BFS was the obvious move and I got there fine.
Clarify the problem constraints (e.g., graph size, whether blocked nodes include start/end) and then propose BFS as the optimal solution for unweighted graphs. Explain how to treat blocked nodes as unvisitable and walk through the algorithm step-by-step, emphasizing time and space complexity.
Pro tip: Mention that BFS is optimal for unweighted graphs because it explores nodes in order of distance, and proactively discuss edge cases like start or end being blocked, disconnected graphs, and large inputs to show thoroughness.
Ask clarifying questions about graph representation, whether blocked nodes include start/end, and expected input size to ensure correct assumptions.
Select BFS because it finds the shortest path in unweighted graphs by exploring level by level, and explain why DFS or Dijkstra would be suboptimal.
Treat blocked nodes as unvisitable: skip them during traversal and check if start or end is blocked, returning -1 immediately if so.
Use a queue to track nodes and distances, a visited set to avoid cycles, and process neighbors while skipping blocked nodes until the end is reached.
State O(V+E) time and O(V) space complexity, and discuss edge cases like disconnected graphs, start equals end, and large graphs.
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This pivot to weighted traversal is where things got interesting.
Model the problem as a weighted graph where blocked nodes have an additional traversal cost, then apply Dijkstra's algorithm to find the shortest path. Discuss how to incorporate the extra cost into edge weights and consider any constraints or optimizations.
Pro tip: Mention that if the extra cost is uniform, you can still use Dijkstra but with modified weights; if it's non-uniform, ensure the graph remains non-negative for Dijkstra. Also, consider if the extra cost applies per node or per edge, and clarify with the interviewer.
Ask clarifying questions: Is the extra cost per blocked node or per edge entering a blocked node? Is it a fixed cost or variable? Are there multiple blocked nodes with different costs?
Represent the grid as a graph where each cell is a node. Assign edge weights: normal moves cost 1 (or given cost), and moves into blocked nodes cost 1 + extra_cost (or the specified extra cost).
Since all edge weights are non-negative, Dijkstra's algorithm is suitable. If the graph is unweighted except for the extra cost, consider 0-1 BFS if extra cost is 1, but Dijkstra is general.
Implement Dijkstra with a priority queue. Discuss potential optimizations like A* with a heuristic, or bidirectional search if applicable. Mention time complexity O(E log V).
Compare with alternative approaches like BFS with state (tracking cost) or dynamic programming. Highlight that Dijkstra is optimal for non-negative weights but may be overkill if extra cost is uniform and small.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.