I knew BFS but initially reached for Dijkstra out of habit.
Model the problem as a shortest path on a graph where each directed edge has weight 0 if traversed in its original direction and weight 1 if reversed. Use 0-1 BFS (deque) or Dijkstra's algorithm to find the minimum cost from source to target. Discuss the trade-offs between these algorithms and handle edge cases like unreachable targets.
Pro tip: Mention that 0-1 BFS is optimal for binary weights and runs in O(V+E), which is more efficient than Dijkstra's O(E log V). Also, clarify that reversing an edge is a one-time cost and the graph remains unchanged for subsequent traversals.
Confirm whether the graph is given as an adjacency list or grid, if edge weights are binary, and if multiple reversals of the same edge are allowed. Ask about the expected input size to choose the right algorithm.
Represent each directed edge as two directed edges: one with weight 0 (original direction) and one with weight 1 (reverse direction). This transforms the problem into finding the shortest path with non-negative weights.
Since weights are 0 or 1, use 0-1 BFS with a deque for O(V+E) time. Alternatively, Dijkstra's algorithm works but is less efficient. Explain why 0-1 BFS is preferred.
Initialize distances to infinity, set source distance to 0, and use a deque to process nodes. If the target is unreachable, return -1 or infinity. Test with small examples and edge cases like source equals target.
State time and space complexity: O(V+E) for 0-1 BFS. Mention that if the graph is large, early termination when the target is popped can save time. Also, note that the graph can be implicit (e.g., grid) to save space.
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