Bit Manipulation - Single Number II (Three Copies)
What is the overall time complexity of the bitwise finite state machine (FSM) approach to solve the Single Number II problem for an input array of size n?
What is the overall time complexity of the bitwise finite state machine (FSM) approach to solve the Single Number II problem for an input array of size n?
medium🧠 Conceptual Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Process each element once
The FSM updates states (ones, twos) for each number in a single pass.Step 2: Constant operations per element
Each update involves fixed bitwise operations, independent of input size.Step 3: Aggregate complexity
Processing n elements with constant time per element results in O(n) time complexity.Final Answer:
Option A -> Option AQuick Check:
Single pass with constant work per element [OK]
Quick Trick: FSM processes each element once in constant time [OK]
Common Mistakes:
MISTAKES- Confusing with sorting complexity O(n log n)
- Assuming nested loops cause O(n^2)
- Misinterpreting bit operations as logarithmic
Trap Explanation:
PITFALL- Bitwise FSM is often mistaken for more complex due to bit operations but is linear.
Interviewer Note:
CONTEXT- Evaluates knowledge of time complexity for bitwise FSM approach.
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