My first instinct was plain BFS and I started coding it before fully thinking through the cost model.
Model the grid as a graph where each cell is a node with a cost: 0 for charged cells, 1 for empty cells, and forbidden cells are impassable. Use 0-1 BFS or Dijkstra's algorithm to find the minimum cost path from any top-row cell to any bottom-row cell, where cost is the number of empty cells activated. If no path exists, return -1.
Pro tip: Clarify whether activating an empty cell is permanent and whether the path can revisit cells; this affects whether the problem is a simple shortest path or requires more complex state tracking. Also, mention that 0-1 BFS is optimal here because edge weights are only 0 or 1, giving O(mn) time.
Ask about grid size, whether activation is permanent, and if diagonal movement is allowed. Confirm that the goal is to minimize the number of empty cells activated, not the path length.
Represent each cell as a node. Assign cost 0 to charged cells, cost 1 to empty cells, and treat forbidden cells as blocked. The total cost of a path is the sum of costs of cells entered (or activated).
Since edge weights are 0 or 1, use 0-1 BFS (deque) or Dijkstra with a priority queue. Initialize the queue with all top-row cells that are not forbidden, with their respective costs.
Process cells in order of increasing cost. When a bottom-row cell is reached, return its cost as the minimum number of empty cells activated. If the queue empties without reaching the bottom, return -1.
State that time complexity is O(mn) for 0-1 BFS and space is O(mn). Discuss edge cases: no top-row start, no bottom-row reachable, all forbidden, and grids with only one row.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.