I had a rough idea of the approach, Eulerian path with a stack and adjacency list sorted lexicographically, and explained it well enough that they seemed to follow.
Model the tickets as a directed graph and use Hierholzer's algorithm to find an Eulerian path starting from the given airport. Perform a post-order DFS, adding airports to the itinerary after exploring all outgoing edges, then reverse the result to get the correct order.
Pro tip: Mention that using a min-heap for each airport's destinations ensures lexical order, and that the algorithm runs in O(E log E) time due to sorting, which is efficient for typical input sizes.
Clarify that we need to use all tickets exactly once, forming a valid sequence starting from a given airport. Recognize this as finding an Eulerian path in a directed graph.
Create an adjacency list where each departure airport maps to a min-heap (or sorted list) of arrival airports to ensure lexical order when multiple choices exist.
Perform a DFS from the starting airport, recursively visiting destinations. After exploring all outgoing edges from an airport, add it to the itinerary (post-order).
Since the post-order DFS adds airports in reverse order, reverse the collected list to obtain the correct itinerary from start to end.
Discuss time complexity O(E log E) due to heap operations, and space O(E). Mention edge cases like multiple valid itineraries (lexical order required) and disconnected graphs (though problem guarantees a valid path).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.