O(n) where n is the number of bits.Final Answer:
Option A -> Option AQuick Check:
32-bit integers have at most 32 iterations [OK]
Quick Trick: Carry shifts left each iteration, max bits iterations [OK]
Common Mistakes:
MISTAKES- Assuming constant time due to fixed integer size
- Confusing bit length with integer value magnitude
- Mistaking linear time with respect to integer value
Trap Explanation:
PITFALL- Thinking fixed 32-bit means O(1) ignores input size scaling in theory.
Interviewer Note:
CONTEXT- Evaluates understanding of bitwise addition time complexity.
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