Took me an embarrassingly long time just to understand what they were asking.
First, clarify the problem and constraints, then propose a binary search on the answer combined with a greedy check. For a given maximum allowed difference D, determine if there exists a subsequence of size n-k where all consecutive sorted differences are ≤ D. This reduces to finding the longest subsequence with gaps ≤ D; if its length ≥ n-k, D is feasible.
Pro tip: Mention that the greedy check can be optimized using a sliding window or DP with binary search, and that the overall complexity is O(n log n log(max-min)). This shows you consider both correctness and efficiency.
Restate the problem in your own words and ask clarifying questions about constraints, edge cases, and expected input/output format.
Sorting simplifies the problem because any subsequence's sorted order is the same as its order in the sorted array. This allows us to work with indices in the sorted array.
The answer lies between 0 and max-min. Use binary search to find the smallest D such that a valid subsequence exists with all consecutive differences ≤ D.
For a fixed D, find the longest subsequence where consecutive elements differ by at most D. This can be done with a greedy two-pointer or DP with binary search, and check if its length ≥ n-k.
After binary search converges, return the smallest D that is feasible. Discuss time and space complexity.
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