Jumped straight to Dijkstra which was the right call, and remembered to add early termination once t gets dequeued.
Start by clarifying the problem constraints (graph size, edge weight properties, memory limits) and then propose Dijkstra's algorithm with a binary heap as the standard solution. Discuss the trade-offs versus alternatives like A* or Bellman-Ford, and mention how you would handle large-scale graphs in a production system like Waymo's.
Pro tip: Mention that for road networks, A* with a consistent heuristic (e.g., Euclidean distance) often outperforms Dijkstra in practice, and that bidirectional search can further reduce the explored search space. Also, note that edge weights must be non-negative for Dijkstra; if negative weights are possible, you'd need Bellman-Ford.
Ask about graph size, whether edge weights are non-negative, if the graph is static or dynamic, and any memory/time constraints. This shows you think about real-world applicability.
For non-negative weights, Dijkstra with a priority queue is optimal for single-source shortest path. For large road networks, consider A* with a heuristic or bidirectional Dijkstra. If negative weights exist, use Bellman-Ford.
Describe using a min-heap to extract the node with the smallest tentative distance, and an array or hash map to track distances. Explain relaxation of edges and early termination when t is extracted.
State time complexity O((V+E) log V) with a binary heap, and space O(V). Compare with alternatives like A* (faster with good heuristic) or Bellman-Ford (O(VE), handles negative weights).
For Waymo-scale maps, mention preprocessing techniques like contraction hierarchies or using A* with landmark heuristics. Also consider real-time traffic updates and distributed graph processing.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.