Knew it was Dijkstra the second I read the problem.
Start by clarifying the problem constraints (e.g., non-negative weights, graph size, single-source vs. all-pairs) and then select the appropriate algorithm. For non-negative weights, Dijkstra's algorithm with a priority queue is optimal; for negative weights without negative cycles, Bellman-Ford is suitable. Explain the chosen algorithm's steps, complexity, and edge cases.
Pro tip: Mention that in real-world systems like Visa's payment network, edge weights often represent latency or cost, and you might need to handle dynamic updates or massive graphs, so discussing scalability (e.g., using A* with heuristics or bidirectional search) can set you apart.
Ask about edge weight properties (negative? zero?), graph size, whether it's single-source or all-pairs, and if the graph is static or dynamic. This determines the algorithm choice.
For non-negative weights, use Dijkstra's algorithm with a min-heap; for negative weights, use Bellman-Ford; for unweighted graphs, BFS. Justify your choice based on constraints.
Describe initialization (distances, priority queue), relaxation process, and termination. For Dijkstra, explain how the priority queue extracts the minimum and updates neighbors.
State time and space complexity (e.g., O((V+E) log V) for Dijkstra with binary heap). Discuss edge cases: disconnected nodes, negative cycles (if applicable), and large graphs.
Mention potential optimizations like bidirectional search, A* with admissible heuristics, or using Fibonacci heaps. Relate to practical scenarios (e.g., dynamic edge weights, distributed graphs).
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