This is basically a graph traversal problem in disguise.
Model the conversion relationships as a directed graph where symbols are nodes and conversion rates are weighted edges. Then, for any query pair, perform a graph traversal (e.g., BFS/DFS) to find a path and compute the cumulative conversion ratio by multiplying edge weights. Handle edge cases like unknown symbols or no path by returning an error or sentinel value.
Pro tip: Clarify upfront whether the graph is guaranteed to be connected and whether rates are consistent (e.g., no arbitrage). This shows you think about real-world constraints and can discuss trade-offs between precomputing all pairs (Floyd-Warshall) vs. on-demand traversal.
Ask about input format, whether the graph is directed, if rates are consistent, and if queries are frequent. This ensures you design the right solution.
Represent symbols as nodes and conversion rates as directed edges with weights. For bidirectional conversions, add reverse edges with reciprocal weights.
Use BFS or DFS to find a path from source to target. BFS finds the shortest path in terms of edges, which is often preferred for simplicity.
During traversal, maintain the cumulative product of edge weights. Once the target is reached, return the product as the conversion ratio.
Return an error if no path exists or symbols are invalid. Discuss optimizations like caching results or precomputing all pairs if queries are frequent.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.