Optimize algorithms and validate inputs

Q: Optimize algorithms and validate inputs

This question evaluates algorithmic optimization, time and space complexity analysis, systematic enumeration of edge cases, input validation and production error-handling competency, and test-case design.

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Question

For a typical medium-difficulty coding task, walk through your approach: enumerate edge cases, justify your initial algorithm, analyze time and space complexity, and propose improvements. Describe production practices for handling invalid or unexpected inputs (validation, error reporting, logging/metrics, safe defaults, and failure modes). Provide example test cases that cover corner scenarios.

Optimize algorithms and validate inputs

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