Recognized it as a union-find problem pretty fast, which felt good.
Model the problem as dynamic connectivity: process logs in timestamp order, union the two riders, and track the number of connected components. When the component count drops to 1, return the current timestamp; if the logs end without full connectivity, return '-1'.
Pro tip: Mention that you can optimize by precomputing the total number of unique riders and using a union-find with path compression and union by rank; also note that if the number of unique riders is 1, the answer is the first timestamp (or '0' if no logs).
Confirm that 'all riders' means all unique riders appearing in the logs, and that connectivity is undirected. Discuss edge cases: no logs, single rider, disconnected groups.
Select Union-Find (Disjoint Set Union) with path compression and union by rank for near-constant time operations. Alternatively, consider BFS/DFS if logs are not streaming, but DSU is optimal for incremental connectivity.
Iterate through logs in order. For each log, union the two riders. Maintain a count of connected components, initially equal to the number of unique riders. Decrement the count when a union merges two different components.
After each union, if the component count becomes 1, return the current timestamp. If the loop finishes without reaching 1, return '-1'.
State time complexity O(N α(N)) where N is number of logs, and space O(R) for R riders. Discuss trade-offs: DSU is efficient but requires mapping rider names to indices; alternative approaches like graph traversal would be O(N * R) if repeated.
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