Solve vault rate and subset-sum

Q: Solve vault rate and subset-sum

This question evaluates algorithmic problem-solving and complexity-analysis skills, focusing on optimization for rate-limited resource allocation and combinatorial subset selection.

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Question

Robber vaults rate: You are given an array vaults of positive integers where vaults[i] is the amount in the i-th vault, and an integer h (hours). In each hour you may steal from only one vault, removing up to k units from that single vault; you cannot split the hourly effort across multiple vaults. Find the minimum integer rate k such that all vaults are emptied within h hours. Describe your algorithm and its time complexity.
Subset sum: Given a set of distinct positive integers and a target, determine whether some subset sums exactly to the target. Outline an algorithm, analyze its complexity, and explain how to recover one valid subset if it exists.

Solve vault rate and subset-sum

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