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What is the time complexity of the optimal UTF-8 validation algorithm that uses a single pass with a continuation byte counter over an input array of length n?

medium🪤 Complexity Trap Q13 of Q15

Bit Manipulation - UTF-8 Validation

What is the time complexity of the optimal UTF-8 validation algorithm that uses a single pass with a continuation byte counter over an input array of length n?

AO(n) because each byte is processed exactly once with constant time bitwise checks

BO(n^2) because nested checks are performed for each byte's continuation bytes

CO(n log n) due to bitwise operations on each byte

DO(1) since bitwise operations are constant time regardless of input size

Step-by-Step Solution

Step 1: Identify the number of iterations
The algorithm iterates over each byte exactly once, so the outer loop runs n times.
Step 2: Analyze operations per iteration
Each iteration performs a fixed number of bitwise operations and conditional checks, all O(1).
Final Answer:
Option A -> Option A
Quick Check:
Single pass with constant work per byte -> O(n) time [OK]

Quick Trick: Single pass with constant work per byte -> O(n) time [OK]

Common Mistakes:

MISTAKES

Confusing bitwise ops as log n
Assuming nested loops cause O(n^2)

Trap Explanation:

PITFALL

Bitwise ops are constant time; nested loops do not exist in optimal solution, so O(n^2) is incorrect.

Interviewer Note:

CONTEXT

Checks if candidate understands complexity beyond superficial code reading.

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