Bit Manipulation - Single Number II (Three Copies)
What is the time and space complexity of the optimal bitwise FSM solution for the Single Number II problem?
What is the time and space complexity of the optimal bitwise FSM solution for the Single Number II problem?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify complexity of outer and inner loops
The algorithm iterates once over the input array (n elements), performing constant time bitwise operations per element.Step 2: Check if recursion stack adds extra space
No recursion or extra data structures are used; only fixed variables 'ones' and 'twos' consume constant space.Final Answer:
Option D -> Option DQuick Check:
Linear time and constant space confirmed by single pass and fixed variables [OK]
Quick Trick: Bitwise FSM uses fixed variables, no extra data structures [OK]
Common Mistakes:
MISTAKES- Assuming sorting or hash map space/time
- Confusing bit operations cost
Trap Explanation:
PITFALL- O(n) time looks obvious but some think bitwise ops add log n factor; space confusion common.
Interviewer Note:
CONTEXT- Checks understanding of bitwise FSM efficiency and space usage
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