## Problem A rescue team must navigate a 2D grid from a start cell to a goal cell labeled `H` (Hope). The grid contains: - `.` passable terrain - `#` impassable wall - `H` the target - `B` a barrier that can be broken exactly once per path (costs 2 moves) Find the minimum number of moves to reach `H` from position `(0,0)`. Moving to an adjacent cell costs 1 move; breaking a barrier costs 2. You may break at most one barrier in total. ```python def min_moves(grid: list[str]) -> int: # Return -1 if unreachable ... ``` **Example:** ``` grid = [ ".#.", "B.H", "..." ] Output: 4 # (0,0)->(1,0) break B (cost 2) -> (1,1) -> (1,2)=H ``` ## Follow-ups - How does your solution extend to allow breaking up to `k` barriers? - What is the time complexity as a function of grid size and `k`? - Modify the problem: barriers have individual break costs listed in a separate dict. How does Dijkstra apply here?

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In Search of Hope - Graph Pathfinding Coding Interview

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Problem A rescue team must navigate a 2D grid from a start cell to a goal cell labeled H (Hope). The grid contains: . passable terrain # impassable wall H the target B a barrier that can be broken exactly once per path (costs 2 moves) Find the minimu…

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