The problem sounds simple on the surface but the recharge timing tripped me up.
Clarify the problem's mechanics: batteries are used sequentially, each provides capacity (usage time) and then requires recharge time before it can be used again. Model this as a scheduling problem where you track the current time, the next available time for each battery, and greedily select the battery that can start earliest and has enough capacity to cover the remaining usage. If no battery is available before the total usage time is covered, return -1.
Pro tip: Discuss the trade-off between a greedy simulation (O(n log n) with a priority queue) and a more complex optimal scheduling approach; interviewers appreciate when you recognize that greedy works if batteries are interchangeable and you always pick the one that finishes recharging soonest.
Ask questions to confirm: Are batteries used one at a time? Can a battery be recharged while another is in use? Is the goal to minimize the number of batteries or just determine if it's possible? What does 'consecutive' mean here?
Identify key variables: total usage time T, arrays capacity[] and recharge[], current time, remaining usage, and a min-heap of (available_time, capacity) for batteries currently recharging or ready.
At each step, pick the battery that becomes available earliest (from the heap). If its available time > current time, advance current time to that available time. Use its capacity to reduce remaining usage, then push it back into the heap with available_time = current_time + recharge_time.
If remaining usage <= 0, return the number of batteries used so far. If the heap is empty and remaining usage > 0, return -1. Also consider initial availability (all batteries start available at time 0).
Time complexity: O(k log n) where k is number of battery uses (could be large if capacities are small). Space: O(n). Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.