What is the space complexity of the recursive bitwise sum algorithm for adding two integers a and b without using '+' operator?

medium🪤 Complexity Trap Q6 of Q15

Bit Manipulation - Sum of Two Integers Without + Operator

AO(1) constant space since no extra data structures used

BO(n^2) due to repeated recursive calls

CO(log(max(a,b))) due to recursion call stack depth

DO(n) where n is the number of bits in the integers

Step-by-Step Solution

Solution:

Step 1: Analyze recursion stack
Each recursive call adds one stack frame; max depth equals number of bits in max(a,b), which is O(log(max(a,b))).
Step 2: Space complexity
Therefore, space complexity is O(log(max(a,b))) due to recursion stack, not O(1) or O(n^2).
Final Answer:
Option C -> Option C
Quick Check:
Recursion depth equals bit length -> space is logarithmic [OK]

Quick Trick: Recursion stack depth equals bit length [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Candidates often ignore recursion stack space, thinking only data structures count.

Interviewer Note:

CONTEXT

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