Part one felt manageable, just run Dijkstra and skip any dangerous node during traversal.
Model the problem as two shortest-path computations: first, remove dangerous stops and run BFS/Dijkstra to find the shortest safe path; second, use a modified Dijkstra where the primary cost is the number of dangerous stops and the secondary cost is path length. Clearly explain the graph representation, algorithm choice, and complexity trade-offs.
Pro tip: Mention that the second problem can be solved by assigning a weight of 1 to dangerous stops and 0 to safe stops, then using 0-1 BFS or Dijkstra with a lexicographic cost (dangerous count, distance) to efficiently find the optimal path.
Ask about graph size, whether edges are weighted, if the graph is directed, and if multiple paths with the same dangerous count should be compared by length. This ensures you handle edge cases correctly.
Remove all dangerous stops from the graph and run BFS (for unweighted) or Dijkstra (for weighted) from start to end. If no path exists, return -1.
Use a modified Dijkstra where each node's cost is a pair (number of dangerous stops, total distance). Alternatively, assign weight 1 to dangerous stops and 0 to safe stops, then use 0-1 BFS to find the path with minimum dangerous stops, breaking ties by distance.
Discuss time and space complexity for both algorithms, and consider edge cases like start or end being dangerous, disconnected graphs, and multiple optimal paths.
Walk through a small example to verify correctness, and mention potential optimizations or alternative approaches (e.g., A* for large graphs).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.