Binary search on the answer, which I knew conceptually but fumbled the boundary conditions at first.
Recognize this as a binary search on the answer problem: the minimum rate k is monotonic, so binary search over k in [1, max(vaults)] and for each k check if the total hours (sum of ceil(vault/k)) is ≤ 8. Return the smallest feasible k.
Pro tip: Mention that the upper bound can be max(vaults) because at that rate each vault takes at most 1 hour, and clarify that hours are integer hours per vault (ceil division) to avoid off-by-one errors.
Clarify that each vault must be processed entirely within an integer number of hours, so time for a vault is ceil(size/k). The total time must be ≤ 8 hours.
Observe that if a rate k works, any larger rate also works. Thus binary search on k from 1 to max(vaults) (or sum(vaults)) to find the minimum feasible rate.
For a given k, compute total hours = sum(ceil(vault/k) for vault in vaults). If total ≤ 8, k is feasible; else not.
Perform binary search: while low < high, mid = (low+high)//2; if feasible(mid), set high = mid; else low = mid+1. Return low.
Test with the given list [3,6,7,11] and 8 hours. Check k=3: hours = 1+2+3+4=10 >8; k=4: 1+2+2+3=8 ≤8, so answer is 4. Also consider edge cases like empty list or k=0.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem: whether it's a decision problem (yes/no) or if we need to find the actual subset. Then, explain that this is the classic Subset Sum problem, which can be solved using dynamic programming or recursion with memoization, and walk through a simple example with the given set to demonstrate the approach.
Pro tip: Mention the trade-offs between different approaches (e.g., DP vs. meet-in-the-middle) and discuss how the solution scales with input size, showing awareness of real-world constraints like memory and time limits.
Confirm whether the task is to return a boolean (exists or not) or to find all subsets that sum to the target. Also, check if the set can contain negative numbers or if it's strictly positive.
Decide between dynamic programming (for small target values) or recursion with backtracking (for small set sizes). Explain the time and space complexity of each.
Apply the chosen approach to the given set {2, 5, 3, 11} and target 10. Show step-by-step how you determine if a subset sums to 10.
Mention pruning techniques (e.g., sorting and early termination) and handle edge cases like empty set, target 0, or large inputs.
State clearly whether a subset exists (e.g., {2, 3, 5} sums to 10) and summarize the reasoning.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.