Clarify whether the graph is directed or undirected, weighted with non-negative or possibly negative edges, and whether we need just the distance or also the path. Then choose the appropriate shortest-path algorithm (Dijkstra for non-negative weights, Bellman-Ford for negative weights) and handle unreachable cases. Finally, discuss time/space complexity and potential optimizations.
Pro tip: Mention that for large graphs, early termination when the target is popped from the priority queue can save time, and that using a Fibonacci heap can improve Dijkstra's complexity to O(E + V log V). Also, relate to ML applications like graph neural networks or recommendation systems to show domain awareness.
Ask about directedness, edge weight constraints (negative?), and whether the path or just distance is needed. This determines algorithm choice.
If non-negative weights, use Dijkstra's algorithm; if negative weights, use Bellman-Ford. Mention that BFS works for unweighted graphs.
For Dijkstra: initialize distances, use a min-heap, relax edges, and stop when target is reached. For Bellman-Ford: relax all edges V-1 times and check for negative cycles.
State time and space complexity (e.g., O((V+E) log V) for Dijkstra with binary heap). Discuss unreachable target, negative cycles, and disconnected graphs.
Mention early termination, bidirectional search, or A* if heuristic available. Relate to ML tasks like graph embeddings or shortest path in knowledge graphs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is the part I fumbled a bit at first.
Decompose the problem into two shortest-path computations: from the source to the intermediate node and from the intermediate node to the destination. Then combine the results, ensuring the algorithm handles directed/undirected graphs and potential edge cases like unreachable nodes.
Pro tip: Mention that for large-scale graphs, precomputing distances from the intermediate node can be beneficial if multiple queries involve the same intermediate node, and discuss the trade-off between precomputation and on-the-fly computation.
Confirm whether the graph is directed or undirected, weighted or unweighted, and whether the intermediate node must be visited exactly once or can be revisited.
Break the problem into two independent shortest-path problems: source to intermediate and intermediate to destination.
Select appropriate algorithms for each segment (e.g., Dijkstra for non-negative weights, Bellman-Ford for negative weights, BFS for unweighted).
Sum the distances and check for unreachable nodes; if either segment is unreachable, the overall path is impossible.
Discuss time and space complexity, and consider optimizations like bidirectional search or precomputation if multiple queries share the intermediate node.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.