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I got the basic Dijkstra part fine, that was muscle memory.
Model the city as a weighted graph where nodes represent intersections and edges represent road segments with time/cost weights. Use Dijkstra's algorithm to find the shortest path, then extend the state space to include the incoming direction at each node to account for turn penalties. This transforms the problem into finding the shortest path in an expanded graph where each state is (node, direction).
Pro tip: Explicitly discuss how to handle multiple transit modes and the trade-off between state space explosion and accuracy when adding turn penalties. Mention that using a priority queue with lazy deletion or a Fibonacci heap can optimize performance.
Ask about the grid size, number of transit modes, whether weights are static or dynamic, and the exact cost model for turns (e.g., fixed penalty or proportional to angle). Confirm if the graph is directed and if there are constraints like one-way streets.
Represent intersections as nodes and road segments as edges with weights (time or cost). For multiple modes, consider separate layers or edge weights per mode. Use Dijkstra's algorithm for non-negative weights; if negative weights exist, use Bellman-Ford but note it's less efficient.
Augment each node with the direction of arrival (e.g., N, S, E, W). Create a new graph where each state is (intersection, incoming_direction). When transitioning, add the turn cost based on the angle between incoming and outgoing directions. Run Dijkstra on this expanded graph.
Discuss the time and space complexity: O((V+E) log V) for Dijkstra, but with turn penalties, V becomes V * D where D is number of directions (e.g., 4 or 8). Mention potential optimizations like pruning, A* with admissible heuristic, or bidirectional search.
Address cases like no path, multiple modes with different speeds, dynamic traffic, and memory constraints. Discuss trade-offs between precomputing turn costs vs. on-the-fly calculation, and between exact algorithms and approximations for large graphs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.