Make a Variable Resolver Safe for Production Use

A variable resolver accepts definitions whose right-hand sides are either integer literals or other variable names. Discuss its time complexity and how you would improve a simple recursive implementation to meet production-code expectations. ### Constraints Preserve the literal-or-single-reference model; arithmetic expressions are not part of this task. Treat duplicate definitions, undefined names, cycles, numeric limits, and definition changes as requirements to clarify. Any caching or concurrency policy must be stated explicitly. ### Clarifying Questions - Is the definition set immutable during resolution, and are there many target queries? - How should missing names, cycles, duplicate definitions, and invalid literals be reported? - What are the maximum chain length and numeric range? ```hint Distinguish a visiting node from a completed value A name encountered on the current resolution path indicates a cycle; a previously resolved name can be a useful cache hit. ``` ### What a Strong Answer Covers - Definition-map construction cost and per-query traversal complexity. - Stack safety, validation, meaningful errors, and cycle detection. - Memoization with explicit invalidation or snapshot semantics and useful tests. ### Follow-up Questions - How would changing one variable affect cached values of other variables? - What would you log to diagnose a cycle without exposing sensitive definitions?