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Model the problem as a graph where each state is (cell, remaining fuel), and use BFS to find the shortest path because each move costs 1. When you reach a gas station, reset the remaining fuel to the full range, effectively creating a new state with full fuel at that cell. BFS guarantees the shortest path in terms of number of steps.
Pro tip: Clarify assumptions upfront: whether refueling is automatic or optional, and whether you can pass through a gas station without refueling. This shows attention to detail and avoids incorrect assumptions.
Ask about grid size, movement directions (4-way or 8-way), obstacles, initial fuel, and refueling rules (automatic vs. optional). Confirm that each move costs 1 unit of fuel and that refueling resets fuel to the maximum range.
Represent each state as (row, col, remaining_fuel). Since fuel is bounded by the maximum range, the state space is finite and manageable.
Use BFS from the start state with initial fuel. For each move, decrement fuel; if the new cell is a gas station, reset fuel to max. Track visited states to avoid cycles.
When moving to a gas station, you can either refuel (reset fuel to max) or not. To minimize steps, always refuel when possible, as it only increases options. However, if refueling is optional, consider both states.
Time complexity is O(R*C*F) where F is max fuel, since each state is visited once. Space is similar. Discuss potential optimizations like early exit when destination is reached.
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