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My first instinct was to just build an adjacency map and do DFS, which worked, but I fumbled the edge case where one of the currencies in the query doesn't exist in the graph at all.
Model the exchange rates as a weighted directed graph where currencies are nodes and rates are edges. For each query, perform a graph traversal (BFS/DFS) from the source currency, multiplying rates along the path until the target is found; if not found, return -1.0. Preprocess the graph to handle unknown currencies efficiently.
Pro tip: Mention that you can precompute all-pairs rates using Floyd-Warshall if the number of currencies is small, or cache query results to avoid redundant traversals. Also, clarify edge cases like same currency (rate 1.0) and negative cycles (not applicable here).
Confirm input format, whether rates are bidirectional (e.g., if A->B is given, is B->A the reciprocal?), and how to handle unknown currencies. Discuss edge cases: same currency, missing path, and floating-point precision.
Decide between adjacency list (sparse) or matrix (dense). For most cases, an adjacency list (hash map of currency to list of (neighbor, rate)) is efficient and easy to traverse.
Use BFS or DFS to find a path from source to target, multiplying rates along the way. BFS finds the shortest path in terms of edges, but any path works for rate multiplication. Consider DFS with backtracking if you need to explore all paths (e.g., if rates could be inconsistent).
For each query, check if currencies exist; if not, return -1.0. If they do, traverse the graph. Optionally, cache results of previous queries to avoid recomputation, especially if there are many repeated queries.
Discuss time complexity: O(V+E) per query for BFS/DFS, or O(V^3) preprocessing with Floyd-Warshall for O(1) queries. Mention space complexity and when to choose each approach based on constraints.
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