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I knew this was Hierholzer's algorithm territory pretty fast, Eulerian path stuff.
Model the tickets as a directed graph and use Hierholzer's algorithm to find an Eulerian path starting from JFK. To ensure the lexicographically smallest itinerary, sort each airport's destinations in reverse order and build the itinerary by adding airports to the front of the result as you backtrack.
Pro tip: Mention that this is a classic Eulerian path problem and that using a min-heap or sorted adjacency list with post-order traversal naturally yields the lexicographically smallest result. Also, clarify that the itinerary must use all tickets exactly once, so the graph is guaranteed to have an Eulerian path.
Recognize that this is an Eulerian path problem on a directed graph where each ticket is an edge. The itinerary must start at JFK and use every edge exactly once.
Construct an adjacency list mapping each departure airport to a list of arrival airports. To facilitate lexicographical order, sort each list in reverse order or use a min-heap.
Perform a DFS from JFK, recursively visiting destinations. After exploring all outgoing edges from an airport, add that airport to the front of the itinerary (or append and reverse at the end).
By processing destinations in sorted order (smallest first) and using post-order insertion, the resulting itinerary will be the lexicographically smallest valid sequence.
Explain that the time complexity is O(E log E) due to sorting, or O(E) if using a min-heap with efficient operations, where E is the number of tickets. Space complexity is O(E).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem: cycles mean multiple repeated edges between the same pair of airports, which can affect algorithms like shortest path or topological sort. Then, discuss how to handle cycles by either detecting them (e.g., DFS with recursion stack) or adapting the algorithm (e.g., using Dijkstra's with a priority queue that handles multiple edges). Finally, mention trade-offs such as time/space complexity and whether to deduplicate edges or keep them for specific use cases.
Pro tip: Show awareness that in real-world flight networks, cycles are common and often represent different flight options; instead of avoiding them, you might need to handle them efficiently by storing edges in a multigraph or using algorithms that tolerate cycles.
Ask whether the graph is directed or undirected, if edge weights matter, and what the goal is (e.g., shortest path, connectivity). This determines how cycles impact the solution.
If the algorithm requires a DAG (e.g., topological sort), use DFS with a recursion stack or Union-Find to detect cycles. Mention that multiple edges between the same nodes can be treated as separate edges or deduplicated.
For shortest path, use Dijkstra's or Bellman-Ford which naturally handle cycles. For traversal, use visited sets to avoid infinite loops. If multiple edges exist, consider storing them in a multigraph or adjacency list with edge lists.
Compare approaches: deduplicating edges reduces memory but may lose information; keeping multiple edges increases complexity but preserves data. Mention time/space complexity of chosen approach.
Conclude with how this applies to Pinterest's scale (e.g., large graphs, real-time recommendations) and emphasize robustness and efficiency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.