Clarify the problem constraints (e.g., graph size, edge weights, whether targets are known upfront) and then propose Dijkstra's algorithm with a priority queue to compute shortest paths from the start node. After computing distances, extract the shortest path to each target, and discuss optimizations like early termination when all targets are reached.
Pro tip: Mention that for multiple targets, you can stop Dijkstra as soon as all targets are settled, and if the graph is static and queries are frequent, precomputing all-pairs shortest paths or using A* with a target-specific heuristic might be more efficient.
Ask about graph size, edge weight properties (non-negative?), number of targets, and whether paths need to be reconstructed. This determines algorithm choice and optimizations.
For non-negative weights, Dijkstra with a min-heap is optimal. If weights can be negative, Bellman-Ford is needed. For unweighted graphs, BFS suffices.
Use a priority queue to explore nodes in increasing distance order. Stop when all target nodes have been finalized to save computation.
Maintain a predecessor map during Dijkstra to reconstruct the actual path from start to each target, not just the distance.
State time complexity O((V+E) log V) and space O(V). Discuss alternatives like A* for single target or Floyd-Warshall for dense graphs with many queries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.