This is a classic single-source shortest path problem on a weighted directed graph with non-negative weights, so Dijkstra's algorithm is the optimal choice. Run Dijkstra from the starting node to compute the shortest time to each node, then return the maximum of these times, or -1 if any node is unreachable.
Pro tip: Mention that if edge weights can be negative, Dijkstra fails and you'd need Bellman-Ford, but since time is non-negative, Dijkstra is safe and more efficient. Also, clarify that the graph may not be connected, so you must check for unreachable nodes.
Confirm that edge weights are non-negative (time delays) and that the graph may have unreachable nodes. Discuss what to return if the start node is isolated or if there are zero nodes.
Select Dijkstra's algorithm for its O((V+E) log V) time complexity with a priority queue, which is optimal for non-negative weights. Mention alternatives like Bellman-Ford if negative weights were allowed.
Initialize distances to infinity, set start node distance to 0, and use a min-heap to repeatedly extract the node with the smallest tentative distance and relax its outgoing edges.
After Dijkstra completes, find the maximum distance among all nodes. If any node still has distance infinity, return -1; otherwise, return that maximum.
State the time complexity O((V+E) log V) and space complexity O(V+E). Walk through a small example to verify correctness, including a case with an unreachable node.
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