What is the auxiliary space complexity of the recursive approach to count set bits using Brian Kernighan's method?

medium🪤 Complexity Trap Q6 of Q15

Bit Manipulation - Number of 1 Bits (Hamming Weight)

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

BO(k) where k is the number of set bits due to recursion stack

CO(log n) due to recursion depth on input size

DO(n) proportional to total bits in the integer

Step-by-Step Solution

Solution:

Step 1: Consider recursion depth
Each recursive call clears one set bit, so recursion depth is k (number of set bits).
Step 2: Relate k to space complexity
Auxiliary space is proportional to recursion depth, so O(k).
Final Answer:
Option B -> Option B
Quick Check:
Recursion stack grows with number of set bits [OK]

Quick Trick: Recursion stack size equals number of set bits [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Candidates often ignore recursion stack space, assuming iterative and recursive use same space.

Interviewer Note:

CONTEXT

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