I got the binary search angle pretty quickly.
Recognize this as a binary search on the answer problem: the minimum rate R lies between 1 and max(piles), and the feasibility of a rate can be checked in O(n) time. Present the algorithm, prove monotonicity for correctness, and analyze complexity.
Pro tip: Mention that the upper bound can be max(piles) because any rate higher than the largest pile doesn't reduce total hours further, and use integer arithmetic to avoid floating-point precision issues.
Restate the problem: given piles and H, find minimal integer R such that sum(ceil(pile/R)) <= H. Confirm that R is an integer and that each pile is processed separately.
Define a function canFinish(R) that computes total hours = sum(ceil(pile/R)) and returns true if total <= H. This function is monotonic: if R works, any larger R also works.
Binary search R in the range [1, max(piles)]. For each mid, check canFinish(mid). If true, search left to find smaller R; else search right.
Argue that the feasibility function is monotonic, so binary search finds the minimal R. Also show that the answer is within the search range: R=1 might be too slow, but R=max(piles) always finishes in n hours (<= H if H>=n).
Time: O(n log(max(piles))) because each feasibility check is O(n) and binary search takes O(log(max(piles))) iterations. Space: O(1) extra space.
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