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My first instinct was to treat it as a pure math problem and I wasted probably two minutes going down that path before realizing the variables form a graph.
Model the equations as a directed graph where each variable is a node and each equation A / B = k creates edges A→B with weight k and B→A with weight 1/k. For each query C / D, perform a graph traversal (DFS or BFS) from C to D, multiplying edge weights along the path; if no path exists, return -1.0. Use memoization or union-find to optimize repeated queries.
Pro tip: Clarify edge cases upfront: variables not in the graph, self-queries (C/C = 1.0), and disconnected components. Mention that using union-find with component tracking can quickly reject impossible queries, but DFS with memoization is simpler and sufficient for most interview constraints.
Create an adjacency list (e.g., HashMap<String, List<Pair<String, Double>>>) where each equation A/B=k adds A→B with weight k and B→A with weight 1/k.
Check if either variable in the query is missing from the graph; if so, return -1.0. Also handle self-queries (C/C) by returning 1.0 if C exists.
For each query C/D, perform DFS or BFS from C to D, multiplying edge weights along the path. If D is reached, return the product; otherwise, return -1.0.
Cache results for repeated queries or intermediate paths to avoid redundant traversals, especially if the number of queries is large.
Discuss time complexity: O(E + Q*(V+E)) for DFS per query, or O(E + Q*α(V)) with union-find. Space complexity: O(V+E) for the graph.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.